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Noise figure of the transistor amplifier Hatton, Walter Lewis 1951

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NOISE FIGURE OF THE TRANSISTOR AMPLIFIER by WALTER LEWIS HATTON A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department ef E l e c t r i c a l Engineering We accept t h i s thesis as conforming to the standard required from candidates f o r the degree of MASTER OF APPLIED SCIENCE Members of the Department of E l e c t r i c a l Engineering THE UNIVERSITY OF BRITISH COLUMBIA A p r i l 1951 A b s t r a c t The n o i s e f i g u r e o f t h e t r a n s i s t o r a m p l i f i e r I s o f s p e c i a l i n t e r e s t s i n c e t h e l a r g e q u a n t i t y o f e x c e s s n o i s e p r e s e n t l i m i t s the u s e f u l n e s s o f t h e t r a n s i s t o r as a l o w - n o i s e a m p l i f i e r . W h i l e the e q u i v a l e n t n o i s e v o l t a g e s g e n e r a t e d i n the e m i t t e r and c o l l e c t o r l e a d s v a r y i n v e r s e l y w i t h f r e q u e n c y , t h e n o i s e f i g u r e does n o t . T h i s v a r i a t i o n f r o m the i n v e r s e f r e q u e n c y c h a r a c t e r i s t i c i s produced by t h e de c r e a s e o f t h e e f f e c t i v e g a i n a t h i g h e r f r e q u e n c i e s . The s u b j e c t o f t h i s t h e s i s i s t h e i n v e s t i g a t i o n o f t h i s v a r i a t i o n * The v a r i a t i o n o f t h e n o i s e f i g u r e w i t h f r e q u e n c y has been measured f o r s e v e r a l d i f f e r e n t t r a n s i s t o r s , w i t h v a r y i n g e m i t t e r and c o l l e c t o r c u r r e n t s . E q u i v a l e n t diagrams have been s u g g e s t e d w h i c h e x p l a i n t h e v a r i a t i o n o f t h e n o i s e f i g u r e w i t h f r e q u e n c y i f t r a n s i t t i m e d i s p e r s i o n i s n e g l i g i b l e . F o r low f r e q u e n c i e s , the n o i s e f i g u r e i s g i v e n by, F = 4-KT-e V a r i a t i o n o f t h e n o i s e f i g u r e due t o t h e s t r a y c a p a c i t i e s i s g i v e n a p p r o x i m a t e l y by 1 The v a r i a t i o n , due t o t r a n s i t t ime e f f e c t s , i g n r o i n g t r a n s i t t i m e . d i s p e r s i o n , i s The o p e r a t i n g c o n d i t i o n s f o r minimum n o i s e f i g u r e o f t h e t r a n s i s t o r a m p l i f i e r a r e dependent on t h e f r e q u e n c y . A t l o w f r e q u e n c i e s , a low v a l u e o f e m i t t e r c u r r e n t s h o u l d be us e d , and t h e l o w e s t p o s s i b l e v a l u e o f c o l l e c t o r v o l t a g e w h i c h i s c o m p a t i b l e w i t h the d e s i r e d g a i n . A t h i g h e r f r e q u e n c i e s a low v a l u e o f e m i t t e r c u r r e n t s h o u l d a l s o be used b u t the v a l u e o f t h e c o l l e c t o r v o l t a g e i s de t e r m i n e d by t h e f r e q u e n c y . The h i g h e r t h e f r e q u e n c y , t h e h i g h e r w i l l be t h e r e q u i r e d c o l l e c t o r v o l t a g e . The b e s t n o i s e f i g u r e s a t h i g h e r f r e q u e n c i e s w i l l be o b t a i n e d w i t h t r a n s i s t o r s w i t h t h e f o l l o w i n g c h a r a c t e r -i s t i c s : ( i ) ITm l a r g e ( i i ) c l o s e s p a c i n g o f p o i n t c o n t a c t s ; ( i i i ) h i g h v a l u e o f r e s i s t i v i t y ( i v ) s m a l l t r a n s i t t i m e d i s p e r s i o n E q u i v a l e n t diagrams have been s u g g e s t e d w h i c h p a r i a l l y a ccount f o r t h e v a r i a t i o n o f the n o i s e f i g u r e w i t h f r e q u e n c y . I t has been s u g g e s t e d t h a t t r a n s i t time d i s p e r -s i o n w j u l d e x p l a i n the r e m a i n i n g d e v i a t i o n o f t h e n o i s e f i g u r e f r o m t h e i n v e r s e f r e q u e n c y characteristic© i TABLE OP CONTENTS I Introduction II General Theory A Noise Measurement 1 Noise Figure 2 Available Signal Power 3 Gain 4 Available Noise Power 5 Effective Bandwidth 6 Noise Figure 7 Noise Figure Measured with Signal Generator 5 8 Noise Figure Measured with Noise Diode 6 9 Comments 7 B Transistor Theory 8 III Description of Equipment 14 A Low Frequency Equipment 15 B High Frequency Equipment 16 IV Theory Applied to Investigations 18 A Low Frequency Case 19 B High Frequency Case 22 1 Neglecting Transit Time 22 2 Neglecting Stray Capacities 25 V Results 28 VI Conclusions 30 VII Literature Cited 34 VIII Bibliography 37 IX Acknowledgment 40 PAGE 1 3 3 3 4 4 4 5 5 i i ILLUSTRATIONS PIG. PAGE 1 Four-Terminal Network 3 2 Diode Noise Generator 6 3 Type-A Transistor 8 4 Circui t Representation of Transistor 10 5 Static Characteristics of Transistor 11 6 Equivalent Circuit of Transistor 13 7 Equivalent Circui t of Transistor 18 8 Low Frequency Equivalent Diagram 19 9 Variation of Noise Figure at Low Frequencies 21 10 High Frequency Equivalent Diagram Neglecting Transit Time 22 11 Variation of Noise Figure Neglecting Transit Time 24 12 High Frequency Equivalent Diagram Neglecting Stray Capacities 25 13 Variation of Noise Figure Neglecting Stray Capacities 27 14 Variation of Noise Figure between Transistors 28 15 Variation of Noise Figure with Collector Voltage 28 16 Variation of Noise Figure with Operating Point 28 17 Variation of Noise Figure for Different Collector Currents 28 18 Variation of Noise Figure for Different Emitter Currents 29 19 Optimum Operating Conditions at Different Frequencies 29 20 Block Diagrams of Test Equipment 40 21 Low Frequency Equipment Circuit Diagram 40 22 Low Frequency Test Set 40 i i i F I G . PAGE 23 H i g h Frequency Equipment C i r c u i t Diagram 40 24 H i g h Frequency T e s t Set 40 NOISE FIGURE OF THE TRANSISTOR AMPLIFIER I Introduction The noise figure of an amplifier i s of the utmost importance, for example the l imit of sens i t iv i ty of an amplifier i s determined by this factor. In the transistor or crystal triode amplifier, due to the large quantity of excess noise present, this rating of an amplifier i s of special importance. Although sufficient gain i s present In an amplifier, unless the signal power output i s large with respect to the noise output, the signal may be masked completely or marred suf f ic ient ly to destroy i t s usefulness as a means of communicating information. The type-A transistor developed at the Be l l System Telephone Laboratories by Drs• Bardeen and