THE REALISATION OF BAND-PASS AMPLIFIER BY UTILISING
NEGATIVE FEEDBACK PRINCIPLE.
JAN 3 1940
LIBR IA
By
it
BHAGWAN DAS TOSHNIWAL
4
M.Sc.,University of Allahabad.
1938.
SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENT FOR THE DEGREE OF
LASTER OF SCIENCE
From the
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
1939.
Signature of Auther ..................
.......
Department of Electrical Engineering, September 25, 1939
Signature of Professor
in charge of Research.-....
Signature of Chairman of Department'
Committee on Graduate Students....
3812
INDEX.
Page.
1. Introduction.
1.
2.Some Fundamental Characteristics of
Feedback Amplifiers.
3.
3.Design of Resistance-Capacity Feedback
Network.
4:
5.
4.Experimental Work.
a. Design of Amplifier.
14.
b. Design of Feedback Circuit.
15.
5.Conclusion.
20.
6.Appendix.
22.
7.Bibliography.
24.
233303
ACKNO WLEDGEM tWENT
The author desires to express his sincere thanks
to Prof. E.A.Guillemin for his help in the design of the
feedback circuit and general supervision throughout the
work.
Thanks are also due to Prof. E.L.Bowles for his
help in the selection of the present thesis problem
and to Prof. W.I.Hall for his useful suggestion during
the experimental work.
THE REALIZATION OF BAND-PASS AMPLIFIER BY UTILISING
NEGATIVE FEEDBACK PRINCIPLE.
INTRODUCTION
The vast amount of literature published on feedback amplifier bears testimony to the incrosing importance of feedback phenomena in the field of electrical
communication. This new tool in the amplifier design
was introduced by H.S.Black
,
with a view to get an
improved frequency response characteristic of the amplifier and to achieve the stabilisation of the effective
amplification in the presence of variations of the
energizing potentials applied to the amplifier tubes,
and to minimise distortion. However as the scientists
became more familiar with t.e feedback principle they
succeeded in utilizing it in diverse fields such as
tone-control'
low distortion volume control
3
,
admittance
neutralization4 and frequency discrimintioa 5
Amplifiers having frequency discrimination
characteristics are widely used these days for various
purposes and from economic considerations it is highly
desirable that this frequency discrimination should be
obtained within the amplifier itself so as to elimanate
the cost of wave-filters. Up till recently all such
amplifiers employed either interstage transformer
-2-
couplings or some other selective networks usually
cosisting of combinations of inductance and capacitance
or their mechenical equivalents. However,since the advent
of high/4-tubes, interstage transformer couplings are,
in most casesbeing replaced by resistance capacitance
couplings, because of their low cost, compactness
and immunity against stray pick-ups. But such resistance
capacitance coupled amplifiers donot give sharp discrimination in trnsmission efficiency for any desired
frequency band. However this sharp discrimination can
be achieved by the use of feedback principle and that
too by the use of resistance-capacitance network alone
in the feedback circuit. Hence the present problem
was undertaken with a view of realizing a narrow bandpass amplifier suitable for use in a superhetrodyne
receiver in the intermediate frequency stage, and it
was further aimed at to use only resistances and condensers in the feedback network.
FUNDAMENTAL CKARACTERISTICS OF FEEDBACK AMPLIFIERS.
In the feedback amplifiers a portion of the output
voltage is fed back into its input terminals through
a feedback circuit or network. The magnitute and phase
relationship of this feedback voltage with respect to
the signal input voltage is governed by the propagation
factors of th:e amplifier and feedback circuit and
determine the feedback characteristic. The propagation
factor of a unit is the ratio of its output voltage
to its input voltage; and it can be represented as a
complex quantity, as the output volyages of both the
amplifier and the feedback circuit differ from the
input voltages in both magnitute and phase and are
functions of frequency.
If i represents the propagation factor of the
amplifier and P3 that of the feedback-circuit, then it
can be shown th.at for an input voltage e , an output
voltage E given by
pze
E
is obtained. The assum-Lpticn as to the sign is such that
when the feedback voltage- opposes the signal voltage it
is
negative.
CONDITIOTS FOR STABILITY.
One of the problems encountered in tne aesign
ana construction of feedback amplifiers is that of
preventing singing at frequencies outside the operating
range of the amplifier. This difficulty may arise due
to a progressive phase shift as the frequency departs
from tle operating range.
