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UNCLASSIFIED
A 43482 0
DEFENSE DOCUMENTATION CENTERFOR
SCIENTIFIC AND TECHNICAL INFORMATION
CAMERON STATION. ALEXANDRIA. VIRGINIA
UNCLASSIFIED
DOTICI: When govezmmnt or other dzavingu, specd-fications or other data ane used for any purposeother than in connection with a definitely relatedgovertmment procurement operation, the U. S.Govermenit thereb~y incurs no responsility, nor anyobiaption vbatsoever; and the fact that the Govern-ment my have formulated, furinished, or in any vaysuppled the oadd drawings, specifioations, or otherdata Is not to be regarded by imPlication or other-wise "a in any imnnr li1cenaing the holder or anyother person or corporation, or conveying mny rightsor peznission to msnutacture, use or sell anypatented invention that my In any way be relatedthereto.
SEL-63121
C* The Design of WidebandW" Transistor Amplifiers by an Extension,-., of the Sampled-Parameter Technique
T by
G. Danon and K. Sorenson
November 1963
Technical Report No. 4815-1Prepared underOffice of Naval Research ContractNonr-225(24), NR 373 360Jointly supported by the U.S. Army Signal Corps, theU.S. Air Force, and the U.S. Navy DDC(Office of Naval Research) r- 7 7 p !
TISIA E
SOUB-STITE ELECTROnICS LMUNITORY
STIIFORB ELECTRONICS LIBORITORIESSTIEFIII EIUI ITY • UTlUEUU KELIFUNII
NO OTS
DDC AVAILABILITY NOTICE
Qualified requestrs may obtain copies of thisreport from DDC. Foreign announcement anddiusemination of this report by DDC is limited.
SEL-63.121
THE DESIGN OF WIDEBAND TRANSISTOR AMPLIFIERS
BY AN EXTENSION OF THE SAMPLED-PARAMETER TECHNIQUE
by
G. Danon and K. Sorenson
November 1963
Reproduction in whole or in partis permitted for any purpose ofthe United States Government.
Technical Report No. 4815-1
Prepared under
Office of Naval Research Contract
Nonr-225(24), NR 373 360Jointly supported by the U.S. Army Signal Corps, the
U.S. Air Force, and the U.S. Navy(Office of Naval Research)
Solid-State Electronics LaboratoryStanford Electronics Laboratories
Stanford University Stanford, California
ABSTRACT
The experiments conducted in nuclear physics laboratories often
require the design of fast-pulse amplifiers. Recent transistors offer
new capabilities in this field. The work presented here centers on the
design of such amplifiers by the sampled-parameter technique, in which
the transistor is characterized by two-port parameters measured at a set
of frequencies through the frequency band of interest. The feedback and
coupling networks are selected by computations based on these sampled
parameters. An application of this technique has led to an iterative
stage using a 2N918 transistor and having the following characteristics:
1. Iterative impedance ................................ 50 ohms
2. Insertion power gain ............................... 10 db
3. Bandwidth ......................................... 400 Mc
4. Rise time .......................................... 1 nsec
5. Overshoot ........................................ < 10 percent
6. Noise factor (throughout the band) ............... 8-10 db
7. Output level, negative pulse ..................... -500 mv
8. Output level, positive pulse ..................... 200 mv
An amplifier of three such stages, cascaded, provided a gain of 30 db,
a rise time of 1 nsec, and a bandwidth of 400 Mc.
SEL-63-121 - ii -
CONTENTS Page
I. INTRODUCTION ........ ...................... . 1
A. Pulse Amplifiers in Nuclear Physics . ........ . 1
B. Recent Advances in Transistor Technology ... ...... 1
C. Continuous-Wave Response and Pulse Response . . . 1
D. Some Recent Achievements ...... .............. 3
E. Two Different Possible Approaches to the Problem . 3
II. LINVILLIS IM CHART ......... ................... 5
A. The LM Plane .......... .................... 5
B. The Po(L,M) Paraboloid and the Pi(L,M) Plane .... 5
C. The Load Admittance (YL) in the LM Plane .... 6
D. The Constant-g Circles ...................... 7
III. THE R-L COLLECTOR-TO-BASE FEEDBACK ..... ........... 9
A. An Equivalent Circuit for the 2N918 Transistor . . 9
B. The Influence of Collector-to-Base Feedback . . .. 13
C. The Constant-(PoO/Pio) Circles ... ........... .. 15
IV. DETERMINATION OF YL(f) AND THE INTERSTAGE NETWORK 19
A. The Mapping of YL: Constant-p Circles and
Constant-p Circles ..... ................. . 19
1. The Input-Admittance Requirement ......... . 19
2. The Power-Gain Requirement ... ........... .. 21
B. The Interstage Network ..... ............... . 21
V. A 400-Mc, 30-db TRANSISTOR AMPLIFIER .......... ... 25
A. The Step-by-step Procedure .... ............. .. 25
1. The 2N918 y Parameters .... ............ .. 25
2. Determining the Feedback Circuit ......... . 25
3. The Constant-g Circles .... ............. . 27
4. The Constant-p Circles .... ............. . 28
5. The Interstage Network .... ............. . 30
B. Bridge Measurements ..... ................ . 30
C. Practical Data ....... ................... . 31
D. Final Summary of Amplifier Performance ........ . 31
REFERENCES AND BIBLIOGRAPHY ...... ................. . 42
- iii - SEL-63-121
TABLES
1. Sampled y Parameters of the Fairchild 2N918 Transistor 9
2. Values of y1 r and y2r for the 2N918 Transistor ..... . 13
3. Computed Values of y{r' YIr' Oand P 'o/PiO.......... 14
4. Restatement of the Sampled y Parameters of the 2N918Transistor .......... ......................... . 25
5. Variation of YF with Frequency ..... .............. . 27
6. The y Parameters of the Transistor with Feedback Circuit
Connected ......... ......................... . 27
ILLUSTRATIONS
1. Electronic apparatus for a nuclear-physics experiment . . 2
2. Two different approaches to the design of wideband amplifiers 4
3. Load admittance in the LM plane ....... .............. 7
4. Locus of constant power gain, g = (Po/Po.)/(Pi/P,0) . . 8
5. A A equivalent circuit for the 2N918 transistor ... ...... 10
