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ENGINEERING EXPERIMENT STATI
AUBURN UNIVERSITY
AUBURN, ALABAMA
A SYSTEM FOR MEASURING THE FREQUENCY
STABILITY OF AN EM TV TRANSMITTER
PREPARED BY
MICROWAVE RESEARCH LABORATORY
M. A. Honnell, Project Leader
FIRST QUARTERLY TECHNICAL REPORT
SEPTEMBER, 1970
CONTRACT NAS8-26193
GEORGE C. MARSHALL SPACE FLIGHT CENTER
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
HUNTSVILLE, ALABAMA
APPROVED BY:
(1 . t -C ajq^-4/
C . C . Carroll
Professor and Head
Electrical Engineering
SUBMITTED BY:
M. A. Honnell
Professor
Electrical Engineering
FOREWORD
This report is a technical summary reporting the progress of
studies conducted by the Microwave Research Laboratory of the
Electrical Engineering Department, Auburn University, under the
auspices of the Engineering Experiment Station toward fulfillment of
Contract NAS8-26193. The report describes a sampled system of fre-
quency measurement directed toward Task 1 dealing with systems
required to yield high frequency stability in wide-band telemetry
transmitters .
ii
ACKNOWLEDGEMENT
The authors of this report wish td express their appreciation
to Mr. G. W. Moreman, Jr., for his assistance in the laboratory work
and to Mr. C. Henderson for the preparation of the figures.
iii
A SYSTEM FOR MEASURING THE FREQUENCY
STABILITY OF AN FM TV TRANSMITTER
M. A. Honnell and J. M. Fontaine
ABSTRACT
This report is concerned with the design and construction of a
system for measuring the frequency stability of an S-band, FM TV
transmitter.
The theory of a phaselock loop relevant to the design of the
frequency measurement system is discussed with emphasis on the design
equations. The design of each unit of the physical system is then
presented along with the design considerations involved in the choice
of system components.
The tests performed on the system are discussed along with a
comparison between test results and calculated performance. Last, but
not least, the results of a satisfactory measurement of the frequency
of an S-band FM television transmitter is presented.
IV
TABLE OF CONTENTS
LIST OF FIGURES vi
I. INTRODUCTION..... 1
II. THEORY OF THE FREQUENCY MEASUREMENT SYSTEM 9
III. DESIGN OF THE SYSTEM. 26
IV. MEASURED DATA AND CONCLUSIONS. 59
REFERENCES..... 66
v
LIST OF FIGURES
1. Illustration of a composite video waveform 2
2. Spectrum resulting from frequency modulation of a TV radio-
frequency carrier with a stair step . 3
3. Block diagram of a possible carrier sampling system 6
4. Representation of the output waveform of the system shown
in Fig. 3 6
5. Block diagram of a simple phaselock loop 10
6. Schematic diagram of a common loop filter 14
7. Simplified schematic diagram of the phase detector 18
8a. Block diagram of a system for sampling at the input to the
phase detector . 23
8b. Block diagram of a system for sampling at the output of
the phase detector. 23
9. Spectrum generated by the sampling technique of Fig. 8a 24
10. Schematic diagram of the voltage controlled oscillator. 32
11. Schematic diagram of the buffer amplifier *'34
12. Schematic diagram of the X3 multiplier and 168-MHz
amplifier * ■ 35
13. Schematic diagram of the IF amplifier and the mixer 37
14. Phase detector output voltage versus phase difference
between the input signals 38
15. Schematic diagram of the M6E mixer connected as a phase
detector - 40
16. Timing diagram 44
17. Simplified schematic diagram of the level shifter 45
18. Schematic diagram of the switching circuit.... 47
vi
19. Schematic diagram of the loop filter and DC amplifier 51
20. System block diagram 55
21. Block diagram of the measurement system test set-up 60
via
I . INTRODUCTION
One of the major considerations in the design of FM transmitters
is frequency stability. The frequency stability requirement is imposed
by the Federal Communications Commission in order to utilize the
frequency spectrum more efficiently. In the case of transmitters
built for space and military applications, the requirements for
frequency stability are made even more stringent by the specifications
of the Inter-Range Instrumentation Group (IRIG) . Naturally, it is
necessary to make measurements to insure that the transmitters meet
the specifications. Often, making these measurements can be a very
complex problem.
There are frequency counters available which can be used to measure
the frequency of a transmitter which is not being modulated or of one
which is being modulated by some type of symmetrical waveform, such as
a sinusoidal wave. All of these devices measure frequency by counting
cycles and averaging the count over some time interval, i.e., they mea-
sure the average frequency. Unfortunately, these devices cannot be used
to measure the frequency of a transmitter which is frequency modulated
by a composite video signal (television picture). The reason for this
will be made clearer by reference to Fig. 1 and Fig. 2. Fig. 1 shows
a general video waveform whose voltage varies from approximately -0.4
volts at the sync tip to about +1.0 volt during the brightest spots
in the picture information. The result of modulating a radio-frequency
1
3
Fig. 2. Frequency spectrum resulting from frequency modulation of
a TV radio-frequency carrier with a stair step.
4
carrier with this video signal is that the carrier is deviated farther
in the high-frequency direction than in the low-frequency direction.
The average frequency of the transmitter is therefore higher than the
unmodulated carrier frequency so ■ that the frequency measured by the
counter is ambiguous. This would not be too much of a problem if the
video signal were constant so that compensation could be made, but this
is not the case. The video signal is dependent on the picture information
and, changes from one scan line to the next. Fig. 2 is a representation
of the frequency spectrum of an FM TV signal which is modulated by a
stair-step composite video signal. The frequency f c in Fig. 2 is the
reference frequency when the video signal is zero volts, corresponding
to the back porch. It can be seen that the average frequency is higher
than the reference, or back porch frequency. In order to make a measure-
ment of the transmitter's frequency stability some method of sampling
the frequency during the back-porch interval must be developed. The
purpose of this paper is to present a method of doing this for a specific
case.
The measuring system described was developed to measure the
frequency of an S~band FM television transmitter which was designed for
George C. Marshall Space Flight Center by Auburn University. The
frequency of this transmitter is controlled by a Sampled Automatic
Frequency Control system (SAFC) [1]. The basic operation of the control
system is discussed below.
The output of the transmitter's voltage controlled oscillator is
sampled once during each horizontal interval of the picture. The
frequency of the VCO is compared to the frequency of a crystal
5
reference oscillator and a voltage, which is proportional to the
frequency difference between the oscillators, is derived. This voltage
is applied to the frequency control element of the VCO (a varactor .
diode) , which shifts the VCO frequency in a direction Ttfhich tends to
reduce the frequency difference to zero.
