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Coherent local oscillators for a 21 cm. supersynthesis experiment Shimozawa, David Tetsuo 1968

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COHERENT LOCAL OSCILLATORS FOR A 21 CM. SUPERSYNTHESIS EXPERIMENT by DAVID TETSUO SHIMOZAWA B.Sc. (E.P,), U n i v e r s i t y of Manitoba, 1963 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE We accept t h i s t h e s i s as conforming to the required standard Research Supervisor Members of Committee Head of Department Members of the Department of E l e c t r i c a l Engineering THE UNIVERSITY OF BRITISH COLUMBIA November, 1968 In presenting this thesis in partia 1 fu1fiIment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shall make i t 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 representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. The University of Brj'tish Columbia Vancouver 8, Canada Department ABSTRACT A method based on phaselock techniques, f o r synchronizing the l o c a l o s c i l l a t o r s i g n a l s in a proposed two-dish supersynthesis at 1420 MHz i s presented. To demonstrate the f e a s i b i l i t y of t h i s method, the design and c o n s t r u c t i o n of a working system that pro-vides phase-coherent, 1390 MHz s i g n a l s at.two s i t e s , separated by a time-varying path length, i s described. The phase accuracy of t h i s system i s -5°. A p r o v i s i o n f o r i n t r o d u c i n g a known phase d i f f e r e n c e between the two s i g n a l s , i n a imanner that i s s u i t a b l e f o r i n t e r f a c i n g with a d i g i t a l computer, i s included. Also, operation of the system oyer a frequency range greater than the expected range of doppler s h i f t i s p o s s i b l e , w i t h -out the r i s k of l o c k i n g to a wrong sideband. T r a n s i s t o r microwave o s c i l l a t o r s at 1.4 GHz are used as v o l t a g e - c o n t r o l l e d o s c i l l a t o r s i n t h i s system. The performance of these devices i s compared with that of the conventional v o l t a g e -c o n t r o l l e d c r y s t a l o s c i l l a t o r / m u l t i p l i e r chain. Test r e s u l t s are given, which i n d i c a t e that the system i s s u i t a b l e f o r use i n an o p e r a t i o n a l environment. i i TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS ' v i ACKNOWLEDGEMENT v i i i 1. INTRODUCTION 1 1.1 Supersynthesis . 1 1.2 The Proposed P e n t i c t o n Supersynthesis Experiment.. 3 1.3 Phase Coherence Requirements..' 5 1.4 I n t r o d u c t i o n of a Programmed Phase D i f f e r e n c e 6 1.5 I n t r o d u c t i o n of a Programmed Frequency Offset 9 1.6 Summary of Requirements f o r the Coherent L.O System 10 2. A REPRESENTATIVE COHERENT L.O. SYSTEM..' 11 2.1 I n t r o d u c t i o n . 11 2.2 The Representative System.... 11 2.3 Disadvantages w i t h the System of Figure 2-1 13 2.4 Design Guidelines f o r the Coherent L.O. System.... 14 3. A PHASE-LOCKED LINK 15 3-1 I n t r o d u c t i o n '. 15 3-2 The Phase-Locked Link — P r i n c i p l e s of Operation.. 15 3-3 The T r a n s l a t i o n Loop as a Sideband Generator 19 3-3.1 Phase and Frequency R e l a t i o n s h i p s 19 3-3.2 Advantages of the T r a n s l a t i o n Loop 19 3-4 The Problem of Wrong-Sideband Lock and i t s S o l u t i o n - - - 21 3-5 The Phase-Locked Link as a Coherent L.O. System... 25 3-6 An A l t e r n a t i v e Phaselock Method 27 4. ANALYSIS AND DESIGN - . 30 4.1 The Linear Loop Equations..... 30 i i i Page 4 . 1 The Linear Loop Equations. 30 4 . 2 Phase Erro r s Due to the T r a n s l a t i o n Loop '.. 33 4 - 3 Phase J i t t e r Due to Noise 35 4 . 3 - 1 I n t r o d u c t i o n 35 4 . 3 . 2 I.F. Noise ' 36 4 . 3 . 3 O s c i l l a t o r Noise 37 4 . 3 . 4 " E l a s t i c " Noise.. . .. '• 38 4 . 3 . 5 "Non-Elastic" Noise 4 0 4 . 4 Choice of a Vo l t a g e - C o n t r o l l e d O s c i l l a t o r (VCO) . . 42 4 . 4 . 1 I n t r o d u c t i o n 42 4 . 4 . 2 The Vo l t a g e - C o n t r o l l e d C r y s t a l O s c i l l a t o r (VCXO) and. M u l t i p l i e r 42 4 . 4 . 3 The T r a n s i s t o r Microwave O s c i l l a t o r (TMO).. 44 4 . 4 . 4 Comparing the VCXO-Multiplier and the TMO.. 46 4 . 5 Intermediate Frequency and I.F. Bandwidth Requirements ' 47 4 . 5 . 1 E f f e c t of I.F. F i l t e r 47 4 . 5 . 2 Choice of I.F. Bandwidth 49 4 . 5 . 3 Choice of the Intermediate Frequency f o r • the T r a n s l a t i o n Loop 4 9 4 . 5 . 4 D e r i v a t i o n of the Other Loop Parameters.... 50 4 . 6 Hold-In Range 51 4 . 7 Lock-In Range 52 4 . 8 Sweep Waveform 53 5 . INSTRUMENTATION • •'. 54 5 . 1 Components 54 5 . 2 C o n t r o l S t a t i o n 55 5 . 3 S a t e l l i t e S t a t i o n 5 8 ' 5 . 4 C i r c u i t r y . 58 i v Page 5 - 5 The Design of the T r a n s i s t o r Microwave O s c i l l a t o r 6 5 6 . PERFORMANCE OF THE SYSTEM 7 4 6 . 1 Testing the Phase-Locked Link 7 4 6.2 Results.' ' 7 5 7 . CONCLUSIONS 7 7 REFERENCES . . . •. 80 v LIST OF ILLUSTRATIONS Figure Page 1-1 Super-synthesis, showing the r e l a t i o n s h i p between the d i s h p o s i t i o n s and the synthesized aperture. 2 1- 2 Proposed Supersynthesis Radio Telescope 4 2- 1 Represenative Coherent L.O. System 12 3 - 1 Phase-Locked Link - Theory of Operation 16 3-2 Basic T r a n s l a t i o n Loop 20 3-3 Sideband Generation by a D i r e c t Method 20 3-4 T r a n s l a t i o n Loop wi t h Sideband D i s c r i m i n a t i o n 22 3-5 Phase Detector C h a r a c t e r i s t i c 24 3 - 6 An A l t e r n a t i v e Phase-Locked Link - . 28 4- 1 The Locked Loop 30 4-2 R e a l i z a t i o n of F(s).by an Operational A m p l i f i e r . 32 4-3 Frequency Response of F(s) 32 4-4 Noise Processes i n the VCO 38 4- 5 Bode P l o t of the Open Loop Response 48 5- 1 Instrumentation - Control S t a t i o n 56 5-2 Instrumentation - S a t e l l i t e S t a t i o n 57 5-3 T r a n s l a t i o n Loop. I.F. Channel, Reference Channel, Loop Phase Detector 59 5-4 T r a n s l a t i o n Loop (shown f o r lower-sideband lock) Lock I n d i c a t i o n C i r c u i t s , Sweep C i r c u i t , Loop F i l t e r 60 5-5 C i r c u i t r y , Control S t a t i o n ; 2 MHz to 4 MHz Mixer, 4 MHz to 2 MHz D i v i d e r 61 5-6 Representation of the T r a n s i s t o r as a Linear Two-Port 67 5-7 Geometrical I n t e r p r e t a t i o n of P. and P 68 1 0 5-8 L i n v i l l Chart f o r 2N 3866 at 1390 MHz 70 v i Page 5-9 Equivalent C i r c u i t of the T r a n s i s t o r and Load 71 5- 10 Frequency and Power vs C o l l e c t o r Current f o r Tran s i s t o r . Microwave O s c i l l a t o r 72 6- 1 Test C o n f i g u r a t i o n ' 74 A - l D e t a i l s of the T r a n s i s t o r Microwave O s c i l l a t o r . 81 v i i ACKNOWLEDGEMENT I wish to express my g r a t i t u d e to my supervisor, . Prof. F. K. Bowers, f o r the guidance and encouragement which he provided during the course of the research l e a d i n g to the w r i t i n g of t h i s t h e s i s . I am indebted to Dr. R. S. Roger and Dr.' C. H. Costain of the Dominion R a d i o a s t r o p h y s i c a l Observatory at Pen t i c t o n , B.C., f o r t h e i r h e l p f u l suggestions and t h e i r a ssistance i n pro-v i d i n g many of the necessary components f o r the system described i n t h i s t h e s i s . A l s o , I wish to thank Dr. M. Kharadly and Dr. L. Young of t h i s , department f o r t h e i r loan of la b o r a t o r y equip-ment which g r e a t l y f a c i l i t a t e d t h i s work. This work was financed by the N a t i o n a l Research Council through Grant A-3295- A l s o , the Council i s g r a t e f u l l y acknowledged f o r the Research A s s i s t a n t s h i p s i t provided i n 1963 and 1967. v i i i 1 1. INTRODUCTION 1.1- Supersynthesis The requirements f o r greater r e s o l u t i o n and s e n s i t i v i t y i n r a d i o astronomy experiments can only be met by r a d i o telescope antennas wi t h apertures l a r g e r than those presently a v a i l a b l e . The high cost and the d i f f i c u l t i e s involved i n the c o n s t r u c t i o n of l a r g e conventional antennas, has l e d to the development of aperture syn-t h e s i s techniques. The s i g n a l d e l i v e r e d to the r e c e i v e r of a radio, telescope can be considered as that r e s u l t i n g from the vector a d d i t i o n of the currents that are induced at each point across the aperture. For a p a r a b o l i c d i s h , t h i s vector a d d i t i o n ' i s accomplished a u t o m a t i c a l l y at the focus. In the case of a multi-element array, the a d d i t i o n can be performed by connecting each of the elements to the r e c e i v e r through equal l e n g t h cables. For an N element array, the current at the r e c e i v e r input terminals that r e s u l t s from an i n c i d e n t plane wave i s ^ ^x ' where 0 i s the phase of the wave at the xth element. The power d e l i v e r e d to the r e c e i v e r would then be given by • N ' .w N • .,; N . N N x^y The f i r s t term i n ( l - l ) , i s simply N times the power received by a s i n g l e element. The terms I I cos (0 - 0 ) correspond to the out-put of a c o r r e l a t i o n r e c e i v e r connected between the xth and the y t h elements. I f , then, i t . were p o s s i b l e to measure separately the currents at a p a i r of elements i n the array, then the r e s u l t s ob-2 tained from a l l such element p a i r s could be combined to provide the same information as would be obtained from the p h y s i c a l array. This, indeed, i s the basis of the aperture synthesis method. The spacing and o r i e n t a t i o n of two small r e c e i v i n g elements i s v a r i e d over an area equivalent to that of the p h y s i c a l aperture that i s to be synthesized. two d i s h antennas are constrained to move along an east-west base-l i n e . Movement of the dishes i n the north-south d i r e c t i o n i s accom-p l i s h e d by making use of the r o t a t i o n of the earth. This can be seen w i t h the a i d of Figure 1-1. In the method of supersynthesis, developed by Ryle, (1) 1-la 1-lb Figure 1-1 Supersynthesis, showing the r e l a t i o n s h i p between the d i s h p o s i t i o n s and the synthesized aperture. 3 During each 24 hour r o t a t i o n of the earth, the p o s i t i o n s of. the two dishes A and B appear as i n Figure 1 - l a , to an observer located, at the source. The locus of B r e l a t i v e to A traces out a s t r i p i n the e l l i p t i c a l area shown i n Figure 1-lb. Thus, by• changing the separation between the dishes i n increments of l e s s than a d i s h diameter, i t i s p o s s i b l e to synthesize a complete e l l i p -t i c a l aperture. The major a x i s of t h i s e l l i p s e i s equal to 2D, where D i s the maximum d i s h separation. The minor a x i s i s then equal to 2D sin<5" , where <£~ i s the d e c l i n a t i o n angle of the source. I t can also be seen from Figure 1-1, that the observation period f o r each d i s h separation d need only be 12 hours, because of the symmetry. Once the aperture has been synthesized, an appreciable area of sky can be scanned without having to make a d d i t i o n a l obser-v a t i o n s . This i s accomplished by i n t r o d u c i n g a progressive phase s h i f t i n the -computations, to " s t e e r " the synthesized beam. On t h i s (2) b a s i s , i t can be shown that the t o t a l observing time required to map a p o r t i o n of the sky with a given r e s o l u t i o n i s of the same order as that required f o r a conventional instrument with the same aperture. In order to use the supersynthesis technique s u c c e s s f u l l y , two conditions must be met. The f i r s t i s that the source be con-stant during the e n t i r e observing period. This i s g e n e r a l l y the case f o r r a d i o sources. The second c o n d i t i o n i s that accurate phase r e l a t i o n s h i p s be maintained during each twelve hour measurement at a given d i s h separation. This l a t t e r c o n d i t i o n becomes i n c r e a s i n g l y d i f f i c u l t to meet at the shorter wavelengths. 1.2 The Proposed P e n t i c t o n Supersynthesis Experiment A new r a d i o telescope employing the supersynthesis p r i n -4 c i p l e i s now under c o n s t r u c t i o n at the Dominion R a d i o a s t r o p h y s i c a l Observatory at P e n t i c t o n , B.C. One of the experiments that w i l l be conducted with t h i s instrument i s a rad i o survey of the northern sky. The frequency range of i n t e r e s t here i s the hydrogen l i n e radio spectrum, which occupies the band 1420 -1MHz. The proposed r a d i o telescope can be described with the a i d of Figure 1-2. L're a i m w 3 3 _ 1000 f t . cable Progm Phase Diff. 3 0 + 1 HHi 1000 f t . cable L .O. 1000 f t . Uomrji: Programmed Freq. .er Switched | Cables vo-cable i-reenr a i x e r 30 + 1 I-1K z 1000 f t . cable Central Location Figure 1-2 Proposed Supersynthesis Radio Telescope 5 The d i s h antennas D and D^  of Figure 1-2 are each mounted on a t r o l l e y . The t r o l l e y s are movable along a r a i l w a y track that i s coincident with an east-west b a s e l i n e , so that the distance d, bet-ween the dishes, 'can be v a r i e d from 30 f t . to 2000 f t . At the focus of each d i s h , the received s i g n a l s are a m p l i f i e d by a low noise microwave p r e a m p l i f i e r and heterodyned w i t h a 1390 MHz l o c a l o s c i l -l a t o r (L.O.) s i g n a l . The r e s u l t i n g 30 MHz I.F. s i g n a l s are then fed through equal length' cables to a c e n t r a l l o c a t i o n f o r s i g n a l processing. 