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Resonance phenomena in conductor-backed asymmetrical coplanar strips Ghanipour, Pejman 2004

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Resonance Phenomena in Conductor-Backed Asymmetrical Coplanar Strips by Pejman Ghanipour B.Sc. (Hons.), University of Brit ish Columbia, 2004 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T OF T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F Master of Applied Science in T H E F A C U L T Y OF G R A D U A T E S T U D I E S (Department of Electrical and Computer Engineering) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 2004 © Pejman Ghanipour, 2004 FACULTY OF GRADUATE STUDIES THE UNIVERSITY OF BRITISH COLUMBIA Library Authorization In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Pejman Ghanipour 08/10/2004 Name of Author (please print) Date (dd/mm/yyyy) Title of "Thesis: Resonance Phenomena in Conductor-Backed Asymmetrical Coplanar Strips Degree: Masters of Applied Science Year: 2004 Department of Electrical & Computer Engineering The University of British Columbia Vancouver, B C Canada grad.ubc.ca/forms/?formlD=THS page 1 of l last updated: 8-Gct-04 Abstract The ground strip of C B A C P S represents a patch antenna supporting unwanted parallel-plate (PP) modes causing numerous resonances. For typical monolithic-microwave integrated circuits in finite substrates and packaging enclosures, these resonance frequencies lie within the microwave frequency region. In order to suppress coupling into these P P modes, several mode coupling suppression methods are proposed, simulated and tested in the frequency range 0.05 to 50 G H z . These methods include variation of line parameters, suspension of the substrate, application of a superstrate with a high dielectric constant and the use of slow-wave structures. It is shown that the resonance frequencies are accurately estimated by our model, which considers the excitation of the first and second PP modes. Furthermore, the mode coupling suppression schemes are verified by measuring the S-parameters of the fabricated C B A C P S lines. This thesis reports the first use of slow-wave electrodes as a mode coupling suppression method for coplanar structures; it is shown that the best mode coupling suppression is achieved by the use slow-wave electrodes along with narrow-width shorted ground strip. i i Contents Abstract i i Contents i i i List of Figures vi List of Tables xiv Acknowledgement xv 1 Introduction 1 1.1 Introduction 1 1.2 Organization of the Thesis 7 2 Theory 8 2.1 Microwave transmission lines 9 2.2 Application of Patch Antenna Theory to C B A C P S Lines 15 2.2.1 Patch Antenna Theory 15 2.2.2 Resonances in Conductor-backed Coplanar Lines 18 2.2.3 Higher-order Modes 20 2.3 Suppression Methods 28 2.3.1 Effect of Ground Strip Width 29 2.3.2 Effect of Air-gap Below Substrate 30 i i i 2.3.3 Effects of High Dielectric Constant Superstrates and Slow-wave Electrodes 33 2.3.4 Effect of Shorting Ground Strip to Back-side Metall ization 36 3 Design and Fabr icat ion 41 3.1 Electrode Design 41 3.1.1 The High Frequency Electromagnetic Software, Sonnet™ 42 3.1.2 Device design 44 3.2 Mask Design 57 3.3 Fabrication 58 3.4 Housing Design 67 4 Results 74 4.1 Measurement Method 75 4.2 Case 1 Results 77 4.2.1 No Suppression Method Used 77 4.2.2 Suppression with Width Adjustment 78 4.2.3 Shorted-ground Strip C B A C P S Lines 84 4.3 Case 2 Results 87 4.4 Case 3 Results 89 4.5 Slow-wave Electrodes 93 4.6 Measurements with No Housing 99 iv 5 Conclus ion 103 5.1 Summary 103 5.2 Discussion 104 5.3 Suggestions for Future Work 107 6 Bib l iography 109 v List of Figures Figure 1.1 Conductor-backed coplanar waveguide ( C B C P W ) . Practical realizations of the C B C P W defer from its ideal form in that the ground conductors are finite. These lines are sometimes referred to as Finite-width conductor-backed coplanar waveguides ( F W - C B C P W ) 4 Figure 1.2 Micro-coplanar strip (MCS) line 5 Figure 1.3 Conductor-backed asymmetric coplanar strips ( C B A C P S ) 6 Figure 2.1 The circuit model of a transmission line of differential length, dz 10 Figure 2.2 Conductor-backed asymmetric coplanar strips ( C B A C P S ) 14 Figure 2.3 A microstrip patch antenna configuration 17 Figure 2.4 Measured |S2 l | of C B A C P S line with wg = 1 mm, s = 28 urn, ws = 120 urn, L = 1 cm, and h = 250 um. The vertical doted lines represent the theoretical locations of resonances caused by the M S L mode, and the vertical solid lines represent the theoretical location of resonances caused by the first higher order mode. The theoretical results were made using equation (2.22) assuming sejf= £ r , i.e., Haydle's method. As can be seen the theoretical predictions of resonance frequencies using this method are highly inaccurate 24 Figure 2.5 Measured |S21| of C B A C P S line with wg = 1 mm, s = 28 um, ws = 120 um, L = 1 cm, and h - 250 um. The vertical doted lines represent the theoretical locations vi of resonances caused by the M S L mode, and the vertical solid line represents the theoretical cutoff of the first higher order mode. The theoretical results were made using equations (2.23) and (2.24), while the cutoff of the HMo.i mode was calculated using equation (2.25). As can be seen the theoretical predictions of resonance frequencies (at least the ones below the cutoff of the HMo.i mode) are more accurate than the theoretical predictions shown in Figure 2.4 25 Figure 2.6 The approximate mode patterns of the relevant modes of a CBACPS line. 26 Figure 2.7 The effective microwave index of the modes shown in Figure 2.6 as functions of frequency. Sonnet™ was used to determine the dispersion of the M S L and coplanar modes, while equation (2.25) was used to estimate the dispersion of the HMo.i mode. The dashed line illustrates where the HMo.i mode is leaky. The open-ground CBACPS line used for this analysis had the following dimensions h = 250 um, ws =120 um, s = 28 um, and wg = 1 mm 27 Figure 2.8 A CBACPS line with an air-gap between the substrate and the supporting backside ground plane (easel CBACPS) 31 Figure 2.9 Comparison of the simulated effective permittivity of the M S L mode and the coplanar mode 32 Figure 2.10 A CBACPS line with a high dielectric superstrate of thickness h,. In order to make the coplanar mode slower than that of the PP modes, the superstrate needs to be relatively thick and have a permittivity higher than that of the substrate (case3 CBACPS). 34 Figure 2.11 A slow-wave CBACPS line 35 Figure 2.12 A shorted-groundCBACPS line 37 vn Figure 2.13 The approximate mode patterns of the relevant modes of a shorted-ground C B A C P S line 38 Figure 2.14 The effective microwave index of the modes shown in Figure 2.13 as a function of frequency. Sonnet™ was used to determine the dispersion of the coplanar modes, while equation (2.25) was used to estimate the dispersion of the HM 0,o.5 mode. The shorted- ground C B A C P S line used for this analysis had the following dimensions ws =120 um, s = 28 um, and wg — 1 mm. As can be seen the two curves cross at approximately 33.5 G H z , around which severe mode coupling is expected 39 Figure 2.15 The effective microwave index of the modes of a shorted-ground C B A C P S line, with dimensions ws = 120 um, s - 28 um, and wg = 0.5 mm, as a function of frequency. Sonnet™ was used to determine the dispersion of the coplanar modes, while equation (2.25) was used to estimate the dispersion of the HMo,o.5 mode 40 Figure 3.1. The design model of 800 micron long caseA C B A C P S slow-wave electrodes, see Table 3.1 for dimensions 47 Figure 3.2 The design model of 800 micron long case5 C B A C P S slow-wave electrodes, see Table 3.1 for dimensions 48 Figure 3.3 The microwave index of a shorted-groundCa^<?4 line as function of frequency. The microwave index has a minimum of about 3.17 which is higher than (s r ) 1 / 2 at 3.13 52 Figure 3.4 The current distribution of CaseA electrodes at 5 G H z . It can be seen that the rectangular capacitors have great effect on the current distribution, and cause the current to be concentrated along the inner edge of the electrode very close to the vi i i opposing electrode. The high concentration of current near the opposing electrode causes the structure to be very lossy 54 Figure 3.5 The current distribution of Case5 electrodes at 5 G H z . Unl ike the case4 structure, the most of current remain travels along the main electrode and a relatively insignificant amount enters the capacitors (fins & pads), making case5 structures relatively low loss 55 Figure 3.6 Comparison of the simulated electrical loss of caseA electrode design and easel electrode designs 56 Figure 3.7 Picture of a segment of a caseA C B A C P S device 62 Figure 3.8 Picture of a segment of a case5 C B A C P S device 63 Figure 3.9 Example of a device with shorted electrodes; our fabrication yield was about 70 percent 64 Figure 3.10 Silver epoxy is used to short the coplanar ground of a case4 type C B A C P S to the back-side metallization 65 Figure 3.11 Silver epoxy is used to short the coplanar ground of a case\(c) C B A C P S line to the back-side metallization 66 Figure 3.12 The copper blocks with groves used as the housing of devices. The picture shows the two different sized blocks used of length 2.2 cm, and 1.2 cm. The sizes of the blocks are compared to the size of a quarter 70 Figure 3.13 The design of the two channels that were fabricated in copper blocks and acted as the housing of the devices. Design (1) is to be used for easel C B A C P S lines, with a = (1.3 ± 0.3) mm, and b = (2.0 ± 0.1) mm. Design (2) is to be used for ix easel C B A C P S lines with a = (1.3 ± 0.3) mm, b = (1.6 ± 0.1) mm, c = (0.20 ± 0.05) mm, and d = (0.25 ± 0.02) mm 71 Figure 3.14 (a) Picture showing a case5 C B A C P S device in a design (2) housing, (b) Same picture as (a) with the addition of white lines to highlight the edges of the channel. A s can be seen there is an air-gap under the device. A lso visible is the silver epoxy used to short the coplanar ground strip to the housing wall 72 Figure 3.15 A top view of the device in Figure 3.14, compared to the size of a quarter. 73 Figure 4.1 A close up of the stage on which the devices were tested 76 Figure 4.2 Measured |S21| of a C B A C P S line with wg = 1 mm, L = 2 cm, w, = 0.120 mm, s = 0.028 mm (case 1(a)). The doted lines represent the theoretical location of resonances caused by the M S L mode, and the vertical solid line represents the theoretical cutoff frequency of the HMo,i mode. A s can be seen, due to the relatively strong coupling to the coplanar mode, HMo,i resonances cause more leakage than the M S L mode resonances 80 Figure 4.3 Measured |S21| of C B A C P S line with wg = 1 mm, s = 28 um, ws = 120 um and L = 1 cm. The doted lines represent the theoretical location of resonances caused by the M S L mode, and the vertical solid line represents the theoretical cutoff of the first higher order mode. Although the spacing between the resonances has increased due to the shorter length, the cut off for HMo,i mode is still at 41.7 GHz.81 Figure 4.4 Measured |S21| of a C B A C P S line with a wg = 0.7 mm, L = 2 cm, w, = 0.120 mm, s = 0.028 mm. The vertical doted lines represent the theoretical location of resonances caused by the M S L mode. Due to the small ground width, higher-order modes are not observed in the above frequency range 82 Figure 4.5 Measured |S21| of a C B A C P S line with a wg = 0.5 mm, L = 1 cm, ws = 0.120 mm, s = 0.028 mm. The doted lines represent the theoretical location of resonances caused by the M S L mode. Due to the small ground width, higher-order modes are not observed in the above frequency range 83 Figure 4.6 Measured |S21| of a C B A C P S line with a wg = 0.5 mm, L = 1 cm, ws = 0.120 mm, s = 0.028 mm with a shorted ground strip. The vertical line represent the theoretical cutoff of the HMo.o.s mode, which is at 37 G H z . Due to the fact that the outer edge of the ground strip is shorted, no resonances below this cutoff are observed 85 Figure 4.7 Measured |S21| of a C B A C P S line with wg = 0.7 mm, L = 2 cm, ws = 0.120 mm, s = 0.028 mm with a shorted ground strip. The vertical line represent the theoretical cutoff of the HM 0 ,o.5 mode, which is at 28.26 G H z . Due to the fact that the outer edge of the ground strip is shorted, no resonances below this cutoff are observed 86 Figure 4.8 Measured |S21| of a C B A C P S line with a wg = I mm, / =2 cm, ws = 0.120 mm, g = 0.028 mm with (0.25+/- 0.03) mm of air under the substrate. The vertical doted lines represent the theoretical location of resonances caused by the M S L mode. 88 Figure 4.9 The thin curve shows the response of the device mentioned in Figure 4.2 ; the thick curve shows the response of a 50 Cl line with similar ground strip dimensions, yet with a 0.650 mm GaAs superstrate. The GaAs superstrate increases xi the microwave index of the coplanar mode relative to the PP modes, hence, decreasing the coupling between the coplanar and PP modes 91 Figure 4.10 The thin curve shows the response of a 2 cm long shorted-ground case\(b) device with a total metallic width, W, of 0.848 mm. The vertical thin line represents the theoretical cutoff of the HMo.o.5 mode for this device, which is at 28.26 G H z . The thick curve shows the response of 2 cm long shorted-ground casei device with as total metallic width, W, of 1.110 mm. The vertical thick line represents the theoretical cutoff of the HM 0,o.5 mode for this device, which is at 21.58 G H z 92 Figure 4.11 The measured relative microwave permittivity of 1 cm long case\{a), case4, case5(a) C B A C P S lines compared to the relative permittivity of the alumina substrate (e r = 9.8) 95 Figure 4.12 The thin curve shows the response of a 1 cm long case 1(a) device, and the thick curve shows the response of a case5(a) device with similar dimensions. The slow-wave structure makes the coplanar mode significantly slower than H M modes, thereby suppressing coupling between the two modes 96 Figure 4.13 The thin curve shows the response of the shorted-ground case\(c) device; the thick curve shows the response of a shorted-ground case5(b) device with similar