Brattain 1# under the direction of Dr. Shockley consists of two small cats' whiskers i n contact with a small block of germanium. One of the probes i s biased i n the positive direction and is called the e m i t t e r . „ The second probe is biased i n the negative direction and is designated the * A l l numbered references given in "Literature Cited" 2 collector* Variation of current i n the e m i t t e r c i r c u i t produces a variation of from two to five times that i n the collector c i r c u i t . Therefore the transistor acts as a current amplifier. Also, because the input c i rcui t i s a low impedance and the output c i rcui t is a high impedance, a voltage gain Is obtained. Power gains of the order of 20 db or 100 times and voltage gains of 30 db or 35 times are easi ly obtained with the type-A transistor. Although the gain of the crystal triode compares well with that of a vacuum triode, the noise figure is much worse* The noise figure of a low-noise vacuum-tube ampli-f i e r i s of the order of 10 db i n a range of 100 cycles up to 30 megacycles. By comparison the transistor amplifier has a noise figure of about 70 db at 100 cycles and of about 30 db at 10 megacycles, with wide variation In individual transistors. In the lower frequency range the noise figure decreases almost inversely with frequency. At higher frequencies of the order of 100 kilocycles to 10 megacycles, variation of current amplification increases the noise figure to values higher than that to be expected from the inverse frequency variat ion. This variation can be explained by the effects of the actual physical capaci-tance of the transistor c i rcui t and of the transit time effects i n the germanium triode. The magnitude of the noise generated In the transistor is nearly proportional to the collector voltage, but the greater the collector voltage, the higher the 3 frequency before the amplifier deviates from the noise spectrum that i s inversely proportional to frequency. The equivalent noise voltage generated i n the emitter and the collector leads have been measured by 2 H. C. Montgomery of the Be l l Laboratories. These noise voltages squared vary nearly inversely with frequency. The noise figure w i l l also vary inversely with frequency at low frequencies. However at higher frequencies the noise figure w i l l no longer vary In this manner. The subject of this thesis i s the investigation of this var ia t ion. II General Theory A Noise Measurement 1. Noise Figure The noise figure F of a four-terminal network has 3 been defined by F r i i s as the ratio of the available signal-to-noise rat io at the signal generator terminals to the available signal-to-ndise rat io at i t s output terminals. OUT POT Circvi t" F i g . 1 Four-Terminal Network 4 Several definitions w i l l be given to make possible a more precise mathematical def init ion of this quantity* 2. Available Signal Power The available signal power 3^ i s the maximum that a generator of impedance /f0 ohms and electromotive force £ can del iver . This is equal to c = E°~ ( l ) 3 . Gain The gain of a network is the ratio of the avai l -able signal power at the output terminals of the network to the available signal power at the output terminals of the signal generator. I f 5 equals the available output power at the output terminals, the gain 4. Available Noise Power The available noise power at the input of the network is that generated by the thermal agitation i n the equivalent internal-resistance of the signal generator. This available thermal noise of Johnson-noise power i s equal to ft7~3f where /C Is Boltzman's constant, 7~ i s the absolute temperature, and B i s the bandwidth, " The available noise power N at the output of the network i s due to a l l the noise sources i n the network and the signal generator thermal noise, i . e . , N = FG KTB (3) 5 5* Effective Bandwidth The effective bandwidth B of the network i s the bandwidth of an ideal band-pass network with gain G which would produce an output of GKTB = [GF KTjf (4) where £f Is the gain at frequency f . Therefore, 6« Noise Figure The noise figure w i l l now be defined in terms of 5j , 5 , KTB', and /V . Repeating, the noise figure F i s the rat io of the available slgnal-to-nolse rat io at the input terminals to the available slgnal-to-nolse ratio at the output terminals. Therefore, F = (S./KT0)(N/5) r K V (6) 7. Noise Figure Measured with Signal Generator I f the signal generator output Is increased . u n t i l the to ta l power output is double that due only to the internal noise of the network and the Johnson-noise i n the generator impedance, then the noise figure KT-6 (7) If t\ = 1.38 x 1 ( T 2 5 j o u l e s / ° C , 7"= 2 9 0 ° Kelvin, this 6 becomes The noise figure can now be determined by calculating the effective bandwidth by manually integrating the gain-versus-frequency curve, 8, Noise Figure Measured with Noise Diode The mean-square noise current of a temperature limited diode is given by the Schottky formula as = 2 e r D B (9) I f t h e diode load Is / f the mean-square-noise voltage due to the diode current and from Johnson-noise i s •p- = + K T n . 8 ( ( 1 0 ) <50 • 5 R = F i g , 2 Diode Noise Generator With the noise generator off, the output noise power i s N = F G K T B With the noise generator on, the total output power i s 7 0 1 7-K-r ' (11) Solving for ^ gives for T « 2 9 0 ° K, F " ( I t f N ^ l ) ( 1 3 ) For the special case where the noise output i s doubled . fr = %0 ID R (14) 9. Comments The noise diode method of measuring noise figure Is far the easiest both from a point of time and equipment. The noise figure can be obtained by a single measurement and an easy calculat ion. On the other hand, for the signal genera-tor method, the bandwidth has to be laboriously plotted and many calculations made, although to a f a i r approximation B can be taken as the distance between half-power points* The advantages of the diode noise source are limited however. At high frequencies the impedance of the generator i s d i f f i c u l t to determine and i t i s necessary to minimize reactive components to prevent variation over the bandwidth. At low frequencies the Schottky formula does not apply due to f l i cker e f fec t . 