1.3 Phase Coherence Requirements The r e s o l u t i o n that can be obtained by supersynthesis i s c r i t i c a l l y dependent upon the degree to which any random d i f f e r e n t i a l phase s h i f t s between the two s i g n a l s a p p l i e d to the c e n t r a l proces-ser are el i m i n a t e d . The allowable phase e r r o r here has been s p e c i -f i e d as - 15° maximum. This corresponds to a r e s o l u t i o n of about 3 seconds of ar c , f o r a 2000 f t . b a s e l i n e interferometer operating at 1420 MHz. There are a number of c o n t r i b u t i n g f a c t o r s which give r i s e to t h i s random phase e r r o r . There i s , f o r example, a l i m i t to the accuracy with which the value of d can be s p e c i f i e d and maintained, using current c i v i l engineering techniques. D r i f t s i n the r e l a t i v e amounts of phase s h i f t that are introduced by the microwave preamp-l i f i e r s are another source of e r r o r . . The most serious f a c t o r , how-ever, i s the v a r i a t i o n i n the length of the cables that d e l i v e r the L.O. s i g n a l s to the dishes. I f , f o r example, the thermal expansion c o e f f i c i e n t of copper and a nominal cable length of 305 meters (1000 f t . ) are assumed, then the change i n length that would r e s u l t from, say, a 2CC°change i n the average temperature of the cable, i s about 10 cm. This corresponds to a phase change of almost 180° f o r a 1390 MHz L.O. s i g n a l . I t i s obvious then, that the requirements f o r phase coherence cannot p o s s i b l y be met, unless steps are taken e i t h e r to reduce t h i s e r r o r , or to compensate f o r i t . Up to the present time, attempts to c o n t r o l the phase e r r o r due to unequal cable lengths have not gone beyond the expedient of simply c u t t i n g the high frequency cables to the same leng t h and burying them a few feet below ground l e v e l . C a l i b r a t i o n t e s t s are run to determine the d i f f e r e n t i a l phase s h i f t through the cables f o r d i f f e r e n t times of the day and year. The phase c o r r e c t i o n s obtained i n t h i s manner are then a p p l i e d to the observation r e s u l t s . This procedure has been s a t i s f a c t o r y at the longer wavelengths. However, at 21 cm, the d i f f e r e n t i a l phase s h i f t f o r buried cables becomes l a r g e and unpredictable to such a degree, that the v a l i d i t y of applying c o r r e c t i o n s based on an e a r l i e r measurement i s open to (3) question. In one published r e s u l t , d e s c r i b i n g a supersynthesis at 21 cm, the d i f f e r e n t i a l phase s h i f t between two buried cables 400 f t . long v a r i e d by as much as 18° over a three hour time i n t e r v a l . What i s required then, i s a system that w i l l provide L.O. s i g n a l s at 1390 MHz to the two dishes, phase coherent to w i t h i n , say, + 5 ° , and independent of the cable lengths. 1.4 In t r o d u c t i o n of a Programmed Phase D i f f e r e n c e The main purpose of the coherent L.O. system proposed i n the previous s e c t i o n would be to el i m i n a t e the phase error due to the L.O. cable runs. I t would be very advantageous though, i f t h i s 7 o b j e c t i v e could be achieved compatibly w i t h two other operations. One of these i s the i n t r o d u c t i o n of a programmable, continuously v a r i a b l e phase d i f f e r e n c e between the L.O. s i g n a l s at the two dishes. The other i s the i n t r o d u c t i o n of a programmable change i n the frequency, of the L.O. s i g n a l . The f i r s t requirement a r i s e s i n the f o l l o w i n g manner. In order to synthesize an aperture whose plane i s normal to the incoming wave front-, the e f f e c t of the path length d i f f e r e n c e , i n Figure 1-2 must be removed. This can be achieved f o r a l l frequencies i n the band oo-^  - Aco-^, by i n t r o d u c i n g a phase d i f f e r e n c e a and a path l e n g t h d i f f e r e n c e h^, as shown i n Figure 1-2. The. phase d i f f e r e n c e between the s i g n a l s at A and B i s then oo, h., w^hv (AUL ) (h-,-h.,) 0 K + - i > •=•-« + - j - 3 ' * c ' <!-2> where o^ = 2rc x 1420 x 10 6 rad/s u>2 = 2 i t x 1390 x 10 6 rad/s oo^  = OJ-^-CO-, = 2ic x 30 x 10^ rad/s c = 3 x 10^ meters/s ' The value of a can be programmed to make the f i r s t three terms of. (1-2) equal to zero. Then, by maintaining h^ = h^, the phase d i f -ference 0 can be made to vanish f o r a l l frequencies i n the band o.^  * A o; . I f a f i n i t e e r r o r 0 i s accepted f o r the edges of the band, then the value of h^ can-be changed i n d i s c r e t e steps, by switching i n cables whose lengths are m u l t i p l e s of a common f a c t o r . For 8 example, i f the maximum allowable e r r o r 0 at the band edges i s 5°, then from the l a s t term i n ( l - 2 ) , the cable length h^ can be switched i n increments of 4.17 meters. For such an increment only 13 separate cables are requi r e d . Any path d i f f e r e n c e up to a maxi-mum of 2000 f t . can then be tracked to w i t h i n 4.17 meters., by a s u i t a b l e combination of these cables. The maximum rate of change of the path d i f f e r e n c e h^ i s given by h,max = W d (1-3) 1 e where W i s angular r o t a t i o n r a t e of the earth about i t s a x i s . For e to d = 610 meters (2000 f t . ) *lmax - 4 - 4 4 c m / s • ' " - • I f the cable delay i s switched i n increments of 4-17 meters, then the shortest time i n t e r v a l - between cable switchings i s t . = -r-^— = 94 seconds mm k lmax When h^ i s changing at t h i s maximum r a t e , the required r a t e of change of the programmed phase d i f f e r e n c e a i s a = 7 5 . 6 % max ' From equation (1-2), i t can be seen, that at each cable s w i t c h i n g , the ote(Ah-r) value of a must change by — —^ ..For Ah^ = 4-17 meters, the change o j i s about 150°. Hence, the programmed phase d i f f e r e n c e a must vary smoothly between cable switchings and undergo a step change when the cable i s switched. Because the value of cx must go through 2 it radians 9 many times during the. observing period and the time i n t e r v a l between cable switchings is r e l a t i v e l y s h ort, a phase s h i f t e r that i s modulo 2% i s d e s i r a b l e . The r o t a r y phase s h i f t e r , ( r e s o l v e r ) which produces an e l e c t r i c a l phase s h i f t p r o p o r t i o n a l to a mechanical angular d i s -placement i s such a device. i 1.5 I n t r o d u c t i o n of a Programmed Frequency Offset The s i g n a l s received at the antennas have superimposed upon them a doppler s h i f t . This doppler s h i f t normally has two com-ponents. These are f , the doppler s h i f t due to the earth's r o t a -t i o n about i t s a x i s and f , due to the motion of the earth about s the sun. The range of these s h i f t s are as f o l l o w s : f = +.1.4 kHz f = + 140 kHz s At the c e n t r a l processer, the I.F. s i g n a l from each d i s h i s to be resolved i n frequency by a 100 channel spectrometer. I t i s thus e s s e n t i a l that a l l doppler s h i f t components be removed p r i o r to t h i s operation. The L.O. frequency therefore, must be programmable over a frequency i n t e r v a l that i s at l e a s t as great as the expected range of doppler s h i f t s . When ex t e r n a l g a l a x i e s are observed, an a d d i t i o n a l doppler s h i f t component due to the motion of the source i s often encountered. This component may be as larg e as 8 MHz. However, the day to day v a r i a t i o n i s so s m a l l , that during the time of observation of the . galaxy, the doppler component associated with the motion of the l a t t e r can be regarded as a constant frequency o f f s e t . The L.O. 10 frequency should, t h e r e f o r e , be manually tunable over a range of - 8 MHz about 1390 MHz. 1.6 Summary of Requirements f o r the Coherent L.O. System I t was e s t a b l i s h e d i n the p r e c e d i n g s e c t i o n s , that i n order to perform a high r e s o l u t i o n supersynthesis at 21 cm, a system that would maintain the phase coherence of the l o c a l o s c i l l a t o r s i g -n a l s was necessary. The requirements that such a system must s a t i s f y can be summarized as f o l l o w s : (a) The L.O. s i g n a l s must be d e l i v e r e d to the dishes phase coherent to w i t h i n - 5°, independent of the L.O. cable lengths. (b) The L.O. power l e v e l at each d i s h must be s u f f i c i e n t to s a t i s f y the requirements of the low-noise mixers - about 10 m i l l i w a t t s are r e q u i r e d . (c) There must be a p r o v i s i o n f o r i n t r o d u c i n g a predetermined phase d i f f e r e n c e between the L.O. s i g n a l s at the dishes. This phase d i f f e r e n c e must be introduced i n such a manner that i t can be c o n t r o l l e d by a d i g i t a l computer. (d) The frequency of the L.O. s i g n a l must be v a r i a b l e over a - 300 kHz range during any 12 hour observing period. This frequency change, must be c o n t r o l l a b l e by a d i g i t a l computer. (e) The L.O. frequency must be mechanically tunable over the range 1390 - 8 MHz. The design of a system that s a t i s f i e s the above r e q u i r e -ments i s the problem to which t h i s t h e s i s i s addressed. 11 2. A REPRESENTATIVE COHERENT L.O. SYSTEM 2.1 I n t r o d u c t i o n The coherent L.O. system that was chosen f o r development i s described i n the f o l l o w i n g chapter. However, before proceeding to t h i s system, one of the other systems that was considered i s discussed. The reasons f o r t h i s are twofold: (1) The system described i n Chapter 3 may at f i r s t glance appear to be an unduly s o p h i s t i c a t e d s o l u t i o n to what i s apparently a s t r a i g h t f o r w a r d problem. A d i s c u s s i o n of the shortcomings of one of the "simpler" s o l u t i o n s should j u s t i f y the need f o r a more complex system. (2) The system to be described here i s not meant to be presented as a v i a b l e a l t e r n a t i v e to the system described i n Chapter 3-I t has, however, c e r t a i n features that are necessary to a l l coherent L.O. systems. A c o n s i d e r a t i o n of these e s s e n t i a l features provides some i n s i g h t i n t o the nature of the design problem. 2.2 The Representative System The simple system p r e v i o u s l y r e f e r r e d to i s i l l u s t r a t e d i n Figure 2-1. A subharmonic of the desired L.O. frequency i s transmitted from the c e n t r a l s t a t i o n to each d i s h . (This i s done to avoid the cable l o s s encountered at 1390 MHz. The a t t e n u a t i o n of 1000 f t . of 0.5 i n c h H e l i a x cable f o r example, i s about 40 dB. On the other hand, the attenuation of the same cable at the n i n t h subharmonic frequency i s only 10 dB.) At each d i s h , part of the s i g n a l i s m u l t i p l i e d up 12 to the L.O. frequency. The remainder i s amplitude modulated by a low frequency s i g n a l and returned to the c e n t r a l s t a t i o n . Here the modulated r e t u r n s i g n a l s from the dishes are f e d i n t o a balanced mixer whose output i s tuned to the modulation frequency com. The mixer output s i g n a l i s given by 2ux V = k K E 0 s i n (—- (R - R, )) cos (to T) m 1 2 c a b m Adjustable Line Figure 2-1 Representative Coherent L.O. System where and E^ are the c a r r i e r amplitudes at the inputs to the balanced mixer. The phase d i f f e r e n c e between the input s i g n a l s to the m u l t i p l i e r s i s then 0, = /s - /S, = -i-a - (2-2) ^d / a / b c c 1 3 The detected envelope of (2-1) can then be used as an e r r o r s i g n a l to adjust the length of one of the l i n e s to make 0^ = 0. 2.3 Disadvantages with the System of Figure 2-1 The method o u t l i n e d above was hot implemented, f o r the f o l l o w i n g reasons: ; (a) In order to maintain the phase accuracy at 1390 MHz to w i t h i n - 5°, i t i s evident that the d i f f e r e n t i a l phase e r r o r of the cables at the n i n t h subharmonic must be made zero to w i t h i n - 5/9°. Thus, while the a t t e n u a t i o n problem has been eased somewhat, the phase accuracy requirement has become almost un-r e a l i z a b l e . (b) For a 10 dB cable l o s s at 154.4 MHz, about 1 watt of power would have to be transmitted i n order to d r i v e the m u l t i p l i e r chains at a l e v e l of, say 100 mW. This would present considerable i s o l a t i o n problems at the inputs to the balanced mixer. (c) In Equation (2-1), the sine f u n c t i o n i s zero f o r two values of the argument, these being 0° and 180°. This r e s u l t s i n an am-b i g u i t y i n the value of 0^ of 90°. A d d i t i o n a l c i r c u i t r y would be necessary at the c o n t r o l s t a t i o n , to overcome t h i s d i f f i c u l t y . (d) The adjustable l i n e of Figure 2-1 i s not s u i t a b l e f o r i n t r o d u c i n g a modulo 2it phase d i f f e r e n c e between the two output s i g n a l s . On the other hand, r o t a r y phase s h i f t e r s do not operate at 1390 MHz. (e) • I f the frequency co^  i s changed, the phases of the 1390 MHz s i g -nals w i l l s h i f t by d i f f e r e n t amounts, unless the m u l t i p l i e r c a v i t i e s have i d e n t i c a l frequency-to-phase r e l a t i o n s h i p s . 14 2.4 Design Guidelines for.the Coherent L.O. System • From Sections 2.2 and 2.3? c e r t a i n design g u i d e l i n e s can be drawn: (a) The phase s h i f t introduced by each cable must be measured over a forward and r e t u r n path. One-half of the d i f f e r e n t i a l phase s h i f t must then be a p p l i e d to the forward path of one of the cables, i n order to b r i n g the s i g n a l s at the end of the cables i n t o phase sy n c h r o n i z a t i o n . (b) In order to avoid e r r o r s due to r e f l e c t i o n s of the transmitted s i g n a l from some point along the cable, the transmitted and r e t u r n s i g n a l s must be distinguishable.. In the system of Figure 2-1, t h i s was done by modulating the r e t u r n s i g n a l . (c) • Use of a subharmonic frequency to equalize the cables i s to be avoided. This immediately introduces the problem of cable a t t e n u a t i o n . (d) Because of the u n s u i t a b i l i t y of adjustable l i n e s f o r the pur-pose, a method of i n t r o d u c i n g the programmed phase d i f f e r e n c e at a lower frequency must be devised. 