6. Transistor model for a frequency of 10 Mc .. ......... . 11
7. Transistor model for high frequencies ... ........... . 12
8. Frequency response considering collector-to-base feedback
only ........... ............................ . 16
9. Matrix of a transistor shunted by an RF-LF circuit . ... 17
10. Superposition of the constant low-frequency and high-frequency
power-gain circles ............ .................. 18
11. Block diagram of the complete amplifier stage . ....... . 19
12. The input and load admittance requirements .. ......... .. 20
13. The power-gain requirements ..... ................ . 22
14. The permissible region for YL at a given frequency ..... ... 23
15. The permissible regions for YL for several frequencies . 23
16. The interstage network ....... ................... .. 24
17. An iterative single-stage amplifier .... ............ 24
18. The YF plane (normalized to 5 mmho) ... ........... . 26
19. The constant-g circles ....... ................... .28
20. Finding the YL location ...... ................. . 29
SEL-63-121 - iv -
Page
21. The interstage network for the 400-Mc amplifier .. ..... 30
22. Schematic circuit of the 400-Mc amplifier .......... ... 32
23. Photograph of the 400-Mc amplifier ... ........... ... 33
24. Insertion power gain vs frequency for the single-stage,two-stage, and three-stage amplifiers ... .......... ... 34
25. Step response of the single-stage amplifier ......... ... 35
26. Pulse response of the single-stage amplifier ...... . 36
27. Dynamic range of the single-stage amplifier ......... ... 37
28. Insertion power gain and noise figure vs frequency forthe three-stage amplifier ..... ................ ... 38
29. Step response of the three-stage amplifier ....... ... 39
30. Pulse response of the three-stage amplifier ......... ... 40
31. Dynamic range of the three-stage amplifier ....... ... 41
- v - SEL-63-121
I. INTAODUCTION
A. PULSE AMPLIFIERS IN NUCLEAR PHYSICS
Experiments in high-energy physics have made necessary, in recent
years, the design of amplifiers for faster and faster pulses. Such
amplifiers are placed at the output of photomultipliers (Fig. 1) in
order to drive a coincidence circuit, or, in some other experiments,
the coincidence circuit is placed at the output of the photomultiplier
while the pulse amplifier is supposed to realize the pulse shaping and
the pulse amplifying before the signal goes to the scaler.
B. RECENT ADVANCES IN TRANSISTOR TECHNOLOGY
Until recently, only the vacuum tube could give a rise time of ap-
proximately 1 nsec. Recent advances in the transistor field make it
possible for transistors to replace tubes advantageously. Some transis-
tors with a maximum oscillation frequency greater than 2 Gc are now com-
mercially available. Because of their small size, one can place, for
some experiments, up to 10 or 12 transistor amplifiers very close to
the scintillators, thus avoiding carrying a low-level signal along a
100-yard cable from the target area tothe measurements area. Moreover,
some recent work seems to indicate that the transistor behavior remains
satisfactory even if it has been submitted to nuclear radiations for a
"reasonable" length of time.
The above remarks explain why the electronics engineers in nuclear
physics laboratories have been so deeply interested, among other things,
in the design of wideband transistor amplifiers.
C. CONTINUOUS-WAVE RESPONSE AND PULSE RESPONSE
As is generally the case, this study was more concerned with band-
width than pulse response. The reason for this is that it is very dif-
ficult to establish a link between desired output pulse characteristics
and the location of transfer-function poles and zeros. Once the band-
width is attained, the phase response can be modified by using an all-
pass phase equalizer, as discussed by Fogarty [Ref. 1], or by modifying
- 1 - SEL-63-121
* SOURCE
SCINTILLATORS
PNOTOMULTI PLIERS TA GETAREA
PULSE AMPLIFIERS
COINCIDENCE CIRCUIT
MEASUREMENTS
REGISTER
FIG. 1. ELECTRONIC APPARATUS FOR A NUCLEAR-PHYSICS EXPERIMENT.
SEL-63-121 - 2-
the bandwidth experimentally. In the case of the 400-Mc, 1-nsec ampli-
fier, it was not necessary to rely on these techniques, since the pulse
overshoot (< 10 percent) was small enough for the intended application.
D. SOME RECENT ACHIEVEMENTS
Many pulse-amplifier designs are to be found in the literature.
Some of the most notable results and the references reporting them are
indicated below:
Reference Transistor Power Gain BandwidthNumber (db/stage) (Mc)
2 M 2039 10 130Western
Electric
fT = 400 Mc
3 2N917 6 2 nsecFairchild rise time
fT = 800 Mc
4M 2107 6 750Western
ElectricfT = 2 Gc
5M 2058 7 200Western
ElectricfT = 550 Mc
E. TWO DIFFERENT POSSIBLE APPROACHES TO THE PROBLEM
Two main ways of approaching the problem are considered:
1. The transistor is represented by a model including R's, C's, andcontrolled sources. An attempt is made to determine the emittercurrent, the load and source impedances which give the maximumgain-bandwidth product, and the values of the associated circuitelements which correspond to a prescribed location for the polesof the transfer function (generally the "maximally flat" location).
2. The transistor is represented by a set of sampled matrix parameters,actually measured at a given value of emitter current. This pro-cedure is J. G. Linvill's sampled-parameter method, the basic ideasof which are developed in Transistors and Active Circuits, by Lin-vill and Gibbons [Ref. 6].
- 3 - SEL-63-121
The first method has the advantage of representing a physical system
with a model: it allows a mathematical analysis and the associated cir-
cuit synthesis through the conventional techniques of network synthesis.
It is also true, however, that this approach is only as good as the model,
and generally raises the question of whether to use a simple model of
limited validity or a more complex model requiring more complicated com-
putations.