4 8 B T r a n s i s t o r Theory The t y pe-A t r a n s i s t o r c o n s i s t s o f a s m a l l b l o c k o f germanium a g a i n s t w h i c h two p o i n t c o n t a c t s a r e made. The germanium used i s s i m i l a r t o t h a t i n h i g h - b a c k - v o l t a g e r e c t i f i e r s s u c h as d e s c r i b e d by T o r r e y and Whitmer. The s u r f a c e i s ground f l a t and t h e n e t c h e d and welded on a b r a s s p l u g . T h i s p l u g i s f o r c e d i n t o the m e t a l b a r r e l o f t h e t r a n s i s t o r as sJtK>wn i n F i g , 3. The p o i n t c o n t a c t s a r e nade F i g . 3 Type-A T r a n s i s t o r o f phosphor-bronze w i r e ,002" t o ,005" I n d i a m e t e r and c u t i n wedge shape t o f a c i l i t a t e c l o s e s p a c i n g . These a r e welded on t o s u p p o r t i n g p i n s on an i n s u l a t i n g p l u g . A f t e r the p o i n t s a r e m a n u a l l y a d j u s t e d u n t i l t he s e p a r a t i o n i s a p p r o x i -m a t e l y ,002", the i n s u l a t i n g p l u g i s pushed i n t o the m e t a l 9 cartridge u n t i l contact is made with the germanium slug. One of the points is biased In the positive direction and is called the emitter. The second point,the col lector , is biased i n the negative direct ion. The brass base makes an ohmic contact with the germanium crysta l . The emitter and the collector can be considered separately as two diodes. The emitter is biased i n the forward direction and the collector i n the backwards direct ion. Therefore, the emitter exhibits a low resistance and the collector exhibits a high resistance. When the emitter is placed suff ic iently close to the col lector , variation of the emitter current w i l l influence the collector current. The variation of the collector current i s actually greater than that of the emitter current, so current amplification takes place. Also, since the emitter c i rcu i t is of low impedance while the collector c i rcu i t i s of high impedance, a voltage gain can be obtained. This current amplification can be explained by the theory of sol id state. Only a br ief summary w i l l be given of one proposed by Bardeen and Brattain.^ The flow of e lec t r i c i ty i n semiconductors consists of negative electrons and positive holes. The negative carriers are excess electrons which are free to move or have energies i n the conduction band of the crystal . The positive carriers are defect electrons or unoccupied energy states i n the f i l l e d band of the crysta l . The 10 germanium u s e d i n t h e t r a n s i s t o r i s n-type w h i c h has an exce s s o f n e g a t i v e c a r r i e r s . The c u r r e n t f r o m the e m i t t e r , w h i c h i s b i a s e d I n t h e p o s i t i v e d i r e c t i o n , c o n s i s t s l a r g e l y o f h o l e s . These h o l e s a r e a t t r a c t e d towards t h e n e g a t i v e l y b i a s e d c o l l e c t o r . The l a r g e s t p a r t o f t h i s h o l e c u r r e n t f r o m t h e e m i t t e r f l o w s i n t o c o l l e c t o r c i r c u i t s i n c e t h e c o l l e c t o r c o n t a c t o f f e r s o n l y a low r e s i s t a n c e t o t h e s e h o l e s . The h o l e c u r r e n t f l o w i n g i n t o t h e c o l l e c t o r c i r c u i t a l s o a l t e r s t h e space charge I n the b a r r i e r l a y e r a t t h e c o l l e c t o r . T h i s change i n t h e b a r r i e r l a y e r charge r e d u c e s the r e s i s t a n c e t o the f l o w o f e l e c t r o n s f r o m the c o l l e c t o r . I n t h i s f a s h i o n a c u r r e n t change i n t h e e m i t t e r c i r c u i t c a n produce a change o f the c o l l e c t o r c u r r e n t o f as much as t e n t i m e s . N o r m a l l y t h i s change I s o f the o r d e r o f two. F o r t u n a t e l y f o r s m a l l s i g n a l c o n s i d e r a t i o n , l i n e a r s i g n a l t h e o r y can be used and t h e o p e r a t i o n o f the t r a n s i s t o r c a n be r e p r e s e n t e d by an e q u i v a l e n t c i r c u i t . The c i r c u i t u s ed most o f t e n i s t h e e q u i v a l e n t T shown i n F i g . 4, F i g , 4 C i r c u i t R e p r e s e n t a t i o n o f T r a n s i s t o r F o r t u n a t e l y t h i s e q u i v a l e n t diagram has a s i g n i f i c a n t p a r a l l e l w i t h t h e a c t u a l p h y s i c a l s i t u a t i o n . The base 11 resistance i s a c t u a l l y the resistance to the flow of current from the germanium to the base. The emitter resistance fe, i s the actual resistance to the flow of current from the emitter into the c r y s t a l . The c o l l e c t o r resistance *2 Is the actual resistance to the flow of current from the c o l l e c t o r into the c r y s t a l . The mutual transfer resistance represents the active property of the network produced by the a l t e r a t i o n of the impedance to the flow of current In the c o l l e c t o r c i r c u i t by the emitter current. This representation of the t r a n s i s t o r i s only applicable at low frequencies. The contact impedances ^ , *e# and ^ are pure resistances In the u s e f u l range of the 7 t r a n s i s t o r . This Is as would be expected from previous measurements on c r y s t a l diodes. However the mutual transfer-impedance w i l l vary at higher frequencies and should be represented by which i s a function of frequency. The equivalent resistances can be determined d i r e c t l y from the s t a t i c c h a r a c t e r i s t i c s of the t r a n s i s t o r . Since the t r a n s i s t o r i s e s s e n t i a l l y a current amplifying device, and because the voltage i s a single-valued variable of the current, the emitter current and the c o l l e c t o r current are selected as independent variables. The s t a t i c c h a r a c t e r i s t i c s of the t r a n s i s t o r are shown In Pig, 5 where £ & and £ c are plotted against and -Tc , Slopes of the d i f f e r e n t curves y i e l d the values of the equivalent c i r c u i t components, Since t he currents are the independent to follow page 11 12 variables, . Ve = / S ) ( 1 5 ) V c = / ^ f ^ , , (16) Expanding these functions in a Taylor series and considering only f i r s t order terms, a V e = i f e ^ r ^ ^ . A r c ( i 7 ) AVC = jgAre + J f c a z * ( 1 8 ) Therefore the general c i rcu i t impedances are as follows: The input Impedance with the output open#circuited for A C i s , R ' - P The output impedance with the Input open-circuited for A C i s , ff ' _ 2 Vc % % ~~ d zc ( 2 0 ) The backward transfer impedance with the input open-circuited for A C i a , R ' = /9- ? T C (21) The forward transfer Impedance with the output open-circuited for AC i s , Rj = (22) Therefore In the stat ic characteristics ftn - slope of curve 5 (a) (23) ff,% - slope of curve 5 (b) (24) R%i - slope of curve 5 (c) (25) = slope of curve 5 (d) (26) From these the c i rcu i t parameters are ascertained, The equivalent diagram so far given does not Include any noise sources that are actually present in the 8 transistor. Peterson has shown that the noise i n a 4-terminal network can be considered as originating i n two noise generators included i n the arms of the network as shown i n F i g . 