PROCEEDINGS OF THE IEEE
54, No. 2
VOL.
FEBRUARY,
1966
Short-Term Stability for a Doppler Radar:
Requirements, Measurements,
and Techniques
D. B.
LEESON,
SENIOR MEMBER, IEEE, AND
Abstract-Short-term frequency stability is an important parame­
Doppler radar designed for operation in a severe vibration and acous­
tic environment. The characteristic of a Doppler radar which leads to
short term stability requirements is its use of a narrow-band receiver
to detect a Doppler-shifted target return which is weaker than clutter.
The system short-term stability requirements are determined by
the following two points:
1) Target return Iinewidth has a direct effect on sensitivity and
velocity resolution j it determines the minimum useful Doppler
filter bandwidth.
Transmitter and receiver local oscillator noise sidebands ap­
1) Altitude Return, caused by direct reflection from
the ground immediately below the aircraft. Since
the aircraft velocity perpendicular to the ground
is small, the altitude return is centered about the
transmitter frequency.
2) l\Tain Lobe Clutter, caused by the antenna main
beam striking the ground. The main lobe clutter is
Doppler-shifted because of the velocity of the air­
craft relative to the ground.2 Main lobe clutter is
a particular problem in a long-range system be­
cause of the small angular separation between tar­
get and ground.
3) Sidelobe Clutter, caused by the sidelobes of the an­
tenna beam striking the ground. The sidelobe
clutter extends from the maximum positive to
maximum negative Doppler frequency determined
by the aircraft velocity.
pearing on clutter determine the maximum possible sub­
clutter visibility.
Short-term stability for a Doppler radar is defined in terms of
Iinewidth and spectrum. Oscillator and crystal requirements are de­
rived from the system requirements. Measurements of linewidth
and spectral purity under quiescent and environmental conditions
are described, and vibration characteristics of quartz crystals are
considered.
INTIWm"CTION
M
Ylanuscript received September 16, 1965; revised 'Jovember 6,
1965.
The authors are with Applied Technology, I nc., Palo Alto, Calif.
Both were formerly with Hughes Aircraft Co., Culver City, Calif.
SENIOR MEMBER, IEEE
A diagram of a typical long range detection situation
is sho\yn in Fig. 1. The return from the moving target
is offset from the transmitter frequency 10, because of
Doppler shift.l For a stationary radar, the ground clut­
ter return and leakage appear at the transmitter fre­
quency as shO\yn in Fig. 2. In an airborne radar the
clutter spectrum becomes complex because of the veloc­
ity of the radar-carrying aircraft. A typical clutter
spectrum consists of these three major components:
scribes system and circuit requirements found in a typical airborne
ODERN airborne radar systems must provide
ever increasing detection ranges. In a typical
long range detection situation, the main lobe
of the narrow-beam radar antenna illuminates both the
target and the ground. Even by range-gating, an ordi­
nary pulsed radar cannot discriminate between the tar­
get and ground clutter at the same range. Because of
this, ground clutter is a severe limitation on a long­
range airborne pulsed radar.
The radar return from a moving target is Doppler­
shifted to a different frequency from that of the ground
clutter. A Doppler radar overcomes the limitations of a
pulsed radar by using this frequency difference to dis­
criminate between target and clutter.
The resolution and range of a Doppler radar are de­
pendent on linewidth and spectral purity, which are de­
termined by short-term frequency stability. For this
reason, short-term frequency stability is an important
parameter in a Doppler radar system. The purpose of
this paper is to outline the reasons for this dependence
in a typical airborne Doppler radar and touch on some
specific requirements for short-term stability.
JOHNSON,
DOPPLER RADAR CHARACTERISTICS
ter affecting resolution and range of a Doppler radar. This paper de­
2)
G. F.
A typical aircraft signal spectrum consisting of target,
clutter, and leakage is shown in Fig. 3. The spectrum at
a missile receiver is different because of the relative
velocity of the missile to the interceptor, but the same
components are present.