15 3 . A PHASE-LOCKED LINK 3 . 1 - I n t r o d u c t i o n .One of the more obvious methods of ob t a i n i n g phase coher-ence at the two antennas was presented i n Chapter 2 . . From an evalu-a t i o n of t h i s method, with i t s shortcomings, i t was e s t a b l i s h e d that the design of an acceptable coherent L.O. system would have to proceed along c e r t a i n g u i d e l i n e s . The f o l l o w i n g system, based on phaselock techniques, was devised using these g u i d e l i n e s . 3 . 2 The Phase-Locked Link - P r i n c i p l e s of Operation The operation of the l i n k can be described w i t h the a i d of Figure 3 - 1 . (a) A c o n t r o l s i g n a l at the d e s i r e d l o c a l o s c i l l a t o r frequency ( t y p i c a l l y 1 3 9 0 MHz) i s obtained from a frequency s y n t h e s i z e r . The frequency and phase of t h i s s i g n a l are represented by ( l ) . The s i g n a l ( l ) and a low frequency reference s i g n a l ( 2 ) are app l i e d to the upper-sideband generator, to produce ( 3 ) . The frequency of the s i g n a l ( 2 ) was chosen to be 2 MHz, f o r reasons that w i l l be developed l a t e r . (b) The s i g n a l ( 3 ) at 1 3 9 2 MHz, i s t ransmitted down the cable, along w i t h the s i g n a l ( 4 ) , which has the same frequency as ( 2 ) , but which has f o r the moment, an unrelated phase. (c) The s i g n a l s ( 3 ) and ( 4 ) a r r i v e at the s a t e l l i t e s t a t i o n delayed • R i n time by — and are represented by ( 5 ) and ( 6 ) r e s p e c t i v e l y . (d) At the s a t e l l i t e , the s i g n a l s ( 5 ) and ( 6 ) are appli e d to the lower-sideband generator, to obtain the output ( 7 ) at a f r e -quency of 1 3 9 0 MHz. This i s the s i g n a l that must be made phase i 1 r o i n Frequency Synthesiser (1) ll  upper Jideband i e n e r a t o i f W2Z V 2 / e 3 -f ^ c V c< (3) - ' l w l + u 2 / e i + " e ? ~ ^  w l "* w 2 ^  v 2 /e - V 2 R (12) 3 = 1 I 1 Shifter 2 / e0 + v , i t I'.axer Ml R = length of cable c = velocity of propagation +• e 0 - 2v R -(6) 1 (a) '2 / " i ' "2 *-•']/ ~c"~ (9) (11) d i v i d e Two (10) ,, / e ? -f- 2WT_R r i i x e r 1-5 2 a* 2 / 2 e 3 + 2wiR (A) Lower Sine ba no Gene r a t e (7) ' / ;,R - 63 vl I e l f = W 1 = 1390 m-t f = v 2 = 2 KHz F i g u r e 3-1 ihase-Locked Link - Theorv of 0-oeration 17 coherent w i t h the c o n t r o l s i g n a l ( l ) . Part of the s i g n a l (7) i s transmitted, down the cable to the c o n t r o l s t a t i o n . (e) At the c o n t r o l s t a t i o n , the s i g n a l (7), delayed i n time by —, i s now given' by (8) . The s i g n a l s (3) and (8) are heterodyned to produce the I.F. s i g n a l (9), at 2 MHz. (f) The s i g n a l (9) i s heterodyned w i t h (4), to obtain (10), at the sum frequency of 4 MHz. (g) The s i g n a l (10) i s a p p l i e d to a divide-by-two c i r c u i t , to give (11), at 2 MHz. (h) The s i g n a l ( l l ) i s given a programmed phase s h i f t a and i s used as the low frequency input s i g n a l to the upper-sideband gener-at o r . So we have w R 0 2 = Q 3 + c ' + a S u b s t i t u t i n g f o r 9 9 i n (7), we have f o r (7) 9, + a The phase d i f f e r e n c e between the c o n t r o l s i g n a l and the output s i g n a l at the s a t e l l i t e s t a t i o n , i s thus independent of the cable length R- and can be made to take on any desired value by an appropriate choice of a. The c o n t r o l s t a t i o n could be placed at one of the antennas and the s a t e l l i t e s t a t i o n at the other. In t h i s case there would be a s i n g l e cable run of 2000 f t . A l t e r n a t i v e l y , the system shown i n Figure 3-1 could be d u p l i c a t e d . The s a t e l l i t e s t a t i o n s would then be l o c a t e d at the dishes and the dual c o n t r o l s t a t i o n at a c e n t r a l point.. The cable runs from the dual c o n t r o l s t a t i o n to each d i s h 18 would then be 1000 f t . long. This set-up would increase the com-p l e x i t y of the system, but would permit the use of l o s s i e r and cheaper cable. 1 9 3 . 3 - The T r a n s l a t i o n Loop as a Sideband Generator 3 . 3 • 1 Phase and•Frequency R e l a t i o n s h i p s The' upper and lower sidebands are generated by phase-locked t r a n s l a t i o n loops, as shown i n Figure 3 - 2 . The input s i g n a l to the loop at frequency oo^ i s heterodyned with the output of the v o l t a g e - c o n t r o l l e d o s c i l l a t o r whose frequency i s C O q . The I n t e r -mediate Frequency s i g n a l and a s i g n a l at a reference frequency GO , are compared i n a phase detector. The f i l t e r e d output of the l a t -t e r i s then used to c o n t r o l the frequency of the o s c i l l a t o r . We have: Upper-Sideband Lock Lower-Sideband Lock GO o \ GO. GO / GO. / 1 O \ 1 wQ = wi + Go r ( 3 - 2 ) GOQ = GO ± - oo p (3-4) 9 = 9. + 9 ( 3 - 3 ) 9^  = 9. - 9 ( 3 - 5 ) o 1 r o i r w ^ / 3 - 3 . 2 Advantages of the T r a n s l a t i o n Loop One might consider, on the basis of Equations ( 3 - 2 ) to ( 3 - 5 ) , the p o s s i b i l i t y of generating the upper and lower sidebands by a scheme of d i r e c t mixing, a m p l i f i c a t i o n and f i l t e r i n g , as i n Figure 3 - 3 • In the case of the upper-sideband generator, s u f f i c i e n t power must be provided at the t r a n s l a t e d frequency to drive the L.O. port of Mixer M^ and to transmit down the cable. The power require-ments at the output of the lower-sideband generator are s i m i l a r . Several m i l l i w a t t s at l e a s t are involved and the scheme of Figure 20 w, / 6. n i x e r ' i f /e i f Voltage \ Control, Csc. Phase Betectoi v /e Loop F i l t e r F ( s ) Figure 3-2 Basic T r a n s l a t i o n Loop Mixer .•iicrowave .'Iraplif i e i F i l t e r w i +  v r Figure 3-3 Sideband Generation by a D i r e c t Method 21 3-3 would r e q u i r e microwave a m p l i f i e r s at 1392 mhz and 1390 mhz. T r a n s i s t o r a m p l i f i e r s g i v i n g 30 db gain at L-band are a v a i l a b l e , but they are very expensive and t h e i r long-term phase s t a b i l i t y i s at best - 4°. . . . The upper and lower sidebands generated by the method of Figure 3-3 are separated by 2a^. I f f i s required by other con-s i d e r a t i o n s to be low, i . e . , 2 .MHz, then a bandpass f i l t e r of the necessary loaded Q becomes u n r e a l i z a b l e . Regardless of oo^ , a nar-row bandwidth at the microwave frequency would be necessary from noise c o n s i d e r a t i o n s . This would r e q u i r e a rnultipole f i l t e r , havin a l a r g e group delay, and the phase s h i f t through the f i l t e r would be i n t o l e r a b l y s e n s i t i v e to frequency changes, or to a d r i f t i n the center frequency of the f i l t e r . The Phase-Locked T r a n s l a t i o n Loop circumvents these d i f -f i c u l t i e s . The sideband frequency i s obtained at the output of an o s c i l l a t o r , and not a mixer; consequently a l a r g e amount of power i s a v a i l a b l e . Only one sideband appears at the output when the loop i s locked, and the loop can be designed to track a change i n input frequency with a very small phase e r r o r . 3.4 The Problem of Wrong-Sideband Lock and i t s S o l u t i o n . The simple t r a n s l a t i o n loop of Figure 3-2- can l o c k to e i t h e r sideband of the input frequency oo^ , these sidebands being separated by 2wp. Normally a wrong-sideband l o c k i s avoided by res t r i c t i n g the frequency range of the VCO to l e s s than 2oj p. In the event, however, that the loop i s required to t r a c k an input whose frequency must be changed over a range greater than t h i s , the pos-s i b i l i t y of a wrong-sideband l o c k i s an immediate problem. From v i f / e i f vco Phase Detect 03 (1) 'dl Loop' F i l t e r ' + oveep C i r c u i t i V i n g g e C i r c u i t Phase S h i f t - 90° Phase Detect. ( 2 ) F i l t e r F (s) 2 V x Translation Loop with Sideband • Discrimination 23 Figure 3-1, the r e s u l t of one of the loops being locked to a wrong sideband i s a frequency d i f f e r e n c e between the c o n t r o l and output-s i g n a l s of 2co . A method of avo i d i n g a wrong-sideband l o c k has been devised and the p r i n c i p l e s can be explained with the a i d of Figure 3-4-The loop i s locked through Phase Detector ( l ) and the Loop F i l t e r . A sweep s i g n a l V , which i s switched on by the output of Phase Detector (2) i s made a v a i l a b l e at the input of the VCO. For the Phase Detectors ( l ) and (2), we have: V d l = K d l cos ( 0 i f - ( 0 r - 90°)) = Kd]_ cos X (3-6) Vd2 = Kd2 c o s ( 9 i f " 9 r ) ' = Kd2 c o s( x-9°°) (3-7) where X = © i f ~ © r + 90° (3-8) Also 0 - K V„ (3-9) o f where V.. = ^ F ^ O O V ^ (3-10) and F(s) i s the t r a n s f e r f u n c t i o n of the Loop F i l t e r . The Phase Detector C h a r a c t e r i s t i c i s shown i n Figure 3-5. When the loop i s locked the output of Phase Detector ( l ) i s at a n u l l , i . e . , = 0. From Figure 3-5 two such n u l l s e x i s t , but only one of these n u l l s corresponds to a phase-locked c o n d i t i o n , and t h i s can be shown as f o l l o w s : Suppose that the loop i s locked to a lower sideband and that V d l i s n u l l e d at (b), where X = (90°). 24 1 v ' ' dl i + K d l j \ / Then Figure 3 - 5 Phase Detector C h a r a c t e r i s t i c and 1 X = ( 9 ± - 9 Q +• 9 0 ° ) ( 3 - l D Let X be perturbed to a s l i g h t l y lower value. V^^ becomes s l i g h t l y p o s i t i v e . This s i g n a l i s then i n t e g r a t e d by the Loop F i l t e r accor-ding to ( 3 - 1 0 ) , and t h i s r e s u l t s i n an i n c r e a s e . i n V^. 9 then increases according to ( 3 - 9 ) , i . e . , the o s c i l l a t o r runs f a s t e r , and from ( 3 - 1 1 ) , X continues to decrease. S i m i l a r l y , i f the i n i t i a l p e r t u r b a t i o n of X were i n the d i r e c t i o n of i n c r e a s i n g X, then X would continue to increase. The n u l l at (b) then, i s unstable f o r a lower-sideband l o c k . By a s i m i l a r argument, the n u l l at (a) i s s t a b l e . For an upper-sideband l o c k the s i t u a t i o n i s reversed; the 25 n u l l at (a) i s unstable and t h e . n u l l at (b) i s s t a b l e . ,So we have; For Lower-Sideband Lock For Upper-Sideband Lock X = -90° X = + 90° Vd2 = Kd2 c o s ( 1 8 0 ° ) = " Kd2 Vd2 = K d 2 c o s ( ° 0 ) = + K d 2 Thus the magnitude and p o l a r i t y of can be used to i n d i c a t e e i t h e r a l o s s of l o c k , or a wrong-sideband l o c k . I f the threshold voltage i s set to - K d 2 < V t ( 0 f o r low er-sideband l o c k 0 (V^_ ( f o r upper-sideband l o c k then the VCO w i l l begin to sweep when l o c k i s l o s t and continue sweeping u n t i l l o c k i s regained. The loop can' be kicked*out of a wrong-sideband l o c k , by employing, f o r example, a sawtooth sweep waveform. 3•5 The Phase-Locked Link as a Coherent L.O. System As a coherent L.O. system, the phase-locked l i n k of Figure 3-1 has s e v e r a l d e s i r a b l e f e a t u r e s . The compensation f o r the changing cable length i s accom-p l i s h e d without the use of l i n e s t r e t c h e r s , servomotors or other mechanical devices. This compensation i s done at the microwave frequency; a c c o r d i n g l y , v a r a c t o r m u l t i p l i e r s , which require' a high d r i v e l e v e l f o r e f f i c i e n t operation and which m u l t i p l y phase e r r o r s , are not used. The transmitted and r e t u r n frequencies are d i f f e r e n t , so that the problem of d i s c r i m i n a t i n g between a r e t u r n s i g n a l o r i g i -n a t i n g at the s a t e l l i t e s t a t i o n , and one that has been r e f l e c t e d 26 from some point along the cable, i s avoided. Use of the phase-locked loops f o r the sideband generators makes a m p l i f i c a t i o n at the microwave frequency unnecessary. Each loop i s , i n f a c t , a t r a c k i n g r e c e i v e r and t r a n s m i t t e r . The input noise bandwidth to the loop i s moved to a'narrow baseband by the loop f i l t e r and a considerable improvement i n s i g n a l - t o - n o i s e r a t i o can be achieved. The loop i s thus capable of l o c k i n g to a weak s i g n a l and r e - t r a n s m i t t i n g a r e l a t i v e l y high l e v e l s i g n a l at the sideband frequency. F i n a l l y , the d e s i r e d programmable phase d i f f e r e n c e between the c o n t r o l and output s i g n a l can be introduced at the reference frequency co . Since co^ i s f i x e d , a phase s h i f t e r of only narrow-band c a p a b i l i t y i s r e q u i r e d . This system does have one shortcoming that i s shared by a l l other coherent L.O. systems that are based on the general p r i n -c i p l e s of Section 2.4.. R e f e r r i n g to Figure 3-1, the phase coherence i s maintained by determining the phase s h i f t due to the cable over a two-way path and then applying one-half of t h i s phase s h i f t to the forward path. The d i f f i c u l t y a r i s e s as f o l l o w s . The phase s h i f t over the two-way path can only be resolved to w i t h i n a m u l t i p l e of 2 it radians. When t h i s phase s h i f t i s di v i d e d by two, there are two p o s s i b l e r e s u l t s . One of these i s the s i g n a l represented by ( l l ) i n Figure 3-1- The other, i s t h i s same s i g n a l , s h i f t e d i n phase by 180°. In the l a t t e r case, t h i s 180° phase s h i f t appears at (7). Thus, i f the system should l o s e l o c k , there i s the p o s s i b i l i t y that the s i g n a l ( 7), may be 180° out of phase when l o c k i s regained. For the d u p l i c a t e system, described at the end of Sec-t i o n 3-2, t h i s problem could be.overcome as f o l l o w s . The phase 27 d i f f e r e n c e between the s i g n a l s ( l l ) from each h a l f of the d u p l i -cate system could be monitored. I f t h i s phase d i f f e r e n c e changes suddenly be 180°, the programmed value of a could be changed by t h i s amount, thus maintaining the co r r e c t phase r e l a t i o n s h i p between the s i g n a l s (7) at the s a t e l l i t e s . Another a l t e r n a t i v e would be to operate the d u p l i c a t e system of Section 3.2, at the second sub-harmonic of the desired L.O. frequency. The s i g n a l s (7) would d r i v e frequency doublers at each d i s h . Any phase r e v e r s a l s at the sub-harmonic frequency, then, would not a f f e c t the phase of L.O. s i g n a l s . This a l t e r n a t i v e , how-ever, r e q u i r e s frequency m u l t i p l i c a t i o n — an operation that should be avoided, f o r the reasons given i n Section 2.3. 