In the second approach the limitations on the validity of the tran-
sistor model pose no problem because one is operating directly on the
measured transistor parameters. (See Fig. 2.) On the other hand, a
set of matrix parameters can hardly be used as a guide in the choice of
the type of associated circuits. It thus appears that good results may
be achieved by combining the two approaches.
Linvill's method consists in "roughing out" the problem with a very
simple equivalent circuit. This first step leads to an appropriate cir-
cuit configuration and gives orders of magnitude for the gain and the
bandwidth. A further step, using the sampled parameters, leads to more
precise values.
APPROXIMATION
TRNITRTRANSISTOX PARAMETERS ASSOCIATED CIRCUITS
MEASUREMENTS CALCULATIONS
FIG. 2. TWO DIFFERENT APPROACHES TO THE DESIGN OF WIDEBAND AMPLIFIERS.
SEL-63-121 - 4 -
II. LINVILL'S IM CHART
A. THE LM PLANE
The two-port parameters and terminal variables are related as follows:
I, = yljEj + Y12E2 ()
12 = Y21 E1 + y22E2 (2)
It is convenient to consider a unit driving voltage:
El = 1 + jO (3a)
The output voltage E2 can be conveniently defined in terms of
variables L and M in the following way. Moreover, the load admit-
tance is found to be related to L and M.
E2 = (L+ jM)- -= -I (3b)
2y22r YL
B. THE Po(L,M) PARABOLOID AND THE Pi(L,M) PLANE
The output power
PO = Re (-E*2I 2 ) = L - (L2 + M2)Iy, 1 2 (4)2y22r 4Y22r
PO(L,M) is a paraboloid, and the coordinates of its summit are (1,0)
where Po is designated as Po0o.
Poo = jy12(5)4y22r
* The problem of selecting (by the sampled-parameter technique) sourceand load terminations of amplifiers to provide a realizable prescribed gain
is discussed in Chapters 11, 18, and 19 of Transistors and Active Circuits
[Ref. 6]. The reader is referred to that reference for background and de-tails. The framework and notation of the reference is outlined in this
section because subsequent development in this report extends the method.
- 5 - SEL-63-121
The input power
Pi = Re E1*I = Y11r + L Re Y + M Im Y- 1 (6)2Y22r 2y22r
Pi (L,M) is an inclined plane. Its gradient line makes an angle 8
with the L axis such that
e = - arg (-Y12Y21) (7)
When L = 1 and M = 0, Pi = Pio = 2 yjjr Y2vr- Re (Y12Y21) (8)2 Y22r
The coordinates L = 1, M = 0 correspond to
YL = Y 2 Pi = Pi0 PO = Poo (9)
The two-port is potentially unstable when (Poo/Pio) < 0, or when the
critical factor
C = 2Po > (10)Pio I~
Moreover, when C < 1, the maximum available gain (Y. = in and YL =Y )
is never larger than 2(Poo/Pio).
C. THE LOAD ADMITTANCE (YL) IN THE LM PLANE
The load admittance is found to be
Y = Y22 + 2r 2yl)
L = L + jM
and G + jB is defined in the following way:
+ Y22 = 2y22r = G + jB (12)YL + Y22 =
Thus a load admittance YL is determined by any one of three sets of co-
ordinates-- (YLr'yLi), (L,M), or (G,B), and we can draw in the IM
plane the constant G and the constant B circles. The chart thus ob-
tained (Fig. 3) is a very simplified version of Linvill's chart but it
contains all the elements which will be needed for the particular pur-
pose of this discussion.
SEL-63-121 - 6 -
IN
B -. Y22,,_ L
G 2Y22 r G =
1.0Y22 r
S +l,0Y22r + =
0. y2
2Y22r
YL * Y22 -17,- G * jB
FIG. 3. LOAD ADMITTANCE IN THE IM PLANE.
D. THE CONSTANT-g CIRCLES
From the charts shown in Fig. 4 two new axes, x and y, are chosen
such that their origin lies at L = 1, M = 0, and such that their angles
with the L axis are e and e + (n/2).
The locus of points for which g = (Po/PoO)/(Pi/PiO) is constant is
a circle:
1 - g(1 + CX) =x2 + y2 (13)
The circles which correspond to different values of g have two
points in common if C > 1 (Fig. 4a), and no point in common if C < 1
(Fig. 4b).
- 7 - SEL-63-121
0 6 43-4~
II
600
SEL-63-121
III. THE R-L COLLECTOR-TO-BASE FEEDBACK
The first step in the design of a broadband amplifier can now be
undertaken. With a given transistora simple equivalent circuit will be
used in order to determine approximately the power gain per stage, the
bandwidth, and the elements of the electrical circuits.
A. AN EQUIVALENT CIRCUIT FOR THE 2N918 TRANSISTOR
The 2N918, which is used in the broadband amplifier, is a Fairchild
NPN silicon, planar epitaxial, double-diffused transistor. (Total max-
imum power dissipation = 200 mw at 25 °C ambient, VCBO = 30 v, and
IC = 50 ma.) Table 1 lists the sampled y parameters of thisCmax
transistor as they can be inferred from the Fairchild data sheet of
May, 1962. (The lO-Mc parameters have been added.)
TABLE 1. SAMPLED y PARAMETERS OF THE FAIRCHILD 2N918 TRANSISTOR
(IE = 5 ma, VCE = 10.0 v)
f Parameter (mmho)
(Mc) Y Y31 y 21 y 22
10 1.7 + j0.65 -0.01 - jO.07 See Footnote 0.08 + jO.13
50 2.5 + j2.5 0.00 - jO.3 80.0 - j60.O 0.1 + jl.O
100 5.0 + j5.0 0.00 - jO.7 40.0 - j60.O 0.2 + jl.3
200 8.0 + j8.0 0.00 - jl.3 25.0 - j55.0 0.5 + j2.5
300 10.0 + jlO.O -0.1 - j2.0 15.0 - j47.0 0.6 + j3.5
400 12.0 + j12.0 -0.2 - j2.7 7.0 - j43.0 0.8 + j4.5
500 17.0 + j14.0 -0.4 - j3.4 0.0 - j40.O 1.0 + J6.0
gm = 100.0 + j40.0 at 10 Mc.