The sampling is done during the back-porch interval of the compo-
site video signal. The back-porch interval is shown in Fig. 1 as .
There is a great deal of circuitry involved in the sampling operation.
The sync pulse is stripped off of the video signal and is used to trigger
a multivibrator which develop a sampling pulse occurring during the back
porch interval. This pulse drives an RF switch, which gates the VCO
output into the discriminator. A second pulse, delayed 30 microseconds,
samples the reference frequency which is also gated into the discriminator.
A voltage derived from the discriminator output signal is used to bias a
varactor in a direction to correct the VCO frequency.
As was mentioned earlier, it is necessary to sample the carrier
during the back— porch interval if a meaningful frequency measurement is
to be made. One possible approach is to use an RF switch which is on
only during the desired interval of time, i.e., during the back— porch
interval of the video waveform. The block diagram of a circuit for
performing this task is shox<rn in Fig. 3. A time domain representation
of the signal at the output of the switch is shown in Fig. 4. The
circuit operation is discussed below.
The modulating signal is applied to the input of the sync stripper,
where the syne pulse is stripped off and passed to the input of the
7
monostable multivibrator. The RC time constants of the multivibrator
are such that it produces an output only during the back-porch interval.
The output of the multivibrator is applied to the control input of a
voltage-controlled RF switch allowing the RF signal from the transmitter
to pass through it. The output of the switch is, therefore, a burst
of RF energy which occurs during the back-porch interval of the video
waveform and is at the frequency of the VCO corresponding to zero
video volts.
Since the duration of the pulse burst is not precisely constant,
the output of the switch is not suitable for use with a frequency
counter. In addition, the digital counter available would not respond
to the RF signal, but responded to the pulse repetition rate. The
counter counted the rate at which the bursts of energy occur, rather
than counting the number of cycles of RF within each burst of energy.
These results were determined experimentally and the exact nature of
the problem is not fully understood. It is believed that the burst
of energy triggers the counter's flip-flop, causing it to count the
repetition rate of the pulse burst. Although this approach seemed to
offer a simple solution to the problem of determining the frequency
of an FM TV transmitter, the problem with the counter meant that
another solution had to be found.
The second approach to the problem proved to be feasible and is
discussed in detail in the remainder of this paper. This second
approach uses a phaselock loop to determine the frequency of the
transmitter. The signal from the transmitter is first down converted
8
and then sampled during the back-porch interval. Then a phaselock
loop is used to phaselock a voltage controlled oscillator to the
down-converted sampled signal from the transmitter. The frequency of
the voltage-controlled oscillator is then counted and used to determine
the frequency of the transmitter. A block diagram of the system is
shown on page 55.
II. THEORY OF THE FREQUENCY MEASUREMENT SYSTEM
Phaselock techniques are often used in low-noise telemetry receivers
in order to obtain a narrow noise bandwidth. Another important applica-
tion of phaselock loops is the control of the frequency of an oscillator.
The frequency measurement system to be discussed makes use of this
second application. In the following paragraphs the theory of phaselock
techniques is examined with special attention given to the frequency
control aspects. Although the following analysis is for the phaselock
characteristics of two continuous wave signals, it presents an insight
into the locking characteristics of a VCO with an FM TV signal.
A block diagram of a simple phaselock loop is shown in Fig. 5.
The loop consists of a phase detector, a voltage controlled oscillator
(VCO) , and a loop filter'. The phase detector compares the input signal
V g having a frequency f and the VCO output signal V^ having a frequency
f v and produces an output voltage which is proportional to the phase
difference between the two signals. The output signal is conditioned
by the loop filter and is then applied to the frequency control element
of the VCO. The result is a change in the phase of the VCO’s output
signal in a direction which tends to reduce to zero the phase difference
between V_ and V . In order to clarify the operation of the loop a
mathematical analysis is given below.
When f g is equal to f , the phase detector output can be represented
9
11
by
v d - WV < 2 -d
where is the phase detector gain constant and 0 g and 0 V are the
instantaneous phase angles of the input signal and the VCO output signal,
respectively. has units of volts per radian and 9 s and 0^ have units
of radians.
The filter has a transfer function given hy
V (s)
F(s) - . (2-2)
V d Cs)
The output of the filter is then
V f (s) = V d (s)F(s) ( 2 - 3 )
or
V f (s) = F(s)K d [0 g (s)-0 v (s)], (2-4)
where 0 s (s), 0 v (s), V^(s), and V^(s) are the Laplace transforms of the
appropriate terms .
The deviation of the VCO from its original frequency f is
Ato = K^V^t) radians/sec. (2-5)
where K v is the VCO gain constant. has dimensions of radians per
second-volt. Remembering that frequency is the derivative of phase,
the deviation of the frequency of the VCO from f may be defined in
c
terms of its phase angle deviation, 0^ (t) , from o^t as
12
d9 v (t)
Aw =
dt
(2-6)
where
d0 (t)
— =K v V f (t). (2-7)
dt
If both sides of the Equation (2-7) are integrated with respect to t,
then
e v (t) = / K v V f (t)dt
or
9 v (t) = K v /
(2-8)
This shows that the phase angle of the VCO output signal is proportional
to the integral of the output of the loop filter. Equation (2-8) may
also be expressed as a Laplace transform which will be more convenient
to use in later work. When this is done equation (2-8) becomes
V f(s)
e v (s) = . (2-9)
s
In order to determine the transfer function of the loop it is
necessary to define 0 (s) in terms of 0 (s). Equation (2-9) is used as
v s
a starting point for this operation.
0 (s)
v
K,V f (s)
>
s
(2-9)
13
but
V f (s) = F(s)V d (s); (2-3)
therefore
K v F(s)V (s)
0 v (s) = . (2-10)
s
V d (s) is given by Equation (2-4) as
v d (s) - K d [e s (s)-e v (s)].