dimensions. The slow-wave structure makes the coplanar mode slower than PP modes suppressing resonances caused by PP modes 97 Figure 4.14 The thin curve shows the response of a 2 cm long shorted-ground casel(b) device with a total metallic width , W, of 0.848 mm. The vertical thin line represents the theoretical cutoff of the HMo.o.5 mode for this device, which is at 28.26 G H z . The thick curve shows the response of 2 cm long shorted-ground casei device with as total metallic width, W, of 1.148 mm. The vertical thick line represents the theoretical cutoff of the HMo.o.5 mode for this device, which is at 20.87 G H z 98 gure 4.15 Comparison of the frequency response of a 1 cm long case 1(a) devices measured in channel, versus outside the channel 102 x i i i List of Tables Table 3.1 The design parameters of the device types on the mask. Note each device type used on the mask had two lengths of 1 cm, and 2 cm 49 Table 3.2 The simulated microwave characteristics of the C B A C P S lines designed on the mask. Note these devices were simulated assuming the outer edge of the ground strip has been shorted to the box walls 50 Table 3.3 The simulated microwave characteristics of the C B A C P S lines designed on the mask to be tested with open ground strip periphery. Note the microwave parameters of these devices are very close to that of devices with shorted ground strips. This shows the microwave properties of devices are not changed significantly by grounding the ground strip 51 Table 3.4 A comparison of the simulated microwave characteristics of case 1(a) line with a case 1(a) line which is at an angle of 0.06° to the lateral box walls 69 Table 4.1 The result of simulations showing the effect of the lateral wall and ground width for shorted-groundca.s'el(a) devices. It is observed that the effect on line parameters is small for ground widths of more than 400 microns 101 xiv Acknowledgement M y deepest gratitude goes to my family for they have been the greatest help to me throughout this work and without their love and support I surely would not have reached this point. Next to my parents, Dr. N . A . F. Jaeger deserves my gratitude and thanks, as without his guidance and support I doubt that I would ever have found an interest in microwave circuitry, an area of research that I truly enjoy, and intend to base my career on. It was truly a pleasure having him as my supervisor and his contributions to this work and beyond wi l l not be forgotten. I am most grateful to Dr. A . Kulpa for her great assistance and insight during device fabrication. A lso, sincere and special thanks go to Dr. J . Bu l l for the endless discussions on electromagnetism and its application to various microwave transmission lines. Although several people stand out in my mind as having made my life as a graduate engineering student tolerable, and even enjoyable, it is hard to say who has contributed what. These people have contributed to this work in so many ways that I could not possibly list everything they have done for me nor can I attach a weight to the importance of my interactions with them. I just would like to give them all my special thanks: S. Chandani, M . Fairburn, A . Guest, W . N. Hardy, T. Mattison, H . Kato, S. Khoramshahi, K. L. Mclean, M . Manarovici , and S. Ristic. Appreciations are due to J G K B Photonics Inc. and the Natural Science and Engineering Research Counci l (NSERC) of Canada for their generous financial support of this work. 1 Introduction 1.1 Introduction Monoli thic microwave integrated circuits (MMICs) are used for a variety of devices, such as microprocessors, amplifiers, oscillators, transmitters, and receivers. Monolithic microwave transmission lines such as microstrip and coplanar lines are basic components of M M I C s . In recent years coplanar lines have increasingly gained popularity in M M I C designs; this is due to the fact that integrated circuits that use coplanar lines have no inherent need for vias, as the ground strips are on the chip surface. Furthermore, coplanar lines exhibit ease of parallel and series connection of both active and passive components. However, coplanar lines can suffer from parasitic problems such as leakage, coupling, and resonance. In particular, the establishment or alteration of such problems can occur once these structures are packaged. This is due to the fact that in packaging mill imeter-wave circuits and components, it is desirable, and generally necessary, to bring coplanar circuits into contact with a metallic base for reasons such as efficient heat removal, improved mechanical strength, better power handling ability, or easy integration with microstrip lines [1]. Such a metal base represents an additional ground strip, which i f introduced in close proximity to the coplanar transmission line, can effectively alter the wave propagating structure, permitting unwanted bulk modes such as surface, parallel plate, and microstrip-like waves to exist [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33]. Without certain mode suppression techniques, these unwanted modes may be excited and propagate along the structures. Furthermore, the coplanar mode may become leaky, coupling to parasitic parallel-plate (PP) modes. The leaked energy propagates in the dielectric and reflects within the structure formed by the surface 1 (planar) and bottom ground planes and any front, back, or side terminations of the coplanar transmission line, forming standing waves at certain frequencies. Depending on the frequency, these standing waves can strongly affect the dominant coplanar mode [6]. As a result, packaging coplanar M M I C s is an extremely challenging task. The suppression or elimination of modes, other than the coplanar mode, has been the subject of extensive studies [2, 4, 5, 7, 9-14, 17-19, 22, 28-30]; however, these studies have been generally confined to the case of conductor-backed coplanar waveguide ( C B C P W ) , which in its ideal form consist of a conducting strip with two semi-infinite side conductors on the surface of a substrate with a conducting back plate (see Figure 1.1). A n attractive alternative to the C B C P W is the micro-coplanar strip (MCS) , which differs from the C B C P W in that it only has a single semi-infinite ground plane, instead of two ground planes (see Figure 1.2). It was first introduced by E. Yamashita [34] as a means to avoid the proximity effect of coplanar grounds near microstrip lines. Practical realizations of M C S deviate from its ideal form in that the ground conductor has a finite width. These lines are called conductor-backed asymmetric coplanar strips ( C B A C P S ) (see Figure 1.3). It is the purpose of this study to contribute new experimental and simulation results for the case of C B A C P S lines. Here, we describe a systematic study of the effectiveness of various methods of suppression of the resonances seen in packaged C B A C P S lines. These methods include variation of line parameters, suspension of the substrate, application of a high dielectric-constant superstrate, and the use of slow-wave electrodes. Two main types of device were fabricated: one with the ground strip shorted to the backside plane along its outer edge, and the other with open (non-conducting) 2 ground strip periphery. The fabricated devices are tested in a metallic box with an open roof and fed with probes. Simulation and experimental results are obtained at frequencies from 0.05 to 50 G H z . It is shown that the resonance phenomenon observed in C B A C P S lines can be explained using patch antenna theory; however, to determine the exact frequencies at which the lines resonate, the proper dispersion of parallel-plate (PP) modes needs to be taken into account. Furthermore, it is shown that although all of the mode coupling suppression schemes proposed, and implemented, are successful in significantly reducing the effects of the resonances in C B A C P S lines, the best results are achieved by using slow-wave electrodes along with narrow-width shorted ground strips. 3 Ground Signal Ground Strip Strip S t r i P Figure 1.1 Conductor-backed coplanar waveguide ( C B C P W ) . Practical realizations of the C B C P W defer from its ideal form in that the ground conductors are finite. These lines are sometimes referred to as Finite-width conductor-backed coplanar waveguides ( F W - C B C P W ) . 4 5 Figure 1.3 Conductor-backed asymmetric coplanar strips ( C B A C P S ) . 6 1.2 Organizat ion of the Thes is Fol lowing this introduction, Chapter 2 provides a theoretical overview of microwave transmission lines with an emphasis on C B A C P S lines. The theory behind guided waves in passive microwave transmission lines is reviewed in detail. Then patch antenna theory and its relevance to the understanding of the resonance phenomenon observed in many conductor-backed coplanar lines, is studied extensively. Final ly, methods of suppressing mode coupling in C B A C P S lines is introduced and analyzed. The analysis is provided in a general form so that it can easily be extended to other conductor-backed coplanar transmission lines. The design and fabrication of C B A C P S lines on alumina substrates are described in Chapter 3. The high frequency electromagnetic software utilized and its method of analyzing multi-layered planar circuits is discussed. Then the design procedure is explained in detail and the simulation results of the designed C B A C P S lines are presented and discussed. Final ly, the fabrication steps are outlined. Chapter 4 contains the results of the measurements made on the fabricated devices. The microwave characteristics of the various C B A C P S lines at frequencies up to 50 G H z are reported and analyzed. A summary and a discussion of the results are provided in chapter 5. A comparison between the measured results and the theoretical model is made and the conclusions drawn are presented. Final ly, some suggestions for future work and possible uses of C B A C P S lines are offered. 7 2 Theory In this chapter, the theory behind C B A C P S line resonances is discussed, and various methods of suppressing coupling into modes which cause these resonances are suggested. A basic review of the properties of microwave transmission lines is contained in section 2.1. This section also includes analytical formulae for the quasi-static impedance and the quasi-static permittivity of C B A C P S lines. Section 2.2 contains a brief summary of the patch antenna theory and its rationalization of resonances observed in C B A C P S lines. This section, also includes a comparison between W. H. Haydle's approach for predicting resonances in conductor backed coplanar lines [13,19] and ours. We show that although the resonance frequencies of higher order P P modes cannot be easily calculated, the frequencies of resonances caused by the lowest order P P mode are well predicted. In section 2.2.2 we discuss four possible methods of suppressing coupling between the coplanar and P P modes in C B A C P S lines. These methods wi l l include narrowing the width of the ground strip, adding an air-gap under the substrate, adding a high dielectric constant superstrate, and using slow-wave electrodes. 8 2.1 Microwave transmission lines In this section we review the theory behind microwave transmission lines, followed by analytical formulae for the quasi-static impedance and permittivity of C B A C P S lines. B y way of review, Figure 2.1 shows the circuit model of a lossless transmission line for a differential length, dz [35]. Considering a differential length of line, dz, having the distributed inductance, L per unit length, and a distributed capacitance, C per unit length, the change in voltage, dV across dz is equal to the product of this inductance and the time rate of change of the current, /. Similarly, the change in current along the length at any instant is merely the current that is shunted across the distributed capacitance. Therefore: 7T = -4 (21> dz dt dz dt Taking the partial derivative of equation (2.1) with respect to distance and of equation (2.2) with respect to time, or vice versa, the following wave equations are obtained: d2V 1 d2V ^-r = - r ~ (2-3) dz2 v2 dt2 and ^ = - L ^ (2.4) dz2 v2 dt2 where 9 I+dl/dzdz V +dV/dzdz dz The circuit model of a transmission line of differential length, dz. Ldz r v f \ V Cdz 10 v represents the velocity of the transverse electromagnetic wave carried by the transmission line, c is the speed of light in vacuum, and n A is the microwave index. As seen from (2.5) the velocity depends on the inductance and capacitance per unit length. Similarly, it can be shown that the ratio of the voltage to the current of a traveling wave at any given point along the transmission line and any given instant, i.e., the characteristic impedance of the line, also depends on the inductance and capacitance per unit length [35]: where R and G are the series resistance per unit length and shunt conductance per unit length of the transmission line, respectively. At higher frequencies (> 3GHz for typical microwave line parameters [36]), the frequency dependant terms of (2.7) dominate the ohmic loss terms, R and G , making (2.6) a good approximation. For conventional, thin, surface deposited, coplanar strips (CPS), asymmetric coplanar strips (ACPS) , and coplanar waveguides (CPW) fabricated on a semi-infinite dielectric substrate, the microwave index, nM, can be approximated by [37]: (2.6) If the electrical loss along the line is accounted for, equation (2.6) becomes [36]: (2.7) II er + 1 2 (2.8) where s r is the dielectric constant of the substrate. The above formula assumes both a semi-infinite substrate and a semi-infinite superstrate (here air), with half the electric field in the substrate and half in the air. The focus in practical M M I C applications, however, is on conductor-backed substrates with finite thickness; due to conductor-backing, more of the electric field wi l l be in the substrate, causing the value of nM to be considerably higher than that given by equation (2.8). For the case of C B A C P S lines (see Figure 2.2), assuming pure, quasistatic, T E M mode propagation with a homogeneous substrate of permittivity e r, and a homogenous dielectric above the strips with permittivity e r t , the microwave index is given by [38]: Pt +Pb (2.9) and the impedance is [38], 12071 bt + P J l-i (2.10) where (2.11) 12 and 9b = K{Pbl) , K{pbr) K{Pbl') K{Pbr) (2.12) s + 2w. (2.13) 8 s + 2wg ' (2.14) Pu = f f *Ps\ sinh ws+-V 2h sinh f ( S) 71 w. + — I ' 2 j 2h V ) (2.15) Pbr sinh *Ps ws+~ V 2y V w r + — sinh 2psh (2.16) and the ratio K(k)/K(k') is the ratio of complete elliptical integrals of the first kind [38]; the primed variables are the complementary parameters defined as (k')2=]-k2. 