3.6 An A l t e r n a t i v e Phaselock Method A phase-locked l i n k that has c e r t a i n s i m i l a r i t i e s to the system described i n Section 3.2 has been developed-independently by Airborne Instruments L a b o r a t o r i e s ^ . This system, h e r e a f t e r r e -f e r r e d to as the A.I.L. system, i s shown i n Figure 3-6. The c o n t r o l s i g n a l co-^ /^ 9-^ , i s obtained from a frequency s y n t h e s i z e r and a p p l i e d to the c o n t r o l s t a t i o n . The low frequency reference s i g n a l ®2' ~*"S §ener&^e& a ^ ^ n e s a t e l l i t e s t a t i o n . I f i n Figure 3-6, the output of the divide-by-two c i r c u i t i s assumed to be ^ / 9^, then i t can r e a d i l y be shown that the output s i g n a l at the s a t e l l i t e s t a t i o n i s co-^ /^ 9-^ . As i n the system of Figure 3-1, a phase d i f f e r e n c e a , between the c o n t r o l s i g n a l and the output s i g n a l can be introduced by i n s e r t i n g a phase s h i f t a between the divide-by-two and the upper-sideband generator. w l l_ ± Control Si)-nal Upper Sideband Gen. ' v:9 Divide by Two I T \U -f- Mr i-nxer Mixer "lT7c 2w, 1"! + ^  Upper Sideband Gen. Lover Sidebanc Gen. T 2,-Mixer v„ V e i Output Signal Control Station II, c Figure 3 - 6 An A l t e r n a t i v e Phase-Locked Link 29 The phase-locked l i n k of Figure 3-1, which, we s h a l l r e f e r to as the P e n t i c t o n system, has s e v e r a l advantages over the A.I.L. system. The Pen t i c t o n system r e q u i r e s two phase-locked sideband generators; the A.I.L. system, three. For the d u p l i c a t e arrange-ment discussed i n Section 3*2, the r e l a t i v e complexity would be four sideband generators f o r the P e n t i c t o n system, as opposed to s i x f o r a l l the A.I.L. system. R e f e r r i n g to Figure 3-6, the i n s t r u -mentation ot the s a t e l l i t e s t a t i o n , f o r the A.I.L. system c o n s i s t s of no l e s s than two sideband generators, a mixer and a s i g n a l gener-ator at frequency civ, • For the P e n t i c t o n system, only a lower-side-band generator Is required at the s a t e l l i t e . Because the space a v a i l a b l e at each d i s h f o r the coherent L.O. system i s l i m i t e d , t h i s d i f f e r e n c e i n the amount of instrumentation required at the dishes i s s i g n i f i c a n t . In the A.I.L. system, the reference s i g n a l i s transmitted from the s a t e l l i t e s t a t i o n to the c o n t r o l s t a t i o n , then back to the s a t e l l i t e s t a t i o n , at the same frequency . This system i s , thus, vulnerable to e r r o r s a r i s i n g from r e f l e c t i o n s of the reference s i g -n a l . To avoid such e r r o r s , two separate cable paths of length R would be necessary. For a d u p l i c a t e system, four a d d i t i o n a l cables would be req u i r e d . This would r a i s e the cost of the system by s e v e r a l thousand d o l l a r s . The A.I.L. system permits phase synchronization over a frequency range of 500 H z ^ . This range i s not adequate f o r the doppler t r a c k i n g requirements of Section 1-6. On the other hand, the Pe n t i c t o n system can e a s i l y t r a c k over the expected range of doppler s h i f t , without l o c k i n g to the wrong sideband. 30 4 . ANALYSIS AND DESIGN • 4 . 1 ' The Linear Loop Equations r-iixer e i " 6 + "n2 n l o 1 + — r ® — vco Phase Detector V 'd Loop F i l t e r Ha) 9. = l 0 = 9 9 n l 9 n2 Figure 4 - 1 The Locked Loop The basic t r a n s l a t i o n loop i s shown i n Figure 4 - 1 , who.ro phase of the input s i g n a l phase of the output s i g n a l phase of the reference s i g n a l contaminating phase disturbance at the Intermediate Fre-quency (I.F.) contaminating phase disturbance at the output of the v o l -t a g e - c o n t r o l l e d o s c i l l a t o r (VCO). When the loop i s locked, the phase detector operates about a n u l l and f o r small v a r i a t i o n s of phase about the locked c o n d i t i o n the output voltage V^ i s approximately a "lin e a r f u n c t i o n of the d i f -31 f e r e n t i a l phase input i . e . , V d ( s ) = K d 9.(s) - 9 o ( s ) + 9 n l ( s ) - 9 r ( s ) l (4-1) a l s o ; 9 Q ( s ) = © n 2(s) + K F ( s ) V d ( s ) (4-2) where i n ( 4 - 2 ) , K q i s the voltage-to-frequency gain constant of the V.CO and F(s) i s the response f u n c t i o n of the Loop F i l t e r . The response of the loop f o r the e x c i t a t i o n s 9^(s), ©n3_(s) a n ^ 9^2(s) i s then; 9 o ( s ) = H ( s ) 9 i ( s ) + H ( s ) 9 n l ( s ) - ( l - H ( s ) ) 9 n 2 ( s ) ( 4 - 3 ) where; K K F ( s ) H ^ = s° + dK oK dF(s) < 4 - 4 ) 1 - H(s) = s + K Q K d F ( s T ( 4 - 5 ) The order of the closed loop response H(s) i s determined by the choice of the loop f i l t e r f u n c t i o n F ( s ) . In order to t r a c k a ramp input phase (a frequency o f f s e t ) , w i t h a f i n i t e steady-state phase e r r o r , a second order system i s requ i r e d . Such a system, i n which the loop gain, damping and bandwidth are independently v a r i a b l e can be r e a l i z e d i n F(s) has the form; A (1 + t„s) F ^ = (1° + A ^ s ) (4-6) F(s) = Vg - A (1 -f t l S ) (1 -f- A t„s) o ^ A - open loop gain of the Operational Amplifier U-7) (P^ -f-R2)C U-8) Figure U-2 Realization of F(s) by an Operational Amplifier 33 Figure (4-2) i l l u s t r a t e s how F(s) i s r e a l i z e d "by using an opera-t i o n a l a m p l i f i e r . The frequency response of F(s) i s shown i n Figure (4-3). When F(s) i s given by (4-6), then H(s) and 1 - H(s) become; 2 co + 2zco s I H(s) = -§ G 2 : (4-9) s + 2zco s + co n n 2 l.-.H(s) = ~2 ~ 2 (4-10) s + 2zco s + co n n where; . v 1 n \ t K K, \ 2 u = | - T - 4 ( 4 - l D z -1 ^ /KK,,\ 2 (4-12) 57 « and 2zco t n \ \ n o 1 N (This l a s t c o n d i t i o n i s true f o r a l l but very narrow band phase locked loops.) 4.2 Phase Errors Due to the T r a n s l a t i o n Loop The purpose of the t r a n s l a t i o n loop i s to t r a n s l a t e the frequency and phase of the input s i g n a l according to the r e l a t i o n s h i p s given i n Equations (3-2) to (3-5). Any d e v i a t i o n of the output phase from these r e l a t i o n s h i p s contributes to the o v e r - a l l system phase e r r o r . The design of the loop, then, involves the choice of loop parameters and components that w i l l tend to minimize t h i s 34 e r r o r . The phase er r o r s introduced by the loop f a l l i n t o three c a t e g o r i e s ; these being d r i f t e r r o r s , t r a c k i n g e r r o r s and phase j i t t e r due to noise. The d r i f t e r r o r s can be a t t r i b u t e d to the change, over a period of time, of the phase s h i f t s introduced by the various e l e -ments i n the loop. This, i n f a c t , i s the s o r t of phase e r r o r that the system was supposed to e l i m i n a t e . Since the main c u l p r i t ' h e r e i s the I.F. a m p l i f i e r , a j u d i c i o u s choice of a m p l i f i e r c o n f i g u r a t i o n i s r e q u i r e d . This, i n t u r n , has a bearing on the choice of the I.F. frequency. More w i l l be s a i d about t h i s point i n a l a t e r s e c t i o n . The second type of phase e r r o r occurs when there i s a d i f f e r e n c e between the frequency being tracked and the free-running frequency of the VCO, i . e . , the frequency that the VCO generates when the output of the phase detector i s zero. This frequency d i f -ference can change i n e i t h e r of two ways: (1) There i s a programmed change i n the desired L.O. frequency, as would occur while a doppler s h i f t was being tracked out. (2) There is a change i n the c h a r a c t e r i s t i c s of the VCO or i t s con-t r o l c i r c u i t ; f o r example, expansion of the o s c i l l a t o r cavity,, or a DC o f f s e t i n the c o n t r o l c i r c u i t . The a n t i c i p a t e d range of the frequency o f f s e t can be estimated as f o l l o w s : Programmed Offset f o r Doppler Tracking Requirements (Based on the a n t i c i p a t e d range of f i n f i n Section 1.5.) 6 S . 142 kHz 35 Offset Due to Expansion of O s c i l l a t o r Cavity (Brass) ( I f the expansion c o e f f i c i e n t of Brass and a temper-ature range of IOC are assumed, then the resonant frequency of the c a v i t y w i l l vary by t h i s amount) 200 kHz Offset Due to D r i f t i n DC Level of VCO Control C i r c u i t (estimate based on measured DC d r i f t s ) 1.5 MHz T o t a l \ 1.84 MHz i The frequency o f f s e t can thus be expected to vary over a range of, say, 2 MHz. Accordingly, the design was i n i t i a t e d by s p e c i f y i n g an allowable e r r o r rate of l°/MHz. For a second-order loop, the steady-state phase e r r o r per u n i t frequency o f f s e t i s j u s t the inverse of the DC loop gain. Hence the required loop gain i s K K,A = 3-6 x 1 0 8 (4-13) o d o ^ \T From Figure 3-1, i t can be seen that i f both loops develop the same e r r o r e, due to a frequency o f f s e t , the r e s u l t a n t phase e r r o r between the c o n t r o l s i g n a l and the output s i g n a l at the s a t e l -3e l i t e s t a t i o n i s ^ • For the chosen value of DC loop gain, t h i s amounts to 3°. Higher values of loop gain could, of course, reduce t h i s e r r o r , provided loop s t a b i l i t y can be maintained. A l s o , f o r the d u p l i c a t e system discussed i n Section 3-2, the output s i g n a l at each s a t e l l i t e s t a t i o n w i l l be a f f e c t e d i n roughly the same man-ner, so that the d i f f e r e n t i a l e r r o r w i l l be l e s s than the above f i g u r e . 4•3 Phase J i t t e r Due to Noise 4.3.1 I n t r o d u c t i o n Apart from the slowly v a r y i n g phase e r r o r s discussed i n Section 4-2, there i s always present the phase j i t t e r r e s u l t i n g 36 from noise i n the phase-locked loop. This phase j i t t e r can be considered as the response of the loop to random inputs 9 ^ and 9n2 w^^-c^ a r e introduced at the I.F. input of the phase detector and at the output of the VCO r e s p e c t i v e l y . (See Figure 4-1) 4.3-2. I.F. Noise The phase-locked loop responds to the random phase s i g -n a l 9 as a l i n e a r system with a response f u n c t i o n H(s). I f i t i s assumed that the I.F. noise that produces the phase j i t t e r 9 ^  (5) can be described by Rice's r e p r e s e n t a t i o n of narrow-band noise , i . e . , n i f ( t ) = n c^" t) c o s w i f ^ + s i n w i f ' t (4-14) where n n = n • n = 0 c s c s , 2 ' 2 2 and n = n = n. „ c s i f with n c and n g having a spectrum from DC to B ^/2, B ^ being the I.F. bandwidth, then the phase j i t t e r at the output of the loop, due to n^^(t) i s U o l = 2(SNR) l f (gj (4-15) where B-^  i s the loop bandwidth, given by B L OO f 2 H(w)| dw = rcto (z + -j—) rad/s ( 4 - I 6 ) 0-> 2 An estimate of U , can be made as f o l l o w s : o l The amount of power provided by the VCO at the c o n t r o l s t a t i o n i s 37 c o n s e r v a t i v e l y , 4 0 m i l l i w a t t s , or +16 dBm. I f , as proposed, 1 0 0 0 f t . of 0 . 5 inch Heliax cable i s used between the s a t e l l i t e and the c o n t r o l s t a t i o n s , the attenuation i s about 40 dB. With the i n s t r u -mentation scheme of Figures 5 - 1 and 5 - 2 , an a d d i t i o n a l 12 dB l o s s at each end i s incurred i n coupling the s i g n a l i n t o and out of the cable. The s i g n a l l e v e l at the input of the mixer of the s a t e l l i t e loop i s then - 4 8 dBm. I f at the s a t e l l i t e loop, the noise f i g u r e of the mixer and I.F. a m p l i f i e r combination i s to say 1 0 dB, the I.F. bandwidth about 3 MHz and the temp erature 2 9 0 ° K e l v i n , then the noise l e v e l r e f e r r e d to the mixer input i s - 1 0 0 dBm. The s i g -n a l - t o - n o i s e r a t i o at the input of the phase detector i s then about B L 50 dB. I f we disre g a r d f o r the moment, the r a t i o -K- i n ( 4 - 1 5 ) , the output phase j i t t e r i s then U Q l(rms) = 0 . 1 4 ° Because the s i g n a l - t o - n o i s e r a t i o at the input of the loop i s high, the r a t i o of to B ^ need not be very much l e s s than one. I f the phase-locked loop were required to t r a c k a s i g n a l that i s buried deeply i n the noise, i . e . , ( S N R ) ^ i s very s m a l l , a loop bandwidth of a few Hz would be necessary. In t h i s ease, however, B^ or e q u i v a l e n t l y , co , can be s e v e r a l orders of magnitude l a r g e r , without s e r i o u s l y i n c r e a s i n g the phase j i t t e r due to noise at the I.F. This r e s u l t w i l l become s i g n i f i c a n t , when the phase j i t t e r due-to o s c i l l a t o r noise i s considered i n the next s e c t i o n . 