PULSED-DIODE DETECTORS FOR RADAR RECEIVERS
A NON-INDUCTIVE FREQUENCY DISCRIMINATOR
By
RICHARD J. STANSFIELD
SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
BACHELOR OF SCIENCE
From the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
1947
Signature of Author
Signature redacted
7
"AoA'
Signature of Adviser
Signature redacted
The author wishes to express his appreciation for the valuable suggestions and
guidance of Mr. E. J. Rhoad and f'or the
suggestion by Professor Radford of a second
topic.
This thesis is wrttten in two sections.
One section
is devoted to Pulsed-Diode Detectors for Radar Receivers,
and the other is on A Non-Inductive Frequency Discriminator.
The thesis subject formally approved was entitled
Pulsed-Diode Detectors for Radar Receivers.
A change of
subject was authorized when it became evident that the
author could not compl-ete in the alloted time,the work
outlined in the original proposal.
The section on pulsed-
diode detectors is, therefore, incomplete, but is of value
because it points out a method of obtaining the desired
solution.
that
It also shows certain difficultiesAwill be
encountered in obtaining a solution.
The section on a non-inductive frequency discriminator
is a report on an article that appeared in the Wireless
Engineer of October 1946.
This article is entitled Linear
Frequency Discriminator and was written by J. R. Tillman,
Ph.D., A.R.C.S.
It is used as the sole source of inform-
ation in writing the theory and as a guide in performing
experiments on the discriminator.
TABLE OF CONTENTS
I.
Preface
II.
Pulsed-Diode Detectors for Radar Receivers
1.
Object.*..... .....
2.
Introduction.......
c0~
(1)
...
(1)
...
....
Transient Analysis.
C.
4.
Conclusions...*...
000
5.
Bibliography .......
(3)
..
C
(9)
...
(10)
A Non-Inductive Frequency Discriminator
Theory..............
3.
Laboratory Set-up...
4.
Discussion of Results.
5.
Bibliography..........
.
2.
(11)
..
.
Introduction........ ...........
.
1.
.............
.....
.
.........
(15)
..(16)
.
.
.
.
.
....
.
*...
g.....
(12)
.1
.
III.
3.
...(19)
.....
6.
Appendix..............
..(20)
PULSED-DIODE DETECTORS FOR RADAR RECEIVERS
Object:
The object of this section can be stated as follows:
1) To study and explain the action of the diode
detector under the conditions found in radar
receivers.
2) To point out the design requirements that must
be met.
3) To make a transient analysis of the detector
action.
Int rodubt ion:
The problems involved in detecting the echo pulses received by a radar receiver are essentially the same as those
found, in detecting amplitude modulated radio signals.
A non--
linear element is required; that is, one which will conduct in
only one direction.
The operation of the diode detector, though
familiar, will be briefly reviewed here.
The conventional cir-
cuit is shown below.
LAST Z.F.
STAGE
70
R
FIG. I.
CAMPLI
FIER
2.
The pulse to be detected can be considered as a
series of sinusoidal oscillations at the intermediate frequency.
The diode will conduct when the voltage on its plate
swings positive with respect to the cathode.
Diode conduction
Between pos-
causes a charge to build up on the condenserC.
itive plate voltage swings the condenser partially discharges
through the resistance R.
The charge retained by the condenser
biases the diode thereby reducing the available charging voltage.
The steady state is reached when the diode conducts enough
each I.F. cycle to just replenish the charge that leaks off
between cycles.
In selecting values for R and C, it is necessary to
consider their product --
the time constant of the circuit.
A long time constant is required to make the output free from
I.F. ripple.
A short time constant is necessary to make the
rise and fall time of the output pulse short.
In addition,
the diode load resistance should be large compared to the diode
conducting resistance to prevent an unfavorable voltage division
between the two.
The condenser should be several times as large
as the interelectrode capacitance of the diode.
A tube satisfy-
ing the conditions of small capacitance and conducting resistance
is a 6AC7 with all the grids connected to the plate.
The condenser shunting the load resistance must be an
effective by-pass for the I.F. voltage.
At the same time, it
must present a high impedance to the highest video frequencies
of interest in the output pulse.
To preserve the shape of the
pulse this highest video frequency is about 3 mcps.
With the
usual I.F. of 30mcps. the highest video frequency is a larger
percentage of the- I.F. than is found in radio receivers.
In
radio receivers the highest audio is about 10 kcps with an I.F.
of 476 kcps.
design.