13 Figure 2.2 Conductor-backed asymmetric coplanar strips ( C B A C P S ) . 14 2.2 Application of Patch Antenna Theory to CBACPS Lines This section is divided into three subsections entitled: patch antenna theory, resonances in conductor-backed coplanar lines, and higher-order modes. The patch antenna subsection provides a brief overview of the patch antenna theory and a general method for calculating the resonance frequencies of parallel-plate (PP) modes, with the assumption that effective permittivity of the modes is equal to the permittivity of the substrate. The subsection "Resonances in conductor-backed coplanar l ines" compares our method of calculating the effective permittivity of the lowest order PP mode with Haydle's method [13, 19]. We wi l l show our method is much more accurate than that of Haydle, and that Haydle's method is only valid for coplanar lines with large width to thickness ratios. The higher-order modes subsection discusses the coupling phenomena between the coplanar and higher-order PP modes. We wi l l estimate the frequency dependant permittivity of these higher-order modes and predict their cutoff frequencies. 2.2.1 Patch Antenna Theory The theory of rectangular patch antennas is well documented [39, 40]. For a rectangular microstrip patch antenna with resonant length L and width W, as shown in Figure 2.3, the fields under the patch antenna may be written as [39]: YYVK | [ nil —-x cos — (2.17) 15 Ex=Ey=0 (2.18) /•(0£0 Ml V0 kl L h cos ^ m7C ^ ^"""" ^ sin Ml (2.19) y kl W h f mil ^ TOT cos — y u (2.20) tfz=0 (2.21) where Vo is the voltage at a patch corner, h is the height of the patch substrate, and m and n depict the mode of operation. The resonant frequencies of rectangular patch antennas are given by the expression 2 ^ ' m N W + (2.22) where e r is the relative dielectric constant, c is the speed of light in vacuum, W and L are the width and the length of the patch, respectively, and m and n are integers, the mode indices. It should be noted that in the above formulae electric-field fringing effects are neglected. 16 Figure 2.3 A microstrip patch antenna configuration. 17 2.2.2 Resonances in Conductor-backed Coplanar Lines Figure 2.2 shows a section of a C B A C P S line. It consists of two coplanar metal strips of finite widths, ws and wg, for the signal and ground strip, respectively. The distance, or gap, between the two strips is denoted by s. The finite width substrate has a dielectric constant er and a thickness h. On the bottom of the substrate there is a ground plane. Later on, the C B A C P S line's length wi l l be denoted by L. A s can be seen in Figure 2.2, the coplanar strips and the grounded back conductor of a C B A C P S line form a parallel-plate waveguide. Parallel-plate (PP) modes are excited at port discontinuities and wil l propagate and couple with the dominant coplanar mode, which has its field distribution confined to the slot region [41]. According to coupled-mode theory [42], power can be exchanged between modes as they propagate and is dependant on the transmission line length. Energy outside the slot cross section of the C B A C P S (s of Figure 2.2) wi l l not be detected by the probe connectors and wi l l resonate in the finite length cavity, formed by the coplanar strips and the grounded back conductor. The resonating P P modes recouple to and interfere with the propagating coplanar mode [5]. For the case of a ground strip with an open (non-conducting) periphery (open-ground C B A C P S lines), the PP mode Z^-field distribution across the ground strip varies as a cosine function in both the x and y directions over the patch in accordance to equation (2.17), i.e., just as in a patch antenna. Hence, given the proper relative effective permittivity, eejf, equation (2.22) can be used to determine the resonant frequencies in open-ground C B A C P S lines with W being the width of the entire metallic structure and not simply the width of the ground strip, i.e., W -w„ + w, + s [5, 33,43]. 18 Previous works, by W. H. Haydle [13,19], attempted to predict the resonant frequencies of C B C P W s by using equation (2.22) with the assumption that the effective permittivities of the P P modes are equal to the substrate permittivity, i.e., zeff = er in equation (2.22). However, application of Haydle's method of calculating the resonant frequencies of conductor-backed coplanar lines, failed to accurately predict the resonant frequencies of the open-ground C B A C P S lines used in this work. This fact is illustrated in Figure 2.4. In this figure, which shows the transmission response of a C B A C P S line, the vertical doted lines represent the theoretical locations of resonances caused by the first order PP mode (later referred to as the M S L mode), and the vertical solid lines represent the theoretical location of resonances caused by the first higher order mode. The theoretical results were made using equation (2.22) assuming eeff = s r , i.e., Haydle's method. A s can be seen, the theoretical predictions of resonance frequencies using this method are highly inaccurate. Therefore, in order to calculate the resonant frequencies of our lines we wi l l use equation (2.22) without assuming that zeg = e r. Instead, here we wi l l divide the P P modes into two subcategories: the zero-cut-off microstrip-like T E M mode (the M S L mode), and the higher-order P P modes. In this work, we wi l l use the proper dispersion of the M S L mode to determine its resonant frequencies but wi l l not attempt to predict the resonant frequencies of the higher-order transverse modes. The resonant frequencies of the M S L mode are obtained using the following equations: P M 5 L L = nn (2.23) where, 19 P _ 2Won^£MSL\JOn) (2 24) MSL c with c being the speed light and /o„ being the nth resonant frequency of the M S L mode. Here, ZMLS (f) was determined • using Sonnet™ Suites Release 7.0, from Sonnet Software Inc., Liverpool, N Y [44]. Figure 2.5 shows the accuracy of equations (2.23) and (2.24) in predicting the resonant frequencies of an open-ground C B A C P S line. In Figure 2.5, the vertical doted lines represent the theoretical locations of resonances caused by the M S L mode, and the vertical solid line represents the theoretical cutoff of the first higher-order transverse mode. The theoretical results were made using equations (2.23) and (2.24). As can be seen the theoretical predictions of resonance frequencies (at least the ones below the higher order mode cutoff) are more accurate than the theoretical predictions shown in Figure 2.4. Therefore, it can be seen that for lines with dimension similar to these used in this work, it is not accurate to assume that the P P modes have an effective permittivity close to the substrate permittivity. Such an assumption is only valid when W» h, which was the case in Haydle's work [13, 19]. It should be noted that equations (2.23) and (2.24) are only accurate at determining resonant frequencies lower than the cutoff frequencies of the higher-order transverse modes. 2.2.3 Higher-order Modes The higher-order transverse modes can be characterized by the combination of two types of transverse modes: modes formed by standing waves in the substrate-thickness direction, and modes formed by standing waves in the lateral direction. 20 Transverse modes formed by standing waves in the substrate-thickness direction are governed by the equation A / 2 = h, where the parameter / denotes an integer value, i.e., / = 1,2,3,.... The approximate effective permittivity of these modes are given by s ^ ( ' 0 ) = e r - (Ix)21 ( M ) 2 [33]. Transverse modes formed by standing waves in the lateral direction, which resemble the higher-order microstrip modes, have their cutoff frequencies determined by the total lateral width, W, of the C B A C P S line. Thus, these modes are governed by the equation nik/2 = W, where W = wg + ws + s, and m = 1,2,3,.... It was found that the frequency dependant relative effective permittivity of these modes is approximately described by 1 £eff°m^ = £ r - (mn)21 (PoW)2. In a more general view, following the notation used by W . Heinrich et al. [33], the higher-order modes can be classified by the two indices / and m and wi l l be denoted by H M / , m in the following. The effective permittivity of mode H M / , m is approximately 1 n 2 + ( UJ I ,w) _ (2.25) The cutoff frequency of the higher-order (HM) modes is defined as the frequency at which the effective permittivity calculated by equation (2.25) goes to zero. Note that for lateral H M modes, this cutoff frequency can also be calculated by patch antenna theory; i.e. using equation (2.22) with n = 0. ' In obtaining this equation, the method used by W. Heinrich et al. [33] to describe resonances in CBCPW lines was followed, taking into account that the higher-order modes in CBACPS lines are not necessarily symmetric. 21 It is important to note that although equation (2.25) can be used to accurately predict the cutoff frequency of the H M modes, i.e., for s ^ ( / m ) = 0, this equation cannot be used to predict the exact location of resonances above the H M mode cutoff. This is due to the fact that the exact dispersion calculations for the H M modes are nontrivial, and that equation (2.25) is merely an approximate solution. Nonetheless, equation (2.25) provides a great understanding of the nature of the resonance phenomena and leakage above the cutoff frequency of the higher-order modes. In this work, substrates of thickness 250 um are used. Since h, being 250 um, is less than A/2 in the frequency range studied here, H M modes with a nonzero / index are disregarded. Figure 2.6 illustrates the approximate open-ground C B A C P S mode patterns, and Figure 2.7 shows the dispersion of the relevant modes of a C B A C P S line with ws = 120 um, s = 28 pm, and wg = 1 mm, (and L - oo). As seen in Figure 2.7, above the cutoff frequency of the first higher-order mode, there exists a finite region in the frequency spectrum in which the effective permittivity of the higher-order mode is less than unity. In this region the mode is leaky, meaning its power decays exponentially with propagation distance, as power is radiated into space. Fortunately, in this work the coupling between the coplanar mode and the leaky mode is small and, therefore, the amount of power that leaks away from the line is relatively low; this is due to the fact that the relative permittivity of the alumina substrate is high, allowing the effective permittivity of the coplanar mode to be much higher than that of the leaky mode. However, leakage in higher-order modes can drastically deteriorate the response of C B A C P S lines if low permittivity substrates, such as quartz, are used; since the effective permittivity of the coplanar mode wi l l be close to that of the leaky mode allowing for significant coupling and leakage. 22 Above this region, where the relative effective permittivity of the higher-order mode is equal to or greater than unity, the higher-order mode becomes bounded. However, as the effective permittivity of the higher-order mode increases and approaches the permittivity of the substrate, the £<$(/) curves of the higher-order mode and the coplanar mode cross each other. In the frequency region around this point strong coupling between the coplanar mode and the higher-order mode can occur, which would deteriorate the response of the line and possibly cause lossy resonances. It should be noted that, due to different symmetry (see Figure 2.6), coupling between the coplanar mode and M S L mode is constrained and generally resonances caused by the M S L mode do not deteriorate the frequency response of the C B A C P S line as much as resonances caused by H M modes, which at certain frequencies strongly couple to the coplanar mode causing sharp, lossy spikes in the frequency response (see Figure 2.5). 23 Figure 2.4 Measured |S21| of C B A C P S line with wg = 1 mm, s = 28 um, ws = 120 um, L = 1 cm, and /i = 250 um. The vertical doted lines represent the theoretical locations of resonances caused by the M S L mode, and the vertical solid lines represent the theoretical location of resonances caused by the first higher order mode. The theoretical results were made using equation (2.22) assuming eeff = er, i.e., Haydle's method. As can be seen the theoretical predictions of resonance frequencies using this method are highly inaccurate. 24 Figure 2.5 Measured |S21| of C B A C P S line with wg = 1 mm, s = 28 um, ws= 120 um, L - 1 cm, and h = 250 um. The vertical doted lines represent the theoretical locations of resonances caused by the M S L mode, and the vertical solid line represents the theoretical cutoff of the first higher order mode. The theoretical results were made using equations (2.23) and (2.24), while the cutoff of the HMo.i mode was calculated using equation (2.25). A s can be seen the theoretical predictions of resonance frequencies (at least the ones below the cutoff of the HMo.i mode) are more accurate than the theoretical predictions shown in Figure 2.4. 