4.3.3. O s c i l l a t o r Noise The contaminating s i g n a l Q ^ i n Figure ( 4 - 1 ) can be iden-t i f i e d w ith the phase j i t t e r of the VCO due to a noisy o s c i l l a t o r 38 s i g n a l . The loop responds to 9 ^ a s a l i n e a r system w i t h a t r a n s -f e r f u n c t i o n 1 - H(s). . Figure 4-4 Noise Processes i n the VCO A simple model of the o s c i l l a t o r i s shown i n Figure 4-4. The o s c i l l a t o r s i g n a l i s generated by a feedback loop of bandwidth and reaches the output terminals of the device through an i n t e r -stage of bandwidth B^. The phase j i t t e r 9 ^ i s "the r e s u l t of two independent noise processes associated with the o s c i l l a t o r . These are shown i n Figure 4-4 as n 0 and n„, . . Both n 0 and n„, are ° • 2a 2b 2a 2b assumed to be narrow-band Gaussian, centered about the o s c i l l a t o r frequency coo and representable by the general form of (4-14) with bandwidths B and B, r e s p e c t i v e l y . 4-3-4 " E l a s t i c " Noise The disturbance n0h i n Figure 4-4 represents the noise 39 that i s added by the output stage a f t e r the o s c i l l a t o r c l o c k f r e -quency has been generated by the feedback loop. This noise could, f o r example, be a t t r i b u t e d to a m p l i f i e r stages and/or m u l t i p l i e r chains at the output of a master o s c i l l a t o r . We can regard as a sequence of random pulses, each of which perturbs the phase of the o s c i l l a t o r s i g n a l . These perturbations are " e l a s t i c " i n the sense that the o s c i l l a t o r phase i s momentarily disturbed when a pulse a r r i v e s , but returns to i t s o r i g i n a l value a f t e r the pulse disappears. Under such co n d i t i o n s and wit h the assumption that the s i g n a l - t o - n o i s e r a t i o i s high, (greater than 15 dB) ^ the mean-square phase j i t t e r due to i s Gn2b = 2TsNiyr ( 4 ~ 1 7 ) b where (SNR)^ i s the s i g n a l - t o - n o i s e r a t i o at the o s c i l l a t o r output I f i t i s assumed that the spectrum of 9 extends from -°b co = 0 to co = — , then an equivalent uniform s p e c t r a l density i s 2 2 W = i f f = - i f 2 (4-18) b "b The phase j i t t e r at the output of the t r a n s l a t i o n loop i s then given by T2 2 U£ = I 0b(co) 1 - H(co)| 2 du (4-19) 4 0 For the second order loop ( 4 - 1 9 ) can be evaluated approximately by i n t e g r a t i n g over simple geometric areas to give U b - 2 T S M X ( 1 - < J f ° r W n < B b ' ( 4 " 2 0 ) b b = 0 f o r co \ B, n / b From equation ( 4 - 2 . 0 ) i t i s apparent that i n order to t r a c k out the phase j i t t e r due to n^b' a -'-arSe %. 0 r l a r § e 1°°P bandwidth i s r e q u i r e d . When the o s c i l l a t o r output bandwidth i s much greater than co^, as i s u s u a l l y the case f o r microwave o s c i l l a t o r s , a small phase j i t t e r can be achieved only by maintaining a high o s c i l -l a t o r output s i g n a l - t o - n o i s e r a t i o . 4-3.5 "Non-Elastic" Noise The noise process n 0 i n Figure 4 - 4 produces a phase d i s - . *_a turbance that i s markedly d i f f e r e n t from that produced by n^b" as i n the case of n2b» ^ e process n 2 a i s considered as a sequence of random pulses, then as before, each pulse s h i f t s the o s c i l l a t o r phase by a minute amount. These phase s h i f t s , however, occur w i t h i n the feedback loop that generates the clock frequency. Each incremental phase change becomes a permanent part of the o s c i l l a t o r phase, with the r e s u l t that the l a t t e r executes a random walk. The e r r o r accumulated over an observing time t , has equal p r o b a b i l i t y of being p o s i t i v e or negative and so has zero mean value. However, the mean-square e r r o r taken over an i n f i n i t e time i n t e r v a l i s not bounded. Van Blerkom has obtained the f o l l o w i n g r e s u l t f o r the (7) mean-square o s c i l l a t o r phase e r r o r due to t h i s " n o n - e l a s t i c " noise. 41 9n2a = 2(SNR) ( 4 " 2 l ) . a where B = bandwidth of the o s c i l l a t o r feedback loop a t = observing time (SNR) = s i g n a l - t o - n o i s e r a t i o i n the o s c i l l a t o r • f e e d b a c k loop a In order to determine the e f f e c t of the o s c i l l a t o r noise n 2 a ° n ^ e P ^ L a s e - i 0 C ^ : e ( ^ 1°°P> a n expression f o r the mean-square phase e r r o r at the output of the loop i s requ i r e d . An approximate r e s u l t can be obtained as f o l l o w s . The unbounded mean-square phase e r r o r of the o s c i l l a t o r s i g n a l due to n Q a r i s e s as the r e s u l t of the a l g e b r a i c a d d i t i o n of the incremental phase e r r o r s introduced by the a r r i v a l of each •new pulse of n^a' o r^- e r ^° m a ^ e t h i s mean-square e r r o r f i n i t e and s m a l l , there must be introduced a "mechanism" that tends to re t u r n the phase e r r o r to zero a f t e r each such incremental phase step. This " r e s e t " must be made w i t h i n a time that i s comparable to the i n t e r v a l between noise pulses and must be made wit h a m i n i -mum of overshoot c o n s i s t e n t with a f a s t response. ' This "mechanism" of course, i s the phase-locked loop. One would expect, t h e r e f o r e , that the mean-square phase e r r o r at the output of the loop would be comparable to that generated by the VCO i n a time t , where t i s the response time of the loop. Using the value t = l/zu)^ f o r a second-order loop, the approximate r e s u l t i s then 42 This r e s u l t , when combined w i t h (4-20), gives f o r the mean-square phase e r r o r at the output of the loop, due to o s c i l l a t o r noise Uo2 = U a + U b = 2(SNR) ZOJ + "2(SNR), ( 4 " 2 5 ) a n D 2 The mean-square phase e r r o r U due to the I.F. noise, has not been inclu d e d . The r e s u l t s of Section 4.3-2, however, show that t h i s component of the.output noise i s s u f f i c i e n t l y s m a l l , that i t can be neglected. 4.4 Choice of a V o l t a g e - C o n t r o l l e d O s c i l l a t o r (VCO) 4.4.1 I n t r o d u c t i o n In order to r e a l i z e the sideband generators of Figure 3-1 using phase-locked t r a n s l a t i o n loops, v o l t a g e - c o n t r o l l e d o s c i l l a t o r s w ith free-running frequencies around 1.4 GHz are required. In t h i s S e c tion, the performance of two types of o s c i l l a t o r s i s discussed and the reasons f o r the choice of one over the other are given. 4.4.2 The V o l t a g e - C o n t r o l l e d C r y s t a l O s c i l l a t o r (VCXO) and M u l t i p l i e r A commonly used method of o b t a i n i n g a pure s i g n a l at a micro-wave frequency i s to v a r a c t o r m u l t i p l y the s i g n a l from a c r y s t a l o s c i l l a t o r . C r y s t a l s w i t h resonant frequencies i n the range 1-10 MHz are u s u a l l y used and voltage c o n t r o l of the frequency i s obtained by a v o l t a g e - v a r i a b l e c a p a c i t o r i n the c r y s t a l o s c i l l a t o r u n i t . In terms of the o s c i l l a t o r model of Figure 4-4, the c r y s t a l o s c i l l a t o r and m u l t i p l i e r chain would correspond to the-feedback loop and the output stage r e s p e c t i v e l y . In such a case, t h e f i r s t term of (4-23) can be made very s m a l l , owing to the very small value of B which i s a 43 determined by the Q of the o s c i l l a t o r c r y s t a l . For frequencies up to 100 MHz or so, the second term i n (4 -23) i s a l s o s m a l l , since (SNR)^ i s l a r g e . The VCXO-Multiplier then, i s a l o g i c a l choice f o r phase-locked loops operating at these lower frequencies. When, however, the required frequency i s i n the GHz range, the second term of (4 -23) dominates. I t has been shown that varac-t o r m u l t i p l i c a t i o n by a f a c t o r N r e s u l t s i n a degradation of the 2 (7) s i g n a l - t o - n o i s e r a t i o of N . I f , f o r example, a 5 MHz c r y s t a l o s c i l l a t o r were used, the degradation of (SNR)^ at 1400 MHz would be about 50 dB. In a d d i t i o n , v a r a c t o r m u l t i p l i e r s , f o r t h e i r e f f i c i e n t operation must be d r i v e n at s u b s t a n t i a l power l e v e l s •— s e v e r a l hundred m i l l i w a t t s at l e a s t . This means that a power ampli-f i e r i s required between the VCXO'and the m u l t i p l i e r chain, which introduces a d d i t i o n a l noise. This noise occupies the bandwidth B^, determined by the Q of the m u l t i p l i e r c a v i t i e s , and at 1400 MHz i s at l e a s t a few MHz wide. The r e s u l t , i n p r a c t i c a l terms, i s that the best frequency synthesizers which generate frequencies by such a method, have s i g n a l - t o - n o i s e r a t i o s of no b e t t e r than 40 dB. Accordingly, the phase j i t t e r at the output of.a t r a n s l a t i o n loop-using a VCXO-Multiplier Chain would be ~2 1 1 2 U o 2 = 2(SNR) b = 2 x 1 Q 4 radians which corresponds to an rms phase j i t t e r of U^rms = 0.5° C r y s t a l o s c i l l a t o r s are by nature of t h e i r high Q, very narrow band devices and t h e i r tuning range, whether by e l e c t r i c a l or 44 mechanical means, i s u s u a l l y r e s t r i c t e d to about 0.2 7°. The required frequency range of -8 MHz at the microwave frequency, would then make necessary the use of more than one c r y s t a l o s c i l l a -t o r u n i t , or of a tapped m u l t i p l i e r chain. The complexity of the VCO-Multiplier Chain and the u n s u i t -a b i l i t y of the l a t t e r f o r wide-band use, l e d to the c o n s i d e r a t i o n of an a l t e r n a t i v e - the T r a n s i s t o r Microwave O s c i l l a t o r (TMO), which i s discussed i n the f o l l o w i n g s e c t i o n . 4.4-3 The T r a n s i s t o r Microwave O s c i l l a t o r (TMO) Any t r a n s i s t o r i s p o t e n t i a l l y unstable at a frequency that i s high enough such that i t s gain as an a m p l i f i e r approaches u n i t y , t h i s p o t e n t i a l i n s t a b i l i t y extending over a range of bias c o n d i t i o n s . In the case of o s c i l l a t i o n s at 1400 MHz, t h i s unstable operation i s p o s s i b l e with a UHP power t r a n s i s t o r operating i n the common base c o n f i g u r a t i o n . The o s c i l l a t o r can then be r e a l i z e d , by coupling t h i s unstable device to a c a v i t y that i s resonant at the des i r e d frequency of operation. The frequency of o s c i l l a t i o n can then be c o n t r o l l e d by tuning the c a v i t y w i t h a v o l t a g e - v a r i a b l e c a p a c i t o r , or by v a r y i n g the bias conditions of the t r a n s i s t o r , the l a t t e r having the e f f e c t of a l t e r i n g the r e a c t i v e load that the t r a n s i s t o r presents to the c a v i t y . Such a TMO was designed and b u i l t using a 2N 3866 UHP power t r a n s i s t o r coupled i n t o a quarter-wavelength c a v i t y at 1390 MHz. Output power i n t o a 50 ohm load was 60 m i l l i w a t t s and frequency con-t r o l over a range of 8 MHz was achieved by v a r y i n g the emitter cur-r e n t . The d e t a i l s of the design and c o n s t r u c t i o n are given i n a l a t e r s e c t i o n . The TMO, considered i n the l i g h t of Equation (4-23) and 45 Figure-4-4, has s e v e r a l i n t e r e s t i n g f e a t u r e s . The output power i s h i g h — 50 m i l l i w a t t s at 1.4 GHz being t y p i c a l . In terms of the o s c i l l a t o r model of Figure 4-4, the band-width of the feedback loop B and that of "the output stage B, are equal and given by CO q, where coQ i s the o s c i l l a t o r frequency, and Q-^  i s the loaded Q of the o s c i l l a t o r c a v i t y . Q-^, however, i s con-s i d e r a b l y l e s s than the unloaded c a v i t y Q, as a r e l a t i v e l y l a r g e amount of power i s coupled out. Because the output s i g n a l l e v e l i s high and d e l i v e r e d at the microwave frequency, without undergoing a m u l t i p l i c a t i o n process, the s i g n a l - t o - n o i s e r a t i o (SNR)^ i n Figure 4-4 i s s u f f i c i e n t l y l a r g e that phase j i t t e r i n (4 - 2 3 ) can be neglected. This i s true i n s p i t e of the l a r g e output bandwidth B^ r e s u l t i n g from the low value of Q-^. I t i s a l s o t r u e , that the ~~2 phase j i t t e r due to the " n o n - e l a s t i c " n o i se, can be made very s m a l l . The reason f o r t h i s i s as f o l l o w s . At the frequency of o s c i l l a t i o n , the gain of the t r a n s i s t o r i n the TMO i s only marginally greater than u n i t y . I t f o l l o w s then, that the s i g n a l l e v e l at any point w i t h i n the feedback loop of Figure 4-4 must be n e a r l y equal to the s i g n a l l e v e l at the o s c i l l a t o r output, so that (SM) i s l a r g e . We have f o r the TMO U o 2 * U l > 2(SHR) ^ ( 4 - 2 4 ) a n where a value of z - 1 has been assumed f o r convenience. I f an o s c i l l a t o r bandwidth of 140 MHz (correspondnng to a loaded Q of 10 at 1.4 G-Hz) and a conservative estimate of (SNR) of a 80 dB are assumed, then the value of f = co / 2TC required to maintain ' • n n' ^ 46 a 1 rms phase j i t t e r i s f = 1 a 1 0 n = 1.8KHz 2 x 1 0 x T36007 A value of f = 50 kHz, which improves the rms phase j i t t e r by a f a c t o r of about 6.5, was chosen, i . e . , f o r oj n = 3.14 x l O 5 . '' (4-25) U rms = 0.15° (4-26) 4 . 4 . 