The time-gating of the pulsed radar can be combined
"'ith the frequency discrimination of a C\i\! Doppler to
reduce the effects of leakage. This leaves clutter as the
principle interfering signal in a pulsed Doppler radar.
Sub-clutter visibility is achieved by use of a narrow­
band receiver at the target frequency. Even though the
total clutter power far exceeds the total target return,
1 The Doppler shift!Dis 2 VfA where V is the radial component of
target velocity as seen by the radar and A is the transmitter wave­
length.
2 hofLe = 2 VfA cos e, where A is the transmitter wavelength, V is
the aircraft velocity, and e is the antenna look angle; V cos e is the
component of aircraft velocity in the direction of the antenna beam.
244
245
LEESON AND JOH:\SON: SHORT-TER�1 STABILITY FOR A DOPPLER RADAR
independent transmi tter and receiver local oscillator
ANTENNA
MAIN LOBE
I
_-------_
---.,
t
/
'will be considered here. In this case, the receiver local
oscillator line\\�idth and noise sidebands are as importallt
\
I
I
as those of the transmitter, because the local oscillator
is mixed with the signal before filtering.
!
Consider first the l i newidth requirement . In the situa­
tion of a filter excited by a narrow -band signal and
Fig. L
broadband noise, narrowing the fiJter bandwidth in­
Sources of clutter signals,
creases its output signal-to-noise ratio as long as the
�0I- L
'
filter bandv,'idth exceeds the signal linewidth. Therefore,
TRANSMITTER LEAKAGE
AND CLUTTER
�
:::i
�
�
in the presence of broadband noise, receiver sensiti vity
and, hence, range i mprove as the receiver bandwidth is
��U
r-------L---��-
narrowed. This improvement continues until the re­
ceiver filter band w idth matches the target li new idth .
FREQUENCY
Fig. 2.
Target line'width is dependent in part upon transmitter
Stationary clutter spectrum.
and local oscillator line\vidths. Thus, line\vidth is a
direct limit on sensitivity--a narrower linewidth makes
possible an increase in radar range.
w
o
::>
i-
�.
::z
<t
SIDE LOBE
CLUTTER'
L
Further, in
TRANSMITTER
LEAKAGE
ALTITUDE RETURN
f
f
MAIN LOBE C,-UTTER
/
velocity resolution. The limit on this improvem ent is
fo +fo
again the
Jinewidtho
Thus line w idth can be defined operationally as the
Airborne clutter spectrum.
narrowest filter band'width
the signal pmver densit'), in the narrmv receiver band­
width can exceed the clutter and noise power density
at the target Doppler frequency, The system require­
ments for short-term stability can be derived from the
requirements for a narrow-band receiver and for sub­
clutter
the same velocity is
system, narrowing the Doppler filter provides increased
FREQUENCY
Fig. 3.
a lmost
and frequency separation are proportional in a Doppler
TARGET
fo
D op pler radar, the ability to discrim­
related to the Doppler filter band w idth. Since velocity
/
A/,.,.�,.,.,.,�/.
..
a
inate between two targets of
visibility.
\yhich
will pass the major
portion of the energy of the sig nal. Transmitter and
local oscillator outputs of a Doppler radar are typically
stable
signals with
incidental
frequency
modulation
caused by no i se . \Vith the narrmy signals required for a
Doppler system, the major portion of the energy lies
within the range of what is ordinarily called the peak- to ­
peak frequency deviation. Since the short-term fre­
quency modulation is typically
SYSTEM FREQl'E�CY STABILITY REQl'IRE:\IE�TS
The system short-term stability requirements are de­
termined by the following two points:
lI oise - like ,
extrapola t i o n
from an rms measurement is more rigorous.
Short term used here refers to frequenc y' variations
which occur at a rate which is faster than the receiver
1) Target return I inew idth has a direct e ffect on sensi­
can trade T y pically , this rate corresponds to a modu­
tiv ity and velocity resolution; it determines the
lating frequenc y smaller than the Doppler filter band­
minim um useful Doppler filter bandwidth .