Reading this table makes an important fact apparent: While
y (f) is approximately a linear function of frequency, y (f) isi2i 12r
approximately a parabolic function. This fact suggests that a a equiv-
alent circuit (Fig. 5) can be used, the feedback admittance being an
rc-Cc series circuit with rcCcW < 1.
- 9 - SEL-63-121
jCe,
g rc Cc C Y12 1 + Jrcc,
Y2 Y22 + Y12
0 VBE 21
FIG. 5. A w EQUIVALENT CIRCUIT FOR ThE 2N918 TRANSISTOR.
For such a circuit the following expression can be written:
jCcW
-12 -+ jrc~w ' rcC c 2 + jCcw (14)
By comparison of the above expression with the parameters in Table 1,
one can calculate that:
cc = 1 pf rc = 30 ohms (15)
At a very low frequency (f = 10 Mc), the transistor can be represented
by the circuit shown in Fig. 6.
At high frequencies, the transistor can be represented by the circuit
in Fig. 7, in which
y= Y + jyli = y + y (16)Yi ir ii 11 1
y = y + jy = y + y (17)2 2r 21 22 12
and gm is complex. The parameters y r and y2r can be computed from
Table 1 in Sec. IIIA. The parameters yli and y21 need not be calcu-
lated since they do not influence the value of (Po0/Pi0).
SEL-63-121 - 10 -
Y* y IC
E
yIr 1. 7 ewho
go100 + A0~ waho
a. The equivalent circuit at 10 Mc
J 1. 7 who YK
b. The equivalent circuit with feedbackat 10 M4C
25 dt
P
YF ("uho)
c. Power gain p vs Y at 10 Mc
FIG. 6. TRANSISTOR MODEL FOR A FREQUENCY OF 10 Mc.
- 11 -SEL-63-121
cc .0 pf
B C
Ylr j yY2r y2i
g,¥
a. An equivalent circuit for the 2N918 transistor withoutexternal feedback
RF LF
CB
Cc
lr Y2r YL Y22
b. Tuning Cc by means of external feedback
B V8 C
~F R F2 CYlr YF Y2rYL Y2r + YF
E
c. Resultant equivalent circuit at amplifier cutofffrequency ,c
FIG. 7. TRANSISTOR MODEL FOR HIGH FREQUENCIES.
SEL-63-121 - 12 -
B. THE INFLUENCE OF COLLECTOR-TO-BASE FEEDBACK
The influence of feedback at a low frequency (lOMc) is considered
first. In the circuit of Fig. 6b, YK is the load conductance. (At low
frequencies the characteristic admittance YK = the load admittance YL-)
YF is the feedback conductance (1 < YF < 10 mmho), and P(YK, YF) is the
power gain of the stage (Fig. 6b). Choosing, for example, YK = 20 mmho,
we can plot P(YF) as shown in Fig. 6c.
It can be seen that when the stage is loaded with 50 ohms, a 200-ohm
feedback resistor from collector to base will reduce the gain to 10 db,
while the input impedance will come close to 50 ohms. Thus it seems
feasible (at least at low frequencies) to design a 50-ohm iterative stage.
The maximum bandwidth which can be expected is determined next. From
the equivalent circuit shown in Fig. 7, the values of y1r and y2r for
frequencies between 200 and 500 Mc are obtained (see Table 2).
TABLE 2. VALUES OF y r AND y2r FOR THE 2N918 TRANSISTOR
Parameter Frequency (Mc)
(mmho) 200 300 400 500
Yr 8 10 12 17
Y2r 0.5 0.5 0.6 0.6
Now Cc =1 pf is tuned with an RF- LF series circuit (RF = 200 ohms),
and YL is chosen such that YL = Y 2 (Fig. 7b). The stage power gain now
nears the maximum value that can be expected with a given RF (determined
by the low-frequency requirements). To calculate this maximum value,
note that Cc, RF, and LF make a resonant circuit which can be replacedby a conductance RFCc2, wc being the cutoff frequency of the amplifier
to be determined. This conductance does not modify y21 appreciably, but
it does modify y22 and y 11 Moreover, within the frequency range of 200
to 500 Mc, y 2 -j40, the "Miller effect" does not modify Yin r' and21
thus the conductance RFCc 2 can be removed and merely placed in parallel
with y2r and with y1r (Fig. 7c).
- 13 - SEL-63-121
Table 3 contains the results of calculating
Y'I = Y + YF (18)ir ir
Y'I = Y + YF (19)2r 2r
and the corresponding value of (Poo/Pio), YL having been chosen such
that YL = 2r
P00 = Y21 12 400
PF 4y y -2Re(y y ) y ,(0jo ilr 22r 12 21 ) r 2r
TABLE 3. COMPUTED VALUES OF Ylr ' Yr AND Po /P
Parameter Frequecy (Mc)
200 300 400 500
y (mmho) 8.3 10.8 13.2 19lr
y' (mmho) 0.8 1.3 1.8 2.62r
Poo (db) 18 14.5 12 9P ioI I
From the above table it is seen that a l0-db power gain up to about
400 Mc can be expected. For this cutoff frequency, the tuning induct-
ance LF = 160 nh and the input impedance is approximately 76 ohms.
(y' = 13.2 mmho). When used in a 50-ohm system the power loss resultingir
from mismatch at the input would be less than 0.2 db, provided that an
appropriate output coupling is designed.
Thus, a very simple equivalent circuit has provided orders of mag-
nitude for RF (200 ohms), LF (160 nh), for the gain-bandwidth product
(1200 Mc), and for the characteristic impedance (50 ohms). But it is
still not known what the frequency response will be between f = 0 and
f = 400 Mc. For a given transistor and feedback network, the response
will depend mainly on the interstage filter. However, for a given inter-
stage filter, it is possible to vary the frequency response by modifying
the feedback circuit.