(2-4)
When Equation (2-4) is substituted into Equation (2-10) the following
equation is obtained
K K F(s)[6 (s)-e (s)3
e v (s) = 2
s
( 2 - 11 )
When Equation (2-11) is solved for G (s) , the solution is
K K F(s)9 (s)
0 ( S ) = -ZJ
s + K^Ffe)
The transfer function of the loop is given by
( 2 - 12 )
H(s)
e v (s)
K K F (s)
v d
s + K^FU)
(2-13)
In order to completely define the loop transfer function it is
necessary to determine the transfer function of the loop filter. Fig. 6
15
is a schematic diagram of a common phaselock loop filter. The filter
may be recognized as the lag compensator ■ found in control systems. The
transfer function of this filter is given by Gardner 12] as
scr 2 + 1
F(s) = . (2-14)
SC(R + R ) + 1
-If R^C is renamed and R 2 C is renamed t 2 then Equation (.2-14) becomes
ST, + 1
F(s) = — f . (2-15)
s ( t 1+ t 2 ) + 1
Equation (2-15) can now be substituted into Equation (2-13) to
obtain the transfer function of a phaselock loop which uses the
filter shown in Fig. 6.
st 2 +1
K K
V s(t^+t 2 )+1
H(s) = — — (2-16)
ST„+1
s + K K ,
v d " :
s ( t i + t 2 )+1
s 2 (t.+t j+s+K K (ST.+1)
12 v d 2
K v K d^ ST 2 +1 ^ ^ ^ T l +T 2^
s 2 + s/ (i 1 +T 2) +K v K d ST 2^ T l +T 2^ + K v K d^ ^ t i +t 2^
16
. K K (sx +1)/( Ti +t )
H(s) = - =—=■
s 2 + s(l+K K t ) + K K / (t 1 +t )
T d 2 12 12
(2-17)
The transfer function can also be found in terms of the damping factor
and the natural frequency of the loop. If the natural frequency w is
n
defined as
0)
n
Vd
T i + V
vl/2
and the damping factor t, is defined as
5 - 1/2
+
(2-18)
(2-19)
then, according to Gardner, H(s) becomes
H(s)
sco n (2? - m n /K v K d ) + ^
9 2
s z, +2t(o s+o)
n n
( 2 - 20 )
The transfer function is an important quantity in any type of
control system, but there are other quantities involved in a phase-
lock loop which give a better indication of the loop’s ability to
control the frequency of an oscillator. Some of these quantities are
the hold-in range, the acquisition range, and the pull-out frequency.
These quantities will be discussed in detail, but first it is
desirable to briefly describe the operation of the phase detector.
17
Dishington [3] did much of the preliminary analytical work on four-
diode phase detectors of the type shown schematically in Fig. 7. This
phase detector is also known as a ring modulator or a doubly balanced
mixer. In the normal locked mode of operation of a phaselock loop the
frequencies of the input signal V and the VCO signal V are equal and
differ in phase by the angle <f>. The output of the phase detector is
then given by
V d = K df sin ^ 2w s t+ 9) + sin<j>]. (2-21)
The first term in the brackets is a high-frequency term which is
removed by an RF filter at the output of the detector. The phase
detector output is then given by
V d = K d sin(f>. (2-22)
If the phase difference between the two signals is small, sin4>
may be replaced by <}> and Equation (2-22) becomes
V d = K d <f>. (2-23)
With the information available it is now possible to determine the
hold- in range. The hold- in range is the frequency range over which the
VCO will track the input signal. The hold-in range is the most
important characteristic of the loop when frequency control is the
18
Fig. 7. Simplified schematic diagram of the phase detector.
19
'prime objective.
The frequency deviation of the VCO, according to Equation (2-5),
can be written as
Aw= K v V f (t) (2-24)
where V^(t) is the output of the filter between the phase detector and
the VCO. When the system is in lock the output of the phase detector,
input to the filter, is a constant and the steady state output of the
filter is
V f (t) = K d F(0H (2-25)
where $= 8^-0^ is a constant. The frequency deviation for this case
can then be written as
Aw = E(0) cj> (2-26)
or if is defined as
K 1 “ K d*V F(0) (2-27)
then
Aw =
(2-28)
20 .
Equation (2-28) holds only when the loop is locked and during this time
sin 4i must be between ±1. .The hold-in range is
Aw h =± K x , (2-29)
The hold-in range can be seen to be a function of the DC gain of the
loop .
Another quantity of interest is the pull-out frequency. This
quantity determines the response of the loop to a frequency step. The
pull-out frequency has been experimentally determined by Viterbi [5]
and an equation has been written which gives the pull-out frequency as
Am = 1.8w (C+I) . (2-30)
po n
It is also useful to determine the rate at which the input
frequency can be changed without causing the loop to lose lock. This
has also been determined by Viterbi and is given by the following
equation.
dAw _ 2
dF" “ W n C2-31)
Two other quantities that are of interest are the lock-in frequency
Aw and the pull-in frequency Aw . The equation for the lock-in
L p
frequency is due to Richman [6] and is
21
Ao) l = 2^. (2-32)
This equation is a measure of the frequency range within which the loop
locks immediately. The pull-in equation is also due to Richman and it
is a measure of the frequency range within which the loop will
eventually lock. The equation is given by Gardner as
2 1/2
Aw = -fl (2 gw K -to ) . (2-qq)
p n 1 n
When K-^ is large. Equation (2-33) reduces to
Aw = 2 /^TkT . (2-34)
p n 1
The basic theory upon which the frequency measurement system
depends has nox<r been presented. The application of this theory to the
measurement system will be examined in the remainder of this section.
It has been shown that the output of the phase detector is
dependent only on the phase difference between the two input signals
when the loop is locked. When the frequency of one of the inputs
changes there is a corresponding change in the phase angle. This
causes a correction in the frequency of the VCO so that the two
frequencies remain equal as long as they are within the hold— in range
of the loop. Therefore, it becomes possible to determine the frequency
of the input signal by counting the frequency of the VCO. This is the
basis of the frequency measurement system.
22
If the transfer function of the loop filter is properly adjusted,
the system can be made to act as a sample and hold circuit. When this
is done, the frequency of the VCO will remain at its value at the sample
time until the next sample is taken. If the sampling is done at the
proper time, the frequency of the input signal can be measured by merely
counting the frequency of the VCO.
There are two possible methods of accomplishing the sampling.
Fig. 8a is a block diagram of a system which switches the transmitter
output into the phase detector only during the back-porch interval.
Fig. 8b is a block diagram of a system which samples the output of the
phase detector during the back-^porch interval. Either of the systems
should perform the required operation, but the system shown in Fig. 8b
has been chosen for the following reason. In Fig. 8a the use of the
RF switch causes the input to the phase detector to be a pulse train
such as that shown in Fig. 4. The frequency spectrum of this wave-
form is shown in Fig. 9. It can be seen that there are many discrete
frequencies in this spectrum and that they appear at intervals which
are multiples of the switching rate f^. This means that there are
frequencies located at (f g ±nf^) Hz. The system cannot distinguish
between these frequencies and it is, therefore, possible for it to
lock up on a sideband instead of the carrier. If this happened, there
would be an error in the frequency measurement. This error would be
a multiple of 15,750 Hz, the horizontal rate. In view of the accuracy
requirements on the transmitter, this could be a significant error.