\\'idth, and can be a fC\I' cyc le s per second or larger .
2) Transmitter
sidebands
local oscillator noise
Other factors such as target motion and target signal
on clutter determine the
modulation due to antenna scanning place a lower limit
and receiver
appearing
on the target line\\'idth "'hich is independent of the
maximum possible sub-clutter visibility.
Both of these statements refer to target and
c l utt e r
as
p resented to the Doppler filter at I F. C orrelation be­
tween the transmitter output and the receiver local
oscillator can be obtained by synthesi zing both from a
COHlmon source. Use of correlation reduces frequency
stability requirements for low modulating frequencies
and short ranges. For high modulation rates and long
ranges , stability requirements can be more severe in the
case of cOl11mon master oscillators." The situation of an
For independent oscillators with u!lcorrelated frequency devia­
);/, the I F signal exhibits a deviation of .,12 ::.j. For common
oscillators with a correlated deviation of .:J./, the IF signal exhibits a
deviation of 2 j.f(sin wmTJiwmT, where w'" is the radian modulation
rate and T is the radar round-trip delay time [2].
3
tions of
transmitter and local oscillator line\\idths. This lower
limit with an X-band radar is in the range of 10 to 50
for t ypi c al airborne targets, and transmitter and re­
ceiver improvements below this level reach the poi nt of
diminishing returns.
The effect of noise sidebands on sub-clutter visibility
can be seen even in the elementary case of a stationary
radar. This exa1l1ple is used because of the simplicity of
the clutter spectrum. Figure 4 shows the statio n ary
radar spectrum of Fig. 2
Subclutter
vis i
w ith
noise sidebands added.
bi lit y is l i mi ted by clutter noise side­
bands at the Doppler frequency. Thus the noise side­
bands, due to very short term frequ en cy variations,
limit
system
sens itivity at
Doppler frequencies for
PROCEEDI)J"GS OF THE IEEE
246
CLUTTER WITH
NOISE
SIDEBANDS-
FEBRUARY
�
.
\
�\�
CLUTTER NOISE SIDEBANDS
lJIRGET
/
-'
r-------,-��---
r
I
..'
•
.. .
�-
mal noise level.
Since narrow filtering of the target return cannot be
accomplished ahead of the receiver mixer, the noise side­
bands on the local oscillator have an effect similar to
transmitter noise. The clutter and other large interfer­
ing signals are modulated by local oscillator noise, re­
sulting in noise power at Doppler frequencies. Any re­
quirements on the transmitter noise spectrum apply to
the receiver local oscillator as well.
In actual systems, the leakage and clutter spectra
may be quite complex because of relative motion be­
tween transmitter, receiver, ground, and targets. How­
ever, the effects of FM noise sidebands are the same as
in the simple example: transmitter and local oscillator
FM noise sidebands cause smearing of clutter energy to
Doppler frequencies which would be clear if noise due to
short term frequency variations were not present. The
effect is shown in Fig. 5, which is the clutter spectrum
of Fig. 3 with noise sidebands added.
Since the clutter spectrum with noise is the determin­
ing factor in sub-clutter visibility, short term frequency
stability requirements can be stated in terms of the
transmitter and local oscillator power spectrum in the
Doppler region. Typical noise spectral density require­
ments for an airborne Doppler radar are that FM noise
sideband levels in one kc/s bandwidth be more than 80
dB below the main line power at modulation frequencies
in the Doppler range.
Short term stability in this connection refers to varia­
tions which occur at rates which result in energy in the
frequency range of expected Doppler shifts. This range
can extend from a few cis up to several hundred kc/s.
OSCILLATOR REQUIREMENTS
The type of system under consideration here employs
solid-state microwave sources for reasons of size, relia­
bility, vibration insensitivity, and long term frequency
stability. The requirement for more than moderate fre­
quency stability implies frequency multiplication from
a lower frequency crystal oscillator. It has been found
empirically that the oscillator is the major source of F M
noise.