6, where = Equivalent noise voltage i n emitter lead 5 Equivalent noise voltage i n collector lead The noise voltage perunit bandwidth has been measured i n 9 some detai l by Montgomery. It has been shown that for the crystal d i o d e , ^ the noise voltage squared per unit bandwidth varies nearly Inversely with frequency. The X F i g . 6 Equivalent Circui t of Transistor 14 Sope of the noise spectrum varies between 0.9 and 1.2. The magnitude of /Vg i s of the order of one-hundreth of the value of h/c • Also, some correlation between the two noise sources has been demonstrated, but i t i s of a highly unpredictable magnitude.^" No compDe te theory of the sources of the excess 1 noise i n semiconductors has been presented. A . Van der Z i e l has shown that i f a suff ic iently wide distr ibution of relaxa* t ion times i s considered the inverse variation of noise power with frequency can be explained. He suggests that this wide distr ibution function could be produced by f ive different sources of noise* These are thermal noise, shot noise* f l i cker effect, l oca l fluctuations i n conductivity due to diffusion of foreign atoms or la t t ice distortions, and spontaneous fluctuations l n temperature* .c Although the cause of the excess noise l n semi-conductors i s not f u l l y understood, considerable improvement has been made with the noise level l n crystal diodes, and i t i s hoped that similar improvements w i l l be made i n the transistor* III Description of Equipment The equipment was designed to measure the noise figure of the transistor amplifier i n the frequency range from 100 cycles per second to 10 megacycles per second* Where possible the noise-diode generator method of measuring the noise figure was used because of this greater ease of 15 Measurement and greater aecuracy* This was done i n the range 75 kilocycles to 10 megacycles where the most extensive measurements were made. In the audio frequency range however, measurement was made by the signal generator nethod* Because of this the equipment divided I t se l f into two test sets, that used at audio frequencies and that used at radio frequencies* A Low Frequency Equipment The low frequency test set, a block diagram of which i s shown i n F ig * 20, consisted of an audio signal generator with, a range of from 10 cycles to 100 ki locycles , a vacuum tube voltmeter for measuring the input signal, an attenuator, the transistor amplifier, a high-gain low-noise preamplifier, a selective amplifier, and a square law out-put meter* The complete c i rcui t diagram is shown i n F i g , 21, The high level of the noise i n the transistor at the lower audio frequencies made this method of measurement pract ica l * The necessary input needed to double the power output of the c i rcui t was obtained with a reasonable attenuation from an easily measurable voltage, ! This fact minimized stray f i e l d consideration which makes this method of measurement d i f f i cu l t at low signal levels . The high gain preamplifier consisted of two 6AK5 pentodes with ample decoupling to ensure s t ab i l i ty and a DC filament supply to reduce hum. The selective amplifier employed a twin-T feedback c i r cu i t with coupling through a cathode follower and a series 16 •onnected amplifier. The output of the selective amplifier 13 was fed to a square-law detector suggested by M i l l e r . The frequency was changed by plug-in resistors i n the twin-T feed-back c i r c u i t . The d i f f i cu l ty with this c i rcui t was the necessity of realigning i t for each frequency and the replotting of the se lect iv i ty curve. It was found necessary to use a long time constant of approximately thir ty seconds i n the output c i rcui t to smooth out periodic fluctua-tions in the noise output . 1 4 Unfortunately this increased the poss ib i l i ty of zero dr i f t during measurement. The whole test set, with the exception of the signal generator and vacuum tube voltmeter, was b u i l t on a single 17" x 13w x 4W chassis, with compartment shielding, and mounted on sponge rubber to minimize i n s t a b i l i t y . B High Frequency Equipment The high frequency test set, a block diagram of which i s shown i n F i g . 20, consisted of a diode noise genera* tor, a preamplifier, the transistor amplifier, a cathode follower, an AR88 RCA receiver, a square law detector similar to that used i n the low frequency range, and a vacuum tube voltmeter output meter. The complete c i rcu i t diagram i s shown on F i g . 23# The noise diode used was a Sylvania type 5722 which has a maximum current rating of 30 ma. With a. load of 1000 ohms, which i s approximately the input resistance for the best noise figure of the transistor amplifier, noise figures up to 600 may be measured for double output power. With an 17 Increase of only one third output power, which i s about the minimum for re l iable measurement, noise figures of up to 1800 can be measured. For noise figures above this a 6AC7 preamplifier whieh had a power gain of about seventeen was used. This made possible the measurement of noise figures up to 30,000, It is well to point out at this time that a l l calculations depend on the fact that the noise figure of a l l c i rcui ts except the transistor amplifier can be ignored. In cascaded amplifiers the principle source of noise Is i n 15 the early stages. The total noise figure is given by F , „ = F, +- -fkff- <87> where i s the noise figure of the f i r s t stage, ^ i i s the noise figure of the second stage, and Q, , i s the gain of the f i r s t amplifier. As the minimum noise figure of the transistor i s 300 with a gain of 10 to 100, and the noise figure of following amplifiers i s 10 or less , a l l noise following the transistor amplifier can be ignored. When the amplifier is used