4 Comparing the VCXO-Multiplier and the TMO. The r e s u l t s of Section 4 .4.2 i n d i c a t e that the best that one could expect i n terms of phase j i t t e r , from a VCXO-Multiplier i s about 0.5° rms. The r e s u l t (4-26) i n d i c a t e s that i f the TMO were used, the rms phase j i t t e r at the output of e i t h e r t r a n s l a t i o n loop could be maintained, f o r a l l p r a c t i c a l purposes, equal to that of the c o n t r o l s i g n a l . The TMC c o n s i s t s of a HHP t r a n s i s t o r and a: C a v i t y . (The 2N 3866 s e l l s f o r about $4.0.0.) The VCXO-Multiplier, on the other hand, .is a complex and expensive device. Emitter-current .control of the frequency of the TMO over the required 300 kHz range and mechanical tuning of the c a v i t y over - 8 MHz are e a s i l y accomplished. The VCXO, however, i s not s u i t a b l e f o r wideband use. The VCXO has the advantage of long-term frequency s t a b i l i t y . This i s of secondary importance here, as the loop o s c i l l a t o r s are locked to a c o n t r o l s i g n a l that provides t h i s s t a b i l i t y . For these reasons, the TMO was chosen f o r use as the VCO i n the phase-locked l i n k . 47 4.5 Intermediate Frequency and I.F. Bandwidth Requirements 4.5.1 E f f e c t of I.F. F i l t e r In the t r a n s l a t i o n loop of Figure 4-1 there i s , i n general, an Intermediate Frequency a m p l i f i e r which can be ch a r a c t e r i z e d by an impulse response h g ( t ) . Introducing t h i s I.F. f i l t e r i s equi-valent to cascading with the loop f i l t e r , a low-pass f i l t e r which has an impulse response h-^(t), given by h B ( t ) = h L ( t ) cos w ± f t ( 8 ) (4-27) In the frequency domain, t h i s means that the equivalent low-pass f i l t e r poles are obtained by s h i f t i n g the pole c l u s t e r at +jco^^. of the I.F. f i l t e r down t c the o r i g i n . * , • Suppose, f o r example, that the I..F. f i l t e r response'is maximally f l a t , w i t h symmetrical 40 dB/decade s k i r t s . The equiva-l e n t low-pass f i l t e r f u n c t i o n i s then M(s) = -3 "I 2~ f 4 " 2 8 ' s + 2ZOJ s + co , n l n l where oo , = B. _/2 z = 0.707 n l i f B . „ = I.F. bandwidth i f The e f f e c t of M(s) on the performance of the loop can be determined by c o n s i d e r i n g the open loop response t r K K , F ( s ) M ( s ) G(s) = H 0 d 1 - H ~ s With F(s) given by (4-6) and M(s) by (4-28), the open loop gain f u n c t i o n becomes 48 K K nA (st„ + 1) b?1 r,f\ o d o 2 n l G-(s) = 2 2 s ( s A o t 1 + l ) ( s + 2 z u n 1 s + w n l) A Bode P l o t of (4-29) i s shown i n Figure 4-5. Figure 4-5 Bode P l o t of the Open Loop Response From Figure 4-5, i t can be seen-that i f the r o l l - o f f term at co ^  i s not present, the loop i s s t a b l e , w i t h a phase margin L, given by L = JC/2 - phase at co = JC/2 - radians. 49 For a damping r a t i o of z = 1 , the phase margin i s 80°. . The I.F. f i l t e r of bandwidth produces an a d d i t i o n a l r o l l - o f f at co^ = radians/sec. In order to prevent the loop performance from being unduly i n f l u e n c e d by the presence of the IF f i l t e r , i t i s necessary to keep the r a t i o of co^ to coc l a r g e . 4 - 5 . 2 Choice of I.F. Bandwidth The a d d i t i o n a l phase l a g introduced at the crossover f r e -quency co i n Figure 4 - 5 , i s a f u n c t i o n of the r a t i o co , /co , and of the damping r a t i o z^. This f u n c t i o n i s tabulated i n most references on servomechanisms. I f we assume a maximally f l a t response f o r which = 0 . 7 0 7 , then, i n order to keep t h i s l a g c o n t r i b u t i o n at the crossover frequency l e s s than, say, 1 0 ° , we must have ^ u>c ^ 8. Now since co , = B./2, and co = 2zco we must have n l i ' ' c n For t y p i c a l loop damping r a t i o s , then, the I.F. bandwidth should be at l e a s t 30 times greater than con f o r the loop. For the value of f = 50 KHz s p e c i f i e d i n S e c t i o n 4 . 4 . 2 , the I.F. bandwidth should be greater than 1 . 5 MHz. 4 . 5 - 3 Choice of the Intermediate Frequency f o r the T r a n s l a t i o n Loop For the required I.F. bandwidth of 1 . 5 MHz, any I.F. greater than say, 1 MHz would s u f f i c e . The lowest p o s s i b l e frequency i s d e s i r a b l e from the point of view of minimizing the e f f e c t of time delay d r i f t s at the I.F. Furthermore, i t i s r e l a t i v e l y easy to obtain high I.F. gains with phase s t a b i l i t y i f a low I.F. i s used. For these reasons, an I.F. of 2 MHz was chosen. The 50 required minimum I.F. bandwidth of 3 MHz was obtained by r o l l i n g o f f the. response of a F a i r c h i l d uA 702C op e r a t i o n a l a m p l i f i e r . 4.5 - 4 D e r i v a t i o n of the Other Loop Parameters . Two of the loop parameters have already been.chosen. These are: K K A = 3 . 6 x 1 0 8 (4-13) o d o oon = 3.14 x 10 5 rad/s ( 4 - 2 5 ) The open loop gain of the uA 702C i s 3000. (This f i g u r e w i l l vary from u n i t to u n i t and t h i s v a r i a t i o n i s compensated f o r by a gain adjustment i n the c i r c u i t design.) Using A q = 3000 i n (4-13), we have K QK d = 1.2 x 1 0 5 (4-30) Using a damping r a t i o of say, z = 1 i n Equations ( 4 - l l ) and (4-12), the loop f i l t e r time constants t-^ and t 2 can be evaluated as f o l l o w s : K K r • t x = = 1.215 x 10 b sec. (4-31) con . * 2 = wT = 6 , 3 6 x 1 0 ~ 6 s e c - (4 - 3 2 ) n The time constants are r e l a t e d t o the element values of the a c t i v e f i l t e r by (4-7) and ( 4 - 8 ) , i . e . , \ - \ C (4-7) t 2 = (R± + R 2)C • ( 4 - 8 ) so that 51 P^/P^ = t 2 / t 1 -1 = 4.24 Choosing . ' R 2 = 10K (4-33 . ) R l = 4724 = 2 ' 3 6 K ( 4 ~ 5 4 ) then, from (4-7) , C = t 1 / R 1 = 515 p.f. (4-35) Choosing a standard value of = 2.2K, t 2 becomes t 2 =6.28 x 10~ 6 sec. . (4-36) and z i s s l i g h t l y modified to become z = w n t 2 / 2 = 0.988 (4-37) The numerical values obtained using these design parameters have been included i n Figure 4-3 and Figure 4-5. 4.6 Hold-In Range The maximum frequency range over which the loop w i l l t r a c k without unlocking can be determined from the steady-state e r r o r equation of the second order loop B s s = i r l V (4-38) o d o where Aco i s the frequency o f f s e t . Now since the phase detector has a dynamic range of - TC/2 radians, the loop drops out of l o c k when the e r r o r exceeds these bounds. The Hold-In Range i s then '52 AGO = K QK dA o it/2 = 3.6 x 10 x 1.07 rad/s, which corresponds to 90 MHz. Such a Hold-In Range i s not p o s s i b l e i n p r a c t i c e , as one of the loop elements w i l l saturate f i r s t . An experimental v e r i f i c a t i o n that Acog meets the t r a c k i n g requirements i s necessary and t h i s i s pro-vided i n Chapter 6. ' •. . 4.7 Lock-In Range I f the loop i s i n i t i a l l y unlocked, and the input s i g n a l (of s u f f i c i e n t s i g n a l - t o - n o i s e r a t i o ) i s introduced, then there i s a f i n i t e frequency range of. the input s i g n a l f o r which the loop w i l l immediately achieve l o c k . This range i s defined as the Lock-In Range, and f o r the second order loop i t has .been shown that the l a t t e r i s equal to the high frequency loop g a i n . ^ ^ Ac^ = K Q K d t 2 / t 1 = 2zcon (4-39) For z = 1 and GO = V2it x 50 x 10 5, . n ' A f L =.b(1iL/2n = 100 kHz ' (4-40) In S e c t i on 4.4.3> a value of f =50 kHz was chosen i n n order to suppress the rms phase j i t t e r at the output of the loop. A smaller value of f could c e r t a i n l y have been s p e c i f i e d without i n c r e a s i n g the phase j i t t e r to an unacceptable value. One of the e f f e c t s of lowering the value of f , i . e . , GO , would be to decrease ° n' ' n' the loop bandwidth and provide a d d i t i o n a l f i l t e r i n g of the input noise to the loop. The r e s u l t s of Section 4-3.1> however, showed tha t the phase j i t t e r due to the I.F. noise was already n e g l i g i b l e . Consequently there i s l i t t l e to be gained by such a change. On the • 5 3 other hand, .Equation 4 - 3 9 i n d i c a t e s that i n order to acquire l o c k q u i c k l y , the largest p o s s i b l e value of co^  should be used. The design value of f = 5 0 kHz then, represents a compromise between a high value of con and the required l a r g e r a t i o of B^/co^ f o r loop s t a b i -i l i t y . 4.8 Sweep Waveform The maximum VCO sweep rate that can be used to acquire l o c k p i s co^. For, i n order to acquire l o c k , the VCO must be w i t h i n a range of frequencies that i s equal to the Lock-In Range, which i s equal to 2zco .. The time taken by the loop to l o c k up i s i n the 2 order of zoo , which e s t a b l i s h e s the maximum sweep rat e at about co . n' . • n I f the sawtooth sweep waveform proposed i n Section 3 - 3 . 3 i s to be employed, then the r i s e time of the l e a d i n g edge of the sawtooth must be f a s t enough to ensure that the loop w i l l be kicked out of l o c k , i n the event that a wrong-sideband l o c k i s encountered. For a 5 MHz sweep width, the required r i s e time i s about 3 0 0 usee. i. 54 5. INSTRUMENTATION 5.1 Components The instrumentation of the phase-locked l i n k discussed i n Section 3.2 i s shown i n Figures 5-1 and 5-2. The v o l t a g e - c o n t r o l l e d o s c i l l a t o r s and a l l of the c i r c u i t r y of Figures 5-3 to 5-5 were designed and b u i l t f o r the p r o j e c t ; however the f o l l o w i n g items were purchased from outside s u p p l i e r s : Mixers Ml, M2, M5 These are Sage Laboratories Inc. balanced mixers: input bandwidth .- 1 . 0-2.0 GHz noise f i g u r e (with a 1.2 dB N.F. a m p l i f i e r ) 7.0 dB i s o l a t i o n between L.O. and s i g n a l ports 25 dB conversion l o s s (2 MHz I.F.) 6.0 dB Mixer M3 Relcom Corp. double-balanced mixer. Input bandwidth 0.2 -500 MHz. D i r e c t i o n a l Couplers DC1, DC2, DC3. DC4 Microlab/FXR Model CA-45N dB d i r e c t i o n a l couplers. I s o l a t i o n i s . 23 dB. o R e s i s t i v e Power Splitters/Combiners RC1, RC2. RC3 Microlab/FXR Model DA-4FN l o s s between any two ports 6.0 dB bandwidth "DC _ 2.0 GHZ . High-Pass F i l t e r s F I , F2 Microphase Corp. Model HT-1000. AB 55 c u t o f f frequency 1.0 GHz i n s e r t i o n l o s s 0.5 dB attenuation at 2 MHz 60 dB 5.2 Control S t a t i o n A block diagram of the c o n t r o l s t a t i o n i s shown i n Figure 5-1. The h i g h - l e v e l transmitted s i g n a l at 1392 MHz and the l o w - l e v e l l e v e l received s i g n a l at 1390 MHz are duplexed to the cable by the d i r e c t i o n a l couplers DCl and DC2. This duplexing i s necessary to prevent the s i g n a l at 1392 MHz from overloading the mixer M2. The 2 MHz s i g n a l which i s propagated down the cable must be prevented from entering the 2 MHz I.F. stage of the upper-sideband generator or the 2MHz I.F. stage that f o l l o w s mixer M2. This i s accomplished by the high-pass f i l t e r F l , which has a 60 dB i n s e r t i o n l o s s at 2 MHz. The r e s i s t i v e power s p l i t t e r / c o m b i n e r RC2 i s used to combine the 1392 MHz and the 2 MHz s i g n a l s f o r propagation down the cable. Such a device produces an output at the I.F. port only i f both the L.O. and input s i g n a l are present. This p a r t i c u l a r choice f o r M3 was necessary i n order to suppress the second harmonic components of the s i g n a l and L.O. frequencies, which appear at 4 MHz. These 4 MHz components add v e c t o r i a l l y to the 4 MHz output s i g n a l of M3 obtained by the mixing of a 2 MHz s i g n a l and a 2 MHz L.O. The addi -t i o n of such a spurious phase term at 4 MHz r e s u l t s i n a phase e r r o r between the c o n t r o l s i g n a l and the output s i g n a l at the s a t e l l i t e , that v a r i e s p e r i o d i c a l l y with changing l i n e l e n g t h . D i v i s i o n by two i s accomplished by i n c o r p o r a t i n g the mixer M4 i n a regenerative loop, tuned to the desired output frequency of The mixer M3 i s a double-balanced or ring-modulator type. Control Signal 1390 i-niz Mixer li-i L.C inpvv I.F. Amp. Limiter 2 1'iHz 1392 Attcn A, 6 dB Phase Detec 2 MHz .imitc Phase S h i f t h" T Ti1 3 dB Directional Couplers ^ Loop F i l t e CQ s ON (V H IFifh 71 Her. i c Co,. L. _Y A rH RC2 F T ].-,u s VCO <—Ce-phas e Deteclf* (2) 2 MI: Limit 1— Terminated Sv/eep Co:,p. u i r c u : Inverting Input DG1 I!on-invert.ing Input Threshold Phase S h i f t oi ~ i r ~ Att en 6 dB T_ 1392 i-'JIs L.UT" inviut Mixer L t t e n A3 1390 MHz 2 PIITs PCI M3 I.F. Double I.F. , 4- MHz ••iixer I.F. ;tmp.i . . l k x l • i i i x e r Arnpl., L i i n i t Ainpl., L i i n i t input Att en -'12 Mover S n l i t -•: i-uiz mVi 2 i-D'Iz input ^ Reference Signal ^ MJIz Figure 5-1 Instrumentation - Control Station 1390 : MHz 2 i-iiiz 1392 KHz o jiCSl £V Coijibii 2 1-11 I z 1392 WIIz i i i gh Pa s s f i l t e i O rH F2 DC3 V liixer l-i5 0. ^ 1390 ut 1-filz Atten. 1-I.F. lAraui. 6 dB Limit 2 I-n-Iz Output 1390 i-Oiz dB D i r e c t i o n a l Couplers yf DC4. "Terminated Pnase Detec ill 2 l-'illz jimit l-'hase S h i f t '0' - 90° I.F. Ampl, Phase Detec (2) Sweep C oiapai Circu .1 j-iimit, Pon-Invertinf Input Inmit Threshold Figure 5-2 Instrumentation - S a t e l l i t e S t a t i o n 58 2 MHz. For t h i s a p p l i c a t i o n , such a method has a d i s t i n c t advan-tage over, say, a binary d i v i d e r . The l a t t e r would provide no output at 2 MHz u n t i l a 4 MHz s i g n a l was a p p l i e d t o the input of the device. When one considers the method by which t h i s 4 MHz s i g n a l i s derived, i t can be seen that considerable d i f f i c u l t y i n g e t t i n g the system to l o c k up could be a n t i c i p a t e d , i f such a d i v i -der were used. In the regenerative mixer of Figure 5 - 1 , the feed-back loop sustains an o s c i l l a t i o n at 2 MHz. This 2 MHz s i g n a l pro-vides the l o c a l o s c i l l a t o r s i g n a l f o r mixer M4 and a l s o serves as the reference s i g n a l f o r the upper-sideband generator. The pro-v i s i o n of t h i s reference s i g n a l and a c o n t r o l s i g n a l enables the upper-sideband generator to l o c k . A 4 MHz s i g n a l then appears at the input of mixer M4, which synchronizes the free-running frequency of the regenerative mixer and l o c k s up the system. 