SWITCH
PHASE
DETECTOR
LOOP
15.75 KC
SWITCHING
LOGIC
V C 0
Fig. 8a. Block diagram of a system for sampling at the input to the
phase detector.
PHASE
DETECTOR
SWITCH
LOOP
FILTER
15.75 KC
SWITCHING
LOGIC
V C 0
Fig. 8b. Block diagram of a system for sampling at the output of
the phase detector.
to
/TThs/nx
25
In the system of Fig. 8b, the transmitter’s output signal is
applied to the input of the phase detector during the entire
horizontal interval. Thus no new RF spectral components are generated
by the sampling technique. Since the transmitter’s VCO is being held
close to the frequency of the crystal reference oscillator during the
sample time, there is no deviation of the transmitter's VCO and
therefore, there are no sidebands present to cause an erroneous lock
condition. The switch used in this system can be an inexpensive
solid-state device. These devices are reliable and readily available.
The output from the switch will, of course, have a sinx/x spectrum,
but this will be centered around zero frequency rather than around f .
s
The loop filter will not allow any of the spectral components other
than the DC value to pass. This means that the sampling can cause
no problems such as those mentioned earlier. The system can perform
all the tasks necessary for the loop to operate, in conjunction with
a standard frequency counter, as a complete frequency measurement
system. The design details of the system are discussed in the next
chapter.
III. DESIGN OF THE SYSTEM
In the design of the measurement system, the most important things
to be considered are the frequency at which the loop is to operate and
the variation that can be expected in the frequency of the input signal.
The first is a function of the transmitter’s center frequency, but it
is limited by practical considerations such as limitations on the
operating frequency of the phase detector and the difficulties involved
in obtaining frequency stability with a high-frequency VCO. The
frequency variation of the input signal from the transmitter determines
the hold-in range necessary for the loop to operate properly. Some
other considerations are the type of switching logic to be used, the
type of device to be used for the switch, whether to use an active or
a passive loop filter, the need for an amplifier in the loop , and the
type of phase detector to be used.
A. Operating Frequency of the Loop
A portion of the output of the first RF amplifier of the transmitter
is applied to the SAFC system through a microdot cable. The signal at
this point is approximately 225 MHz, which is much more convenient to
measure than the S-band output. A coaxial tee can be inserted into the
line so that part of the signal can be used as the input to the fre-
quency measurement system. This doesn’t require any permanent modifi-
cation of the transmitter and the tee is easily removed when testing
of the transmitter is completed.
26
27
Most phaselock loops are designed to operate in the 1-MHz to 25-MHz
frequency range, but it is possible to design loops that operate up to
60 or 70 MHz. This means that the frequency of the 225-MHz signal from
the transmitter is too high to be used directly as the input to the
phase detector. There are good mixers commercially available in the
200-MHz frequency range, so that a heterodyne technique can be used to
down-convert the transmitter signal to a frequency that can be effect-
ively used in the phaselock loop. The problem of local oscillator
frequency stability must still be solved if unnecessary measurement
errors are to be avoided.
When the loop is locked, the frequency of the input signal and that
of the VCO are equal. If some multiple of the VCO frequency is used as
the LO for the mixer, the problem of local oscillator drift is avoided.
The frequency of the VCO is given by
f
v
f *~Nf v ,
(3-1)
where N is the multiplication factor.
The frequency of the input signal is given by
f s = (N+l)f v . (3-2)
The selection of the multiplication factor is fairly arbitrary but it
should be low number for two reasons. The first reason is that it
i.s difficult to obtain a high order frequency multiplication in a one
stage multiplier and it is undesirable to have more stages than are
necessary in any type of electronic system. The second reason Is that
the number of undesired signals increases as the multiplication factor
28
is increased. These signals are difficult to get rid of without the
use of 'complicated filtering. If they are not filtered out, they
combine with the input signal in the mixer to produce signals that
could cause problems in the phase detector. For these reasons , N was
chosen to be three. It is now possible to determine the frequency of
the VCO by use of Equation (3~2) . The frequency of the transmitter
during .the back porch is actually 224.48 MHz. The required "VCO
frequency is
f = (N+l) f
s v
(3-2)
f
v
224.48
4
MHz
f = 56.12 MHz.
v
This is a good operating point for the phase detector and it is also
a frequency at ttfhich the design of the VCO is not difficult.
Once the operating frequency of the loop has been determined, it
is -convenient to determine the tracking range required and the overall
loop bandwidth. The tracking range of the measurement system is a
function of the frequency stability of the transmitter. The transmitter
specifications require that its frequency be i^ithin ±0.01% of the
design frequency under all specified environmental conditions . Since
the measurement system is required to track any frequency drift that
occurs during the back-porch interval, it is necessary to determine
the amount of drift, Af, that can be expected. Assuming the value of
29
+ 0.01 7 0> Af is calculated below.
-4
Af = ±(1.0X10 )f,
bp
= ±(1.0X10~ 4 ) (2.2448X10 8 )
= ±2.2448X10 4
Af = ±22.448 kHz (3-3)
The hold-in range required by this frequency variation can now be found.
Aw = ±2rrAf
H
Aw r = ±2r (2. 2448X10 4 )
Aco^ = ±1.41X10^ rad/sec. (3-4)
From Equation (2-29), the loop gain constant required for a given
hold-in range is
4 "h " ±K 1 ;
therefore
(2-29)
= 1.41X10^ rad/sec.
This is the value of -gain at which the loop would lose lock if the
frequencies of the input signal and the VC0 were separated by ±22.448
kHz. This is the absolute limit of proper operation of the loop and
if the drift should be more than the specified amount it would not be
30
possible to obtain data on the excess drift. For this reason, the loop
is designed to track a frequency variation of ±200 kHz. Equation (2-28)
gives the deviation of the VCO as a function of and <J>, the phase
difference between the input signals to the phase detector. Because $
is small when the signals are in phaselock, sin<{> has been replaced by (j>.
For convenience, equation (2-28) is presented here as equation (3-5).