preceding the transistor, the noise figure i s above 1800 so that the noise of the preamplifier with a gain of 17 and a noise figure of 10 need not be considered* The AR88 receiver was especially suitable because of i t s low frequency range. The receiver was l inearized by operating with the beat frequency osc i l la tor on # The operation of the set was very simple, allowing rapid compilation of data in the frequency range most desired. The only d i f f i cu l ty of design was in minimizing the input capacity to the transistor amplifier. Since the 18 5732 diode has an Internal capacity of this input capacity could not be reduced much below tO/^^f &s • Rather than tune this capacity out, i t was taken Into account i n the theoretical calculation to follow. The high frequency test set, except for the radio receiver, the vacuum tube voltmeter and the power supplies, was also mounted on a 17"1 x 13rt x 4" chassis as a complete unit . Both sets have b u i l t - i n controls to vary and measure the emitter and the collector current. Prim these two readings the operating point on the characteristic curves may be determined since the emitter and collector voltages are both dependent variables of the emitter and collector currents. IV Theory Applied to Investigations An analysis of the transistor w i l l now be made from the consideration of the theoretical equivalent 16 c i r c u i t . A f i r s t analysis w i l l be made for low frequencies where capacitive and transit time effects can be ignored. This w i l l then be extended to include capacities which may Pig . 7 Equivalent Circuit of Transistor 19 be ignored, except at the highest frequencies. Then variation of the noise figure due to^^aloAe w i l l be oonsidered* A Low Frequency Case The noise figure has been defined as the available signal-to-noise rat io at the signal generator to the available signal-to-noise rat io at the output terminals. Consider the equivalent c i rcu i t diagram of the transistor shown i n F i g . 8 # The available signal power v S at the input terminals /f i s . The available noise power at the input terminals is KTB. Therefore, the available signal-to-noise rat io at the input terminals i s The available signal power at the output terminals 2-2 w i l l now be calculated. The current flowing In c i rcu i t two due to the vo l tage^in one F i g . 8 Low Frequency Equivalent Diagram (28) 20 where/) is the c i rcui t determinate and/^^Is the minor obtained by cancelling row 1 and column 2. Therefore, the signal output power i s P s = ( ^ ) ^ l ^ ^ (30) The output noise power due to A / , the t'ermal noise i n the generator, i s s imilar ly PN^^X+KTB ( S 1 ) The output noise power due to the noise generator Nela the emitter lead is The output power due to the noise generator He i n the collector lead is , N c [ 0 1 C (33) Since the noise voltages are s t a t i s t i c a l l y independent events, thdir output powers may be added arithmetical ly. This gives a tota l noise output power 2. (34) A poss ib i l i ty exists of He and tfc not being completely independ* ent but the correlation has not been determined as yet, and therefore w i l l not be considered. 21 p a available signal at input y, noise at output available noise at input" signal at output (55) Actually any correlation between and nfc should be taken into account, but for simplifying purposes /l4 w i l l be ignored, since i s approximately 50 db. below A/. 1 7 t and -^P* i s never larger than about 35, / l ^wi l l only s l ight ly affect the noise figure. Therefore, since F ~ +«rffRj irZfit J ( 3 6 ) If f^c varies inversely proportional to frequency This variat ion of goise figure is shown on F i g . 9* t o f o l l o w page 21 lb 70 db 60 Noise Figure 1 10 1 0 2 1 0 3 1 0 4 l o 5 F r e q u e n c y i n C y c l e s F i g . 9 V a r i a t i o n of Nols© F i g u r e at Low F r e q u e n c i e s 22 B High Frequency Case 1. Neglecting Transit Time For higher frequencies the equivalent c i rcui t diagram of the transistor amplifier i s as shown In F i g . 10, Fig.10 High Frequency Equivalent Diagram Neglecting Transit Time Cf Is the input capacity, £ ^ i s the capacity between the emitter and the col lector , and C3 i s the barrier layer capacity. 18 This model was suggested by Br a dne r-Brown. As In the low frequency case, the available signal-to-noise rat io at the input terminals i s L~ To obtain the output powers, f i r s t write the general mesh equations for the active network, ignoring /Ve # 23 Z„ L, -h~ l,% -j- Z,3 i-j -h Z^t^. -f Z^tj- ~ £r Z^ i, -h Z % ^ i % -hZ%.-3 L3 + Z-tf-t>4_-j-ZVJT^' O Z 3 < L , + Z3^o^+Z53 t>3 + Z^c^^ Z35- if A/^-h-r^ (c;-fcJ(38) Z6/ c, +ZS% 01. + ZSs -l-Z$+ c+.-hZtfs*j - 0 T h i s can be r e w r i t t e n i n the p a s s i v e f o r m a s , Z,, -h Z/% L x. -h Z,3 13 ~h Z/ 4-6 4- -t- zt Z+* —On Z& -h Z3t. i j_ + Z3 3 6 j -r-Zs £><^ 4-Z3 r = /V c Zj, c, -hZjr%c%. -hZs 3 <o -h-Z4+l+. +Zs?is ~ o where - / -7 / *-31~ = ^3 X rrt, Z3S Z+i = +• r-tr, z i 6 It t h e c i r c u i t d e t e r m i n a n t Z// ^ix ^-13 Z-I+Z-IS Z%( Z. Z%.j Z^f. Zxjr Z3, Z33 Z'3sr Z*i Zs% Z S 3 Z s + Z s 5 the o u t p u t s i g n a l I q u a l s a- _ 2. D = and t h e o u t p u t n o i s e power e q u a l s (39) (40) (41) (42) 24 T h e r e f o r e , t h e c i r c u i t n o i s e f i g u r e (43) where, A. = - re z++ Z,* = 0 Z.s = o Z31 - Zs, - 0 - 0 Z33 ~ - O Zj+ = Z53 - 0 z%, = </ ^ / Z35 - Zs+ - ii *3 7 -*- a-a -Z+i = T h i s formula becomes, after considerable manipulation, g/^YAfr *ASJAX ^  Z *~ 'V f/tj *• r<H-rhf 7 +- irj> + r~,)2' (44) where«^ e^and/"is in megacycles per second and cf)^»} + ^3 are in/{/{/Vs. A typical curve for variation o f A i s shown in P i g . 11 for c f = / * , ~ * C 3 ^ /. t o f o l l o w page 24 e lOdb 20 Noise \ \ \ \ \ \ \ \ \ \ -i 2 3 4 5 10 20 30 40 50 Frequency in Megacycles Fig. 11 Variation of Noise Figure Neglecting Transit Time 25 At a l l but very high frequencies F * (45) It ia seen that stray capaclites except for frequencies above 10 megacycles* i f kept to the smallest possible values* have l i t t l e effect on the variation of the noise figure* Therefore* i f -h (46) 2. Neglecting Stray Capacities In the previous section, It has been shown that stray capacities have very l i t t l e effect on the noise figure, for below 10 megacycles* The equivalent diagram may therefore be shown i n P ig . 