25 (a) Coplanar Mode (b) MSL Mode (c) HMo.i Mode Figure 2.6 The approximate mode patterns of the relevant modes of a C B A C P S line. 26 3.5 2.5 1.5 0.5 • HM01 (Leaky) -HM01 (Bounded) -MSL 'Coplanar 10 15 20 25 30 Frequency (GHz) 35 40 45 50 Figure 2.7 The effective microwave index of the modes shown in Figure 2.6 as functions of frequency. Sonnet™ was used to determine the dispersion of the M S L and coplanar modes, while equation (2.25) was used to estimate the dispersion of the HMo,i mode. The dashed line illustrates where the H M 0 , i mode is leaky. The open-ground CBACPS line used for this analysis had the following dimensions h = 250 pm, ws = 120 pm, $ - 28 pm, and w„ = 1 mm. 27 2.3 Suppress ion Methods In this section we discuss various ways of improving the frequency response of CBACPS lines. There are two main ways of improving the response of these devices; one is to reduce the coupling between the coplanar and PP modes, the other is to move the cutoff frequency of the H M modes out of the frequency range of interest. A reduction of mode coupling between the coplanar and PP modes can be achieved by, either, increasing the effective permittivity of the coplanar mode, or by decreasing the effective permittivity of the PP modes. The latter method can be implemented by placing an air-gap under the substrate, while the former method can be implemented by application of a high dielectric constant superstrate, or by utilization of slow-wave electrodes. Increasing the cutoff frequency of H M modes above the frequency range of interest can be accomplished by either narrowing the ground strip or by placing a large enough air-gap under the substrate. In the following subsections, the inherent advantages and disadvantages of each of these methods (narrowing the width of the ground strip, having an air-gap under the substrate, having a high dielectric constant superstrate, and using slow-wave electrodes) will be discussed. Furthermore, there will be a subsection describing the effects of shorting the outer edge of the ground strip to the backside metallization, as a mean of eliminating the M S L mode. 28 2.3.1 Effect of Ground Strip Width At the resonant f requenc ies , / m n , there is significant leakage into the relevant P P mode causing a considerable decrease in the impedance of the line [14]. A s a result, fhe/ f f l,„ correspond to frequencies at which the radiated and reflected power is significantly increased. From equation (2.22), it can be observed that having W and L lower than certain values, could cause all /„,,„ to be higher than the maximum operating frequency. In short, below a certain frequency, resonances caused by H M modes can be avoided by making W small enough so that the C B A C P S line cannot support any H M modes, and M S L mode resonances can be avoided by making L less than A,MSI/2. This "finite-ground" C B A C P S , wi l l exhibit no resonances and no power loss, excluding thermal losses, over the operating frequency range. However, for complex coplanar M M I C s with a mesh of coupled ground planes or for devices on high dielectric constant substrates requiring relatively long transmission lines, the approach based on "finite-ground" coplanar lines is not practical. One method of suppressing lossy resonances while keeping a certain length, L, would be to minimize the width of the ground strip. This may cause the H M 0 , i mode to have a cutoff frequency above the frequency range of interest; however, it wi l l not affect the resonances caused by the M S L mode. 29 2.3.2 Effect of Air-gap Below Substrate Another method of suppressing the coupling to P P modes at their resonances is by having an air-gap under the substrate (see Figure 2.8). Since most of the electric field lines of the coplanar mode are located near the surface of the substrate, the air-gap wi l l not have a significant effect on the propagation constant of that mode; however, it wi l l decrease the effective permittivity of the P P modes considerably, as most of the electric field lines of the P P modes are vertical. As a result, coupling between the coplanar mode and the PP modes is inhibited. Figure 2.9 shows a comparison of the effective permittivity of the coplanar and the M S L modes of a C B A C P S line with a 250 pm air-gap under the substrate. The results show that an air-gap of 250 microns drastically lowers the effective permittivity of the M S L mode from near 9.8 to 6, at high frequencies. Since, H M modes are effectively higher order M S L modes, it is expected that the air-gap wi l l also substantially decrease the effective permittivity of the H M modes. Furthermore, a decrease in the effective permittivity of an H M mode results in an increase in the cutoff frequency of that mode; therefore, an air-gap could be used to move the cutoff of H M modes above the frequency range of interest. However, care needs to be taken to make sure that the air-gap is not so large as to allow modes with standing wave patterns in the z direction. In this work, it was found that an air-gap of 254 pm was, indeed, large enough to move the cutoff of the H M 0 , i mode above the maximum frequency studied, i.e., 50GHz. 30 Figure 2.8 A C B A C P S line with an air-gap between the substrate and the supporting backside ground plane (easel C B A C P S ) . 31 32 2.3.3 Effects of High Dielectric Constant Superstrates and Slow-wave Electrodes It is also possible to inhibit the coupling between the coplanar mode and the P P modes by making the coplanar mode significantly slower, i.e., have a higher microwave index, than the PP modes. This can be achieved by having a relatively thick, high dielectric constant superstrate (see Figure 2.10). The addition of a high dielectric constant superstrate wi l l significantly increase the propagation constant of the coplanar mode, as about half of its field lines wi l l be in the superstrate. However, since most of the electric field lines of the PP modes are located in the substrate, between the top and bottom metallization, the propagation constant of the P P modes are not as effected by the superstrate as the propogation constant of the coplanar mode. Similarly, it is possible to slow the coplanar mode, by capacitively loading the coplanar electrodes of a transmission line. Such slow-wave electrodes (see Figure 2.11) wi l l increase the propagation constant of the coplanar mode while having little effect on the P P modes. It is possible to design slow-wave electrodes that provide enough capacitance per unit length to make the coplanar mode significantly slower than the P P modes, and thereby reducing the coupling from the coplanar mode to the P P modes. This thesis reports the first use of slow-wave structures to suppress unwanted modes in conductor-backed coplanar lines; experimental results wi l l be covered in section 4.5. 33 Figure 2.10 A C B A C P S line with a high dielectric superstrate of thickness ht. In order to make the coplanar mode slower than that of the P P modes, the superstrate needs to be relatively thick and have a permittivity higher than that of the substrate (caseh C B A C P S ) . 34 Figure 2.11 A slow-wave C B A C P S line. 35 2.3.4 Effect of Shorting Ground Strip to Back-side Metallization B y shorting the outer edge of the ground strip of the coplanar line to the metal plane at the bottom of the substrate (shorted-ground C B A C P S ) , as seen in Figure 2.12, we can eliminate the M S L mode. However, this method does not suppress all resonances. Instead, the change in boundary conditions gives rise to other allowed mode patterns which must exhibit zero field at the outer edge of the ground strip and maximum field along the outer edge of the signal strip (see Figure 2.13). The Ez distribution now varies as a sine function in x and a cosine function in y: To estimate the effective permittivity of the mode as a function of frequency, equation (2.25) still applies with m replaced by odd multiples of 0.5. Therefore, the lowest order H M mode wi l l be HM 0,o.5, which has a lower cutoff frequency than the H M 0 , i mode, which exists in open-ground C B A C P S lines (see Figure 2.14). However, the cutoff frequency of the HM 0,o.5 mode can be increased by narrowing the width of the shorted ground strip, see Figure 2.15. By comparing Figure 2.14 with Figure 2.15, it is seen that as the width of the ground strip is decreased from 1 mm to 0.5 mm, the cutoff of the HM 0 >o.5 mode increases from 21 G H z to 37 (2.26) G H z . 36 Figure 2.12 A shorted-groundCBACPS line. 37 X (a) Coplanar Mode Figure 2.13 The approximate mode patterns of the relevant modes of a shorted-ground C B A C P S line. 38 3 2.5 c 1.5 0.5 — HMO.0.5 (Bounded) - HMO.0.5 (Leaky) —Cop lanar 10 15 20 25 30 Frequency (GHz) 3 5 40 45 50 Figure 2.14 The effective microwave index of the modes shown in Figure 2.13 as a function of frequency. Sonnet™ was used to determine the dispersion of the coplanar modes, while equation (2.25) was used to estimate the dispersion of the HMo,o.5 mode. The shorted- ground CBACPS line used for this analysis had the following dimensions ws= 120 um, s = 28 um, and wg = 1 mm. As can be seen the two curves cross at approximately 33.5 GHz, around which severe mode coupling is expected. 39 3 2.5 c 1.5 0.5 • HMO.0.5 (Leaky) -HM0,0.5(Bounded) -Coplanar 10 15 20 25 30 Frequency (GHz) 35 40 1 5 50 Figure 2.15 The effective microwave index of the modes of a shorted-ground CBACPS line, with dimensions ws = 120 jam, s = 28 um, and wg = 0.5 mm, as a function of frequency. Sonnet™ was used to determine the dispersion of the coplanar modes, while equation (2.25) was used to estimate the dispersion of the HMo,o.5 mode. 40 3 Design and Fabrication In this chapter the design and fabrication of C B A C P S lines and their housings are described. The design and fabrication information is contained in four sections entitled: electrode design, mask design, fabrication, and housing design. The electrode design section begins with a brief description of the computer aided design (CAD) software used. Then information regarding how the software was used to design C B A C P S lines is given. Finally, the dimensions of the chosen C B A C P S lines are outlined. The mask design section contains the mask specifications information, while the fabrication section outlines the processing steps involved in the fabrication of devices. The housing design section, describes how the C A D software was used to design the housings of the devices. It also outlines the dimensions of the housings chosen. 3.1 Electrode Design This section is divided in to two subsections. The first subsection, contains a brief description of the C A D software used, namely, Sonnet'" Suites Release 7.0. This subsection also contains information regarding the utilization of this software in simulating coplanar transmission lines. The second subsection, presents the result of the Sonnet™ simulations and gives the dimension of the different types of C B A C P S designs chosen. The different types of C B A C P S lines selected wi l l be used to test the various mode coupling suppression methods mentioned in Section 2.3. The result of these tests are presented in Chapter 4. 41 3.1.1 The High Frequency Electromagnetic Software, Sonnet The C B A C P S electrodes were designed using the high frequency electromagnetic software package, Sonnet™ Suites Release 7.0. The model used by the software consists of a metallic box fil led with several dielectric layers. The top and bottom conductors of the metallic box can have non-zero resistivity values, while the side walls are lossless. The software performs electromagnetic analysis of transmission lines and other 3-D planar circuits by solving the current distribution on the circuit conductors (the metallization) using the method of moments [44]. The metallization is modeled as zero-thickness conductors between dielectric layers. The analysis begins by subdividing the circuit's metallization into small rectangular subsections. The size of the individual subsections depends on the required accuracy of the simulation as well as the wavelength of the electromagnetic wave for which the circuit is being analyzed. Then the electric field everywhere within the box, due to the current in each subsection, is evaluated. Hence, the "coupl ing" between each possible pair of subsections is effectively calculated (see [45]). The problem is then solved by assuming current on all subsections simultaneously, and adjusting these currents such that the total tangential electric field goes to zero everywhere that there is a conductor. The solution wil l be the current distribution on the metallization. Once the currents are known, the S-parameters follow (see [45]). If the metallization is not lossless, the boundary condition is modified such that the tangential electric field wi l l be proportional to the current, rather than being zero. The constant of proportionality used is the surface resistivity (Ohm's Law). For a 2 port device one can get the impedance, loss and microwave index from the S-parameters as follows [36]: 42 S\2S2l 'OR S22 SU —TJ(^ + s\2S21 SUS22^ ^S2\ (3.1) a + /S = —In L 1 + SnS2i SUS22 2s + 21 1 + sns2X S\\S22 2s2X -1 (3.2) and S t 2nf (3.3) where Z0R is the impedance reference (= 50 Q in this work), L is distance between the ports, a is the attenuation coefficient (in Np/cm if L is in cm), P is the microwave propagation constant, c is the speed of light in vacuum, and / i s the frequency of the microwave signal. For equation (3.1) the solution for which Re{Zo} is positive is chosen and, similarly, for equation (3.2), the result which gives a positive value for a is chosen. Having modeled conductors as infinitely thin sheets of metallization, Sonnet™ calculates the total, frequency dependent, surface impedance of the conductors according to [46] z _ d + j)RRF4f l - e R d c (3.4) where RRF and Roc are provided by the user and are defined as R DC at (3.5) 43 and In the above equations t represents the conductor thickness (m), a is the bulk conductivity (S/m), and u is the conductor magnetic permeability (in this work JJ . = uo = An X 10" H/m). It should be noted that (3.6) is only valid when the skin depth of the current is less than half the conductor thickness [46]. 