Ato = K^. (3-5)
Through use of Equation - (3— 5).,. it is possible to obtain the value of., gain
necessary for the loop to track the input signal with some given amount
of phase error. If the .phase error is set at 0.1 rad. then the gain
required to track the input signal over a ±200 kHz range can be found
from Equation (3-5) .
• = Aw_
1 $
= 2n (2 . OXit) 5 )
0.1
K = 1.256X10 7
(3-6)
The values of the phase detector and VCO gain constants must be
determined before it can be decided if the above value of is realis-
In most phaselock loop applications the bandwidth of the loop is
tic.
31
made very narrow in order to reduce the noise power at the input to
the VCO, but in this measurement ^-system noise is not a consideration.
This means that the choice of loop bandwidth can be made on the basis
of such things as spectral component removal and acquisition time.
As was mentioned in Chapter II, the sampling produces- a sinx/x
frequency spectrum in which spectral lines appear at multiples of the
sampling rate, in addition to the desired low-frequency component
produced by the phase detector. If these components are allowed to
pass through the filter to the VCO input, they can cause the measured
frequency to be in error. Since the lowest frequency produced by
the sampling is 15,750 Hz, the loop bandwidth should be somewhat less
than 15,750 Hz. The bandwidth of the loop is selected to be 5.0 kHz.
Before any other calculations involving the entire loop are made, it
is necessary to examine some of the loop components .
B. Voltage Controlled Oscillator
There are a number of configurations that can be used for the VCO
and there is really not much reason, other than designer preference,
to select one over the others. The configuration chosen for the
measurement system VCO is a modification of a Colpitts oscillator.
The VCO is shown in schematic diagram form in Fig. 10. Once an operating
point is selected from the transistor’s characteristics, all that is
required is to design the tuned circuit. The output poorer of the VCO
is set at a fairly low level, about 5 mw, to improve the frequency
stability of the oscillator.
The value of can be obtained by measuring the change in
frequency of the VCO when the bias on the varactor is changed by one
ERROR
SIGNAL
BIAS
u>
N>
Fig. 10. Schematic diagram of the voltage controlled oscillator.
33
volt. The value of for the VCO used in the frequency measurement
system is 125.5 kHz/ volt.
C, Buffer Amplifier
The VCO is followed by a buffer amplifier in order to prevent
loading effects from causing unwanted frequency changes. The buffer
amplifier is a-class-A amplifier' with a fairly low power gain.
The gain of the buffer is approximately 7 dB. A portion of the
output of the buffer is applied to the phase detector and to a frequency
counter, and the remainder of the buffer's output is applied to the
input of the X3 frequency multiplier, fig. n is a schematic diagram
of the buffer amplifier.
D. X3 Frequency Multiplier
The X3 frequency multiplier is a class C amplifier whose output
circuit is tuned to the third harmonic of the input signal. The output
frequency is, therefore, 168.36 MHz. In order to maintain a high
loaded Q in the output circuit of the multiplier, the inductance used
in the tuned circuit should be kept as small as possible. The
inductor used was approximately 20 nH.
As was mentioned earlier, it is desirable to remove all unwanted
signals at the input to the mixer. To help remove these signals, the
multiplier is followed by an amplifier which has a double-tuned output
circuit. The amplifier provides some power gain at the desired
frequency and it also provides attenuation at the frequencies of the
unwanted signals. A schematic diagram of the X3 frequency multiplier
and the amplifier is shown in Fig. 12..
35
15 V
36
E. Mixer
The mixer used in the measurement system is a Relcom M6E mixer.
This mixer is a diode-bridge balanced mixer, which, has excellent conver-
sion characteristics. It provides a conversion efficiency of approxi-
mately -6.5' dB at the frequencies of interest and it presents an attrac-
tive alternative to the design of the mixer for the system. A 3 dB
resistive attenuator is provided at the LO input to the mixer, to assure
that the input power is at an acceptable level.
F. IF Amplifier
An IF amplifier -is provided at the output of the mixer to provide
some gain at the intermediate frequency, and to provide rejection of the
undesired mixer products. The amplifier is a class A amplifier, with
both the input and output tuned to the 56.12 MHz intermediate frequency.
A schematic diagram of the IF amplifier and the mixer is shown in Fig. 13.
G. Phase Detector
It is difficult to design a good phase detector at frequencies much
above 25 MHz and for this reason phaselock loops are seldom designed
to operate above this frequency. The main problems are the sensitivity
of the diodes used and the design of the transformer needed for
coupling the input signals into the actual detector circuit. During
the preliminary research of the measurement system, it was found that
the manufacturers of the M6E Relcom mixer discussed earlier, recommended
the unit as a possible phase detector. A curve, found on the data
sheet for the mixers, which shows the output as a function of phase
difference between the input signals is shown in Fig. 14. This is a
age
39
general curve, which will vary somewhat at different input frequencies
and power levels, but it provides an insight into the mixer's
performance when used as a phase detector. Fig. 15 is a schematic
diagram of the m6e mixer connected for use as a phase detector. It
can be seen that the mixer is essentially the same as the ring modulator
discussed in Chapter II. The output of the phase detector is zero
when the phase difference between the input signals is 90 degrees . This
is accounted for in the equations by considering one of the inputs to
be a sine wave and the other to be a cosine wave. The phase detector
output can be seen to be more of a sinusoidal function when the power
levels of the input signals are high. This means that if linear
operation is desired the input levels should be kept fairly low,
approximately 1 mw. In the case of the frequency measurement system,
this is not a strict requirement and there was no effort made to
restrict the inputs to this level.
The value of can be estimated by considering the 0 dBm curve of
Fig. 14 to be a linear function of <f).
K d - (V volts/1.571 rad.)
Kj = 0.333/1. 571 volts/rad.
= .212 volts/rad. (3-7)
II . Sampling Circuit
The sampling circuit can be broken down into two parts, the
sampling switch and the control circuitry. The design of the control
40
41
circuitry is straight-forward, but the choice of the device to be used
as the switch is not so simple. There are several devices that might be
used, such as relays or various solid-state devices. Most of the devices
have inherent characteristics that make them unsuitable for use in the
measurement system.