SEL-63-121 - 14 -
The following observations can be made on the basis of what has al-
ready been learned from the equivalent circuit.
1. A frequency-response curve similar to that represented in Fig. 8acan be smoothed with two inductors in the feedback circuit, onebeing a ferrite coil and the other an air coil (Fig. 8b). Whilethe air coil tunes Cc at 400 Mc, the ferrite coil tunes Cc ata lower frequency f1 , the material being chosen such that thecorresponding inductance is negligible at 400 Mc.
2. A frequency-response curve similar to that represented in Fig. 8ccan be smoothed with a parallel damping resistor RD.
The foregoing ideas based on the transistor equivalent circuit were
not developed mathematically. Qualitative considerations of those ideas,
however, were very helpful during the experimental step of our procedure.
C. THE CONSTANT-(PoO/Pio) CIRCLES
The second step in the computations will lead to more precise values
for LF, RF, the maximum gain-bandwidth product, and to the design of
the interstage two-port.
Consider again the expression for (PoO/Pio) [Ref. 6, p. 248]:
-00 Y j 1 (21)Po 0 j j
P 4y y - 2 Re(y yllr 22r 12 21
In this relation, [y] is the matrix of a two-port which is shunted by
an RF-LF circuit (Fig. 9). That is,
[y] = [YTl + [YF ] (22)
1 F (231where Y = YF YF23)
1
and YF - jL F = F + OF (24)
- 15 - SEL-63-121
POWER GAIN
itRF LFIfI
cc(a) '400 Mc f
RF 1F 1F2then can give
cc (b) fb
F LFI LF 2
If givyes
I1 f
cc (c) f
then IIFFLFLF can give
RD(d) 400 Mc
cc
FIG. 8. FREQUENCY RESPONSE CONSIDERING COLLECTOR-TO-BASE FEEDBACK ONLY.
SEL-63-121 - 16-
Thus,
P00 _ 21T - gF - JbF 1 2
'io 4 ( y rT+gF) (y 2 2 rT+gF) - 2 Re (y12T -yF) (y 21T-yF
(y2 1rTgF)2 + (y2liTbF)
2
4(y llT+g F)(y22r'rF) - 2 ((Y12rTgF)(YrT-gF) - (Y21T-bF )(y21iT-bF))
(25)
R F LF
- I RANSIS3TOR- :I -
[yl = [yT'J + [YF]
FIG. 9. MATRIX OF A TRANSISTOR SHUNTED BY AN RFL F CIRCUIT.
For a given value of (Poo/Pio) = p, the above relation is the equation
of a circle. This fact suggests a simple method of determining RF,
LF, and p. Consider, on a Smith chart (Fig. 10), the constant RF
circles. For each of these values of RF (Fig. 6c), there is one value
for p (low-frequency power gain with a given value of Y K)" The con-
stant (Po/Pio) circles can be drawn on the same chart. For a given
desired power gain p, RF must be simultaneously on the two corres-
ponding circles. Figure 10 clearly shows that the highest value for p
corresponds to two tangent circles and that any lower value will lead to
two values for RF (and LT).
Thus, for a given value of YK, knowledge of the y parameters at a
very low frequency f0 and the y parameters at any other frequency
f leads, in a straightforward way, to an estimation of the maximum
power gain (within 3 db) which can be expected from a video amplifier
having a bandwidth B = f - fo, and to knowledge of the RF- L feedback
circuit.
- 17 - SEL-63-121
1. 0C-4 0I . .l.O 4L
R F
5 db
-00
0
I6
-J l.o
FIG. 10. SUPERPOSITION OF THE CONSTANT LOW-FREQUENCY AND HIGH-FREQUENCY
POWER-GAIN CIRCLES. In this illustration the highest value for thepower gain, p max' corresponds to the two tangent circles for which
SEL-63-121 - 18 -
IV. DETERMINATION OF YL(f) AND THE INTERSTAGE NETWORK
A. THE MAPPING OF YL: CONSTANT-p CIRCLES AND CONSTANT-p CIRCLES
At this point, RF and LF are known, and for a required bandwidth
B, the maximum power gain p which can be expected with a given load
admittance YL = YK is also known. The transistor with its feedback
circuit now behaves like a new transistor, characterized by y para-
meters for a set of sampled frequencies. The following question shall
now be answered. How can the interstage filter be designed in order to
achieve, in the band B (Fig. 11), a constant input admittance Yin = YK,
and a constant power gain p 7
INPUT POWER pi(f) OUTPUT POWER Pom
TRANS ISTOR INTERSTABE
Yinput + FILTERFEEDBACK YK
YL
FIG. 11. BLOCK DIAGRAM OF THE COMPLETE AMPLIFIER STAGE. The generalrequirements are that Yinput = YK and Po/Pi = p.
1. The Input-Admittance Requirement
An arbitrary value po is chosen for the input reflection co-
efficient, and the new requirement on the input admittance Yin is
formulated by stating that, for any frequency, the input admittance of
the amplifier must lie on a Smith chart, inside the constant po circle.
But it is known that Yin is related to YL in the following way:
-Z (26)L =
2 2 Yin-y 1
Thus, two circles that correspond to each other can be drawn on two
separate Smith charts (Fig. 12), one for the input admittance and one
- 19 - SEL-63-121
a,_ . 0 n. u ad0ta c chrt Th h d d r g o i h atc
inpLoa admittance chart. The shaded region i the locus of Yinfor any input reflection coefficient .0
SEL-63-0. - 20
for the load admittance. For any load admittance inside the right shaded
circle, the transistor will present an input reflection coefficient less
than po
2. The Power-Gain Requirement
It is specified that within the band B, the stage power gain
must not differ from p by more than Ap. That is,
p - Ap stage power gain g p + Ap
But it is known that on the iX plane, and consequently on a Smith chart
(Fig. 13), the load admittances YL that provide power gains p - Ap
and p + Ap are located on two circles. The load admittances that pro-
vide power gains between those two values are to be found between those
two circles.