The mathematical investigation
of the problem of stability was underte:n by Nyquist6
who showed that if
the vector productlk is
plotted
on a polar coordinate paper, then for complete stability
vector
the/ 5 O/envelope and its conjugate for all frequencies
should not intersect or enclose the point (1,jO). This
deduction was latter on varified experimentally by
Peterson, Kreer and
Vare 7 .
The expedients adopted for the prevention of
singing, in general, require some sacrifice of the
effective amplification so that the magnitute of
becomes less than unity before its phase angle assumes
such a magnitute so as to cause oscillations.
DESiGIT
OF T 1E RESISTANCECAPACITY FEE'DBACK NLTWORK.
The problem of designing tLe feedback
circuit was
attacked with a view to get a band elimination network
so that when the output voltage is fed back through
this network to the input terminals a reverse effect,
that is, band-pass characteristic property is obtained
within tie amplifier. It was also aimed at to comletely
stop feedback voltage in the effective band width so
that no sacrifice in the over-all gain of the amplifier
is affected in the useful range.
In the design of feedback network symmetrical
lattice was used as a basic structure,as this form of
structure provides a more general and flexible approach
for the desig7n of a selective network. The following
treatmen~t shows a graphical method very conveniently
adopted to resistance-capacity filter design.
Let figure 1 represents a symmetrical lattice
structure having impedances Zao and Zbo in the cross
arms, and for simplicity let us assume t1at it is
R
zdO
A,'
A62
,
E740
/JY.
1.
designed to work into a load impedance of resistance R,
- 6 -
which is equal to the internal impedance R of the
generator of voltage El. The generator can be replaced
LL/R, and
by a constant current source of current I1 -the above figure can be modified as follows:
/r =KE,/g
z7
I'
/:
2
which can be further modified as
shown in figures 3
and 4.
R
'1
I1
F/G. 3
//G.
4.
where Zao stands for a parallel combination of Za and
R, and Zbo for a similar combination of Zb and R.
Then we have
-1
E2
_ Z 6 o -Za.
2
anl if R is unity tie propka6ation factor
is given by
Thus if we plot the impedance vector diagram of
Zao and Zbo we can very easily determine the magnitute
and phase relationship of
f3.
Conversely if we wish to
- 7 -
have a predetermined characteristic curve for
we can
do so by introducing modifications in the individual
values of Zao and Zbo
Afterwards, the component ele-
ments of Zao and Zbo can be determined and finally the
symmetrical lattice structure can be converted into
some more convenient equivalent network.
Considering the structure of Zao and Zbo from the
view point of resistance-capacitance combination alone
we can resolve any complicated structure into a series
combination of a number of individual units consisting
of a condenser in parallel with a resistance as shown
in figure 5.
RI
R2
RA
RN
C/
C2
Cx
C
The impedance vector diagram of the Kth branch in
the above figure is shown in figure 6, in whic. at
X
Xx
p
P
zocius
R
0
I/ G.
6.
O'A
first the admittances due to Rk and Ck are added to
give the straight line OkXk which is the admittance
vector diagram of the Kth branch. In the figure the
point P" is the inverse of the point P, and the lower
semi-circle being the inverse of straight line OkXk
is the impedance vector diagram of the Kth branch.
The angle
where RkC
O,
is given by
w
Likewise vie can draw the vector impedance diagrams
for other branches and add them up to give the over-all
vector impedance locus.
In the design procedure the final combination of the
elements of the branches Zao and Zbo were those as
shown in figure 7,
and the impedance vector diagram
OOhm
/Ohm
of both Zao and Zbo is shown in figure 8. It is seen
-that the two locii intersect at the same frequency
given by W. =RC' , and hence at this frequency
the propagation factor
CO
,
being zero no voltage is fed
back through the feedback network.
In plotting the impedance vector diagram of Zao
-
and Zb,
the resistancesR
were also considered to be
unity for the sake of convenience.
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As the symmetrical lattice network has some
inherent didadvantages froi
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it is always converted into equivalent 7
orT-network
or thier combination,if possible. In the present case
the symmetrical lattice network was found to be equivalent to the
parallel combination of two T-networks
as shown in figure 9.
R
C
C
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For detail study of the above network it was
subjected to mathematical investigation (Appendix)
and its frequency response curve is shown in figure
10, in which linear scale is used for both E2/El
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using db scale for E2 /Ei
and logarithmic scale for
frequency. Figure 10 does not show that the circuit is
selective enough to be used for band elimination purpose. However when such a circuit is used in the
feedback path of an amplifier, shLarp seleutivity can
be obtained because of the
A'
vector, since the over-
all amplification with negative feedback is given by
The effect of different values of /W on the
selectivity of an amplifier is shown in figure 12.