Hence the radar receiver detector requires better
The detector in television receivers are similar in
this respectto-radar receiver detectors.
In practice a low pass filter is connected across the
load resistance to accomplish the above action. This low-pass
filter
takes the fonm of a pi-section in which the input
capacitance of the video amplifier which follows is used as
one of the legs.
Transient analysis:
When a high frequency (I.F.) signal is applied to a
diode detector the condenser does not become fully charged
until several cycles have passed through.
The detector has
been analyzed mathematically for the steady state condition
but, to the author's knowledge, not for the transient build-up.
This transient is particularly important in radar receivers
because the shape of the pulse must be retained.
The simplest type of diode detector using only.a resistor and a condenser will be treated here.
The following
assumptions are made;
1) The diode interelectrode capacitance is negligible.
2) The diode resistance is infinite for negative plate
to cathode voltages and is a constant for positive
plate to cathode voltages.
DIODE
CHAR A CTER I $TIc
TRANSIENT
SrEADY
I
,
a,
I
STATE
I
Cowostro 1
I
'
T
----I
I
I
I
-- eb-)
I
I
j
!
S
CURRENT
DioDE
Edc
E sin wt
-
-
I~
z
-*
ET
A
Esvn tA
TS1EAOY
PLATE
VbLTAGE
FiG. 2.
1*
EQUIvALEvr
Ar
two
E -e
CIRcu IT
4.
3) The signal input is a pure sine wave beginning
at the start of the pulse and continuing at a
constant amplitude until the end of the pulse.
4) The load resistance and capacitance are ideal.
The circuit to be analyzed is shown in Fig. 1.
Fig. 2
is a graphic interpretation of detector action using the idealized diode characteristic curve.
For the first conduction period of the diode two
equations can be written.
= ir
E srwti
E
+
U
-U ,) RL
(1.)
~wid
rp
off
(2.)
Eliminating i. in equations (1) and (2) gives
dt
+
r+ R,
r, RLC
.E
9,
to C
sin Wt := 0
W+ + RLC
3
(3.)
The solution of equation (3) results in an expression
for i which is good for the first
diode.
pulse of current through the
The constant of integration has been evaluated from the
initial condition that i.= o at t = o.
solution of equation (3).
r+JRL
+RL
Equation (4) is the
5.
Since the coefficients
cf
the three terms are constants
the current can be expressed in more compact form.
i=
A J/in0e
*8 cos W
- B
c
~~~
(5)
'(
5))
AWI4AD~~7Z
E
/C
'3
-- i
The output pulse is called Ed cand by using equation (5)
is now possible to obtain an expression for it.
Two circuit- equations can be written down as before
E
-
(6)
E,:n e)Z'-,r
E-7)
Eliminating i, a differential equation is obtained.
+
Substituting (5)
E4.,=
(
C
C
into (8) and solving
A'sIntJ
'
t
.
+
I
--
'
"'" (9)
'
13
B
(
+
d i-
-
it
(
E
6,.
C
C
Equation (9) gives the output voltage for the interval
from t
=
o until the diode ceased to conduct.
The time at
which' the diode ceases to conduct occurs when the instantaneous
voltage at its plate is equal to the voltage at its cathode.
This time will be called ti.
d-F
i
Ai
A
E
(10)
+ 13'cosc.*, +jC~cik*wt~cd
D~611
Equation (11) cannot be solved explicitly for tl.
It re-
and error solution.
quires a trial
o t the diode no longer conducts and
Beginning at t
the condenser begins to discharge through the load resistance.
Hence the voltage Ed-c decreases exponentially from its initial
=
Le.
t,
until the diode again conducts at t
F
RLC
=
t
2
'
value at t
~~,
(12)
The time at which the diode begins to conduct again is
given by equation (13).
7.
=
d-c
(13)
From equation (14) t2 can be determined if t, is already
known.
At tinb t = t 2 the cycle repeats itself.
There are
similar differential equations to solve which have different
boundary and initial conditions.
The complexity of these bound-
ary and initial conditions make the equation for Ed-c successively
more complicated.
The results thus far obtained can be checked to see if the
order of magnitude is correct and to see approximately how fast
the pulse is building up.