12* ^ — ( S ) — I — ® — ^ ^ H Q -4. Pig. 12 High Frequency Equivalent Diagram Neglecting Stray Capacities 26 The noise figure i s then and since i s very small with respect to >cr = — f*k±!*±* ) ( 4 Q ) where ^ is some functionof frequency* In consideration of the filamentary transistor, 1 9 Shockley, Pearson and Haynes have developed a formula which gives the variation of <*ewlth frequency. This expression takes into account the recombination of holes with electrons and the time delay of holes passing to the col lector . It can be shown t h a t ^ i s equivalent t o - ^ r — , and therefore any variation of with/ 1 w i l l be duplicated i » ^ » They hawe given Ke^VC'+A)^ ( 4 9 ) where cooFt +(rt/Tf>) (50) 72 i s the transit time, 7p i s the hole l i fet ime, ^Is the fraction of the emitter current carried by holes, and 6 i t the rat io of the mobility of electrons to the mobility of holes. Hence, for the filamentary transistor, iion -h(-n/rP) <51> or 7*. = ^ ' ^ ^ ^ r ^ r T ^ ^ - ^ f <5 2> 27 •7 20 Bardeen has g i v e n t h e h o l e l i f e t i m e as 2 x 10 seconds ana -7 21 t h e t r a n s i t t i m e o f t h e h o l e s as .5 x 10 s e c o n d s . Then Hrrsq I I +e-**'*-Invasion. (53) and, as a f u n c t i o n o f f r e q u e n c y . The v a r i a t i o n of/Srith f r e q u e n c y f o r t h e p a r t i c u l a r case h a v i n g 7p*< 2 x 1©~ 7 seconds and/£ a .5 x 10""7 seconds 11 shown i n P i g . 13. T h i s v a r i a t i o n does n o t i n c l u d e t h e e f f e c t s due to t r a n s i t t i me d i s p e r s i o n . I n the type-A t r a n s i s t o r , the p a t h that a l ) . the h o l e s f o l l o w i s n o t the same. The h o l e s on l e a v i n g the e m i t t e r tend t o f o l l o w the p o t e n t i a l g r a d i e n t * The shape of t h i s f i e l d caused b y two n o n - p o i n t s o u r c e s I n c o n t a c t w i t h a r e l a t i v e l y l a r g e body h a v i n g d i f f e r e n t p o t e n t i a l s , i s extemely comples. I t i s f u r t h e r c o m p l i c a t e d b y the p r e s e n c e o f space charges and a r e c t i f y i n g b a r r i e r . Even i f t h e shape o f the f i e l d c o u l d be d e t e r m i n e d , the p r o b l e m i s s t i l l f u r t h e r c o m p l i c a t e d by t h e e x i s t e n c e o f two d i f f e r e n t t y p e s o f c u r r e n t c a r r i e r s w h i c h must be c o n s i d e r e d s t a t i s t i c a l l y . T h e r e f o r e , no attempt has been made t o p r e d i c t the v a r i a t i o n of F~due t o t r a n s i t t i m e d i s p e r s i o n * 28 V R e s u l t s The v a r i a t i o n o f t h e n o i s e f i g u r e o f t h e t r a n s i s t o r a m p l i f i e r w i t h e m i t t e r c u r r e n t , c o l l e c t o r c u r r e n t , and f r e q u e n c y was measured. I n P i g . 14 i s shown t h e v a r i a t i o n o f the n o i s e f i g u r e f o r f o u r d i f f e r e n t t r a n s i s t o r s i n the f r e q u e n c y range 100 k i l o c y c l e s t o 10 m e g a c y c l e s . I t i s e a s i l y seen t h a t t h e r e i s v e r y l i t t l e u n i f o r m i t y i n t h e r e s u l t s o b t a i n e d f r o m v a r i o u s t r a n s i s t o r s . A t one megacycle, t h e n o i s e f i g u r e s v a r y f r o m 600 t o 32,000, a range o f 17 db. V a r i a t i o n o f the magnitude o f u n d e r s i m i l a r o p e r a t i n g c o n d i t i o n s w i l l r e s u l t i n wide v a r i a t i o n o f the n o i s e f i g u r e , s i n o e F i s i n v e r s e l y p r o p o r -t i o n a l t o ^tn s q u a r e d . T h i s a l o n e would not account f o r the wide v a r i a t i o n o f t h e n o i s e f i g u r e , b u t p r o b a b l y t h e n o i s e v o l t a g e s g e n e r a t e d v a r y c o n s i d e r a b l y i n d i f f e r e n t u n i t s . I n P i g . 15 t h e v a r i a t i o n o f n o i s e f i g u r e w i t h \/c i s shown f o r a s i n g l e u n i t a t a f r e q u e n c y o f 500 k i l o c y c l e s . The d e v i a t i o n o f t h e c u r v e f r o m t h e g e n e r a l p a t t e r n a t t h e low e r v o l t a g e s i s due t o t h e i n c r e a s e o f t r a n s i t t i m e e f f e c t s . I t I s seen t h a t t h e n o i s e f i g u r e i s v e r y n e a r l y p r o p o r t i o n a l t o t h e c o l l e c t o r v o l t a g e . I n P i g . 16 t h e v a r i a t i o n o f n o i s e f i g u r e f o r a t r a n s i s t o r a m p l i f i e r i n t h e range f r o m 100 c y c l e s t o 10 mega-c y c l e s i s shown f o r two d i f f e r e n t o p e r a t i n g p p i n t s . The v a r i a t i o n o f t h e n o i s e f i g u r e i n t h e f r e q u e n c y range f r o m 100 k i l o c y c l e s t o 10 megacycles i s shown i n P i g . 17 f o r d i f f e r e n t v a l u e s o f c o l l e c t o r c u r r e n t . The n o i s e f i g u r e t o f o l l o w pag© 28 1 \ 5 ® OJ ca O H 1 2 3 4 5 6 7 8 9 10 Frequency I n Megacycles F i g . 13 V a r i a t i o n o f Noise F i g u r e N e g l e c t i n g S t r a y C a p a c i t i e s t o f o l l o w page 28 c 3 .4 .5 1 2 Frequency i n Megacycles F i g . 14 V a r i a t i o n o f Noise F i g u r e between T r a n s i s t o r s t o f o l l o w page 28 t o f o l l o w page 28 0 tOi&M I c = 2 ma \ x \ \ 0 « O PS 1 0» V "v - x — \ \ . \ \ \ \ -^_\_ ^ \ \ H \ • \ ^ \ \ \ \ \ \ ^ \ s —g _^ ios lo 6 IO1? Frequency i n C y c l e s F i g . 16 V a r i a t i o n of Noi3e F i g u r e w i t h O p e r a t i n g P o i n t t o f o l l o w page 28 o .1 0 2 .3 04 .5 1 2 3 4 5 10 ' Frequency i n Megacycles F i g . 17 V a r i a t i o n o f Noise F i g u r e f o r D i f f e r e n t C o l l e c t o r C u r r e n t s 29 variation i n the frequency range from 100 kilocycles to 10 megacycles is plotted i n P ig . 18 for different values of emitter current. These curves indicate that the noise figure decreases at some rate less than Inversely proportional to frequency at radio frequencies. In fact , the noise figure increases above a certain frequency. The lower the voltage on the col lector , the lower is the frequency at which these effects become important. The variation i n both the curves of noise figure for different collector and emitter currents can be attributed to the changes i n collector voltage. However, the lowest noise figure at a particular frequency is not obtained with the highest collector voltage. Pig . 