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14 -
EXPERIMENTAL WORK.
Design of amplifier. As the selectivity in a feedback
amplifier increases directly with the gain, an amplifier
with a high gain of about 60-db was considered to be
necessary. Such an amplifier should have a minimum
phase shift taking place within its internal coupling
circuits so as to avoid regenaration and consequent
oscillations at the higher and lower end of the amplifier
frequency range. Thus a resistance -capacity coupled
amplifier was considered most suitable for the purpose.
Now as each tube introduces a phase shbft of 7F between
the input voltage fed into the grid-cathode circuit
and the output voltage taken out from the plate-cathode
circuit,
it
was essential that the amplifier should
have an odd number of tubes for negative feedback action.
At first
an attempt was made to get the required ampli-
fication by using only one single
recently introduced
high-transconductance tube 1851. But it was found that
for the frequencies under consideration a voltage gain
of more than about 100 could not be obtained in this way.
Hence
it became inevitable to build a three stage
amplifier. Any of thie regular pentode tubes used for
high frequency work could have been used.
Using 6K7a
tubes, tie amplifier shown in figure 13 was built.
almost
This amplifier gave/constant gain of 60-do from about
5 Lc to about 100 Kc.
;
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4F
- 15 -
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ro
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Such a high4gain amplifier is very much susceptible to
hum and other stray pick-ups unless proper care is taken
in its design and construction, because a very small
voltage induced in the first stage will be highly amplified at the end of the final stage. Therefore as
necessary precautionary measures, twisted wires were
used for suppling the current to the filaments, the
grid in the first stage was carefully shielded and a
well filtered source of D.C. voltage was used to supply
the plate voltage. The screen voltage was obtained
by the use of a bleeder resistance across the supply
voltage.
The feedback circuit. The feedback circuit was designed
to work in
the vicinity of 50 Kc.
For this purpose the
resistance R was a fixed carbon resistance of 6000
Ohms, and the condenser C was a variable condenser of
500
maximum capacity.
equally proportioned.
The other eleirents were
---------
- 16 -
The feedback circuit tuned to 50 Ko was introduced
in
the amplifier as sLown in
the figure through a
coupling condenser Cc. This condenser should be suffiently large so as to avoid appreciable phase shift
--
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Iedbaeick
e,cjj
INP1/Trtr
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down to the lowest frequency. For instance it was noticed
that when Cc was 0.l4f,
formance of the ampi
0.5
1 Uff
iotor-boating marred the perfier, but when it
was increased to
this trouble disappeared.
The frequency response curve of the above arrangement is shown in figure 15, and is quite in agreement
with the theoretical prediction.
In taking the experi-
mental data the measured input was taken from a General
Radio Standard Signal Generator and the output was
measured by a "--R vacuum-tube voltmeter. Another feedback circuit tuned to 55 ac,
when used alone in the
amplifier gave the frequency response curve similar
to that shown in figure 15. But as soon as the two
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feedback circuits were joined in cascade and connected
in the feedback path, the amplifier began to produce
self-oscillations. The frequency cf these selfoscillations was determined by means of an oscilloscope
and was found to be very nearly 33 Kc.
In order to investigate the cause of these oscillations the phase shift of individual parallel T-networks
was calculated and the result is shown in figure 16.
+4
-
t4
Ti
f
I
-
iL
!tr,
-
-
t
T4
T
r+
tr
t
,i
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-
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t7
Thus if aw.is 50 Ko, then at 151 K c each individual
parallel T-.network introduces a phase shift of about
80 degrees and hence the two together produce a phase
shift
shift of 160 degrees. A phase/of 20 degrees might be expected to arise within the amplifier coupling networks and
hence the self-oscillations at 151 Kc was quite natural.
There were two ways of stopping these selfoscillations. Either the amplification should have been
-
19
-
reduced to such an extent that the product
at 33 Kc
became less than unity or some phase correcting network
should have been introduced. But unfortunately the
frequency of self-oscillation was so close to the frequency of the tuned feedback circuit that either of
not
these expedients could have been successfully employed
without impairing otier desired properties of the
amplifier. As a result it was concluded that the use
of two or more parallel T-networks in cascade in the
feedback path of the amplifier was not the solution
of the problem.
- 20 -
CONCLUSION.