3.1.2 Device design In order to test the validity of our theory in explaining the resonance phenomena observed in C B A C P S lines [47], regular C B A C P S lines (lines with single layer substrates and no superstrates (easel)) of varying length and width, were designed and tested. Furthermore, to test the effectiveness of various mode coupling suppression methods, C B A C P S lines with air-gaps under the substrate (case2), C B A C P S lines with high dielectric constant superstrates (case3), and C B A C P S lines with two types of slow-wave electrode [48, 49] (caseA and caseS) were to be simulated and implemented in the design. The dielectric layers used in modeling the easel, caseA and case5 lines used in this work, from bottom to top, are as follows: 250 urn of alumina having er = 9.8 and loss tangent = 1 x 10"4 , and 1 mm of air having s r = 1. For easel lines, a 250 um layer of dielectric having er = 1, was added under the alumina substrate. The dielectric layers used for modeling case3 lines were the same as the ones used for easel lines, expect a 650 um layer of GaAs having zr = 12.9 [50] was added between the alumina substrate and the 1 mm air above it. 44 The electrodes used in the simulation were made of gold having a = 3.42 x 10 7 S/m, and a thickness of 1.6 urn. The bottom of the metallic box, used as the housing in the Sonnet™ simulation, was made lossless. In order to simulate devices that are not shielded (do not have a metallic top), the top of the box was simulated having a resistivity of 377 ohms per square (impedance of free space). Using Sonnet™, it was found that the microwave characteristics of C B A C P S lines do not vary significantly between open-ground, and shorted-ground lines of similar dimensions; furthermore, the microwave characteristics of the line remained relatively constant as the width of the ground strip was decreased from 1000 pm to 500 pm (see Table 3.1, Table 3.2, and Table 3.3). In short, the width of the ground strip has little effect on the impedance and microwave index i f its value exceeds a few hundred microns. However, according to our theory, the size of the ground strip is directly correlated to the resonance frequencies observed. In order to test our theory, ground strips of widths 500, 700, and 1000 pm were designed; see Table 3.1. Moreover, every type of device designed on the mask was given two lengths, 1 cm and 2 cm. Casel C B A C P S lines of varying ws and s (see Figure 2.2) were simulated to achieve a 50 ohm line. From previous work [47,51], it was known that Sonnet™, by ignoring the thickness of the conductors, underestimates the capacitance and hence overestimates the resulting impedance by, typically, about 2 ohms. So the simulated impedances of casel lines chosen were slightly higher than 50 ohms; see Table 3.2 & Table 3.3. For casel and case2 lines, the chosen ws and s were 120, and 28 micrometers respectively. For case3 lines, the size of ws and 5 devices were changed to obtain a 50 Q. impedance; ws was decreased to 70 pm while s was increased to 40 pm. In addition, two types of slow-wave electrode were designed and simulated, namely caseA and case5. Figure 3.1 schematically illustrates the caseA slow-wave electrodes. The 45 dimensions of the line are shown in Table 3.1. As seen in the figure, caseA electrodes were composed of periodic rectangular capacitors along the C B A C P S lines. The capacitors were positioned 200 urn apart along the entire length of the C B A C P S lines. A s compared to easel electrodes, this formation increases both the capacitance and inductance per unit length of the C B A C P S line in such a way as to increase the microwave index while keeping the impedance at approximately 50 Q.; see Table 3.2 & Table 3.3. Note that the size of the capacitors is significantly smaller than the microwave wavelength at the frequencies of interests, allowing the microwave characteristics to be uniform along the length of the line. The microwave index of the coplanar mode traveling along a caseA line was simulated to be larger than 3.17 (see Figure 3.3). This value is considerably higher than the estimated microwave index of the relevant H M modes in the frequency range of interest (see Figure 2.7). The significantly higher microwave index of the coplanar mode, as compared to H M modes, should suppress any coupling between the two modes. The electrode loss is primarily dependant on the gap between the strips and the width of the strips [49]. The larger the gap and the wider the main strips, the smaller the loss. However, as long as the width of the main strips are larger than several skin depths, the electrode loss is chiefly dependant on the inter-strip gap rather than on the width of the strips [46]. A decrease in the gap between the strips increases the electric field between them and this in turns increases the current density near the edge of the strips, which leads to a higher resistive loss. The addition of the rectangular capacitors to C B A C P S lines in caseA electrodes, periodically decreases the inter-electrode gap between the signal and ground strips. A s seen in Figure 3.4, this significantly alters the current distribution on the main electrode and causes lossy current crowding at the edge of each capacitor. Therefore, as expected caseA electrodes were simulated to be significantly lossier than easel lines (see Figure 3.6). 46 Figure 3.1. The design model of 800 micron long caseA C B A C P S slow-wave electrodes, see Table 3.1 for dimensions. 47 Figure 3.2 The design model of 800 micron long case5 C B A C P S slow-wave electrodes, see Table 3.1 for dimensions. 48 Device s wf Wp h d Type (um) (Mm) (um) (um) (um) (um) (um) (um) Case\ (a) 1000 120 28 -Casel (b) 700 120 28 -Casel (c) 500 120 28 — - -Casel (a) 1000 120 28 - - - -Casel (b) 700 120 28 - — - -Casel (c) 500 120 28 Case3 1000 70 40 • — CaseA 852 48 8 120 160 200 Case5 (a) 956 72 8 32 24 10 190 200 Case5 (b) 456 72 8 32 24 10 190 200 Case's (c) 956 72 6 32 24 10 190 200 Table 3.1 The design parameters of the device types on the mask. Note each device type used on the mask had two lengths of 1 cm, and 2 cm. 49 Device Z 0 a Type («) (Np/cm) Case\ (a) 50.7 2.44 0.053 Casel (b) 50.8 2.44 0.053 Casel (c) 50.7 2.44 0.053 Casel (a) 55.0 2.40 0.052 Casel (b) 55.1 2.40 0.052 Casel (c) 55.0 2.40 0.052 44.2 3.49 0.080 CaseA 53.6 3.18 0.065 Case5 (a) 56.9 3.15 0.056 CaseS (b) 56.6 3.17 0.058 Case5 (c) 55.5 3.23 0.059 Table 3.2 The simulated microwave characteristics of the C B A C P S lines designed on the mask. Note these devices were simulated assuming the outer edge of the ground strip has been shorted to the box walls. 50 Device Z 0 a Type («) (Np/cm) Casel (a) 50.7 2.44 0.053 Casel (b) 50.7 2.44 0.053 Casel (c) 50.7 2.44 0.053 Casel (a) 54.9 2.40 0.052 Casel (b) 55.0 2.40 0.052 Casel (c) 55.0 2.40 0.052 44.2 3.48 0.080 CaseA 53.6 3.18 0.064 Casei (a) 56.9 3.15 0.056 Gzse5 (b) 56.6 3.17 0.058 Case5 (c) 55.4 3.22 0.059 Table 3.3 The simulated microwave characteristics of the C B A C P S lines designed on the mask to be tested with open ground strip periphery. Note the microwave parameters of these devices are very close to that of devices with shorted ground strips. This shows the microwave properties of devices are not changed significantly by grounding the ground strip. 51 20 25 Frequency (GHz) 40 Figure 3.3 The microwave index of a shorted-groundCase4 line as function of frequency. The microwave index has a minimum of about 3.17 which is higher than (s r) 1 / 2 at 3.13. 52 A n ingenious design for slow-wave structure was first proposed by R.G. Walker et al. [48] and later improved by N.A.F . Jaeger et al. [49], in which fins and pads replaced the rectangular capacitors (see Figure 3.2). The addition of fins and pads, as compared to case 1 electrodes, increases the capacitance per unit length of the line, while keeping most of the current along the main electrodes (see Figure 3.5). Therefore, case5 electrodes which employ fins and pads to get similar impedance and microwave index values as caseA electrodes (see Table 3.2, & Table 3.3), have a significantly lower loss. However, due to the complexity of case5 electrodes and hardware limitations, actual length electrodes could not be simulated. Typically a length of 800 microns, which is equivalent to 4 times the fin period, d, was used. In our theory and design, we implicitly assumed that the electrode length does not affect the microwave characteristics of devices, at non-resonant frequencies; in short, infinitely long electrodes were assumed. This is expected to be a fair assumption in the simulation of these devices as long as the length is larger than the substrate thickness [44]. Since the substrate thickness is only 250 microns, results of the case5 simulations can be trusted to be fairly accurate. However, it should be noted that even though the microwave characteristics (impedance, microwave index, loss per unit length) of case5 electrodes can be accurately simulated by using shorter electrodes, the length dependent resonant behavior of the devices cannot be accurately simulated. 53 Figure 3.4 The current distribution of CaseA electrodes at 5 GHz. It can be seen that the rectangular capacitors have great effect on the current distribution, and cause the current to be concentrated along the inner edge of the electrode very close to the opposing electrode. The high concentration of current near the opposing electrode causes the structure to be very lossy. 5 4 Figure 3.5 The current distribution of Case5 electrodes at 5 GHz. Unlike the caseA structure, the most of current remain travels along the main electrode and a relatively insignificant amount enters the capacitors (fins & pads), making case5 structures relatively low loss. 55 0.18 i 0 _| , , , , , , , , 1 0 5 10 15 20 25 30 35 40 45 Frequency (GHz) Figure 3.6 Comparison of the simulated electrical loss of caseA electrode design and casel electrode designs. 56 3.2 Mask Design This section describes the placement of the C B A C P S lines on the mask as well as giving the specifications of the mask. The mask for the electrodes included 25 types of asymmetric coplanar strips (ACPS) (some of which were copies of each other). Theses types included, casel A C P S lines with ground strip widths, wg, of 1 mm, 0.7 mm and 0.5 mm, casel) and caseA A C P S lines with w g = 1 mm, and case5 A C P S lines with wg - 1 mm and wg = 0.5 mm (see Table 3.1). A l l devices mentioned above were designed for use with the shorted ground strips and floating (open) ground strips; see section 3.4. A l l types of electrodes were designed with two lengths of 1 cm, 2 cm. A l l types of lines were located parallel to one another at 2 mm intervals. The mask was laid out using the Sonnet™ Suits Release 7's Project Editor [44]. Compressed forms of the mask files in GDSI I format were sent to Adtek Photomask Inc., Montreal, Quebec, for mask fabrication. The mask was made on a 4 " x 4 " x 0.06" soda lime substrate using optical pattern generation with a precision of ± 1.0 micrometers. The mask was a dark-field mask; that is, the A C P S lines were transparent while the spacing between electrodes was opaque with an anti-reflection chrome coating. 57 3.3 Fabrication In this section we describe the steps involved in the fabrication of the devices after the mask was made. Two alumina substrates with A C P S electrodes on the surface were fabricated at the University of Brit ish Columbia's (UBC 's ) Center for Advanced Technology in Micro-fabrication. One of the substrates was fabricated with conductor-backing and one was fabricated with no backside processing. The fabrications were done using a single-step cholorobenzene lift-off process [52, 53, 54] and involved the fol lowing steps: 1. The substrates were cleaned by first putting them in a beaker of acetone and slowly heating the beaker to a temperature of 50° C . The substrates were then transferred to a second beaker of Acetone at 50° C , where they sat for approximately 5 minutes. 2. The samples were rinsed with deionized water for about 3 minutes, and then blown dry with N2 gas. 3. 212 A of chromium followed by 10,000 A of gold were evaporated onto the backside of one of the substrates using a thermal evaporation system from Carl Herman & Associates Inc. ( C H A ) , Menlo Park, C A . Since gold does not bond very well to alumina, the chromium is added to serve as an adhesion layer between the gold and the alumina. 4. Shipley's SI818 negative photoresist, from Shipley Company Inc., San Jose, C A , was spun on the front side of both samples at 4700 rpm for 40 seconds. 58 5. The photoresist was softbaked at 95° C for 25 minutes. In this process, water and other solvents are evaporated from the newly applied photoresist and as a result, the photoresist hardens and adheres better to the substrate [55]. 6. After cooling down to room temperature, the substrates along with the fabricated mask mentioned in section 3.2, were put in the Karl-Suss M J B 3 contact mask aligner, from Kar l Suss America Inc., Waterburgh, V T . Through the mask, the photoresist was exposed to U V light at a wavelength of 320 nm for 90 seconds. 7. The samples were soaked in chlorobenzene for 8 minutes. 8. Immediately after removal from cholorobenzene, the samples were blown dry with N2 gas. The samples were left for about 20 minutes to allow for complete evaporation of the remaining chlorobenzene. 9. The photoresist was developed in Shipley's MF-319 developer for 4 minutes and 30 seconds. 10. 216 A of chromium and 8011 A of gold were evaporated on the front side of both substrates using the thermal evaporation system. 11. The samples were immersed in acetone to remove the photoresist and the unwanted metal on it. The acetone was heated up to 50° C to speed up the process. After a few minutes the metal on top of the photoresist peeled off as the photoresist dissolved in the acetone. 12. The samples were removed from the acetone and blown dry with nitrogen gas. The samples were checked under a microscope to make sure all the photoresist was removed. If any photoresist remained, the samples were placed back into the acetone and the above process was repeated. This was done a number of times; 59 unfortunately, some of the photoresist had become too hard (possibly due to the heat generated in the thermal evaporation system) and was not removed by the acetone after repeated attempts. This was the main reason for our fabrication yield being only about 70 percent. 13. The back of the samples were adhered to a sapphire substrate using Dynatex's 1.3 M I L standard wafer grips, from Dynatex International, Santa Rosa, C A . 