The cascode amplifier by Glenn B Coughlan A THESIS Submitted to the Graduate Faculty in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering Montana State University © Copyright by Glenn B Coughlan (1956) Abstract: The primary purpose of this thesis was to determine the characteristics of the cascode amplifier and to develop equations for the design of such an amplifier. This entailed developing equations from the equivalent circuit of the cascode amplifier and then confirming these expressions by making measurements on an amplifier in the laboratory. Fairly good agreement existed between predicted and experimental results. THE GASCODE AMPLIFIER

by

GLEHN B0' COUGHLAN ■h

A THESIS

Submitted to the Graduate Faculty

i n

partial fulfillm ent of the requirements

for the degree of

Master of Science in Electrical Engineering

a t

Montana State College

Bozeman5 M ontana J u ly 5 1956 M57I C -2 - TABLE OF CONTENTS

Acknowledgment

A b s tr a c t

Introduction

Theory-

Method of Investigation

Discussion of Results

Conclusions

A ppendix

Experimental Circuit Diagram (Fig. I)

Response Curves (Fig. 2)

Graph, Gain vs. R^ (Fig. 3)

Graph, Bandwidth vs. R^ (Fig. U)

Tabulated Results (Table I)

Sample Calculations

Literature Cited and Consulted

119224 —3—

ACKNOWLEDGMENT

This investigation was undertaken at the suggestion of Professor

R. Ce Seibel. of the Department of E lectrical' Engineering, Montana

State College. The author wishes to express his appreciation to all

of the electrical engineering staff for their help and suggestions and in particular to Professor Seibel under whose supervision this thesis was completed.

Bozeman, Montana Glenn B. Goughian •July, 19^6 ABSTRACT

The primary purpose of this thesis was to determine the charac­

teristics of the caseode amplifier and to develop equations for the

design of such an am plifier.

This entailed developing equations from the equivalent circuit

of the caseode am plifier and then confirming these expressions by making measurements on an am plifier in the laboratory.

Fairly good agreement existed between predicted and experimental r e s u l t s . INTRODUCTION

In low frequency radio systems where the greatest sources of noise, such as atmospherics, are external to the radio set itself, the small amount of tube and circuit noise generated within the set. is not important. However, in the very-high frequency range, where atmospherics are not so severe, minimum signal discernibillty is often determined by noise generated within the receiver itself. Now, the signal entering a vhf receiver is usually very weak and although this signal can be amplified easily, any noise generated in the -input stages of the receiver w ill be amplified along with the signal. Noise gener­ ated in subsequent stages is not so important since its magnitude is small compared to the signal which has already been amplified many times. Thus, the maximum attainable signal/noise ratio of a vhf receiver is set by the signal/noise ratio of the input stages. For this reason, low-poise r-f amplifiers are very important in vhf receivers.

It is well known that the random division of cathode current between plate and screen in a pentode makes the partition noise of a pentode three to five times that of the same tube connected as a triode % therefore, it is desirable to use a triode tube in the first stage of apy vhf receiver,

Triode am plifiers that must function over a wide frequency range, such as in television receivers, are very difficult to stabilize unless they are heavily loaded. Since one heavily-loaded triode tube has low c- voltage gain, it would seem desirable to use two triodes at the input of a vhf receiver to improve its noise figure. -6 -

Two triode tubes can be cascaded in nine possible ways but the cas-

code circuit has proved to be the best combination with regard to low noise figure, stability and gain.

■ The cascode am plifier is a low-noise amplifier and although two tri­ ode tubes are employed, the circuit as a whole has the stability, and high gain characterized by the pentode. Much has appeared in the literature concerning the low-noise properties of the circuit but very little has been published about practical design considerations.

This investigation was undertaken to study the gain, bandwidth, input impedance, and stability characteristics of the cascode amplifier and to develop equations and present curves that would be useful in designing a cascode circuit. I

- 7 -

THEORY

The cascode am plifier as shown in Figo 1 ( a ) an d 1(b) consists of a

conventional grounded-cathode am plifier V- feeding a grounded-grid a$p- 1 lifier . In both circuits the tubes arp series-connected as far as the a-c signal is concerned 5 how ever5 Pig. 1(a) shows the plate voltage applied to the tubes in series, and Fig. 1(b) shows the tubes paralleled acrpss the plate supply. There are advantages and disadvantages to both circuits.