19 shows the optimum values of-ZTcfor varying emitter currents. z c Ze /=~ O. 1m: /•Om 7V-0 o<h* //SO / <• t o 3fo % o 0- o 370 •• % o 0-7O 3 f 370 f 3f 30 %70 I* 3 f 3 70 * 3 S Pig , 19 Optimum Operating Points at Different Frequencies The above tabulation" shows that the best noise figure i s obtained with a low emitter current and that the best collector current depends on the frequency. t o f o l l o w page 29 30 VI Conclusions (a) The noise figure of the transistor amplifier i s very nearly inversely proportional to frequency at frequencies where the transit time Is not important. This agrees with the low frequency equivalent diagram for which r 2. F = _ _ A ^ r j > & ± ^ - ^ f (55) ^ +KTB ^ l r b - h r * 1 This agreement depends on the Inverse frequency characteristic of He. (b) The variation of the noise figure with frequency w i l l be further changed by the stray capacities as shown i n Pig . 11 and r --^Fa^i (rA+rM)>- 7(56) This only becomes important above 7 or 8 megacycles, and is usually overshadowed by other effects. (c) The variation of noise figure w i l l be modified by change i n w i t h frequency. This variation i s produced by recombination of holes with electrons during the time taken for the holes to pass from the emitter to the collector and the reduction due to the time of transit being comparable with the period of the s ignal . The noise f igure, as plotted i n F ig . 13 is given by _ W T 6 fi. I / y-e-**"^ i f ^ s T6 j ( 5 7 ) 31 Only a t h i g h c o l l e c t o r v o l t a g e where the t r a n s i t t i me i s h i g h do the above v a r i a t i o n s e x p l a i n the ob s e r v e d changes o f t h e n o i s e f i g u r e w i t h f r e q u e n c y . The n o i s e f i g u r e a t h i g h e r f r e q u e n c i e s i s c o n s i d e r a b l y above t h a t t o be e x p e c t e d . T h i s i n c r e a s e p r o b a b l y can b e s t be e x p l a i n e d b y t r a n s i t time d i s p e r s i o n s . That I s , some h o l e s l n p a s s i n g f r o m the e m i t t e r t o t h e c o l l e c t o r , do not f o l l o w the d i r e c t p a t h b u t f o l l o w a round-about p a t h . T h e r e f o r e , n o t a l l t h e h o l e s w i l l have the same t r a n s i t t i m e , and as a r e s u l t a t the h i g h e r f r e q u e n c i e s d e c r e a s e s t h e e f f e c t i v e kralue o f t h e t r a n s f e r impedance . (d) Where t h e n o i s e l e v e l i s o f p r i m a r y i m p o r t a n c e , some g e n e r a l r u l e s f o r t h e o p e r a t i o n o f t h e t r a n s i s t o r a m p l i -f i e r c a n be g i v e n . A t low f r e q u e n c i e s , a low v a l u e o f e m i t t e r c u r r e n t s h o u l d be u s e d . A l s o , t h e l o w e s t p o s s i b l e v a l u e o f c o l l e c t o r v o l t a g e s h o u l d be u s e d t h a t Is c o m p a t i b l e w i t h t h e d e s i r e d g a i n . A t h i g h e r f r e q u e n c i e s a low v a l u e o f e m i t t e r c u r r e n t s h o u l d be used but t h e v a l u e o f the c o l l e c t o r v o l t a g e i s dete r m i n e d by the f r e q u e n c y . F i g . 19 i n d i c a t e s the v a r i a t i o n o f t h e b e s t o p e r a t i n g c o l l e c t o r v o l t a g e s a t s e v e r a l r a d i o f r e q u e n c i e s * (c) Some g e n e r a l c r i t e r i a c a n be e s t a b l i s h e d as t o t h e c h a r a c t e r i s t i c s t h a t a r e most d e s i r e d f o r o p e r a t i n g w i t h t h e l o w e s t p o s s i b l e n o i s e f i g u r e . 32 The l a r g e r t h e v a l u e o f fm t h e l o w e r t h e n o i s e f i g u r e o— w i l l be s i n c e / ^ i s v e r y n e a r l y i n v e r s e l y p r o p o r t i o n a l t o . T h i s a p p l i e s a t b o t h h i g h and low frequencies» The h i g h f r e q -uency n o i s e f i g u r e can be improved b y r e d u c i n g the t r a n s i t 22 t i m e e f f e c t s . The t r a n s i t t i m e 7? - • *-yrS* (58) and t h e r e f o r e t h e c l o s e r t h e s p a c i n g , t h e s m a l l e r t h e t r a n s i t t i m e . The v a l u e o f - Z ^ i s d e t e r m i n e d by o t h e r c o n s i d e r a t i o n s and t h e r e f o r e c a n not be g r e a t l y a l t e r e d . A l s o , t h e h i g h e r t h e v a l u e o f t h e r e s i s t i v i t y ^ ? , t h e l o w e r t h e t r a n s i t t i m e . i 23 Bradnsr-Brown has shown v a r i a t i o n s o f °C ewith f r e q u e n c y , w i t h spa.cing, c o l l e c t o r c u r r e n t , and b u l k r e s i s t i v i t y . The l a r g e s t r e d u c t i o n o f ^ w i t h f r e q u e n c y i s caused by t r a n s i t t i m e d i s p e r s i o n . T h i s has b e e n r e d u c e d by u s i n g m agnetic b i a s i n g and by making t h e t r a n s i s t o r i n t h e f o r m o f a f i l a m e n t . I n t h e f i l a m e n t a r y t r a n s i s t o r , v e r y l i t t l e d i s p e r s i o n can take p l a c e , and would v e r y n e a r l y a p p l y . W i t h magnetic b i a s i n g as used by 24 25 Bradner-Brown , and S h o c k l e y and S u h l , t h e magnetic f i e l d t e n d s t o make t h e h o l e s t r a v e l f r o m t h e e m i t t e r t o t h e c o l l e -c t o r w i t h i n n a r r o w e r t i m e l i m i t s , t h u s r e d u c i n g t r a n s i t t i m e d i s p e r s i o n . V a r i a t i o n w i t h f r e q u e n c y o f t h e n o i s e f i g u r e o f the t r a n s i s t o r a m p l i f i e r has been p l o t t e d and t h i s v a r i a t i o n has been p a r t l y e x p l a i n e d due t o c a p a c i t a n c e and t r a n s i t time 33 e f f e c t a I t has been s u g g e s t e d t h a t t h e o b s e r v e d v a r l i i o n s f r o m the t h e o r y c o u l d be caused by t r a n s i t time d i s p e r s i o n . Some g e n e r a l r u l e s f o r low n o i s e o p e r a t i o n o f t h e t r a n s i s t o r have been g i v e n and a l i s t o f d e s i r a b l e c h a r a c t e r i s t i c s have been g i v e n f o r low n o i s e o p e r a t i o n . 34 LITERATURE CITED 1 Bardeen, J . , and Brattain, W. H . , "The Transistor, a Semiconductor Triode, " The Physical Review. Vol.74, p . 231. 2 Montgomery, H. C . , "Background Noise i n Transistors," Be l l Laboratory Record. Vo l . 28, p. 401. 3 P r i i s , H. T . , "Noise Figures of Radio Receivers," Proceedings of the Institute of Radio Engineers. Vo l . 32, p. 419. 4 Van der Z i e l , A . , "On the Noise Spectra of Semi-Conductor Noise and of Fl icker Ef fec t , " Physlea. Vol . 16, p. 367. 5 Torrey, H. C. and Whltmer, C. A . , Crystal Rect i f iers . McGraw*Hill Book Co. , Inc. , New York, 1948, p. 361. 