5 - 3 S a t e l l i t e S t a t i o n A block, diagram of the s a t e l l i t e s t a t i o n i s shown i n Figure 5-2. The instrumentation i s s i m i l a r to that used f o r the- upper-sideband generator at the c o n t r o l s t a t i o n . Here, however, the t r i g g e r c i r c u i t f o r the sweep has been changed to provide a lower-sideband l o c k and the sweep waveform has been i n v e r t e d so that the VCO i s i n i t i a l l y d r i v e n to a lower frequency and i s then swept toward a higher frequency. 5.4 C i r c u i t r y  Figure 5 - 3 The I.F.. a m p l i f i e r , A l , i s a F a i r c h i l d uA 702C op e r a t i o n a l a m p l i f i e r . The r e s i s t o r s R l and R4 and the compensating c a p a c i t o r A l l T's'are 20 turns %U Formex b l f i l a r vound on P h i l i p s zft -S33 3 -a/rz, f e r r i t e core. A l l RPC's are P h i l i p s z+zz-sss"- ao/sv A l l t r a n s i s t o r s are 2N /j.124. A l l diodes are IP lr15U A l l by-pass C s are O.luf. unless otherwise T3 _ r r r \ P29 22 T5 06 63pf 0.2 PPG rrr\ A n R3<£ 4.7K R37 3.2K S 6G0-Figure 5-4 T r a n s l a t i o n Loop(:.;hown for lower-sideband lock) Lock Indication C i r c u i t s , Sweep C i r c u i t , Loop F i l t e r ,o> o 62 C2 were chosen to provide a closed-loop gain of 54 dB and a video bandwidth of 4.5 MHz. The a m p l i f i e r response was r o l l e d o f f at the lower end at 50 kHz by choosing C l = .022 uf, to provide an I.F. bandwidth of about 4 MHz wit h a center frequency of 2 MHz. This ensures that the I.F. bandwidth requirements of Section 4.5-3 are met. In Section 4.5.1, the need to keep the I.F. f i l t e r i n g to a minimum was emphasized. ' Having e s t a b l i s h e d the I.F. bandwidth by shaping the frequency response of A l , the other I.F. stages were d e l i b e r a t e l y made broad-band. The l i m i t e r stage A2, i s a F a i r c h i l d uA 703C emitter-coupled RF a m p l i f i e r , with a DC to 150 MHz' c a p a b i l i t y . Hard l i m i t i n g w i t h -out s a t u r a t i o n i s achieved by l o a d i n g the output of the uA 703C wit h R5. Wide-band i n t e r s t a g e coupling i s r e a l i z e d by using b i f i l a r -wound d i s t r i b u t e d - l i n e transformers, of the type described by xiuthroff. ' The transformers used i n the c i r c u i t s of Figures 5-3 to 5-5 e x h i b i t a f l a t response from 20 kHz to 15 MHz. These b i f i l a r - w o u n d transformers are a l s o used i n the unbalanced-to-balanced hybrids which d r i v e the loop phase detector, quadrature phase detector, phase s h i f t e r and mixer M4.'. Under the assumption that the transformers are i d e a l over the frequency range of i n t e r e s t , i t can r e a d i l y be found t h a t : (1) The balanced arms are i s o l a t e d from each other, w i t h the im-pedance l o o k i n g i n t o e i t h e r unbalanced port equal to one-half the impedance across the balanced arms. (2) When the unbalanced arms are terminated to ground by equal 63 impedances R, the output impedance at e i t h e r balanced arm to ground i s 2R. The balanced arms are i s o l a t e d from each other. ( 3 ) I f a s i g n a l i s appl i e d to each unbalanced port, then the sum of these s i g n a l s appears at one of the balanced ports and t h e i r d i f f e r e n c e at the other balanced port. j The loop phase detector i s of the 4-diode type, d r i v e n from two unbalanced-to-balanced hybrids. I t can be seen from Figure 5-3 that the device c o n s i s t s of a p a i r of conventional 2-diode phase detectors placed back-to-back. The advantage of the 4-diode c i r c u i t i s that when the I.F. and reference s i g n a l s are i n quadrature, the r e s u l t i n g n u l l i s i n s e n s i t i v e to .-.unbalances i n e i t h e r or both of these s i g n a l s . The 90° phase s h i f t required f o r the l o c k i n d i c a t i o n scheme of Section 3 « 3 . 3 i s introduced i n t o the reference channel of the loop phase detector by R 3 1 and C6 which are connected across the balanced arms of the hyb r i d made from transformers T5 and T6. Figure 5-4 The loop f i l t e r , which uses a uA 702C op e r a t i o n a l ampli-. f i e r , has already been described i n Section 4.1. The output of the loop f i l t e r d r i v e s t r a n s i s t o r Q10, which i n turn c o n t r o l s the c o l l e c -t o r current of Q l l . In the absence of a sweep s i g n a l , t r a n s i s t o r Q l l acts as a current sink that determines the c o l l e c t o r current of the t r a n s i s t o r o s c i l l a t o r and the frequency of o s c i l l a t i o n of the l a t t e r . The reference s i g n a l at C, which i s 90° out of phase with the reference s i g n a l a p p l i e d to the loop phase detector, i s coupled to the hard l i m i t e r A5 through transformer T i l . The output of A5 64 and. the I.F. s i g n a l are appli e d to the unbalanced arms of the hy-b r i d T12, T13. The sum and d i f f e r e n c e of these s i g n a l s appear across CR5 and CR6 r e s p e c t i v e l y . The detected output currents are summed by the r e s i s t i v e network, to give a s i g n a l that i s pro-p o r t i o n a l to the phase d i f f e r e n c e . For the case of a lower-sideband l o c k , t h i s s i g n a l i s ap p l i e d to the non - i n v e r t i n g input of compar-ator A6, as shown i n Figure 5-4. The threshold of the comparator i s adjusted by p o t e n t i o -meter A6. When the loop i s locked to the lower sideband, the v o l -tage at p i n 3 of A6 i s negative and l e s s than V"., where V^ . i s the threshold l e v e l . I f the loop l o s e s l o c k or l o c k s to the upper sideband, the voltage at p i n 3 becomes greater than V".. A6 then goes to the ON s t a t e . The l o s s of l o c k i s i n d i c a t e d by a lamp which i s d r i v e n by t r a n s i s t o r Q9. T r a n s i s t o r s Q8, Q17, and Ql6 form a t r i g g e r c i r c u i t that turns on the astable c i r c u i t c o n s i s t i n g of Q14 and Q15. The output of the astable c i r c u i t i s d i f f e r e n t i a t e d and DC rest o r e d by C13, R75 and CR9, to produce a sawtooth waveform. • The sweep waveform d r i v e s the current sources Ql2 and Q13. The l a t t e r ; are connected i n push - p u l l , and sweep the c o l l e c t o r current and con-sequently, the frequency of the t r a n s i s t o r o s c i l l a t o r . The clock r a t e of the astable c i r c u i t i s approximately 2 Hz, which r e s u l t s i n a sweep.rate f o r the VCO of about 4 MHz/sec. For the upper-sideband generator, r e s i s t o r R50 i s connected to p i n 2, i . e . , the i n v e r t i n g , input of comparator A6. Al s o , the sweep waveform i s i n v e r t e d , by.reversing CR9 and connecting R75 to the +12 v o l t supply. 65 Figure 5-5 The I.F. s i g n a l from mixer M2 i s a p p l i e d to p i n E i n Figure 5-5. The I.F. stage f o r mixer M2 c o n s i s t s of an a m p l i f i e r A8, f o l -lowed by a bandpass" f i l t e r at 2 MHz cf 250 kHz bandwidth. The 2 MHz I.F. s i g n a l at p i n G i s then fed to the s i g n a l port of the double-balanced mixer MJ. The output of the mixer M3 at - p i n H i s a m p l i f i e d by A9, hard l i m i t e d by A10 and f i l t e r e d by a 4 MHz bandpass f i l t e r c o n s i s -t i n g of L2, C21 and R103. The bandwidth of the l a t t e r i s 750 kHz. The l i m i t e d s i g n a l at 4 MHz i s then fed to the s i g n a l port of the balanced mixer M4. The I.F. output of t h i s mixer i s ampli-f i e d and l i m i t e d by A l , f i l t e r e d at 2 MHz and fed back from the emitter of Q23 to the L.O. port of M4. Since the L.O. s i g n a l appears i n phase at both balanced output ports of the h y b r i d T17, T18, the diodes CR13 and CR14 are switched a l t e r n a t e l y at the 2 MHz L.O. frequency. In the absence of a s i g n a l at the input of mixer M4, the feedback loop sustains a free-running o s c i l l a t i o n at 2 MHz. The 4 MHz s i g n a l from M3 then synchronizes t h i s free-running o s c i l l a t i o n to perform the d i v i s i o n by two of the 4 MHz frequency. The d i v i d e r output i s taken from the emitter of Q24, attenuated 40 dB by R114, R115, R116, R117 and then fed to the reference input of the upper-sideband generator. This a t t e n u a t i o n can be reduced as necessary, when the r o t a r y phase s h i f t e r i s placed between the d i v i d e r and the upper-sideband generator. 5.5 The Design of the T r a n s i s t o r Microwave O s c i l l a t o r The design of the o s c i l l a t o r involved two steps. These were: 66 (a) The s e l e c t i o n of an a c t i v e device that was p o t e n t i a l l y unstable at the frequency of i n t e r e s t and that was capable of p r o v i d i n g a s u f f i c i e n t amount of power at t h i s frequency. (b) The choice of a resonant s t r u c t u r e that would u t i l i z e the i n s t a b i l i t y of (a) and allow the power generated by the a c t i v e device to be d e l i v e r e d to an e x t e r n a l load at the desired f r e -quency. Several UHF power t r a n s i s t o r s were evaluated f o r t h e i r s u i t a b i l i t y f o r use as o s c i l l a t o r s at. 1390 MHz. For each t r a n s i s t o r , common base y-parameters at 1390 MHz were measured f o r a range of c o l l e c t o r - t o - b a s e voltage and c o l l e c t o r current values. The s t a -b i l i t y of the t r a n s i s t o r s • f o r each set "of bias conditions was s t u d i e d , u s i n g a m o d i f i c a t i o n of a method developed by L i n v i l l , as f o l l o w s : The t r a n s i s t o r , on a l i n e a r b a s i s , can be represented by a two part network that i s d r i v e n by a source of admittance Y and terminated s by a load of admittance Y-^ . For some s p e c i f i e d source and l o a d , the' voltages and w i l l appear at the input and output terminals r e s p e c t i v e l y . Furthermore, because the system i s l i n e a r , the source can be scaled so that "V^  takes on a value of u n i t magnitude with zero phase. This s c a l i n g i n no way a f f e c t s the input and output admittances or the power gain of the t r a n s i s t o r . The s u b s t i t u t i o n theorem can then be invoked, to replace the source with a voltage generator ( u n i t magnitude and zero phase) and the l o a d w i t h a voltage source that a p p l i e s to the output terminals the same voltage as that taken by the l o a d . This r e p r e s e n t a t i o n i s shown i n 67 Figure 5-6. Thus any e x c i t a t i o n and load a p p l i e d to the t r a n s i s t o r can be simulated by a s u i t a b l e choice of the q u a n t i t i e s L and M, i n the complex voltage generator ^2' V-L = l / o ! (5-1) (L + jM) (5-2) Figure 5-6 Representation of the T r a n s i s t o r as a Linear Two-Port The input power P^ i s then p Mr T ^ Re(y y )L Im(y 2 y g )M i = R e ( V 1 I 1 * ) = g l l - + —TJZ (5"3) and the output power i s P o =-Re(V 2I 2*) (5-4) which r e s u l t s i n (L - i ) 2 + M2 = 1 - 4 { 5 ' 5 ) | y 2 l l In the three-dimensional space of L, M and P, where P represents power, (5-3) i s the equation of a plane and (5-5) the equation of a 68 paraboloid. The curve P Q = 0 i s a c i r c l e of u n i t r a d i u s , centered at L = 1, M = 0 l y i n g i n the L-M plane. The p r o j e c t i o n of grad P^ on the L-M plane and the l i n e of i n t e r s e c t i o n of the P^ and L-M planes can be e a s i l y determined from ( 5 - 3 ) . R e f e r r i n g to Figure 5 - 7 , we have _! I m ( y 1 2 ^21^ 0 = tan" -Re(y, 0 y ( 5 - 6 ) 12 J21' The l i n e of i n t e r s e c t i o n , i . e . , P^ = 0, i s perpendicular to the gradient d i r e c t i o n and has an M-intercept given by -2 g 2 2 s l l = ^ ^ 1 2 ^ 2 1 } ( 5 - 7 ) P paraboloid o P. plane unstable region Figure 5 - 7 Geometrical I n t e r p r e t a t i o n of P^ and P Q 69 I f the load admittance i s given by Y L = g L + j b L (5-8) the above can be mapped i n t o the L-M plane by the r e l a t i o n s h i p T L ="vf ( 5- 9 ) Equation ( 5 - 9 ) maps the admittance plane i n t o the P Q = 0 c i r c l e i n the L-M plane. This map, the s o - c a l l e d L i n v i l l Chart, can be obtained from the Smith Chart by t r a n s l a t i n g the l a t t e r one u n i t to the r i g h t and a r o t a t i n g through 180°. The load conductance g-^  and the load susceptance b-^ , are then r e l a t e d to the q u a n t i t i e s r and x of the Smith Chart, by the f o l l o w i n g : g L = g 2 2 r (5-10) b L = g 2 2 x - b 2 2 (5-11) The y-parameters f o r the 2N 3866 at f = 1390 MHz, V c b = 18 v o l t s , I =50 mA were as f o l l o w s : c ^11 = (^.8 - j 7.6) mmhos. y12 = ("31-5 - 3 2.1) mmhos. y 2 1 = (0 - j 40.0) mmhos. y 2 2 = (35 +3 70) mmhos. The p o s i t i o n of the input power plane r e l a t i v e to the L-M plane, f o r the above data, i s shown i n Figure 5-8. 70 Figure 5-8 L i n v i l l Chart for 2K 3366 at 1390 MHz 71 I t i s of i n t e r e s t that i n Figure 5-8, the input power plane i n t e r s e c t s the L-M plane w i t h i n the area of the u n i t c i r c l e . Over the crosshatched region i n Figure 5-8, P^ i s negative f o r p o s i t i v e values of P . The t r a n s i s t o r w i l l then o s c i l l a t e when o terminated i n any load value that corresponds to the values of L and M f a l l i n g w i t h i n t h i s r egion. On the b a s i s . o f Equations (5-10) and (5-11) and the measured data, i t can be seen that t h i s unstable region corresponds low values of load conductance and a negative, load susceptance. Just such an admittance i s that presented by an anti-resonant c i r c u i t that i s s l i g h t l y below anti-resonance at 1390 MHz. short Figure 5-9 Equivalent C i r c u i t of the T r a n s i s t o r and Load 72 i L t r : i ; 11 Tiff- -crrrr • .M..U-r t t i : tttt 4 - r H ••pxp ::tjxp •+-FR--rhr- 4+1+ _.