To secure the same operating point, the plate voltage for the spries connection must be twice that for the parallel connection. Fewer com­ ponents and adjustments are necessary, however, in the series-connected

' ‘ cascode am plifier and it seems to be the most widely used circuit,.

Another .important consideration is that avc voltage applied to fhe grid of w ill control both tubes if they are series-connected, whereas avc voltage must be applied to the grids of V and V separately in the I d. parallel-connected circuit to obtain the same amount of gain control

In both circuits the grid-bias resistors R, and R1 are adjusted so that both triodes are operating at the same point on the linear portion of their characteristic curves. Adjusted this way, both triodes may be assum­ ed to have the same tube coefficients. The by-pass capacitors are se­ le cted so that they have negligible reactance at the operating frequency.

The tank circuits consisting of L and C are parallel resonant at the operat­ ing frequency and the radio-frequency choke, in the parallel-connected cir­ cuit, is selected to have a high reactance at the operating frequency.. .

Neglecting interstage shuhting effects in.the parallel-connected cascode circuit, as they can be if RFC presents a high reactance to the signal 8

FIG. I(O).- SERES D-C CONNECTED CASCODE AMPLIFIER.

I _l_ !

FIG. 1(b).- PARALLEL D-C CONNECTED CASCODE AMPLIFIER. - 9-

V o lta g e 5 the series-connected cascode and the parallel-connected cas­

cade amplifier have the same a-c equivalent circuit 5 t h e r e f o r e 5 the equat­

ions derived in this investigation w ill apply equally well to both circuits.

The grounded grid stage Vg is inherently stable and because of its very low input impedance (approximately equal to the transconductance of

?g)1s it reduces the gain of the first stage by heavy loading. Stabil­

ity in both circuits is thus achieved. Contrary to the claims of many

W r i t e r s 5 who have failed to specify the degree of loading used on

their cascode am plifiers, laboratory tests indicated that the circuit has

some tendency to oscillate unless the second stage is loaded. This w ill be discussed later.

The reasons for the low-noise characteristics of the circuit are quite involved and have been treated thoroughly elsewhere.^

As far as the a—c signal is concerned, the cascode circuit is essentially two tubes connected in series. If the polarizing voltagps on the tubes are adjusted so that they are operating on a linear portion of their characteristic curve, and if the exciting signal is not allowed to drive the tubes out of their linear region, then we may represent the circuit by the equivalent circuit of Fig. 2. Since both tubes have the same operating point, their tube coefficients Jjls gm, an d r , are the '

"V alley, G. E., and Wallman, H., Vacuum Tube Am plifiers, New York; McGraw-Hill, 19^8, pp 6^7. 2 ■ Reintj.es, J. F.; and Coate 3 G. T., Principles of Radar, New Y ork; M cG raw -H ill,. 195>2, 'p p !429. " ” V aliman, H., MacNee5 A. B., and Gadsdens C. P . 5 "'A Low-Noise -A m plifier,M Proc. IRE-., June 5 I 9U8, pp 700-708. • = 10— same,, If a negative-going signal is applied to the input of the amplifier and designated as -Eg 5 then the first tube may be considered as an ar-c generator of volts with an internal resistance rp equal to the h-c plate resistance of the tube. The same a-c plate current I flows through both tubes, and the signal driving the second tube will be minus the drop in the plate resistance of or (jjEg-- ipFp.) ° With th is driving voltage and an amplification factor the second tube Vg may be repre­ sented as a generator of " iprp) volts with an internal impedance equal to r^. Writing Kirchoff1s voltage equation around the circuit in

F ig . 2 .

Xp(2,rp4"20 (I) where represents the combined impedance of the plate tank circuit and any coupled load. Solving Eq. (I) for

I ir - P (2 )

The output voltage Eq w ill be IpZjj and the voltage gain of the stage w ill be s—

A (3 ) where the minus sign indicates that when Z is resistive, there is a. Li 180-degree phase sh ift between Eg and Eq..

To derive the bandwidth equation, we w ill first convert the constant? voltage equivalent Pipcpit-Of-Fig. 2, to the constant-*- current equivalent ’ ll-

WV

J l ^

FIG. 2 - CONSTANT-VOLTAGE EQUIVALENT PLATE CIRCUIT.