6 Bardeen, J . , and Brattain, W. H . , "Physical Principals Involved i n Transistor Act ion , " The Physical Review. V o l . 75, p. 242. 7 Bardeen, J . , and Brattain, W. H . , "Physical Principals Involved i n Transistor Act ion , " The Physical Review. Vol . 75, p . 258. 8 Peterson, L . C . , "Space Charge, Signal and Noise i n Microwave Tetrodes," Proceedings of the Institute  of Radio Engineers. V o l . 35, p. 1270. 9 Becker, J . A . , "Transistors," E l e c t r i c a l Engineering. Vol . 69, p. 62. 10 M i l l e r , P. H . , "Noise Spectrum of Crystal Rect i f i e r s , " Proceedings of the Institute of Radio Engineers. Vol . 35, p. 253. 35 11 Montgomery, H. C . , "Background Noise i n Transistors," B e l l Laboratory Record. Vo l . 28, p. 402, 12 Van der Z i e l , A . , "On the Noise Spectra of Semi-Conductor Noise and of Fl icker E f fec t , " Physlea. Vo l . 16, p.359. 13 M i l l e r , P. H . , "Noise Spectrum of Crystal Rec t i f i e r s , " Proceedings of the Institute of Radio Engineers. Vol . 35, p. 254. 14 Bain, W. A . , Spectral Distribution of Noise. M. A. Sc. Thesis i n Engineering Physics, U. B. C . , May 1950, p. 8. 15 Torrey, H. C. and Whitmer, C. A . , Crystal Rect i f iers . McGraw-Hill Book Co. , Inc. , New York, 1948. p . 29. 16 Ryder, R. M . , and Kircher, R. J . , "Some Circui t Aspects of Transistors," Be l l System Technical Journal. Vo l . 28, p. 369. 17 Bardeen, J . , and Brattain, W. H . , "Physical Principals Involved i n Transistor Act ion , " The Physical Review. Vol . 75, p . 596. 18 Bradner Brown, C . , "High Frequency Operation of Transistor," Electronics . July 1950, p . 83. 19 Shockley, W., Pearson, G. L . , and Haynes, J . R., "Hole Injection l n Germanium - Qualitative Studies and Filamentary Transistors," Be l l System Technical  Journal. V o l . 28, p. 363. 20 Bardeen, J . , and Brattain, W. H . , "Physical Principals Involved i n Transistor Act ion , " The Physical Review Vol . 75, p . 274. 36 21 Bardeen, J . , and Brattaln, W. H . , "Physical Principals Involved in Transistor Act ion , " The Physical Review. V o l . 75, p . 258. 22 Bardeen, J . , and Brattain, W. H., "Physical Principals Involved in Transistor Act ion , " The Physical Review. Vol . 75, p. 274. 23 Bradner Brown, C , "High Frequency Operation of Transistors," Electronics . July 1950, p. 82. 24 Bradner Brown, C . , "Magnetically Biased Transistors ," The Physical Review. Vo l . 76, p. 1736. 25 Shuhl, H. and Shockley, W., "Concentrating Holes and Electrons by Magnetic F ie ld s , " The Physical Review. Vol . 75, p . 1617. 37 BIBLIOGRAPHY Aisberg, E . , "TransIstron • Transistor - ?, Toute l a Radio. Vol . 16, pp. 218-220. Bain, W. A . , Spectral Distribution of Noise. M. A. Sc. Thesis ln Engineering Physics, U. B. C . , May 1950. Bardeen, J . , "Surface States and Rectif ication at a Metal Semiconductor Contact," The Physical Review. Vo l . 71, pp. 717-725, Bardeen, J . , and Brattain, W. H . , "Nature of Forward Current i n Germanium Point Contacts," The Physical Review. V o l . 74, p. 231. Bardeen, J . , and Brattain, W. H . , "The Transistor, a Semi-conductor Triode," The Physical Review. Vo l . 74, p. 231. Bardeen, J . , and Brattain, W. H . , "Physical Principals Involved i n Transistor Act ion , " The Physical Review. V o l . 75, pp. 215-221. Bradner Brown, C , "Magnetically Biased Transistors ," The Physical Review. V o l . 76, p. 1736. Bradner Brown, C , "High Frequency Operation of Transistors," Electronics . July 1950, pp. 81-83. Becker, J . A . , "Transistors," Electrieel Engineering. V o l . 69, pp. 58-63. Becker, J . A . , and Shive, J . N . , "Transistor - a New Semi-conductor Ampli f ier , " E lec t r i ca l Engineering. Vo l . 68, pp. 215-221. 38 Goldberg, H . , "Some Notes on Noise," Proceedings of the  Institute of Radio Engineers. Vol . 36, pp. 1205-1215. Goldman, L . , Frequency Analysis..Modulation and Noise. McGraw-Hill Book Co . , Inc. , New York, 1948. F r i i s , H. T . , "Noise Figures of Radio Receivers," Proceed- ings of the Institute of Radio Engineers. Vol * 32, pp. 419-422. Mllman, I . J . , "Noise Generators and Measuring Technics," Tele-Tech. May 1950, p. 28 and June 1950, p. 26. M i l l e r , P. H . , "Noise Spectrum of Crystal Rect i f iers " , Proceedings of the Institute of Radio Engineers. V o l . 35, pp. 252-256. Montgomery, H. C . , "Background Noise i n Transistors," B e l l Laboratory Record. V o l . 28, pp. 400-403. Peterson, L . C , "Space Charge, Signal and Noise i n Micro-wave Tetrodes," Proceedings of the Institute of  Radio Engineers. V o l . 35, pp. 1264-1272, Ryder, R. M. , "Type A Transistor," B e l l Laboratory Record. V o l . 27, pp. 89-93. Ryder, R. M . , and Kircher, R. J . , "Some Circui t Aspects of Transistors," Be l l System Technical Journal. V o l . 28, pp. 367-400. Shockley, W., and Pearson, G. L . , "Modulation of Conducti-v i ty by Surface Charges," The Physical Review. Vol . 74, p. 233. Shockley, W., Pearson, G. L . , and Haynes, J• R., "Hole Injection i n Germanium • Qualitative Studies and Filamentary Transistors, w B e l l Sy8tem Technical Journal. V o l . 28, pp. 344-366. Sueur, R., "The Transistron Triode Type PTT 601," Onde. E l e c . V o l . 29, pp. 389-397. Shuhl, H . , and Shockley, W., "Concentrating Holes and Electrons by Magnetic F i e l d s , " The Physical Review. V o l . 75, p. 1616. Torrey, H. C . , and Whitmer, C. A . , Crystal Reeti f iers . McGraw-Hill Book Co. , Inc. , Hew York, 1948. Van der Z i e l , A . , "On the Noise Spectra of Semi-conductor Noise and of Fl icker Ef fect , " Physica. Vo l . 16, pp. 359-372. 40 Acknowledgment The author wishes to express his indebtedness to those who have assisted him throughout the course of this research; especially to Dr. F . Noakes for his guidance and encouragement* Acknowledgment is also made to the Defence Research Board of Canada whose grant made this invest i -gation possible. W.L. Hatton VTVM OSC. Trans !• s t o r Amp. P r e -Amp. Se l e c t ' i v e Amp. Squar Law Det. Output .Meter Low-Frequency B l o c k Diagram Diode Noise Gen. P r e -Amp. T r a n s i s t o r Amp. C a t h . Follow, e r AR88 R e c e i v e r Square Law Output Meter Hlgh-Frequency B l o c k Diagram F i g . 20 B l o c k Diagrams o f T e s t Equipment P i g . 21 Low f r e q u e n c y Equipment C i r c u i t Diagram F i g . 23 High Frequency Equipment C i r c u i t Diagram 

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