Typical values for the constants in
-a radar receiver detector are as follows:
50
MAC
PS
C =
f f
rp = 200 Ohms
E
= Ovol+s
20,0oo oIs
The equation for Ed-c during the first cycle of I.F.
becomes
Ea
=-
.6 z
sin t
3.30 coswt + 3.16 L
The maximum value of Ed-C during the first I.F. cycle
occurs at t = tl.
From equation (11)
8.
Wt
= 112.7
0
Fd-=
9ZZ Volts
el-C
The order of magnitude is correct indicating that the
solution.is mathematically correct. The value is obviously
too high since it indicates that the transient is nearly over
on the first I.F. cycle. In seeking to explain this result
it is well to review the assumptions made at the beginning.
The constancy of the diode conducting resistance is open to
serious question. An experimental curve of this resistance
as a function of plate to cathode voltage is sketched in Fig.3.
This shows clearly that the resistance does vary with plate to
PLArTs R ESIST ANCE
V.s.
PLATC
-To CATMODE
VOLTAGE
Sao
6AC7
E
-C 4ob I
(GR1s
COkIECTED
To
THE PLATE)
aoo
0
0
I
eb (vo/i+s
I
I
z
3
9.
cathode .voltage especially at low values of this voltage.
It
must be remembered that the parallel RC network biases the
cathode of the diode to the point where the instantaneous
plate voltage never becomes more positive than the cathode
by rcre than a few volts.
Conclus ione:
A transient analysis of the diode detector is not a
simple thing to obtain.
Any transient analysis must take
into account the variation of -conducting resistance with plate
to cathode voltage.
A fairly simple mathematical expressions
could probably be found which would approximate the curve obtained experimentally.
The usefulness of a solution would be greatly enhanced
by expressing the result as a continuous function of time from
the initial instant until the steady state is reached.
Such a
solution would not predict the output voltage at a partieblar
instant but would give the average value over a short interval
of time at that instant.
100
Radio Engineers' ,Handbook
- F. E. Terman
Communication Engineering
-
Everett
Television Simplified (96-103) - M.S. Kiver
irinciples of Television Engineering (320-324)- Fink
Design Formulas for Diode Detectors - H. A. Wheeler
Proc. I.R.E. 26, 745-780 June 1938
*
*
**
*
*
*
-
.~4.
Ernest Frank
*
Pulsed Linear Networks
110
A NON-INDUCTIVE FREQUENCY DISCRIMINATOR
Introduct ion:
A frequency discriminator is a circuit in which the
output is a direct voltage that is linearly proportional to
The frequency discriminator
the frequency of the input signal.
is used in frequency-modulated systems to convert the F.M. signal
It is also employed in
into an amplitude-modulated sIgnal.
automatic frequency control systems.
The most common type of frequency discriminator makes
use of the resonant property exhibited by a parallel combination of an inductance and a capacitance. At the frequency to
which this circuit is tuned the output is a maximim and will
decrease rather rapidly as the frequency is raised or lowered.
The discriminator usels two such circuits tuned to slightly
different frequenciesf1
and f2 .
The center frequency - the
frequency at which the discriminator output is zero - is then
fl~f2''
A direct current output is obtained by rectifying
the voltages developed with separate rectifiers and placing the
output of the rectifiers
in series opposition.
A well-designed discriminator using the above principle
to
can be made very linear and fairly stable as regard/the shift
of the center frequency with temperature aid age.
The failure
to maintain a constant center frequency is the most undesirable
characteristic 'a discriminator can have.
The inductors used in
12.
the above discriminator are apt to cause instability since
commercial inductors are further from ideal than resistors
and condensers.
Commercial inductors are themselves unstable.
From this standpoint, a discriminator that does not use inductance is very desirable.
Theory:
The resistance-capacitance discriminator is based on
the output vs. frequency characteristics of the Wlien bridge
near the balance frequency.
output is zero.
At the balance frequency the
jThe output increases as the frequency is
made greater or less than the balance freqtency.
The Wien
bridge is related to the twin T network shown in Fig. 1.
It is this network that will be used in the discriminator.
C,
-
---->R, -C
'-- \.
FIG. I.
C,
13.
The design formulas
for the twin T network for any
value of balance frequency f, is. given below:
w1 R
C,
=
The discriminator consists of two such circuits with
slightly different balance frequencies f, and f 2 so chosen
that the square root of the product is equal to f0 --
balance frequency of the discriminator.
the
Fig. 2 indicates
how the two twin T networks can be connected to give discriminator action.
A
BALANCE
\f,-
RE~quency
B
FIG. 2.
14.