FIG. 3 . - CONSTANT-CURRENT EQUIVALENT PLATE CIRCUIT

i -1 2 -

circuit of Fig. 3» From Eq. (2)

T = E g Q - I u) p H l - + fP ( Z p j)

K /ȣs = Ip &L +Iprpft+-^)

I t i s w e ll Icaown t h a t JJssg r and dividing by r we get m p 9 m E -L JL L 2 -b jj *" rP(2>>) + XP (k) Both sides of Eq. (U) are expressions for current. In fact this equat­

ion describes the circuit of Fig. U(a)$ where I is the current flowing

through the load and (2+/^) is ^he current flowing through the

shunting impedance rp(2 4yU). The sum of these two currents as expressed b y Eq0 (U) i s 3 the constant-current source.

The load impedance may be a resonant circuit as shown in Fig. U(a)

Tithere R is the damping resistance due to coil loss and any coupled load.

We may simplify this circuit to that of Fig. U-Cb) by combining the two resistances into a total dampimg resistance R given by

rP(2 tP ) R R t ~ (5 ) *P (E + p ) + R

The quality Q of this parallel tank is given by

R y Q LD L

^Cruft Electronics Staffs Electronic Circuits and Tubess New Yorks M cG raw -H ills 19U75 pp 2 # 3 .

^Martins T. L.s Ultra-high Frequency Engineeringt New Y ork; P r e n t i c e - H a l l s 19lO s pp 13UT -'" -13-

and th e>bandwidth BW is

B W — 3 l oj>L Q RT (6)

where f is the resonant frequency of the tank circuit, r The input impedance of an amplifier is not infinite mainly be-

•caause of signal currents flowing to ground through the inter-electrode

capacitance of the tube. The a~c grid current I consists of two compon?

ents as shown in Fig. £jj the current Igjc flowing through the grid-to-

cathode capacitance Ogjc5 and the current Ig^ flowing through the grid-tov-

plate capacitance Ggp, These currents may be expressed as

1 J P - J tu ^

Now assuming a resistiv e'2- as would occur at the resonant.frequency 5 E L o and Egp are i 80 degrees out of phase and their sum is the a-c plate volt­

age Ep- of therefore, we may write

Assuming voltages polarized as shown in Fig, 2«, Ep^ is

e Pi =

t h e r e f o r e

E9 r — Eg — Ip&fp " h / ^ % - E X p D p tj.

Substituting the expression for I given by Eq. (2) we arrive at the -14-

FIG. 4. - CONSTANT-CURRENT EQUIVALENT PLATE CIRCUIT. -1 5 - following '

Ei9P = Ef (/J+I)

== % p J + [ I 4- I) 2 4~y P • 4* ^L/fp^

Now I gp=- jc*jCgpEjP — jw C^p% ^ 4 i){j +; 2 +-/>+• s y rp] and

Ig - V +■ I9K " J a j S C 9 K ^ C ^ p ^Ai ^ 0 ( I 2 4-yU +■ t h e r e f o r e

:a ■3 Ju j [C 9R + C3P(>+i)(i - 5 1 ^ 2 7 ) ] ( 7 )

If the load impedance Z is a pure resistance, that is if the plate is . L resonant, then the bracketed expression in the denominator of Eq« (7) is a pure capacitance called the input capacitance«

Q n — - C ^ k + Cs 2,-fcJj +* fp

This can be sim plified to

Caw 4“ Ce C in ( 8)

This equation for the casCode am plifier input capacitance can be compare^ with the well-known expression for the input Capacitance of a Conventional triode am plifier, Eq« (9)- The only difference between Eq. (8) and Eq« (9) -16-

- L G,

FIG. 5 - EQUIVALENT INPUT CIRCUIT SHOWING INTERELECTRODE CAPACITANCE.

V is in the expression within the brackets.

C m "■ 9K + C3p [ | + IrP + H l , (9 )

With the circuit parameters given in Fig. I of the Appendix and .

assuming a of 10 K Ohms3 Eq. ( 8) gives, 6.75) U^jf for the. input capa­

citance of the cascode amplifier. Assuming that in Fig. I of the Ap^-._

pendix was operating as a conventional triode amplifier with the operating

conditions as given in the figure, the input capacitance from Eq. (9) would b e 31.8

T h u s3 it appears that the input capacitance of a cascode amplifier em­

ploying a pair of triode tubes is less than the input capacitance of a cqn-

ventional triode amplifier using one of the same triodes. This gives the

cascode amplifier another advantage over the conventional triode amplifier

in the vhf range where capacitance shunting effects must be. held to a mip^.,.

inum .