Although, the use of two parallel T-networks as
discussed above has
failed to give the desired band-
pass characteristic to the feedback amplifier; it is
possible to get any percentage of band width by using
two separate feedback circuits in parallel in the feedback path. One of these circuits should be designed
to give sharp low-pass characteristic and the other
the sharp high-pass characteristic. But, such lowpass
and high -pass circuits with sufficient sharp cut-offs
were not obtained by simple arrangement of resistances
and capacitances alone and
ience further attempts on
this line were given up, as the very aim of simplicity
was endangered in the complexity of the circuit
structures.
However further attempts were made to get better
results by using slightly modified form of one parallel
T-network alone in the feedback path, but witihout much
success. For instance it was found that mistuning of the
circuit could give higher peak at the cut-off frequency
but did not result in the increase of band width. In
another attempt the circuit was modified by putting a
high resistance of about 10CR as shown in figure 17,
IOR
0
- 21 -
and then it was introduced in the feedback path. But this
arrangement :.ave only a slight increse in the band
width, which was not sufficient for the purpose and
that too at the sacrifice of gain at the tuned frequency.
From one point of view this loss in gain was not a very
serious disadvantage, because what-ever feedback was
introduced had
the stabilising effect on the over-all
working of the amplifier.
owever further work on the design of a band
elimination circuit should enable us to find a more
favourable comnbination of resistance capacitance elements whose cut-off range extend over th.e required
band width. Such a circuit when used in the feedback
path would give us narrow band width with good selectivity in the band-pass amplifier. The design of filter
circuits based on symmetrical lattice structure when
approached graphically as outlined previouly, presents
a very good method in the
design of resistance capacity.
networks and further work on these lines is highly
desirable.
-
22-
APPENDIX
A T-network can be replaced by its equivalent 7Tnetwork. Thus
C
6?
a
where
and
/CW
g=
1eg -g exg*
Similarly
I
R
R
T 2C
/
where
0
%,/IW
/ ji'a'C
and
R (/4jRCw)
And finally we can replace the parallel combination
of the above two T-networks by a 7T-network as shown
below
R
2
I
where ZA =
i+i ACw
and ZC
:4'
( /+ 1 4 CW)
J C IV)
- 23
-
Now,
Impedance to the right of 33' -. Z3
Impedance to the right of 22?
+
Z
R 2 +Z4
3
z_7z
Impedance to the right of 11'
-f Z3
-7c
ZII Zz
=1ZI
Z,,2Z
And total impedance z
Therefore current I
.-
-z
Current 12
Z
4
,7 Z 2
Current I
// 71----z
And E 2 = 3R
2
R2 - z
~
Z(ZEZ2
1(*+
(zo
(Z
Z)
72,,+Za)(
Theref ore,
6;
65
(Z -Z)R *Ig) +(R
R,~~rz
/
R 2 (/ -AXZCia9(
Let R=
f
R
and R 2
9 ACiC&)
fJCtOR(
0
2
4 A,014A2 +
z+A
-:2(
+
72
Z
-t
2
2#,+4X
R
Then
2- # +&/)
2~~~~~
-c
And if
C
fS(
+R
9
10
'f~/+
t4
4is a very large quantity and /)o very small
we get
6/
ia-J
-
'9'
4
X2
- 24 -
BIBLIOGRAPHY.
1. H. S. Black, "Stabilised Feedback Amplifiers,"
Electrical Eng.,Vol.53, p.ll 4 , Jan. 1934.
2. P. K. Turner, "Negative Feedback," Wireless World,
Vol. 41, p.386. Oct. 1937.
3.
B. J. Stevens, "Low Distortion Volume Control,"
Wireless Eng.,Vol. 15,
p.143, March,1938.
. E. W. Herold, "Admittance Neutralisation,"- Proc.
I.R.E.,Vol. 25, p. 1399, Nov. 1937.
5.
. H. Fritzenger, "Frequency Discriminationby
Inverse Feedback,"Proc.I.R.E., Vol. 26. p.207
February,
1938.
H. H. Scott, "A New Type of Selective Circuit and
Some Applications," Proc. I.R.E., Vol. 26,
p. 226, Feb. 1938.
6. H.Nyquist, "Regeneration Theory," Bell.Sys.Tech.Jour.,
Vol. 11, p.126, July, 1932.
7. E. Peterson, J. G. Kreer and L. A. Ware,"Regeneration
Theory and Experiment," Bell. Sys. Tech. Jour. Vol.,13.
p. 680, October, 1934.