At a frequency below the center frequency one of
the twin T networks will have a greater output than the other.
This will cause more current to flow through its rectifier than
flows through the other rectifier.
In this way a potential
difference is built up between point A and B in Fig. 2.
This
potential difference will go through zero and change sign as
the frequency is increased up to and past the center frequency.
The linearity of the discriminator can be improved by
the addition of a simple RC circuit.
The circuit is added to
each twin T network as shown in Fig. 4.
The relationships
R 3 and 03 must satisfy are given below:
R, >> R,
WioR- 3 C=
_ __E_
C3
E_ C_
BALANACE
-V3
ViFREQUENJCY
FIG.
4.
300v
300 ~l
-~
35K
S1G~IIAL
7.5'I(
*
bAG r
GE,,
C,
HAAA*A*A
6F0
ToR
60o
4o
"'Cl50SL
w
FIG. 3.
CI
15.
Laboratory Set-up:
In order to run tests on the R-C discriminator,
it
is
necessary to have a signal whose frequency is variable but
known at all
used.
rms.
times.
The General Radio signal generator was
This generator has a maximum output of about one volt
Since the diode detectors need a signal of a few volts
to operate satisfactorily, the output of the signal generator
was amplified.
The amplifier that was built uses a 6AG7 and
has a gain of approximately 20.
Tie twin T networks-'An
parallel have a very low impedance.
It was necessary to
insert a cathode follower between the bamplifier and the networks to prevent loading the amplifier.
A cathode follower
has a gain that is somewhat less than unity, but it will work
into a low impedance load.
The input impedance of the cathode
follower was several megohms, while the output impedance was
approximately 400 ohms.
Fig. 3 is a schematic diagram of
the entire system.
In the twin T network R, and C, must satisfy the design equations at the chosen balance frequency.
Either Rl or
Cl must be set to an arbitrary value before the other can be
determined.
Choosing a large value for R, makes C1 small
andhence, increases the value of input impedance.
If Cl be-
comes too small, the stray capacitance in a practical circuit
may cause trouble.
In the set-up used, it was found that
a value of Cl equal to 50 mmf gave good results.
.
works were tuned by varying R1
The net-
16.
Discussion of results:
The output of the twin T network as a function of
frequency was the first test made in the laboratory.
The
signal generator was connected directly to the network and
the network output was not rectified.
The input and output
voltages were obtained using vacuum tube voltmeters.
One
network was tuned. to 1.030 mcps. and the other to .885 mc.
The two independent curves obtained are plotted on curve
sheet 1 in. the appendix.
Curve sheet 2 shows the output that would theoretically
be obtained if the networks of curve sheet 1 were used for a
discriminator.
This curve was obtained by
two curves on curve sheet 1.
substracting the
The center frequency of the
predicted discriminator output figures out to be .955 mcps.
A quantity which expresses the bandwidth of the discriminator is called m.
=SALAIJCF
FIQUECY
The value
B
oF: Hi--NETWORK
WF~En
APJD
It is defined below.
.'
BALANCE
Fr-REQUENCY
of m for the curve on curve sheet 2 is 1.08.
OF LO-NETWoRK
A discriminator
designed with m = 1.08 should give a linear output tor all
values of
between .92 and 1.08.
The curve obtained is
fairly linear throughout this region.
Curve sheet 3 gives the output of the discriminator
with a center frequency of 491 kcps.
This curve was obtained
17.
using the entire circuit shown in Fig. 3.
m used was 1.06.
The value of
The output voltage was read directly on
the d-c scale of a V.T.,V.M.
The effect of the added R3 C3
network can be seen by comparing curve sheet 3 with curve
sheet 4.
They show that the added network increases the
linearity a great deal while it decreases the sensitivity.
Whether the R3 C3 network should be used depends upon whether
the increase in linearity is important enough in a given application to tolerate the decrease in sensitivity incident
to obtaining it.
The last two plots on curve sheets 5 and 6 were taken
using a value for m of 1.13 without and with the R303 network
respectively.
Increased linearity with decreased sensitivity
was again observed using the added network.
Unlike conventional inductive discriminator;, the R-C
discriminator output does not fall off outside the desired
band.of frequencies.
If the presence of other signals d.is-
turbs the operation of the discriminator, a band pass filter
may be required at the input.
Since the sensitivity is low
amplification may be necessary to operate the discriminator.
There is no practical limit on the magnitude of the input
signal.