+ -~ r r r r ' 73 The required anti-resonant s t r u c t u r e was r e a l i z e d by the two transmission l i n e s T^ and T^ i n p a r a l l e l , as shown i n Figure 5-^ 9. The l i n e T^ i s terminated i n a short c i r c u i t and T^ i s t e r m i -nated by a tuning stub, represented by the v a r i a b l e capacitance C . s The t r a n s i s t o r i s probe-coupled to the j u n c t i o n of the two l i n e s at P. The probe coupling capacitance i s represented by C . The le n g t h 1^ + ±2 i s about 15$ shorter than one-quarter wavelength at 1390 MHz and the capacitance C can be adjusted so that the admit-tance Y-^ , seen by the c o l l e c t o r terminals of the t r a n s i s t o r , f a l l s w i t h i n the unstable r e g i o n of Figure 5-9. The o s c i l l a t o r can then be mechanically tuned with C and the frequency of o s c i l l a t i o n p u l l e d ' by v a r y i n g the c o l l e c t o r current.- The l a t t e r changes the value of the t r a n s i s t o r output capacitance C . The d e t a i l s of the construc-t i o n of the o s c i l l a t o r are shown i n the Appendix. The design and c o n s t r u c t i o n of the VCO centered at 1392 MHz i s s i m i l a r . The v a r i a t i o n of the frequency and the power output of the TMO as a. f u n c t i o n of the c o l l e c t o r current i s shown i n Figure 5-10. The frequency i s l i n e a r w i t h c o l l e c t o r current f o r only a l i m i t e d range of the l a t t e r . Over the i n t e r v a l of - 1 MHz about 1390 MHz the o s c i l l a t o r gain constant i s approximately 330 kHz/mA. The output power i n Figure 5-10 e x h i b i t s an almost l i n e a r v a r i a t i o n w i t h frequency. About one-tenth of the output power would I be fed to the L.O. port of the 1420 MHz-to-30 MHz mixer at the s a t e l -l i t e antenna. The r e s u l t i n g change i n L.O. l e v e l would then be about 1 mW, over a 2 MHz t r a c k i n g range. More p r e c i s e c o n t r o l of the power l e v e l could be obtained with the use of a PIN diode l e v e l l e r . 74 6. PERFORMANCE OF THE SYSTEM 1390 HP 614A i -UlZ -Control otat ior 2MHz Attenuator Tek t r . 191 Chan.A GR LK-20L a d j . l i n e Chan. B S a t e l l Static-: Figure 6-1 Test C o n f i g u r a t i o n 6.1 Testing the Phase-Locked l i n k The performance of the phase-locked l i n k was checked, using the t e s t c o n f i g u r a t i o n of Figure 6-1. The c o n t r o l s i g n a l and the 2 MHz reference s i g n a l were obtained from .a Hewlett-Packard 614A L-band s i g n a l generator and a Tektronix Model 191 s i g n a l generator r e s p e c t i v e l y . The frequency at the output of the s a t e l l i t e s t a t i o n was monitored with a Beckman Model 6146 counter f i t t e d . w i t h a Model 609 Heterodyne U n i t . Phase comparisons were made d i r e c t l y . a t the microwave frequency, by applying the c o n t r o l and output s i g n a l s to the A and B channels r e s p e c t i v e l y , of the HP 140A sampling o s c i l l o s c o p e . The attenuation of the cable and i t s time v a r y i n g path length were simulated by a 75 v a r i a b l e attenuator and a GR Model LK-20L adjustable l i n e . The system steady s t a t e phase e r r o r f o r a frequency o f f s e t was measured by f i r s t l o c k i n g the system and then changing the f r e -quency of the c o n t r o l s i g n a l . With the sampling o s c i l l o s c o p e t r i g g e r e d on channel B, the r e s u l t i n g phase e r r o r was measured from the displacement of the trace on channel A r e l a t i v e to that of chan-n e l B. The Hold-In Range was determined by observing with the coun-t e r , the range of the c o n t r o l s i g n a l frequency over which the system remained i n l o c k . The Lock-In Range was determined by unlocking the loop, then slowly changing the c o n t r o l frequency u n t i l l o c k was a t t a i n e d . F i n a l l y , the performance of the system with regard to i t s a b i l i t y to t r a c k out e r r o r s due to changes i n the cable length was checked. A 20 CM. change i n l i n e l e n g t h was introduced by means of the adjustable l i n e , while the c o n t r o l and the output s i g n a l s were, observed on the sampling o s c i l l o s c o p e . 6.2 Results The steady-state phase e r r o r r a t e f o r each t r a n s l a t i o n loop was set to a value of l°/MHz, by a d j u s t i n g the values of r e s i s -t o r R22 and potentiometer R21. Since no s t a b i l i t y problems were e v i -dent f o r t h i s value of loop g a i n , the value of the l a t t e r was then increased by a f a c t o r of three, i n order to decrease the steady-state phase e r r o r r a t e to 0.3°/MHz. This corresponded to i n c r e a s i n g the values of co^  and z f o r each t r a n s l a t i o n loop by a f a c t o r of 1.6, since both these loop parameters are p r o p o r t i o n a l to the square root of the DC loop g a i n . This increase i n loop- gain d i d not introduce any apparent d i f f i c u l t i e s with regard to l o c k a c q u i s i t i o n . The 76 steady-state phase e r r o r r a t e between the c o n t r o l s i g n a l and the output s i g n a l at the s a t e l l i t e loop was then measured and found to be 0.5°/MHz. This i s about 1.5 times the e r r o r generated by one of the t r a n s l a t i o n . l o o p s as predicted i n Section 4.2. In Section 4.2, the t o t a l frequency o f f s e t that could be introduced i n t o the loop was estimated to be 2 MHz. On the basis of t h i s estimate, the increased value of loop gain would then r e s u l t i n a system phase e r r o r of l e s s than 1.5° maximum. The Hold-In Range which was l i m i t e d by the dynamic range of the loop f i l t e r A7, was measured and found to be -8 MHz about 1390 MHz. The l o c k - I n Range was measured and found to be -200 kHz about 1390 MHz. In the f i n a l t e s t , the sampling o s c i l l o s c o p e observations i n d i c a t e d that the change i n cable l e n g t h of one wavelength at 1390 MHz was tracked out by the system to w i t h i n a small e r r o r . This e r r o r appeared as a p e r i o d i c displacement of one of the traces r e l a -t i v e to the other, with a maximum d e v i a t i o n of 1.5°. A f t e r i n v e s t i -g a t i o n , t h i s phenomenon was a t t r i b u t e d to the generation of spurious second harmonic components of the L.O. s i g n a l at the output of mixer M3. This e r r o r could be f u r t h e r reduced by r e p l a c i n g mixer M3 with a u n i t that has a lower harmonic content. 77 7. CONCLUSIONS A new method of obta i n i n g phase-coherent l o c a l o s c i l l a t o r s i g n a l s f o r a two-dish supersynthesis at 1420 MHz has been devised. The f e a s i b i l i t y of t h i s method has been demonstrated by the design and c o n s t r u c t i o n of a system that provides phase-coherent, 1390 MHz s i g n a l s at two s i t e s that are separated by a time-varying path length. Tests performed i n d i c a t e that i n a l a b o r a t o r y environment the phase e r r o r of the system i s w e l l w i t h i n the allowable l i m i t s of -5° maximum. F i e l d t e s t s , which would have brought out the phase er r o r s due to temperature e f f e c t s on the system components, were not p o s s i b l e at t h i s time. However, these temperature e f f e c t s are a n t i c i p a t e d to be sm a l l , as both the c o n t r o l s t a t i o n and the s a t e l -l i t e s t a t i o n w i l l be operated i n a temperature c o n t r o l l e d environment during the a c t u a l experiment. The.periodic phase e r r o r described i n Section 6-2, although w i t h i n the design l i m i t s , could be f u r t h e r reduced by using a double-balanced mixer that b e t t e r suppresses the second harmonic components of the input s i g n a l s . Such mixers are commercially a v a i l a b l e . During the lab o r a t o r y t e s t s the maximum attenuation that was introduced between the control.and s a t e l l i t e s t a t i o n s was 30 dB. With more atte n u a t i o n , the loop at the s a t e l l i t e s t a t i o n no longer h a r d - l i m i t s the incoming s i g n a l . I f , as proposed, the more economi-c a l 0.5 inch H e l i a x cable i s to be used, the att e n u a t i o n f o r a 1000 f t . run would be .40 dB.. The a d d i t i o n a l 10 dB l o s s could be made up by r e p l a c i n g the r e s i s t i v e power s p l i t t e r s / c o m b i n e r s RC2 and RC3 by a r e a c t i v e coupling scheme. For example, the 2 MHz s i g n a l could be coupled to the cable through a shunt arm that i s s h o r t - c i r c u i t e d at 78 1390 MHz by a s u i t a b l e c a p a c i t o r placed one-quarter wavelength along the shunt arm. A l t e r n a t i v e l y , the I.F. gain of the s a t e l l i t e loop could be increased by 10 dB. I t would be advisable to add t h i s gain as a wide-band stage i n order not to introduce more I.F. f i l t e r i n g . This wide-band gain could be achieved by cascading with the l i m i t e r stage A2, another uA.702C l i m i t e r stage. . The d u p l i c a t e system, which c a l l s f o r two s a t e l l i t e s t a -t i o n s and a dual c o n t r o l s t a t i o n d r i v e n from a s i n g l e c o n t r o l s i g -n a l at 1390 MHz, i s p r e s e n t l y being considered f o r implementation. The reasons f o r t h i s choice- are as f o l l o w s . The instrumentation f o r the s a t e l l i t e s t a t i o n i s simpler than that required f o r the c o n t r o l s t a t i o n . The d u p l i c a t e system permits the use of a s a t e l l i t e s t a t i o n at each d i s h , where space i s at a premium. A l s o , f o r a 2000 f t . b a s e l i n e , •the cable runs need . only be 1000 f t . long. For the d u p l i c a t e system the steady-state phase e r r o r due to a frequency o f f s e t of the c o n t r o l s i g n a l , w i l l tend to be the same f o r each d i s h , i f the loop gains are equal. The d i f f e r e n t i a l t r a c k i n g e r r o r , then, can be made much l e s s than the t r a c k i n g e r r o r f o r a s i n g l e system. The d i f f e r e n t i a l phase s h i f t due to the cables can.be con-v e n i e n t l y monitored i n the d u p l i c a t e system. In Section 3 - 5 , i t was pointed out that t h i s i n f o r m a t i o n could be used to detect and c o r r e c t f o r the r e v e r s a l i n phase of the L.O. s i g n a l s that may occur when the system regains l o c k a f t e r a momentary l o s s of l o c k . " A d u p l i c a t e system, of course, r e q u i r e s the c o n s t r u c t i o n 79 of another system s i m i l a r to the one that has already been b u i l t . A l s o , the frequency s y n t h e s i z e r that generates the c o n t r o l s i g n a l and the r o t a r y phase s h i f t e r - have yet to be i n t e r f a c e d w i t h -the PDP-9 computer. These tasks are not considered to be extremely d i f f i c u l t . This system was developed f o r a s p e c i f i c a p p l i c a t i o n i n radi o astronomy. However, the technique i s qu i t e general and could be a p p l i e d to many s i t u a t i o n s r e q u i r i n g the phase synchronization of s i g n a l s at two s i t e s that are separated by a time-varying path l e n g t h . This method, with l o w - n o i s e . c i r c u i t components and a narrow loop bandwidth to suppress the I.F. noise, could be used with s u i t -able antennas, over a broadcast path of many mi l e s . For operation of the l i n k at higher microwave frequencies, the requirements f o r the VCO could p o s s i b l y be met by a Gunn O s c i l l a t o r . The system described i n t h i s t h e s i s represents a consider-able improvement over e x i s t i n g methods of o b t a i n i n g phase coherence of L.O. s i g n a l s i n r a d i o astronomy interferometer and supersynthesis experiments. With the continuing i n t e r e s t i n supersynthesis at short wavelengths, the technique should prove u s e f u l i n future experiments. 80 REFERENCES 1. -Ryle,.M. , "The New Cambridge Radio Telescope", Nature, V o l . 1 9 4 , No. 4828, May 1 2 , 1 9 6 2 , pp. 5 1 7 - 5 1 8 . 2 . Ryle, M., and Hewish, A., "The Synthesis of Large Radio Teles-copes", Monthly Notices of - the R.A.S., V o l . 1 2 0 , No. 3 , I 9 6 0 , pp. 2 2 0 - 2 3 0 . 3. Fomalont, E.B., and Wyndham, J.D., " P o s i t i o n s f o r 3C Revised Radio Sources", Observations of the Owens V a l l e y Radio  Observatory, C a l i f o r n i a I n s t i t u t e of Technology, Pasadena, C a l i f . , 1 9 6 6 . 4. Haneman,.F., and F l a t t a u , T., "Remotely S y n c h r o n i z i n g ' O s c i l l a -t o r s Over Time Varying Paths", I.E.E.E. Spectrum, October, 1 9 6 7 , pp. 5 . 5 . R i c e , S. 0 . , " S t a t i s t i c a l P r o p e r t i e s of a Sine Wave Plus Random Noise", B e l l System Technical J o u r n a l , V o l . 2 7 , 1 9 4 8 , pp. 109-157. 6 . Gardner, Floyd M., Phaselock Techniques, John Wiley and Sons, New York, N.Y., 1966, pp. 1 7 - 2 7 , 28 - 5 4 . 7. Van Blerkom, R., and Anema, S. L., "Considerations f o r Short Term S t a b i l i t y of Frequency M u l t i p l i e r s " , I.E.E.E. Journal  on Aerospace and E l e c t r o n i c s Systems, V o l . AES 2 , No. . 1 , Jan. 1966, pp. 36-47. 8. V i t e r b i , Andrew J . , P r i n c i p l e s of Coherent Communications, McGraw-Hill, New York, N.Y., 1966, pp. 36-39-9. Ruthroff, C.L., "Some Wide Band Transformers", Proc. I.R.E., V o l . 4 7 , No. 7 , pp. 1 3 3 7 - 1 3 4 2 . 1 0 . L i n v i l l , John G., and Gibbons, James F., T r a n s i s t o r s and A c t i v e C i r c u i t s , McGraw-Hill, New York, N.Y., 1 9 6 1 , Chap-t e r 1 1 . 81 APPENDIX 

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