The device finally selected for the switch is the junction field
effect transistor. The characteristics of the EET, when used as a
switch, have been described by several authors. Wollesen [7],
Neal 18] ,and Bergersen [9] are three who describe useful circuits as
well as theory. The operation of the FET is such that a signal applied
to the source will appear at the drain when the device is turned on by
a control voltage applied to the gate. The switching time of the
device is very fast, a few nanoseconds, and the only loss is a small
ohmic drop. The loss is a function of the drain-to— source resistance
which can be made small by proper choice of the particular FET to be
used. The loss can be further reduced by using a fairly high value of
load resistance. The< device selected for use in the measurement system
is a VCR4N, n-channel FET, manufactured by Siliconix, Inc. The drain-
to-source resistance of this device is approximately 200 ohms. Since
the load resistance is approximately 50,000 ohms the loss through the
switch is insignificant. In addition to its low on resistance, the FET
has an extremely high value of off resistance so that the output of the
phase detector during the off-time of the switch does not leak through
the switch. If leakage occurred, it could introduce errors into the
system.
42
In order to insure that the sampling takes place during the back—
porch interval, it is necessary to maintain precise timing between the
signal In the measurement system and the TV signal. It is, therefore,
necessary to find some readily identifiable characteristic of the trans-
mitter’s input or output that can be used as a time reference. Tire
video signal that modulates the transmitter can easily be used as the
time reference since it is derived from a test signal generator
which is not limited in available .output power. The back porch would
seem to be the most obvious choice for use as the time reference, but
it is not convenient to use because it represents zero signal level.
The only point in the video signal that is convenient to use as a time
reference is the sync pulse, but before it can be used it must be
separated from the remainder of the video waveform by the sync stripper.
The sync stripper used in the measurement system is identical to
the circuit used to perform the same function in the TV transmitter.
The active element of the sync stripper is a SN52710 differential-
voltage comparator. The input circuit is arranged so that only the
negative-going portion of the video waveform is applied to the sync
stripper. The only negative- going portion of a standard video signal
is the sync pulse and thus the sync pulse is separated from the
remainder of the video waveform. The output of the sync stripper is
a positivergoing pulse which occurs during the sync pulse of the
video signal.
A monostable multivibrator is used to obtain a pulse that occurs
during the back porch of the video signal and that is the required
length. The monostable multivibrator is an SN5380 integrated circuit
43
which triggers when the input changes from a positive voltage to a
zero voltage. Through the adjustment of two RC time constants, it
is possible to vary the time delay between input and output of the
multivibrator and to vary the length of the output pulse. In the
case of the measurement system, it is required that the output of the
multivibrator occurs during the back-porch interval and, therefore,
the delay can be set at zero. In order to assure that the sampling
circuit turns off before the end of the back porch, the multivibrator
output pulse is made somewhat shorter than the length of the back porch.
The length of the back porch is approximately 3.8 ysec. and the length
of the pulse is set at 3.5 ysec. A timing diagram which shows the
relationship between the sync pulse and the output of the multivibrator
is shown in Fig. 16. As can be seen in Fig. 16, the multivibrator’s
output is 4.0 v except during the pulse interval, when it is zero.
This is not compatible with the requirements of the FET switch. An
n-channel FET requires a negative voltage on the gate to turn it off,
and a zero or slightly positive voltage to turn it on. This means
that some kind of level shifting circuit is required due to the opera-
tional characteristics of the integrated circuits used for the control
circuitry. This problem is discussed in detail below along with a
basic circuit arrangement.
The circuit shown in Fig. 17 can be used to shift the output of
the multivibrator to the levels required by the FET. The operation
of the circuit can be explained as follows: as long as the input to
the circuit is positive the transistor is turned on and the output is
44
Fig. 16. Timing diagram.
46
at -V volts. When the input becomes zero the transistor is turned off
and the output is at 4y volts. The output of the circuit is shown
in the timing diagram of Fig. 16.
A schematic diagram of the complete sampling circuit is shown
in Fig. 18. The diodes between the level shifter and the FET are
used to prevent the positive portion of the control signal from appear-
ing as a signal at the drain of the FET. It was found experimentally
that two diodes in series are required to perform this task properly.
If only one diode was used, a slight positive voltage was found to
appear at the drain when the input signal at the source was zero. The
diodes are selected so that their capacitance characteristics match
those of the FET. This helps to improve the switching characteristics
of the FET. A more complete discussion of this phenomenon can be
found in the literature [7].
I. Loop Filter
The loop filter is the component which is primarily responsible
for determining the overall operating characteristics of the loop. It
determines such things as the loop bandwidth, response time, tracking
range, pull-in frequency, and pull-out frequency. If properly designed,
along with an amplifier, it can correct for certain deficiencies in
other components of the loop. These include such things as low values
of and K. . In the design of the loop filter for the measurement
system it is necessary to select a filter that can be used in a sample
and hold circuit. The lag filter discussed in Chapter II is essentially
an integrator and thus it can be used in a sample and hold circuit. The
loop bandwidth has already been chosen to be 5.0 kHz and it is now
48
possible to design the filter.
Gardner gives an equation for loop bandwidth in terms .of the
natural frequency and damping factor of the loop.
0 ) 1
B - ~ tC + — 3 (3-8)
L 2 4r
In Equation (3-8) there are two unknowns, w and and it is necessary
to select a value of one before the equation can be solved for the
other. In many control and phaselock system problems the value of
£ is chosen to be 0.707. Gardner shows curves which indicate that
this will be a reasonable value for the loop damping factor.
2
w =
n .707 + 1/(4) (.707)
w
n
A
= lXio 4
1.061
3
oj = 9.43X10 rad/sec.
n
The two time constant, and of the filter can now be found,
is given by
(3-9)
49
and T 2 is g lven by
T
2
(3-10)
Then,
n
1.25 6X10 7
t 2
(9.43X10 J )
1.256X10 7
8. 9X10 7
t, = .141 sec.
1
and
2 (.707)
1-
1 9.43X10
_. 1.414
9.43X10 3
T
2
1.5X10
sec.
50
Since x = R-.C and x„ = R C it is necessary to select a value for one
of the variables so that the other two can he calculated. Selecting C
to be 3.3 yF,
R 1 = l^lXlO" 1
3.3X10 -6
= 4.27X10 4 ohms,
and
T2 — R£C
R 2 = 1.5X10" 4
3 . 3X10" 6
R = 4 . 55X10 ohms .
2
A value of 43 kfi is used for R^ and value of 45f2 is used for R 2 -
The loop filter is shown schematically in Fig. 19.
J. Loop Gain Constant
It is now possible to calculate the value of using the loop
parameters that have been measured or calculated. is given by
Equation (2-27) as
52
\ = w (o) -
F(0) is the steady-state DC gain of the loop filter and for the type
of filter used, the steady-state DC gain is equal to one. has
been measured to be 7,881X10“* rad/sec-volt and K, was found to be 0.212
d
volt/rad. is then,
Kj_ = (7.881X10 5 ) (2.12X10~ 1 ) (1)
K = 1.671X10 5 1/sec.