Tf in Eq. (7) is not a pure resistance, then contains a real

and a reactive component. For any Z^ 3 the reactive component w ill be capa­

citive but the input resistance may"be either positive or negative. A pos­

itive input resistance results when the load impedance in the plate cir­

cuit is capacitive, while a negative resistance is obtained with an induct­

ive load. A negative input resistance indicates that energy is being fee}

from the plate circuit back to the grid circuit; moreover, for a certain

range of.inductive plate circuit loads, the magnitude and phase of this

feed-back voltage w ill be such -that the amplifier w ill oscillate. The -1 8 - magnitude of this feed-back voltage may be reduced below that required fqr oscillation by loading the amplifier heavily 0 - 19- '

METHOD OF INVESTIGATION

During gain measurements3 a ll quiescent voltages and the input volt-?-

age Eg were held constant; The plate circuit was kept tuned to 30 mcps at

a ll times. The General Radio model 1001-A signal generator was tuned

above and below this frequency (E^ being kept constant) to qbtain the re­

sponse curves in Fig, 3 in the Appendix, To study the behavior of the

amplifier under various Ioads 3 the tank circuit was shunted with several

different external resistors R^. This R^ is included in the R of Fig. It3

page ill. Input and output voltages were- measured with Hewlett-Packard

model,LlO-B vacuum-tube voltm eters.

Calculation of the bandwidth of the am plifier from Eq» (6 ) r e q u ir e d

a value of L and R1^, The inductance L was removed from the amplifier

output tank circuit and measured on a General Radio model 916-A r-f

bridge. An average of several measurements was taken as the final value

(0.96 micro-henries).

Considerable difficulty was experienced in measuring the effective

tank resistance R . This resistance was too.high to measure accurately

at 30 mbps on the r-f bridge used to measure L. "A General Radio model

82I-A Twin-T impedance bridge designed to measure conductance was found

to give much more consistent results. After much experimentation, it was found that R depended upon the placement of the inductance in relation ^o

near-by metal objects such as the Chassis 3 and th e e x a c t p o s i t i o n i n .whig}}

the external load resistors R^ were fastened. Whether the tube filamentg

were hot or not also made considerable difference. For this reason, R T. was measured with L and R in the exact positions that they were in during L '—2 O.. the corresponding gain measurement and the filament power was supplied.

Only in this way could serious discrepancies between experimental data and theoretical calculations be resolved.

Since the input impedance of the am plifier given by Eq. (7) was also very high,, the twin-T r-f bridge was found to be more satisfactory than the conventional r-f bridge for input impedance measurements. The tank was kept resonant during these measurements so given by Eq. (?) was purely capacitive. This capacitance was so small that it was necessary to take into account the capacity of the leads connecting the r-f bridge to the amplifier input term inals. The capacitance of these leads alone was measur­ ed and subtracted from the input capacitance measurement. -21-

DISCUSSIOM OF RESULTS

The values of components used in the experimental circuit, operating

voltages, and 'tube coefficients are given in Fig..I of the appendix. Thg

calculated and measured frequency response, gain, and bandwidth for var­

ious plate loads are graphed in Figs. 2, 3, and h» These curves can hes used to design series- or parallel-connected caseode amplifiers of given bandwidth and gain, providing the same tube and polarizing voltages are used. The data used to plot the graphs is tabulated in Table I of the

Appendix. The left column in this table gives the d-c or color-code resistance of the external plate-circuit load. The next column gives the measured value of the to tal equivalent plate load resistance Rir,. The graphs and tabulated results substantiate the theoretical equations.

In all cases the deviation between predicted and measured values is with­ in experimental error. All the calculated values depended upon at least one impedance measurement at 30 mcps, and it was found that the balance qf the r-f bridges could be changed markedly by a slight vibration of the instruments or by a small movement of connecting leads. Averages of several measurements had to be taken in all cases.