14. Each of the 150 devices on both substrates was cut out using a dicing saw from Micro Automation Inc., Ancaster, Ontario, with a Dynatex™ Diamond Dicing Blade. The Blade had a thickness approximately 0.08 mm, so each device, having an original width of 2 mm on the substrate, had a width of approximately 1.92 mm after dicing. 15. The sapphire substrates were placed in Shipley's SVC28 solvent and heated to -50° C to remove the adhesive wafer grip. After a few minutes the 150 devices were separated from the sapphire substrate and were individually immersed in isopropanol for cleaning. 16. The devices were removed from isoproponal and blown dry with nitrogen gas. 17. Conductor-backed devices, which were to have their coplanar ground strips shorted to the backside metallization, were separated from the other devices. Colloidal silver l iquid (a type of silver epoxy), from Ted Pella Inc., Redding, C A , was used to short the ground strips of these devices to the backside metallization along the entire edge of the substrate. See Figure 3.10 and Figure 3.11. For devices with no conductor backing, the ground strips were shorted to the side walls of the housings using colloidal silver l iquid. The design of the housing is explained in section 3.4. 60 Colloidal silver is not very viscous and so when attempting to short the ground strips to the backside metallization or housing walls, care must be taken not to have the liquid silver epoxy leak into the gap between the ground and signal strips. Unfortunately, while applying the liquid silver epoxy, some of the devices' signal lines were shorted to the ground strips, effectively destroying the structure of the device. 61 Figure 3.7 Picture of a segment of a caseA C B A C P S device 62 Figure 3.8 Picture of a segment of a case5 C B A C P S device. 63 Figure 3 .9 Example of a device with shorted electrodes; our fabrication yield was about 70 percent. 64 Figure 3 .10 Silver epoxy is used to short the coplanar ground of a caseA type CBACPS to the back-side metallization. 65 66 3.4 Housing Design In this section we describe the design and fabrication of the housings, in which the devices were placed during microwave measurements. The results of these measurements are presented in chapter 4. The housings of the devices were to be narrow groves made in blocks of copper. The copper blocks used were designed to be 2 cm wide and 6 mm thick with lengths of 2.2 cm and 1.2 cm for devices of length 2 cm and 1 cm, respectively. Two sets of grove design were made. One set was designed for devices with conductor-backing and the other set was designed for devices with no conductor-backing, which were to have an air-gap under the substrate. The design of the channels is shown in Figure 3.13. For the case of devices with conductor-backing the channel was designed to be 1.3 mm deep and 2 mm wide (Figure 3.13(a)). Since the devices were only 1.9 mm wide, the design allowed the devices to be easily placed in the channel. However, the extra 0.1 mm of air-gap between the device and the side walls of the housing, prevented devices from being perfectly aligned with side walls, and therefore, caused small changes in the electromagnetic fields of the microwave as it traveled along the length of the device. For geometrical reasons, the above problem should be more noticeable in shorter devices, i.e. 1 cm long devices. However, even for 1 cm long devices, the 0.1 mm gap can at most cause an angle between the edge of the substrate and the walls of the channel of only 0.6°. Therefore, it is safe to assume that when a device is placed into the copper channel, its microwave properties remain relatively constant along the length of the device. Simulations done using Sonnet™ show this to be true (see Table 3.4). As seen from Figure 3.13, the design of the channel for casel devices is very similar to the channel design for other devices. The difference is that a secondary channel with a width of 67 1.5 mm and a depth 0.25 mm is made inside the main channel. The secondary channel is to be fi l led with air as the substrate sits above it (see Figure 3.14). To test the effect of an air-gap under an A C P S line, the width of the air-gap under the substrate would ideally be the same as the width of the substrate; however, the air-gap in the design is slightly narrower so that the substrate can be supported. The effect of the narrower air-gap was simulated using Sonnet™. The results of the simulation showed that the narrower air-gap had negligible effect on the microwave properties of a casel line. The fabrication of the channels in the pieces of copper was done at U B C ; however, due to equipment limitations, the channels fabricated did not have very smooth surfaces, and had an error of up to 10% in dimension sizes. These factors caused the loss of the devices to be more than we anticipated from the simulation results. However, the location of the P P mode resonances in the measured frequency spectrum and their suppression are not significantly effected by the minute changes in the dimension sizes of the channels and the surface roughness of the channel walls; therefore our theory and mode coupling suppression methods can still be tested, with imperfect housings for the devices. 68 Device Zo a Type («) (Np/cm) 1 cm long Case 1(a) 51.10 2.43 0.052 1 cm long Casel (a) at an angle of 0.06° to the box walls 50.89 2.44 0.051 Table 3.4 A comparison of the simulated microwave characteristics of case\{a) line with a case 1(a) line which is at an angle of 0.06° to the lateral box walls. 69 Figure 3.12 The copper blocks with groves used as the housing of devices. The picture shows the two different sized blocks used of length 2.2 cm, and 1.2 cm. The sizes of the blocks are compared to the size of a quarter. 70 ( 1 ) a b (2) Figure 3.13 The design of the two channels that were fabricated in copper blocks and acted as the housing of the devices. Design (1) is to be used for easel C B A C P S lines, with a = (1.3 ± 0.3) mm, and b = (2.0 ±0.1) mm. Design (2) is to be used for casel C B A C P S lines with a = (1.3 ± 0.3) mm, b = (1.6 ± 0.1) mm, c = (0.20 ± 0.05) mm, and d = (0.25 ± 0.02) mm. 71 (a) Figure 3.14 (a) Picture showing a caseS CBACPS device in a design (2) housing, (b) Same picture as (a) with the addition of white lines to highlight the edges of the channel. As can be seen there is an air-gap under the device. Also visible is the silver epoxy used to short the coplanar ground strip to the housing wall. 72 Figure 3.15 A top view of the device in Figure 3.14, compared to the size of a quarter. 73 4 Results The results of microwave measurements on the fabricated devices are presented in this chapter. Section 4.1 contains the description of the apparatus, as well as the details of the microwave measurement technique used in this work. Then the microwave measurement results, unique to each device type, are presented in sections 4.2, 4.3, 4.4, and 4.5, each type having its own section. The final section, section 4.6, contains the results of measurements done on casel devices outside of the copper housings. These results are compared with those of devices inside the housings. 74 4.1 Measurement Method In this section we describe the microwave measurement apparatus, and the measurement method used in this work. The S-parameter measurements were made using an Agilent 85IOC Vector Network Analyzer, from Agilent Technology Inc., Palo Al to, C A . The microwave probes used were Picoprobe™ 50A-GS-150-P, and 50A-SG-150-P models by G G B Industries Inc., Naples, F L . During the measurements, the model 50A-SG-150-P was damaged and had to be replaced by a Picoprobe™ P-9-4484-D model, see Figure 4.1. A l l probes had a pitch of 150 microns between signal and ground. The probes were connected to 00RHT3LC00024 phase stable cables from Semflex Inc., Mesa, A Z , which were then connected to the network analyzer. The probes were short, load, open and through (SLOT) calibrated using a Picoprobe™ CS-8 calibration substrate. For measurements, each device was placed in its proper copper housing, and then placed on top of a vacuum-pumped Teflon stand. The probes were lowered into the channel to contact the signal & ground strips at each end of the device. Data were taken at 801 equally spaced frequency points between 50 M H z and 50 G H z . The microwave line parameters were calculated from the S-parameters using equations (3.1), (3.2), and (3.3). 75 Figure 4.1 A close up of the stage on which the devices were tested. 76 4.2 Casel Results The casel results information are divided into three subsections: 4.2.1, 4.2.2, and 4.2.3 Section 4.2.1, contains the microwave measurements results for devices which do not utilize any mode coupling suppression schemes. The section includes a comparison of the frequency response of a 1 cm case1(a) device with that of a 2 cm casel(a) device. The results verify our theory that, while the spacing between M S L mode resonance frequencies is inversely proportional to the length of the C B A C P S line, the cutoff of the higher order (HM) modes is independent of the length of the line. In section 4.2.2, the frequency response of casel(b) and casel(c) devices are presented. These devices have narrower ground strips than the case\(a) devices. Comparison of easel (a), casel(b) and casel(c) results wi l l show that it is possible to increase the cutoff frequency of the H M modes above the frequency range of interest by simply narrowing the ground strip. Section 4.2.3, contains the measurement results of shorted-ground casel devices. It wi l l be shown that the results verify our theory regarding shorted-ground C B A C P S lines. 4.2.1 No Suppression Method Used Figure 4.2 shows the transmission response of a casel (a) C B A C P S line in its copper housing with L = 2 cm, ws = 120 um , s = 28 Lim, and wg = 1 mm. The doted lines in the figure correspond to the theoretical resonance frequencies, fon, of the M S L mode and the solid line corresponds to the theoretical cutoff frequency of the HMo ,i mode, which is at 41.7 G H z for this device. As can be seen, the M S L resonance frequencies are well predicted by our theory. A lso as predicted, lossy resonances, caused by the coupling and interference of the coplanar and HMo,i modes, appear right above the cutoff frequency the H M 0 , i mode; however, due to the fact 77 that the exact dispersion of the HMo.i mode is difficult to compute, the location of these resonances along the frequency spectrum are not predicted. Figure 4.3 shows the response of a device with the same structure as the one shown in Figure 4.2, but with L = 1 cm instead of 2 cm. In Figure 4.3, again, the doted lines represent the theoretical locations of resonances caused by the M S L mode, and the solid line represents the theoretical cutoff frequency of the FfMo,i mode. As can be observed, when compared to Figure 4.2, the spacing between adjacent M S L mode resonances in Figure 4.3 has increased as predicted by equations (2.22) and (2.23). However, since the width of the ground strip has not changed, the sharp, lossy resonances, caused by the existence of the HMo,i mode, are still in the same region of the spectrum with the theoretical cutoff still at 41.7 G H z . 4.2.2 Suppression with Width Adjustment One way of eliminating resonances, in the frequency response of C B A C P S lines, caused by H M modes, would be to decrease the total width, W, of the lines such that W < A. m i n /2, where A,mj„ is the lowest operating wavelength of interest. This technique would not affect the resonance frequencies of the M S L mode; however, it causes the HMo,i mode to have a cutoff frequency above the frequency range of interest. To test this, we compare the frequency response of a case] device with wg = 1 mm, i.e., casel(a), with a case] device with wg = 0.7 mm, i.e., case](b). A caselQo) line has a theoretical H M 0 , i mode cutoff at 56.5 G H z , as compared to 41.7 G H z for the case]{a) line. Since we can only measure the scattering parameters up to 50 G H z , HMo.i resonances should not be visible in the frequency response of the case](b) device. Figure 4.4 shows the transmission response of a case](b) device with L = 2 cm. Comparing Figure 4.4 with Figure 4.2, the transmission response of a case\(a) device with L = 2 cm, one can see that, even though the location of the M S L mode 78 resonances in the frequency responses of the two devices are the same, there are no signs of lossy resonances, caused by the H M 0 > i mode, in the frequency response of the case\(b) device (Figure 4.4). Similar results were observed in the transmission response of a 1 cm long casel device with wg = 0.5 mm, i.e. casel(c). This devices has a theoretical HMn,i mode cutoff at 74 G H z , and, as expected, it's transmission response does not show any sign of sharp, lossy resonances caused by that mode, see Figure 4.5. This proves that resonances caused by the H M modes can easily be moved out of a frequency range of interest by simply narrowing the width of the ground strip of the C B A C P S line. However, care needs to be taken in ensuring that the impedance, loss, and microwave index of the line are not significantly altered by the reduction in ground strip width, wg. 79 Figure 4.2 Measured |S211 of a C B A C P S line with wg = 1 mm, L = 2 cm, ws = 0.120 mm, s = 0.028 mm (casel(a)). The doted lines represent the theoretical location of resonances caused by the M S L mode, and the vertical solid line represents the theoretical cutoff frequency of the HMn,i mode. As can be seen, due to the relatively strong coupling to the coplanar mode, FfMo,i resonances cause more leakage than the M S L mode resonances. 