If both the input-admittance requirement and the power-gain re-
quirement are to be taken into account simultaneously, YL must be chosen
inside the region that belongs to the two regions just specified. This
region will be the permissible region for YL at a frequency f (Fig. 14).
Proceeding in the same way for each sampled frequency leads to as
many permissible regions as there are sampled frequencies. These regions
will be drawn on a single Smith chart (Fig. 15), or more effectively, on
two superimposed reversed Smith charts, as shown in Fig. 20. (See also
Chapter 14 of Ref. 6.)
B. THE INTERSTAGE NETWORK
The interstage network (Fig. 11) transforms YK into YL(f). A
ladder type, nondissipative filter will be chosen. Usually a single A
(or a T) section will give satisfactory results (Fig. 16). Although
some advanced mathematical methods are available for the design of such
a ladder [Ref. 6, Chap. 141, experience shows that a few trials on the
Smith chart will bring the input admittances at the different frequencies
inside the corresponding permissible regions. Finally one arrives at
the stage represented in Fig. 17. It will be found later that, for the
400-Mc amplifier, the interstage filter can be reduced to a single in-
ductor. The design and realization of such an amplifier will be consid-
ered in the next chapter.- 21 - SEL-63-1l2
II
a. LM Plane
P -jBSI
00.
b. Smith chart
FIG. 13. THE POWER-GAIN REQUIREMENTS. The shaded regions are the lociof power gains between p - 1p and p + Ap.
SEL-63-121 - 22-
p -L
-0.
P L0
FIG. 14. THE PERMISSIBLE REGION FOR YL AT A GIVEN FREQUENCY. To meetthe requirements on both power gain and input admittance, YL must belocated in the shaded region.
o7
il-0.
FIG. 15. THE PERMISSIBLE REGIONS FOR YL FOR SEVERAL FREQUENCIES. Theinterstage network transforms YK into Y(f) such that for the
sampled frequencies fI, f2' f3d f4;''', Y Ls image on the chartcomes into the corresponding shaded region.
- 23 - SEL-63-121
0I I T 1
FIG. 16. THE INTERSTAGE NETWORK.
FIG. 17. AN ITERATIVE SINGLE-STAGE AMPLIFIER.
SEL-63-121 - 24-
V. A 400-Mc, 30-db TRANSISTOR AMPLIFIER
A. THE STEP-BY-STEP PROCEDURE
The step-by-step procedure leading to the design of a 400-Mc, 30-db
transistor amplifier is now presented.
1. The 2N918 y Parameters
In Table 4 the sampled y parameters of the 2N918 transistor
are restated for reference purposes.
TABLE 4. RESTATEMENT OF THE SAMPLED PARAMETERS OF THE2N918 TRANSISTOR, [YT]f)
(IE = 5 ma, VCE = 10 v)
Frequency Parameter (mmho)
(Mc) Y 11 Y 1Y21 Y22
10 1.7 + jO.65 -0.01 - jO.07 See Footnote 0.08 + jO.13
50 2.5 + j2.5 0.0 - jO.3 80 - j60 0.1 + jl
100 5 + j5 0.0 - jO.7 40 - j60 0.2 + jl.3
200 8 + j8 0.0 - jl.3 25 - J55 0.5 + j2.5
300 10 + jlO -0.1 - j2 15 - j47 0.6 + j3.5
400 12 + j12 -0.2 - j2.7 7 - j43 0.8 + j4.5
500 17 + j14 -0.4 - j3.4 0.0- j40 1 + j6
Sh 21 = 62.5 at 10 Mc.
2. Determining the Feedback Circuit
Figure 18 contains, in the YF plane, the constant power-gain
circles for YK = 20 mmho and for a very low frequency (10 Mc). These
circles correspond to p = 9, 10, 11 and 12 db. Also contained in the
YF plane are the constant (Po0 /Pio) circles for f = 400 Mc. Consider-
ing the intersections of these circles, it is seen that p = 11 db could
be chosen, but since the transistor y parameters specified in Table 4
are merely typical parameters, p is chosen to be 10 db. It is to be
noted further that in Fig. 18 there are two intersections of the l0-db
- 25 - SEL-63-121
circles, thus yielding two solutions for the normalized feedback impedance:
ZF norm 0.7 + J5.0
and (27)
ZF norm 0.7 + jO.5
o9
F F -40F
RF = 4 om!(9
F!9 dFIG. 18. THE Y. PLANE (NORMALIZED TO 5 mmho). YK 20 inmho; f =400 Mc;
11 db < pm < 12 db. Choosing p = 10 db gives KZ F = 0.7 + j0.5 or
Z F = 0.7 T'15.0.
In order to preserve midband gain, ZF norm = 0.7 + j5.0 is chosen.
ZF = (0.7 + J5.0) x 200 = 140 + J1000 ohms (28)
RF = 140 ohms (9
LF = 0.4 ph
The feedback admittance YF(f) is calculated from the foregoing values
for RF and LF , and the results are listed in Table 5.
SEL-63-121 - 26 -
TABLE 5. VARIATION OF YF. WITH FREQUENCY
Parameter Feuny(c50 100 2003040
YF(norm)* O.8-JO.7 O.35-JO.6 O.l-JO.37 O.05-jO.25 O.03-JO.2
YF(mmho) 14 -j3.5 1.75-j3.0 O.5-jl.85 O.25-jl.25 0.15-jl.0
Normalized to 5 mmho.
3. The Constant-g Circles
The y parameters of the transistor with its feedback circuit
connected (Table 6) can now be determined.