Nowhere in this work are the d-c resistance values of the external tank-circuit loads mentioned. The reason for this is that the a-c re­ sistance Values at 30 mcps Could not be'predicted from the measured d-c value. For instance, a resistor with a measured d-c resistance and color- code marking of 68 K ohms was found to load the tank circuit much more ttym. a resistor of the same type with a 33 K ohm d-c resistance. Also a 1^0 K ohm load resistor yielded a gain much lower than a 100 K ohm resistor. The -2 2 -

results tabulated on page v of the Appendix indicate that the loading

effect of the resistors was not a predictable function of the d-c resist­

ance. ,According to theory, for any particular type of resistance of a.

given size and geometrical configuration, the ratio of the a-c resistance

to d-c resistance w ill depend only upon the product of frequency and d-c resistance and w ill be independent of the particular value of resistance.

The opinion of the author is that the apparent discrepancies Tpetween a-c and d-c resistance in this investigation were results of non-uniform resistance manufacture.

The most important practical application of the cascode circuit is ap a very-high frequency am plifier. Used this way, the circuit always has a tuned tank in the grid circuit. The circuit was connected this way at the beginning of this investigation and was found to oscillate unless either loaded or neutralized. Many writers describe the circuit as being very- stable, and claim that neutralization is used only to improve the poise figure. Although two different mechanical layouts were tried, and all well-known precautions were observed, the circuit was very unstable unless loaded. With the tuned-plate, tuned-grid arrangement, the circuit was stable for less than about 8 K ohms. For R^ between 8 K ohms and 9 K ohms the gain measurements were erratic and for R1^1 above 9 K ohms, the cir­ cuit broke into oscillation. Tb eliminate this difficulty, the grid-tank circuit was replaced by a 300?% ohm resistor. Connected this way, there was no sign of instability.

Of course the cascode circuit is normally used well above 30 mcps and at the higher■frequencies the maximum attainable tank-circuit Q1s . decrease. Hence, it is reasonable- to suppose that the circuit would be more stable at frequencies above those used in this investigation. CONCLUSIONS

This investigation indicates that with moderate loads, the cascode

amplifier has the high-gain and stability characteristic of pentode cir­

cuits; moreover, it is well-known that the cascode circuit has a much low­

er noise figure than amplifiers employing pentodes. At one time the cas­

code . am plifier, because it employed two tubes, was not as economical to

build as the one-tube pentode am plifier. This is no longer true, now that

duo-diodes have been developed especially for use in the cascode circuit.

In fact, the 'cascode am plifier is now beginning to replace both une high-

gain pentode and the low-noise triode in high-fidelity audio-frequency amp­

lifiers. In this application no tank circuits are involved, so instability

is no problem.

It is doubtful if the cascode circuit w ill ever replace the conVeht-

ional pentode amplifier in r-f applications below 30 mcps where very good selectivity is important and can be obtained only by using high-Q timed circuits and hence high impedance plate-circuit loads.

In its present stage of development, it appears that the cascode amplifier is lim ited to use in the vhf range where high-Q tuned circuits can not be constructed practically, and to use at audio frequencies -yrhere tuned circuits are not used at all. - 2 5 -

■ APPEiroix '

Page

Circuit Diagram,, Experimental Circuit (Fig. I) i

■Response Curves (Fig. 2) ii

G raph5 ' G ain v s . R1^ ( F ig . 3 ) i i i

G raph5 Bandwidth vs. R^ (Fig. Ii) iv

Tabulated Results (Table I) • v

Sample Calculations • vi

Literature Cited and Consulted - vii i

CIRCUIT PARAMETERS

R,- 300 K ohms Cb 1 0 0 0 M i f Rk- 220 ohms C - 5 0 M Rfc4- 5 0 K ohms L - 0.96^ 1 RhR2" 100 K ohms Vh Vfe- 6B07A Plate voltage on each section ISO volts Grid bios voltage on each section -2 volts Filament voltage 6.3 volts a-c

j j - 39, gm = 6400 ^m hos1 rp = 6100 ohms

FIG. I - CASCODE AMPLIFIER EXPERIMENTAL CIRCUIT. if

O l ______29.0 30.0 30.5 Frequency in Megacycles

FIG. 2 - FREQUENCY RESPONSE CURVES. Voltoge Gain I. OTG GI v. OD RESISTANCE. LOAD vs. GAIN VOLTAGE - . 3 FIG. K O I K IO K 3 od ssac R - esistance R Load hoeia Curve v r u C Theoretical xeietl Curve Experimental