80 I I I I I I I I I « I -8 - i ! ! ! ! ! ! ! ! ! -9 - ! ! ! ! i ! ! ! ! ! -10 -I r-1 , 1 , 1 1 1 , 1 1 ' , 1 r—J-" 1 1 0 5 10 15 20 25 30 35 40 45 50 Frequency (GHz) Figure 4.3 Measured |S211 of CBACPS line with wg = 1 mm, s = 28 um, w, = 120 um and L = 1 cm. The doted lines represent the theoretical location of resonances caused by the M S L mode, and the vertical solid line represents the theoretical cutoff of the first higher order mode. Although the spacing between the resonances has increased due to the shorter length, the cut off for H M 0 , i mode is still at 41.7 GHz. 81 0 -1 — -5 - . j | j | j ! ! ! ! ! ! ! ! I ! I ! ! ! OJ f 1 I I i I i i t t i f » i i i i i i — i i ! i > I ! I ! i ! i i i i i I i ! -6 - ; | | | j j ] ; | j | | | ] | | ] j | -7 --8 - ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! -9 - ! ! I ! ! ! ! ! ! I ! ! ! ! ! ! ! ! ! -10 -I 1 r-< 1 , 1 ' , 1 ' i 1 ' I 1 "-1 1 ' L - i 1 " - i ' ' 0 5 10 15 20 25 30 35 40 45 50 Frequency (GHz) Figure 4.4 Measured |S211 of a C B A C P S line with a wg = 0.7 mm, L = 2 cm, ws = 0.120 mm, s = 0.028 mm. The vertical doted lines represent the theoretical location of resonances caused by the M S L mode. Due to the small ground width, higher-order modes are not observed in the above frequency range. 82 -3 - ! ! ! ! ! i ! ! ! -i - ! I ! ! i ! j i ! 2" ! ! ! ! ! ! ! ! ! •o J J , , J J ( I i ^ -5 - j j ; ] j j j | ] W ' I ! I I I i i I — I ! ! ! ! ' ! ! ! -6 - ! ] | j | i i i ! -7 - ! j ! j ! j j j | -8 - ! I i ! ! ! ! ! ! -9 ! ! ! ! ! ! ! ! i -10 -I 1 - 1 1 — 1 1 — ' 1 ' 1 ' 1 1 1 ' 1 — ' 1 — 1 0 5 10 15 20 25 30 35 40 45 50 Frequency (GHz) Figure 4.5 Measured |S21| of a C B A C P S line with a wg = 0.5 mm, L - 1 cm, ws = 0.120 mm, s = 0.028 mm. The doted lines represent the theoretical location of resonances caused by the M S L mode. Due to the small ground width, higher-order modes are not observed in the above frequency range. 83 4.2.3 Shorted-ground Strip C B A C P S Lines. According to our theory, by shorting the outer edge of the ground strip of the chip to the metal plane at the bottom of the substrate, we can eliminate the M S L mode; however, the change in boundary conditions should give rise to newly allowed modes which must exhibit zero field at the outer edge of the ground strip and maximum field along the outer edge of the signal strip. The predicted cutoff frequencies, /,„,o, of the new PP modes are given by equation (2.22) with m replaced by odd multiples of 0.5 (see section 2.3.4). Results of the transmission response of a l c m long shorted-ground casel(c), i.e., wg = 0.5 mm, C B A C P S is shown in Figure 4.6. In this figure, the vertical line represent the theoretical cutoff of the HM 0,o.5 mode, which is at 37 G H z . The results, demonstrating the predictions of our theory, show a significant amount of leakage at frequencies higher than the cutoff. A more drastic effect of the coupling between the coplanar and HM 0,o.5 modes is observed in the transmission response of a 2 cm shorted-ground casel (b) device, see Figure 4.7. In this figure, as in Figure 4.6, the vertical line represent the theoretical cutoff of the HMo,o.5 mode; since wg = 0.7 mm, the HM 0,o.5 cutoff frequency of this device is lower than that of the casel(c) device. For this device the theoretical cutoff the HMo,o.5 mode is at 28.26 G H z . The shorted-ground devices were observed to be slightly lossier than the devices having the periphery of their ground strips open. This was true even at frequencies lower than the HM 0,o.5 cutoff. One possible explanation for this could be the loss associated with the silver epoxy used to short the ground strip to the backside metallization. Although the resistivity of the silver epoxy is quite low, it is still much higher than the gold evaporated on the substrates; furthermore, since the silver epoxy was applied by hand, the surface of the applied silver epoxy on the shorted-grounddevices was not smooth and increased the surface resistivity. 84 . 1 0 - | , , , , , , • r 1 , , 1 0 5 10 15 20 25 30 35 40 45 50 Frequency (GHz) Figure 4.6 Measured |S21| of a C B A C P S line with a wg = 0.5 mm, L = 1 cm, ws = 0.120 mm, s = 0.028 mm with a shorted ground strip. The vertical line represent the theoretical cutoff of the HMn,o.5 mode, which is at 37 G H z . Due to the fact that the outer edge of the ground strip is shorted, no resonances below this cutoff are observed. 85 Figure 4.7 Measured |S211 of a C B A C P S line with wg = 0.7 mm, L = 2 cm, w, = 0.120 mm, s = 0.028 mm with a shorted ground strip. The vertical line represent the theoretical cutoff of the HMo.o.s mode, which is at 28.26 G H z . Due to the fact that the outer edge of the ground strip is shorted, no resonances below this cutoff are observed. 86 4.3 Case 2 Results In this section, we present the result of microwave measurements on easel devices. These measurements test whether having an air-gap under the substrate is an effective method of suppressing the coupling between the coplanar and H M modes in C B A C P S lines. B y having an air-gap under the substrate the effective permittivity of the H M modes should decrease, thereby reducing the coupling between these modes and the coplanar mode. Moreover, the decrease in the effective permittivity of these modes could possibly move the cutoff of the H M modes above the frequency range of interest. This theory was successfully tested by measuring the microwave transmission response of a case2(a) device, with L = 2 cm, ws = 120 um , s = 28 um, and wg = 1 mm, that was placed in a design 2 housing (see Figure 3.13(b)). The response of this device is shown in Figure 4.8. Due to the fact that the size of the air-gap cannot be accurately measured nor can it be assumed that its size is constant along the length of the device, the theoretical model cannot accurately predict the resonance frequencies of this device. This is illustrated by the fact that the vertical doted lines of Figure 4.8, which represent the theoretical location of the M S L mode resonances, assuming a constant 254 um air-gap below the substrate, do not lie exactly on the resonance peaks of the frequency response. However, when compared to Figure 4.2, it can be seen that the spacing between the M S L resonances has increased, which shows that the air-gap has indeed decreased the microwave index of the M S L mode. Furthermore, Figure 4.8 shows no sign of resonances caused by the H M 0 , i mode, demonstrating that the air-gap has successfully increased the cutoff of that mode above the frequency range of interest. 87 Figure 4.8 Measured |S21| of a C B A C P S line with a wg = 1 mm, / =2 cm, ws = 0.120 mm, g = 0.028 mm with (0.25+/- 0.03) mm of air under the substrate. The vertical doted lines represent the theoretical location of resonances caused by the M S L mode. 88 4.4 Case 3 Results Microwave measurements were performed on case3 devices to test whether one can successfully suppress the coupling between the coplanar and PP modes, by having a high dielectric constant superstrate. If the superstrate has a significantly higher dielectric constant than the substrate, the coplanar mode should become much slower than the PP modes, thereby, decreasing the coupling between the coplanar and H M modes. To test this, microwave measurements were done for a 50 Q case3 device, with L = 2 cm, wg = 1 mm, ws = 70 pm, and s = 40 pm, by placing a 650 pm thick GaAs (e r =12.9) piece on top of the device. The superstrate was 1.95 cm long and 2 mm wide. According to simulations performed using Sonnet™, this configuration should make the coplanar propagation index considerably higher than the PP mode propagation index (see Table 3.2, & Table 3.3). The superstrate was slightly shorter than the substrate to allow for probing of the devices. The response was compared to that of a device with similar L and W dimensions with no superstrate (see Figure 4.9). A s can be seen from the figure, although PP mode resonances can still be observed, the fact that there is less coupling between the coplanar mode and the H M 0 , i mode makes the response of casei devices, which have GaAs superstates, smoother than the response of casel devices at frequencies above the H M 0 , i cutoff. In fact, resonances caused by the HMo,i modes are hardly noticeable. As mentioned in section 4.2, shorted-ground unloaded C B A C P S lines have significant loss at frequencies above the HMo,o.5 mode cutoff. By using with case3 electrodes along with a high dielectric superstrate in shorted-ground C B A C P S lines, the coupling from the coplanar mode to the HMo.o.s mode at high frequencies can be effectively eliminated. 89 Unfortunately, since some of the devices were damaged during fabrication, transmission responses from shorted-ground casel and case3 devices with similar widths, i.e., with similar HMn,n.5 mode cutoff frequencies, could not be obtained and compared. Figure 4.10 shows a comparison of the transmission response of a 2cm long shorted-ground casel and case 3 C B A C P S lines, with different HMo.,0.5 mode cutoff frequencies. In Figure 4.10, the thin curve shows the response of a 2 cm long shorted-ground case 1(b) device with a total metallic width, W, of 0.848 mm, the vertical thin line represents the theoretical cutoff of the HMo.,0.5 mode for this device, which is at 28.26 G H z , the thick curve shows the response of 2 cm long shorted-ground casei device with as total metallic width, W, of 1.110 mm and the vertical thick line represents the theoretical cutoff of the HMo.o.s mode for this device, which is at 21.58 G H z . From the figure, it can be observed that even though the casei device has a lower HM0,o.5 cutoff, its transmission response is much better than that of the casel(b) device. Figure 4.9 and Figure 4.10 illustrate the effectiveness of using high dielectric superstrates for the purpose of suppressing mode coupling between the coplanar and H M modes. 90 -8 -9 -10 10 15 20 25 30 frequency (GHz) 35 40 45 50 Figure 4.9 The thin curve shows the response of the device mentioned in Figure 4.2 ; the thick curve shows the response of a 50 Q, line with similar ground strip dimensions, yet with a 0.650 mm GaAs superstrate. The GaAs superstrate increases the microwave index of the coplanar mode relative to the PP modes, hence, decreasing the coupling between the coplanar and PP modes. 91 0 10 15 20 25 Frequency (GHz) 30 35 40 4 b 50 Figure 4.10 The thin curve shows the response of a 2 cm long shorted-ground case 1(b) device with a total metallic width, W, of 0.848 mm. The vertical thin line represents the theoretical cutoff of the HMo,o.5 mode for this device, which is at 28.26 GHz. The thick curve shows the response of 2 cm long shorted-ground case3 device with as total metallic width, W, of 1.110 mm. The vertical thick line represents the theoretical cutoff of the HMo,o.5 mode for this device, which is at 21.58 GHz. 9 2 4.5 Slow-wave Electrodes In this section, results of measurements done on caseA and caseS C B A C P S lines (lines with slow-wave electrodes) are presented. We wi l l show that using slow-wave electrode is an effective way of suppressing mode coupling in C B A C P S lines. Figure 4.11 shows the effective permittivity of the coplanar mode of the slow-wave structures case4, and case5, shown in Figure 3.1 and Figure 3.2, respectively, each with wg = 1 mm. A s is observed, the effective permittivity of the slow-wave structures, similar to that of case3 C B A C P S lines, is higher than the permittivity of alumina, allowing very low coupling between the coplanar mode and the higher order modes. The coplanar mode of an unloaded easel (a) line, on the other hand, has an effective permittivity which is close to the effective permittivity of the HMo,i mode (see Figure 4.11), hence, there wi l l be significant coupling and leakage from the coplanar mode into the HMo,i mode at frequencies above the HMo.i mode cutoff. In Figure 4.12 a comparison of the response of an unloaded (case 1(a)) line and a capacitively loaded (case5(a)) line are shown. The slow-wave structures of the electrodes make the devices slightly lossier than the unloaded devices, however, the lack of pronounced resonances caused by the H M 0 , i mode, make them attractive alternatives to the unloaded transmission lines for packaging purposes. Furthermore, N.A.F. Jaeger et al. [49] have shown that the loss associated with slow-wave electrodes can be significantly reduced by optimizing the design of the fins and pads. B y using slow-wave electrodes in shorted-ground C B A C P S lines, the coupling from the coplanar mode to the HMo.o.5 mode at high frequencies can be effectively eliminated. Figure 4.13 shows a comparison of the transmission response of a shorted-ground unloaded C B A C P S 93 versus a shorted-ground slow-wave C B A C P S of similar demensions. It can be seen that the response at frequencies above 40 G H z is dramatically enhanced by using slow-wave electrodes. Another example of this kind of improvement in the transmission response of shorted-ground casel devices is shown in Figure 4.14. Figure 4.14 shows a comparison of the transmission response of a shorted-ground unloaded, casel, C B A C P S versus a shorted-ground slow-wave, case5, C B A C P S of slightly different width. Due to the difference in the total metallic width of the devices, the two (casel and case5) devices have slightly different cutoff frequencies. In Figure 4.14, the thin curve shows the response of a 2 cm long shorted-ground case 1(b) device with a total metallic width , W, of 0.848 mm, the vertical thin line represents the theoretical cutoff of the HMo.o.5 mode for this device, which is at 28.26 G H z , the thick curve shows the response of 2 cm long shorted-ground case5(a) device with as total metallic width, W, of 1.148 mm, and the vertical thick line represents the theoretical cutoff of the HM0,o.s mode of the shorted-ground case5(a) device, which is at 20.87 G H z . It can be seen, from the figure, that even though the HMo,o.5 mode cutoff frequency of the case5(a) devices is lower than that of the case 1(b) device, the transmission response of the case5(a) device is much better than that of the case 1(b) device. Figure 4.12, Figure 4.13, Figure 4.14 illustrate that the greatest improvement in the transmission response of C B A C P S lines is achieved by util izing a combination of mode coupling suppression techniques: use of slow-wave electrodes along with narrow width shorted-ground strips. 94 13.00 12.00 11.00 10.00 CO 9.00 \ 8.00 7.00 6.00 5.00 4.00 -t 10 15 20 25 30 Frequency (GHz) • case5 * c a s e l " case4 - E r 35 40 45 50 Figure 4.11 The measured relative microwave permittivity of 1 cm long case 1(a), case4, case5(a) CBACPS lines compared to the relative permittivity of the alumina substrate (er = 9.8). 