The desired value of was found to be 1.256X10^ 1/sec. It is obvious
that some adjustment must be made if the measurement system is to
perform satisfactorily. Is it possible to make the necessary adjustment
without redesign of the phase detector and the VCO? Fortunately, the
adjustment is quite easy to make.
The deviation of a VCO is increased if there is frequency multi-
plication at the output of the VCO. The new deviation is NAF where
N is the multiplication factor and Af is the original frequency
deviation. The output frequency of the VCO is effectively multiplied
by a factor of 4 in the measurement system as can be seen from
examination of Equation (3-2). With this multiplication, the loop
gain constant can now be represented as
K x = NKyKjF (0)
(4) (1.671X10 5 )
53
— 6.684X10 1/sec. (3
This value is still too low for the measurement system to operate as
desired, but there is another adjustment that can he made.
The phase detector gain constant is effectively increased by
using a DC amplifier at the output of the phase detector, thus
increasing by the gain factor, A, of the amplifier. If the
amplifier is placed after the loop filter, it can be used to
compensate for any loss that occurs in the filter. If a high gain
operational amplifier is used, it will tend to reduce errors that
can be caused by loading effects of the filter since the operational
amplifier has an extremely high input impedance (several megohms) .
The required gain of the loop DC amplifier can be calculated from the
following equation.
\ = ANKK d F(0) (3-12)
A = ... Kl
NiyCjFCO)
1.25 6X10 7
A = -
(.4) (7.881X10 5 ) (2.12X1CJ
A = 18.8 (3-13)
A schematic diagram of the amplifier used in the measurement system
is shown in Fig. 19. The active device in the amplifier is an LM301
54
integrated circuit operational amplifier. The design of the circuit
is straight-f orward once the active device is selected. Care must be
taken to assure that the input voltage is not sufficient to saturate
the amplifier since this can cause lock-up problems and measurement
errors . The gain of the amplifier is given by
A =
(3-14)
R^ is selected to be 6.2 kfl and A has been calculated as 18.8, then
R* = AR,
r l
= (18.8) (6.2X10°)
Rf = 1.167X10"
R f = 116.7 kfl .
A value of 120 kfJ is used for R^.
(3-15)
K. The Complete System
The design of the frequency measurement system is now complete. A
block diagram which shows the interconnection of all the system
components is shown in Rig. 20. When the system is used to measure
the frequency of a television transmitter it may be necessary, at
times, to manually lock the loop by adjusting the bias on the VCO's
varactor diode. Provision has been made for this by using a
56
potentiometer in the varactor bias circuit. Although it is possible to
design a circuit to indicate a locked condition, this was not done. An
oscilloscope can be used to determine if lock has occurred, if it is
connected to the phase detector output. The loop is locked if the
output is a DC signal. If the output is an AC signal the varactor bias
should be adjusted in a direction that reduces the frequency of the
phase detector’s output signal. This will eventually result in a
locked condition.
L. Calculated System Parameters
At this time some of the system parameters mentioned earlier will
be calculated so that they may be compared to the measured values
presented in the next chapter. The hold-in range is given by Equation
(2-29) as
Aw = ±K . (2-29)
n ±
Substituting in the calculated value of gives
Aw = 1.256X10^ rad/sec.
H
The maximum rate of change of input frequency that the system can
follow is given by Equation (2-31) as
57
dAw _ 2
— - — = 0 )
dt rt
(2-31)
= (9.43X10 )
= 8. 9X10 ' rad 2 /sec 2
dt
The pull-out frequency of the loop is a measure of the loop’s
response to a frequency step. Below the pull-out frequency the loop
remains in lock but above the pull-out frequency the loop will lose
lock, at least temporarily. The pull-out frequency is given by Equat-
ion (2-30) as
Aw =1.8w (c+1) (2-30)
po n
= (1.8) (9.43X10 3 ) (1.707)
4
Aw = 2.8X10 rad /sec.
po
The lock-in frequency is a measure of the maximum difference
permissible between the input signals if the loop is to lock immediately.
By Equation (2- 32) the lock-in frequency is ,
A® 2e» n ; (2-32)
therefore.
A« L = 2(.707) (9.43X10 3 )
Am-^ = 1.33X10^ rad/sec.
The last system parameter of interest is the pull-in frequency.
This is the maximum frequency separation allowable between the VCO and
the input signal if the loop is to eventually lock. The pull-in
frequency is given -by Equation (2-34) as
Am = 2/ £m K . (2-34)
Substituting in the required values,
Am = 2 /(.707) (9.43X10 3 ) (1.256X10 7
P
Am = 5.78X10 3 rad/sec.
P
This concludes the design of the system. The remaining chapter
presents the measured data and makes comparisons between the calculated
and measured data.
IV. MEASURED DATA -AND CONCLUSIONS
The measurement system was constructed using the circuits dis-
cussed in Chapter III. Initial testing of the system was done using
a Hewlett-Packard Model 608 signal generator as the source for f .
This was done so that the actual frequency of the source could be
measured using a standard counter. The test set-up is shown in Fig.
21 .
The pulse generator is used to provide a trigger signal for the
switching circuitry. The oscilloscope is used as a lock indicator.
The two counters measure the frequencies of the VCO and of the signal
generator.
The first parameter measured x-ras the hold-in range, Ao^. This
test was performed by first increasing the frequency of the generator
f - t
until the loop lost lock and then decreasing the frequency until lock
was again lost. The frequencies at which lock is lost are the limits of
the hold-in range. The frequency limits measured are given below:
f H+ = 226.979 MHz
f R _ = 221.013 MHz.
The center frequency of the generator was 224.480 MHz. The frequency
differences are then given by
59
Fig. 21. Block diagram of the measurement system test set-up.
61
Af H+ “ f H+ “ f s
Af H+ = 2.499 MHz
and
Af H- = f s “ f H-
Af H _ = 3.467 MHz.
The hold-in limits are given in terms of radian frequency by
Aw H+ “ 2irAf H+
Awg-j. = 1.57 x 10 2 rad/sec
and
A^H- = 2lfA ^H-
Ao)jj_ = 2.18 x 10 2 rad/sec.
The hold- in range is seen to be wider 'in the low-frequency direction
than in the high-frequency direction. This is accounted for by the
fact that the sensitivity of the VCO is greater in the low-frequency
direction. This is inherent in the capacitance vs. voltage character-
istics of the varactor diode and it is not possible to correct this
over a wide frequency range.