------Bandwidth in Kilocycles I. . BNWDH s LA RESISTANCE. LOAD vs. BANDWIDTH - 4. FIG. od ssac R - esistance R Load Theoretical Experimental K O K IO K 6 iv

—V—

D-C V alue of El M easured C a lc u la te d rt ' Gain J a in '10 K ohms „ 5>.06 K' ohms 32 31 l £ IC ohms 5>i,3 K ohms 3k 32 30 K ohms Sok K ohms hi 39 5>0 K ohms 7 .1 5 K ohms HS Lt3 . 33 K ohms 8.68 IC ohms 55 52 XSO K ohms 9.74 K ohms 63 ■ 59 • 100 K ohms 11.3 K ohms Tl ,68 No Load lit.75 K ohms 92 87

D-C V alue M easured C a lc u la te d o f Rjj r T B andw idth B andw idth

1 0 .K ohms 5.06 K ohms 1020 Kc. 1070 Kc. 15 IC ohms 5. 3 K ohms ■980 Kc. 1020 Kc. 30 K ohms 6 .It K ohms 800 Kc. ' 850 Kc. 50' IC ohms 7.15 K ohms 760 Kc. 750 Kc. 33 K ohms 8.68 K ohms 680 Kc. 620 Kc. 150 K ohms 9.7lt K ohms 600 Kc, 550 Kc. 100 IC ohms ll.lt IK ohms 530 Kc. It 80 ICc. No Load lit.75 K ohms It50 Kb . 370 Kc.

D-C VciluG M easured C a lc u la te d Rt O f E i Cln Gin

10 K ohms 5.06 K ohms 6 50 K ohms 7.l5 K ohms 8 jsjrt 6 150 K ohms 1 1 .3 K "ohms 9 ' y w f 7 No Load lit.75 K ohms 11 jijfi 8

TABLE I - TABULATED RESULTS v i

SAMPLE CALCULATIONS

G ain

Rrp = Zjj — 5.06 K ohms

rp ~ 6„1 K ohms

/ » = 3 9 A — pCp-hl) _ 3 9 0 + 3 ^ I f ^ ( a + ^ ) ' + jfegfc+39)

B andw idth

Rrp =• 5).06 K ohms

L = 0.96 y^h f r — 30 mops

r - f3TT>f30x|06)fo.96x|0'‘6) BW fjoxio6;= /070 KtOa R - r T - ■ 5 0 6 0 ' -

Input Capacitance Rt = Zpj — 5>.06 K ohms c,„= CaK + Cg, ^ 0( l - Manufacturers data givess s ja ,Af + 1.1^39+1^1------Cgk = 2. BSyupf 2 + 3 9 + S |5 2

cgp = lll5ZTjf = 6 J^UcF JU = 39

r _ = 6100 P

V v i i

LITERATURE CITED AND CONSULTED

Sruft Electronics Staff, Electronic Circuits and Tubes, New York: McGraw- H ill Book epos, IShl* »

Martin, T. L., Ultra-high Frequency Engineering, New York; Prentice-Hall, i?5o„

Reintjes, J„ F.-, and Coate, G. T., Principles of Radar, New York: McGraw- Hill Book Co., 1#2.

Terman, F. E., and P ettit, J. M., Electronic Measurements, New York^ McGraw-Hill Book Co., 19#.

Valley, Ge E ., and Wallman, H., Vacuum Tube Am plifiers, New York: McGraw- Hill Book Co., 19#. ~

Wallman, H., MacNee, A. B., and Gadsden, Ce p ., t»A Low-Noise Am plifier," Proc. of IRE., June, 19^8.

'■-Llrki

119224 MONTANA STATE UNIVERSITY LIBRARIES

762 100 3392 3

W57G :826c 119224 cop.2

poughlan, G. B. The cascode amp-i-x^ier

R , oTTi V iCaa^ fyo^ :s

!A,- OCT 2 9 ^ 1 , ,. / r% V • '

j i1—£ J j - — ® r ■ S 'J tlr & A .

H s n a M (u C o p . 2

W 0IM *;