TABLE 6. THE y PARAMETERS OF THE TIRANS ISTOR WITHFEEDBACK CIRCUIT CONNECTED
[y](f) = tYT](f) + [YFI(f)
Frequency Parameter (mmho)
(Mc) y y 12y 21y2
10--------
50 6.5 - jl.0 -4.0 + j3.2 76 - j57 4.1 - j2.5
100 6.75 + j2.0 -1.75 + j2.3 38 - j57 2.0 - jl.7
200 8.5 + J6.15 -0.5 + jO.6 25 - j53 1.0 + jO.65
300 10.3 + J8.8 -0.35 - 30.75 15 - J46 0.9 +~ j2.3
400 12.2 + jil -0.35 - jl.7 7 - j42 1.0 + j3.5
On the LMd plane, the constant-g circles for f = 100, 200, 300, and
400 Mc are plotted in Fig. 19 using the following relationships:
X2 + y2 =l1-_g(14+-Cx) (30)
= (P 0 /Pi) p (1
6g = o(2
oor(32)
In the present situation, p = 10 (10 db) and Ap = 1 db.
- 27 - SEL-63-121
jM
jM 9db
/db
0. f. 100Me, C-2; 9.Th
b. 112OMe.. 0-2.6; 890o
jJM
TOISR 1 SAN TLAT 0bA
10d CIRCLE.
FIG. 19. THE CONSTANT-g CIRCLES.
4. The Constant-p Circles
With p = 1/3, the insertion power loss is less than 0.5 db.
The constant-p circles and the constant-g circles are plotted in Fig. 20,
using Smith-chart coordinates for YL
SEL-63-121 - 28-
a2a
;rt
29 SEL63-12
5. The Interstage Network
A few investigations lead to the two-port shown in Fig. 21.*
The input admittance of this two-port, when loaded with YK falls into
the regions determined in Fig. 20.
60 nh
0.8 Pf j 50 ohms
FIG. 21. THE INTERSTAGE NETWORKFOR THE 400-Mc AMPLIFIER.
B. BRIDGE MEASUREMENTS
After arriving at design values for the individual circuit elements,
the following bridge measurements are made: *-
1. Measurements of the transistor y parameters,
2. Measurements of the y parameters of the transistor with feedbackcircuit connected, adjusting the feedback circuit so that theparameters approach the design values as closely as possible, and
3. Measurements of the y parameters of the complete stage, consistingof transistor, feedback circuit, and interstage network. Duringthese measurements the interstage inductor can be adjusted so thatthe y parameters of the complete circuit correspond to an iterativestructure with a characteristic impedance of 50 ohms and an in-sertion gain of 10 db.
For an extensive discussion of the design of coupling networks, seeChap. 14 of Transistors and Active Circuits, by Linvill and Gibbons[Ref.61
A General Radio 1607-A Transfer-Function and Immittance Bridge was usedfor these measurements during the realization of the 400-Mc amplifierdescribed in this report.
SEL-63-121 - 30 -
During the course of these measurements and adjustments, it is helpful
to keep in mind the fact that, at high frequencies, the circuit elements
behave like distributed rather than lumped elements.
C. PRACTICAL DATA
A detailed schematic circuit of the 400-Mc amplifier realized by
the foregoing methods is shown in Fig. 22. Slight adjustments of the
emitter currents were used to improve the response shape. In order to
permit transistor interchangeability, voltage and current adjustments
were provided for each stage.
Figure 23 is a photograph of the amplifier. Shields were used be-
tween stages, each emitter was grounded with a very short connection,
and each transistor case was grounded. Stand-off insulators and transis-
tor sockets were avoided, except for a teflon stand-off insulator used
at the base of the input transistor The base leads of the second and
third transistors were connected directly to 50-ohm bulkhead female
microconnectors in order to permit optional independent connection to
any one of the individual stages.
D. FINAL SUMMARY OF AMPLIFIER PERFORMANCE
Figures 24 through 31 summarize the performance of the 400-Mc ampli-
fier. From these figures it can be seen that the three-stage amplifier
has a gain of 30 db, a rise time of 1 nsec, and an overshoot of less than
10 percent.
The three original transistors were replaced by three others. Slight
modifications of the emitter currents made it possible to regain the
original amplifier characteristics, the adjustment process being rapidly
"convergent" when carried out using a sweep-frequency generator. Although
such a single trial cannot be considered conclusive, it indicates that the
amplifier might be reproducible on a production basis.
- 31 - SEL-63-121
L F - cLF CF LFI CF
RI
RF RD LF R L F2 RFR RD LF2
LI LF LF Li C~IC2C 12 2T 3
R8 RC R R8 j ) RCI R B RC I
C FT CFT CFT CFT CFT CFT
IV 0 K..C HF" HIGII-FRKQIJEKIC RITORS D.0K, 1
RD~ ~ ~ ~ ~~f - ... HR IH-RQECYRSSOR,20OHS / K
RF-IR loxF" IHFRQEC REIS ORS 150 OHS /
CB - 0.01 A CERMI ISC-FCAPUCITORSISOS -K /
RC - 0.01 f CEFRMI DISC CAPACITRSISOS .K /
RFD - CERAMC "FEDTHROGHFRQ C CAPACITO RS , 275 0 OHS,1/
FIG7 UNS. 2.W SHEDATICNE CIRCUIT LOFG THE21 INSIDE DAMELIER.
SE -6 -1 2 TUN 32. 20-GSLDTNE IEI ELNSEEEWUDO EEA EAISTR
FIG. 23. PHOTOGRAPH OF THE 400-Mc AMPLIFIER.
- 33 - SEL-63-121
8
ww
z
0 0N 2 L
(qp)N~V9~3M~ NOI~S"
SEL-6-121 34W
I flsec/cm --- a
a. Input step
C4'
I nsec/cm -
b. Output step for amplifier plus IO-db attenuator.
FIG. 25. STEP RESPONSE OF THE SINGLE-STAGE AMPLIFIER.
- 35 - SEL-63-121
5 nsec/cm--m
b. utpt plsefora.mIpuie pus 1-bateut
I26 PUSREPNEOTHSIGESAEAPIIRSEL-63-1 2-3
U
U
C
5 nsec/cm *---P
a. Positive output
S
00
5 nsec/cmb. Negative output
FIG. 27. DYNAMIC RANGE OF THE SINGLE-STAGE AMPLIFIER. Input pulse
varied in 3-db increments in both (a) and (b).