95 -9 — -10 J 1 1 1 1 . 1 1 1 1 0 5 10 15 20 25 30 35 40 45 50 frequency (GHz) Figure 4.12 The thin curve shows the response of a 1 cm long casel (a) device, and the thick curve shows the response of a case5(a) device with similar dimensions. The slow-wave structure makes the coplanar mode significantly slower than H M modes, thereby suppressing coupling between the two modes. 9 6 10 15 20 25 f requency (GHz) no 3b 40 4b 50 Figure 4.13 The thin curve shows the response of the shorted-ground casel(c) device; the thick curve shows the response of a shorted-ground case5(b) device with similar dimensions. The slow-wave structure makes the coplanar mode slower than PP modes suppressing resonances caused by PP modes. 97 25 Frequency (GHz) Figure 4.14 The thin curve shows the response of a 2 cm long shorted-ground case 1(b) device with a total metallic width , W, of 0.848 mm. The vertical thin line represents the theoretical cutoff of the HMo,o.5 mode for this device, which is at 28.26 GHz. The thick curve shows the response of 2 cm long shorted-ground case3 device with as total metallic width, W, of 1.148 mm. The vertical thick line represents the theoretical cutoff of the HM0,o.5 mode for this device, which is at 20.87 GHz. 98 4.6 Measurements with No Housing In this section, the effect of the proximity of the probe tips to the lateral walls of the channel wi l l be studied; furthermore, the results of microwave measurements on casel C B A C P S lines which were not placed in copper housings wi l l be presented. These results wi l l be compared to those of measurements done on devices in the copper housings. Since the devices were put into groves made on copper blocks, for measurement purposes the probe tips had to be lowered into the copper channels. This put the probes in close proximity of the lateral walls. In order to see the effect of a lateral conducting wall on the microwave line parameters, simulations using Sonnet™ were performed (see Table 4.1). From these simulation results, it was found that a distance of 400 microns between the signal line and the lateral wall was sufficient to keep the effect of the wall on the value of line parameters less than 0.1%. Since the probes were always more than 400 microns away from the lateral walls of the copper channels, it was assumed that the results of the measurements would not be significantly affected due to the presence of the lateral walls near the probe tips. Furthermore, measurement of crosstalk between the two probes 100 micron apart had shown a crosstalk of less than 35dB up to 50GHz [56], suggesting that the lateral walls of the channel were far enough away so as to not interact with the probes. However, when the responses of devices with conductor-backed substrates were measured outside the housings, on the Teflon stage shown in Figure 4.1, the results were significantly different from the responses of the same devices measured in housings (see Figure 4.15). It was observed that the location of P P mode resonances in the frequency spectrum were the same in both in-channel and on-Teflon measurements; indeed, the frequency response from both types of measurement were quite similar below the cutoff of the H M modes, however, the 99 loss associated with H M mode resonances was much more pronounced in measurements done outside the housings (Figure 4.15). This phenomenon can be explained by the fact that the M S L mode is bounded, while the H M modes are leaky near their cutoffs [57]. When the devices are in the channel, the power radiated by these H M modes is reflected by the lateral walls, and, in effect, is partially trapped in the channel. The trapped power travels down the channel and is received by the receiving probe. When the measurement is done with the device outside the channel, i.e., on the Teflon stage, the radiated power is not reflected back and the leaky mode simply radiates the power into space. 100 G r o u n d width (wg) Z„ a (nm) («) (Np/cm) 100 49.72 2.417 0.0510 200 50.45 2.432 0.0520 300 50.63 2.438 0.0523 400 50.70 2.441 0.0525 500 50.74 2.443 0.0526 1000 50.74 2.443 0.0526 Table 4.1 The result of simulations showing the effect of the lateral wall and ground width for shorted-groundcasel(a) devices. It is observed that the effect on line parameters is small for ground widths of more than 400 microns. 101 Figure 4.15 Comparison of the frequency response of a 1 cm long casel (a) devices measured in channel, versus outside the channel. 102 5 Conclusion This conclusion consists of three sections entitled: summary, discussion, and suggestions for future work. In the summary section, we review the result of this work. In the discussion section, we discuss the various advantages and disadvantages of each of the mode coupling suppression methods. This section contains comparisons of the different mode coupling suppression methods, and presents guidelines for using each method. The last section contains suggestions for future works. It provides recommendations for the industrial use of C B A C P S lines, as well as suggestions for gaining a better understanding of the resonance phenomena in C B A C P S lines. 5.1 Summary It has been shown that the ground strip of a C B A C P S behaves like an overmoded patch antenna supporting PP modes with analytically predictable resonance frequencies for simple rectangular geometries. Several mode coupling suppression methods, including shorting the outer edge of the ground strip patch to the backside metal plane, the use of an air-gap under the substrate, use of a high dielectric constant superstrate, and the use of slow-wave electrodes, was investigated. It has been shown that shorting the ground strip patch eliminates resonances caused by the M S L mode, however resonances related to the higher order (HM) modes, which appear at high frequencies, are not suppressed and are merely shifted in frequency. The use of an air-gap, under the substrate, lowers the effective permittivity of the PP modes shifting resonance 103 frequencies caused by higher order P P modes out of the range of interest. Furthermore it was shown that using slow-wave electrodes or superstrates with a relatively high dielectric constant can significantly reduce the coupling to P P modes. 5.2 D iscuss ion It was observed that low frequency M S L mode resonances observed in the frequency response of devices with an open ground strip periphery, had spacings that directly correlated with the length of the devices, in accordance with equation (2.23). It was also observed that the cutoff frequency for the HMo,i mode in C B A C P S lines was directly correlated to the width of the electrodes, in accordance to equation (2.25). Furthermore, it was observed that the M S L mode resonances can be eliminated by shorting the outer edge of the ground strip to the backside metallization of the C B A C P S lines; however, this shorting allows the existence of the HM0,o.5 mode which has a lower cutoff frequency than H M 0 , i mode, observed in devices with open-ground C B A C P S lines. The above observations are all in accordance to our theory and show that model does indeed explain resonant phenomena seen in the frequency response of C B A C P S lines. In general, shorting the outer edge of the ground strip of C B A C P S lines to the backside metallization was the best way to eliminate M S L mode resonances at low frequencies. However, care needs to be taken so that shorting the ground strip does not increase the resistance of the line. In this work silver epoxy was used for this purpose; however, it is recommended that wire bonds be used instead to improve the insertion loss of the device. Although shorting the ground strip eliminates the M S L mode, it does not eliminate the H M modes and in fact, lowers the cutoff frequency of H M modes. To ensure that resonances associated with these higher order modes are not within the frequency range of interest, one needs to design the C B A C P S line in such a 104 way that the total width of the structure, W = ws + s + wg, is less than a quarter of the wavelength of the relevant H M mode, at the highest frequency of interest. It was observed that devices with an air-gap under the substrate did not support any H M modes below 50 G H z . This was attributed to the fact that the air-gap lowered the effective permittivity of the PP modes and hence put the cutoff frequency of the first H M mode outside the range of interest. To increase the frequency range at which no H M modes exist, using this method, the air-gap below the substrate needs to be enlarged; however, the air-gap cannot be increased so much as to allow modes in the depth direction. Therefore, the use of air-gaps to suppress H M modes, is best suited for relatively low frequencies. Moreover, since the microwave line properties of devices with an air-gap are heavily dependant on the size of the air-gap, small variations in the fabrication of the housing wi l l have significant effects on the performance of the device. Consequently, for more reliable and repeatable device fabrication, other methods of mode suppression are recommended. Suppression of coupling to the H M modes was successfully achieved by the use of a high dielectric constant superstrate. However, due to the ever present port discontinuity, this method did not eliminate PP mode resonances. Using a high dielectric constant superstrate to suppress P P mode resonances in C B A C P S lines is cheap and easily implemented. However, placing a high dielectric constant superstrate on top of a case\ C B A C P S line, increases the capacitance per unit length of the line and in order to maintain a 50 Q impedance, the inductance per unit length of the line should be increased as wel l ; this is achieved by narrowing the signal strip, which has the unwanted effect of increasing the loss of the line. Therefore, for devices which require lower loss transmission lines, other methods of mode coupling suppression should be used. Likewise, since this method requires the 105 circuit to be surrounded with dielectric material, it is best suited for devices with a planar circuitry; for non-planar devices, the use of other methods is recommended. A similar success in suppression of H M mode resonances was observed in devices with slow-wave electrode structures. Similar to casei devices, slow-wave devices, especially devices with the caseA electrode design, had high losses. However, unlike case3 devices, slow-wave electrodes can be used in non-planar devices, without increasing the cost of fabrication. Furthermore, N . A . F. Jaeger et al. [49] have shown that slow-wave electrode structures similar to case5 electrode structures can be designed in way as to minimize the loss associated with these devices. In fact, it may be possible to design slow-wave structures that are less lossy than unloaded C B A C P S lines of similar dimensions. The use of low-loss, slow-wave electrode structures with a shorted ground strip would combine two methods of mode coupling suppression and would have great advantages over other methods. 106 5.3 Suggest ions for Future Work In this work, we were able to show that the frequencies at which M S L modes resonate in C B A C P S lines can be predicted by our theory using the microstrip dispersion model. The cutoff frequency of H M modes was also well predicted by the theory assuming seff = er for these H M modes. However, the exact location of the resonant frequencies of H M modes and the frequency response of devices above the H M mode cutoff frequencies could not be predicted using the above assumption. Furthermore, the exact field structure of the various modes and the coupling mechanism between them was not studied extensively. For a better understanding of the resonances observed in C B A C P S lines, it is suggested that the proper field structure of the various modes and the proper dispersion of the H M modes be theoretically modeled. This thesis provides a study of the effects of packaging A C P S lines, and their frequency response up to 50 G H z . The devices and casings fabricated were designed to show that packaging these devices does indeed cause resonances in the frequency range of interest, and to test the mode coupling suppression techniques proposed in this thesis. However, there was no effort made to optimize the devices and the packaging. For the devices to be useful in commercial systems, the structure of the C B A C P S lines along with the packaging process needs to be optimized to take advantage of the particular microwave characteristics these lines have to offer. Even though the optimization and the design of a transmission line is dependent on a particular application, here, we provide a few general guidelines to improve the performance of C B A C P S transmission lines: 1) As mentioned in [49], the insertion loss associated with caseS electrode structures can be greatly improved by adjusting and fine tuning the design parameters mentioned in 107 Table 3.1 and Figure 3.2. For example, minimizing wp and // and maximizing ws should significantly improve the insertion loss associated with case5 devices. Another mode coupling suppression method would be to short the ground strip to the backside metallization using vias located near the inner edge of the ground strip. In order to suppress resonances by shorting the outer edge of the coplanar ground strip to the backside metallization, one needs to make sure that the ground strip has a width less than a quarter of the wavelength of the microwave that wi l l travel along the transmission line. That means, in order for a C B A C P S line on alumina to have a bandwidth of 50 G H z it would need to have a width of no more than 480 um; this puts a severe constraint on the width and shape of the substrate. Therefore it's recommended that where large substrates are needed, vias be used for shorting the coplanar ground strip. However, in some applications, the use of vias increases the cost of fabrication dramatically, and lowers the advantage of C B A C P S lines over microstrips. 108 6 Bibliography [I] S. K i m , H. Yoon, and H. 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