For most applications the value of m ranges from 1.05
to 1.10.
The linearity of the discriminator is good even at
high values of m.
In comparing curve sheet 5 with curve sheet 3
it is seen that a large value of m gives a slightly greater
18.
sensitivity in the region near the balance frequency.
In
addition, a high value of m gives greater linearity over the
same band width.
It therefore appears desirable to design
the circuits for a larger value of m than will be used.
Linear Frequency Discriminator
Wireless Engineer
(281-286) October, 1946.
-
J.R.Tillman,Ph.D., A.R.C.S.
Discriminator Linearity
Electronics
-
L. B. Arguimbau
March,
1945.
Theory and Application of Parallel-T Resistance-Capacitance
*
***
-
*
Frequency-Selective Networks
Proc. I.R.E. Vol.34, No.7
(447-456) July, 1946.
L. Stanton
20.
A P P E N D I X
Ila11
-I
-"-t-
-.
+i
1t4TtI4
-1 -k+
-4-;
If
iv -
tiiji:
,!
11-:7 i
4.4-4-
,4
H
4-4.
.- 1I
-
-4L-I
.4L
:L--
-,
f41
-T-I
~~i-4i
-4- 4d
L~
T
Aldl t-H4 -1
1
TFf
t
I
- I
j4-M
W-1
-I
i
44
-11-
+
t--
rn
- - -,
i
-H , -. 1-t
-+-I4.1-ft
Tri
I
4-1-
-t r
~4~4Ifflj~4
MV
I
+
Ellhh2tiY2
444T-4r-r-14-1111 -4+4114141
"AOL&
~44F1r1~
-"-ORR
Lk
Luld
4rjT 4V
44t11i4
4t_ jj-n
f+
LIU-! 1
tiltlt~
Hj4F+-',+
t#1
1IIH
IF
+444-f-
y
-i-14 1-+-4-
TI
-f-+
I-
-111
1+4
1V4
~4
-j1f
If+t
I
-I
F Tr-T!
hIfU
..
:
t
fifi-H
-
42
It-t-ll
I~4~
4 -t-,4--;1
zL
[j
L i
-
Ei I
;-- i4Tftff
vi -- A-+-
th-ittii4
7-fl
, H#
-1411
-4,J4.-F
H-H-
M,~ft
-H
11
-i I- -H-++-
Lt t
U
H~uTh~t
will
444-
L14t44t
ii-
if:
A-
-I
L
TtiIJH- 7
~
hit
<V~44-&4-~
t 1 ~
r
4i
-~
t~iflZL1
-I
11-
iiriitr44t4Ih~kij
t
H r-14 It4ftH'1tJIIr~' HHitI+it9trIhH
VA 4AiEThTAThiitVTh~H~i~Vi4-4
if:
'1+11 I
4
CT
+
+
1
V 1 I1'4+U~
H
4~f
4
lit-F
itit
Thi~ A
it-
P4
1
4-
ItH-
4
111
11-I II tHA~
I
;
+H
il
i 'i I
J+ H+f+
ff am_
-4- -1 1.
1
IT
I-'-L 4-1+4 - +4
T H--f1 L{ U-
14
I-
L~i KLIIIKI[J~iLW
f~ThTh~LIk~Th tAl
I
TI
fit
r
4 :--E
,L
2:71
I'm
-- I
I
I , H - -11"
As I Iff-M
fit
4L
T
...Lit
1
1 11 H +-H
444-- TM++ I
4 4-1+
-4-+-4-
-I
I!4+ IIi mii aii +
f
-1j
ii l M
lI-H
t-i-
U2--
~TP~-
-f-4-
0.
-f
r
44~
tpt
~
fr
4 -~
~
~ ~
~-
L
-r
4~4V
U2
r%-j-,
4-
,,*
4
-~
-
,-
+
~-f
1-
4-
-p
4
4-1
-~
~-t-
ft
2
~
~
jf-~~
.- *~
f+~-t1 4
h
-~
p
i~
T44L
-4
A-
41~
~
rt
7---
E
--
-
4-
4-1
4
-4-
44 H44-Hi4
-4
Ar4~A~44
-~
-I-A-1
-4i-
-ii
+
-41H
IF- I
i i
I---H
~ IL IP
i~4-..-i>
~
V R P iI ii iI...........
II N
~<1~
I
-H 1 F -H--H-
#ti*41
I, i i
I'III,
44J-~vt
4