The measured value of the hold-in range is seen to be larger than
the calculated value. This is accounted for, in part, by the gain of
62
the amplifier being somewhat higher than the value used in the
calculations. The measured value of K is also a source of error
v
which could account for some of the difference in the measured
and calculated values of Aar,.
H
The second parameter of interest is the lock-in range. Aw .
J-r
It was found during testing of the system that it is not practical
to measure the lock-in range. Problems arose in trying to set the
signal generator frequency so that the difference between the VCO
frequency and the frequency of the IP amplifier output signal was
within the required ±13 kHz. It is believed that the lock-in range
is at least as wide as the calculated value and it appears to be
somewhat wider.
In measuring the pull-in range, the beat frequency signal out
of the phase detector was used as an indication of the frequency
difference between the two phase detector input signals . The loop
was first unlocked and then the frequency of the signal generator was
adjusted until the beat frequency was close to the calculated value
of Aajp. The frequency of the generator was then adjusted in small
increments until the loop pulled into lock. The pull-in range mea-
sured in this way was approximately ±60 kHz. This is about 30% less
than the calculated pull-in range, but the measured value and the
calculated value are not really the same parameter.. The calculated
value of Aajp is the difference frequency at which the loop will
eventually pull into lock. This process might take a considerable
time. The measured value is the frequency difference at which the
63
loop will rapidly pull into lock and so it would be expected to be
somewhat less than the calculated value.
v_
Another important system variable which was not mentioned before
is the power of the input signal. The response of the system to various
levels of input power was checked by locking the loop and then reducing
the input power until the loop lost lock. It was found that the loop
lost lock when the input power to the system reached —26 dBm. The
power was then increased until the loop regained lock which occured at
an input power level of from -18 dBm to -16 dBm.
The input power was also found to have an effect on the pull-in range
of the loop. Varying the input power caused the loop to pull into lock
when the frequency difference between the two inputs was greater than the
60 kHz obtained in the measurement of Aw . It is believed that this is
P
due primarily to changes in the phase detector output voltage which cause
the VCO to begin to change frequency. This has the same effect on the
loop as does manually changing the frequency of the signal generator.
A. System Test with the Transmitter
The system test with the transmitter was divided into two phases .
The system was first tested with no modulation on the transmitter. This
was done by using a pulse generator to simulate the sync pulse input to
both the transmitter and the measurement system. The frequency of the VCO,
when the loop was locked, was found to be 55.4975 MHz. The modulation
on the transmitter's VCO was then shorted to ground and the frequency of
the transmitter's VCO was measured and found to be 221.990 MHz. The actual
frequency measured by the system can be found from Equation (3-2) as
64
f s = 221.990 MHz.
Some error was found in the last three digits of the measured frequency,
i.e.jthe digits corresponding to less than 1 kHz variation. This error
is due to the response time of the loop and to the fact that the sample
and hold circuit is not perfect. An error of 1.0 kHz in the measurement
represents a percent frequency error of less than 0.0005% which is
insignificant. The frequency of the transmitter was varied from 220 MHz
to 229 MHz with results comparable to those above.
In the second phase of system testing, a video test signal (a stair-
step) was used to modulate the transmitter. Part of the video signal was
applied to the measurement system to provide a trigger for the switching
circuitry. The measurement system locked up with no problem and appeared
to track the transmitter in the desired manner.
The output of the switch was monitored with an oscilloscope for
the lock indication in this phase of the testing. This was done because
the output of the phase detector is a beat frequency which is dependent
on the deviation of the transmitter except during the back porch interval.
It was found to be difficult to separate this beat note from that caused by
a normal unlock condition.
It might be useful to remove the vertical blanking on the video sig-
nal during testing. The blanking occurs at a 60— Hz rate and causes sidebands
65
to be present which could cause -a false lock condition. This should not
cause much measurement error because of the closeness of the sidebands
to the carrier, but the possibility of erroneous measurements should be
avoided where possible.
The overall performance of the measurement system is well within the
requirements discussed in Chapters I and II. It is believed that the
system will be very helpful in the testing of any future television trans-
mitters. It is also believed that the system can be used, with slight
modifications, in the testing of other types of transmitters where the
modulation prevents the use of standard frequency measurement techniques.
Radar or PCM transmitters are examples of transmitters where the system
could be applied.
REFERENCES
1. M. A. Honnell and W. E. Faust, "The Development And Analysis of A
Sampled-Data Automatic— Frequency— Control for a Frequency Modulated
Transmitter," Final Report (Task I), NAS8-11184, Engineering Experi-
ment Station, Auburn University, Auburn, Alabama, July, 1970.
2. Floyd M. Gardner, Phaselock Techniques , New York, N. Y., John Wiley
and Sons, Inc., 1966.
3. R. H. Dishington, "Diode Phase-Discriminators," Proceedings of the
IRE, Vol. 37, pp. 1401-1404, December, 1949.
4. E. W. Pappenfus, W. B. Bruene and E. 0. Schoenike, Single Sideband
Principles and Circuits , New York, N. Y., McGraw-Hill Book Company,
Inc., 1964.
5. A. J. Viterbi, Principles of Coherent Communication , New York, N. Y.,
McGraw-Hill Book Company, Inc., 1966.
6. D. Richman, "Color-carrier Reference Phase Synchronization Accuracy
in NTSC Color Television," Proceedings of the IRE , vol. 42, pp. 106-
133, January, 1954.
7. D. L. Wollesen, "Analog Switching— High Speed with JFET’s," EDN, vol,
15, No. 2, January 15, 1970.
8. G. Neal, "FET’s as Audio Switches" Electronics World , vol. 84, No. 2,
August, 1970.
9. T. B. Bergersen, "Field Effect Transistors in Chopper and Analog
Switching Circuits," Application Note AN-220 , Motorola Semiconductor
Products Inc., February, 1966.
10. R. Jaffe and E. Rechtin, "Design and Performance of Phase-Lock Circuits
Capable of Near-Optimism Performance Over a Wide Range of Input Signals
and Noise Levels," IRE Transactions — Information Theory, vol. 1, pp.
66-76, March, 1955.
11. Applications Engineering Section, Handbook of Operational Amplifiers ,
Tucson, Arizona, Burr-Brown Research Corp., 1963.
12. J. J. D’Azzo and C. H. Houpis, Feedback Control System Analysis and
Design , New York, N. Y., McGraw-Hill Book Company, Inc., 1960.
66