- 37 - SEL-63-121
I-8
2
C-4
0 000
NOp 3unouI 3s*N# 9 NIVS W3MOd NOIJMI3SNI
SEL-63-121 - 38-
I nsec/cm -
a. Input step
-Ut
Insec/cm -
b. Output step for amplifier plus 30-db attenuator
FIG. 29. STEP RESPONSE OF THE THREE-STAGE AMPLIFIER.
- 39 - SEL-63-121
E
5 nsec/cm
b. utpt plseforam Iputie pus 3-batna
FI.3.PLERSOSEFTETRESAEAPIIR
SEL-3-12 - 4
in
5 nsec/cm-*
a.Positive Output Pulse for 8 values of input pulsediffering in amplitude by 3 db
5 nsec/Cm -
b. Negative output pulse for 11 values of input pulsediffering in amplitude by 3 db
FIG. 31. DYNAMIC RANGE OF THE THREE-STAGE AMPLIFIER.
- 41 - SEL-63-121
REFERENCES AND BIBLIOGRAPHY
1. J. D. Fogarty, "Lattice Networks for Phase Correction,"Sperry Engineering Rev., Mar 1961.
2. J. C. de Broekert and R. M. Scarlett, "A Transistor Amplifier with100 Mc Bandwidth," TR No. 514-1, Contract AF33(600)-27784, StanfordElectronics Laboratories, Stanford, Calif., Jan 1959.
3. P. J. B6n6teau and J. A. MacIntosh, "Getting Fast Pulse Response withVideo Amplifiers," Electronics, 13 Oct 1961. Also in FairchildApplication Note No. APP 38, 1961.
4. V. R. Saari, et al, "Circuit Applications of a Coaxially EncapsulatedMicrowave Transistor," 1960 Solid-State Circuits Conference Digestof Technical Papers, Philadelphia, Pa., 1960.
5. W. E. Ballentine and F. H. Blecher, "Broadband Transistor VideoAmplifiers," 1959 Solid State Circuits Conference Digest of TechnicalPapers published 1959, pp. 42-43.
6. J. G. Linvill and J. F. Gibbons, Transistors and Active Circuits,McGraw-Hill Book Company, Inc., New York, 1961.
ADDITIONAL SOURCE MATERIAL:
J. B. Angell, "High Frequency and Video Amplification," Handbook ofSemiconductor Electronics, Second Edition (Ed. by L. P. Hunter),McGraw-Hill Book Co., Inc., New York, 1962.
G. Bruun, "Common Emitter Transistor Amplifiers," Proc. IRE, 44,Nov 1956, pp. 1561-1572.
J. Fisher, "Emitter Peaking Improves Video Amplifier Response,"Electronics, 19 May 1961.
M. S. Ghausi and D. 0. Pederson, "A New Design Approach for FeedbackAmplifiers," IRE Trans. on Circuit Theory, CT-9, Sep 1961.
L. S. Nergaard, "Amplification--Modern Trends, Techniques, andProblems, R.C.A. Rev., Dec 1960.
R. S. Pepper and D. 0. Pederson, "Designing Shunt-Peaked TransistorAmplifiers," Electronics, 2 Dec 1960.
R. L. Pritchard, et al, "Transistor Internal Parameters for SmallSignal Representation," Proc. IRE, 49, Apr 1961, pp. 725-738.
G. Reddi, "Transistor Pulse Amplifiers," Semiconductor Products,Aug 1961.
J. Sardella, A. Caggiano, and others, "Silicon Video Amplifiers,"U. S. Govt. Res. Repts., 15 Apr 1960, PB 138051. (Facility:Raytheon Mfg. Co., Newton, Mass. Available on microfilm or photocopyfrom Library of Congress.)
D. E. Thomas and J. L. Moll, "Junction Transistor Short CircuitCurrent Gain and Phase Determination," Proc. IRE, 46, Jun 1958,pp. 1177-84.
SEL-63-121 - 42 -
P. H. Thomas, "Wide-Band Video Amiplifiers Using Compound Feedback,"Electr. Design News, Nov 1960.
F. D. Waldhauer, "Wide-Band Feedback Amplifiers," IRE Trans. onCircuit Theory, CT-4, Sep 1957, pp. 178-190.
- 43 - SEL-63-121
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-2- 2/64
UNIV2"ITIES
School of Engineering Harvard University Dynamic Analysis and Control Lab.
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4600 Oak Grove St. 3503 1. Engineering Bldg.
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Berkeley 4, Calif, Ann Arbor, Mich.
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Univ. of Florida 1515 W. Wisconsin Ave. Raleigh, N.C.
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M.I.T. Dept. of Elect. Engr.
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Electrical Engineering Dept.
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kU.K.) Ltd.
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1 Mt__ 1.n iS, D. urich, SWITZERLAND1 At in: Prof. N.J.O. Strutt
Prof. F.Hi. Itboderick
Mach-erstr Co1 lege of Science ProfS Btebo'k
ao Ie, Ii .crn t* 1 y1v~ of Liv.A.1 Manchestr 1, ENGLANtD Insti tute of Physique
'!1 Rue de NamorMr. Bruit ib,,toia Louvain. t BIlgiumt
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P1rof. rlitto -noo I.aay-L-MoulintauxFacult o od Enleevr rnSineI FRANCEtoivernits ot lI "k, I Attn: Solid-State and ElectronBonkun-ito, tkto Devices
I JAPANProf. Karl Stinbuct
Dr, \tein, 1. %--ur tInstitute uf( t chrichtenver-
P hysc Dept. arbeltung tindThe technicl tltniversity Nachrichtenubrtragung
of Dettttri rechtiache Hochscitule KarlsruheLoIndtof level 100h, I-vttgt'v 1 Karlsruhe, GERMANY
1 IWt)(t
Prof , G. tteoottnRoyai Irchtnical t'nieersit y
of fietnankttstIervolgsttt' 10, 0. 4eotsOL
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