Oscillator instabilities are increased by the multiplica­
tion ratio. A factor of 100 is typical. Linewidth and
modulation index increase directly with the multiplica-
I.
THERMAL
NOISE LEVEL
...........
J"
--
fo
Fig. S.
Frequency relationships for stationary radar
with noise sidebands.
which clutter noise sidebands exceed the receiver ther­
•.
fo+ fo
FREQUENCY
FREQUENCY
Fig. 4.
TARGET
-
RECEIVER THERMAL
NOISE LEVEL
Clutter spectrum with noise.
tion ratio, and FM sideband power increases as the
square of the ratio. A typical 10 Gc/s requirement of
100 cis linewidth and noise sidebands down 80 dB in
the Doppler region would require that a 100 "\;lc/s crys­
tal oscillator have 1 cis linew'idth and FM sidebands
down 120 dB. These stringent requirements are also
placed on spurious outputs due to varactor multiplier
instabilities. "\;lodulation due to AM is ordinarily sup­
pressed in multiplication, so the FM requirement pre­
dominates except in special systems such as a homodyne
altimeter.
Short-term instabilities in the oscillator are related to
the signal-to-noise ratio at the input of the oscillator
amplifier. For modulation rates higher than the oscil­
lator feedback loop bandwidth, an approximate calcula­
tion of signal-to-noise ratio can be made. If the signal
level at the oscillator input is -10 dBm and the thermal
noise level including a 4 dB noise figure is
- 140
dBm/(kc/s), the best expected signal-to-noise ratio is
130 dB referred to 1 kc/s bandwidth far from the center
frequency. In practice, this limit is not achieved, and
noise level increases rapidly as the carrier is approached.
The role of drive level in determining signal-to-noise
ratio is fairly clear; the highest drive level consistent
with long term stability requirements appears to give
the best signal-to-noise ratio. The effect of noise en­
hancement by multiplication prompts the choice of a
high oscillator frequency for a Doppler radar--this has
generally been upheld in practice.4 Reduction of noise
sidebands by narrow-band filtering is possible in a
single-frequency application.
Since linewidth and low-lying sidebands are impor­
tant to system operation, the effect of environment on
these parameters is important. An airborne or missile­
borne system must provide the required stability while
experiencing high vibration and acoustic levels. Not
merely the average frequency, but the detail spectrum
and small frequency deviations at rates up to hundreds
of kilocycles per second are important during environ­
mental stress. A typical environment includes random
vibration of 5 g's rms from 20 to 2000 cis and an overall
sound pressure level of 130 dB above 0.0002 dynes/cm2
with energy up to 100 kc/s.
• This calculation is independent of resonator Q. For m�dulatioll
.
rates of the order of the feedback loop bandWidth,
the ?etalls <: f the
noise spectrum are dependent upon resonator Q, which tYPically
decreases as the inverse of the oscillator frequency.
1966
247
LEESON AND JOHNSON: SHORT-TERM STABILITY FOR A DOPPLER RADAR
TABLE I
quirement of a high mount resonant frequency with no
CRYSTAL SPECIFICATIONS
induced stress in the crystal blank. In theory, three short
ideal ribbons will remove the six degrees of freedom of
Crystal Specification No. 1004
the blank without any redundancies. In practice, two­
1. Series resonant frequency
fo = 90 to 100 Mcls
2. Electrical capacity
Co = 3.S pF ± 10 percent
employs three short ribbons which position the blank
3. Motional capacitance
Cm=SXlO-4 pF±10 percent
parallel to the base of a standard TO-5 can. The lowest
4. Mode number
=S
S. Crystal cut
=AT
6. Series resistance
R$�80 ohm
7. Frequency and series
resistance of spuriolls
responses
-40 dB
R,'/R, within ±1O kc/s
wire mount. At the same time, aging characteristics are
- 20 dB
R,' IR, within ± so kc/s
not degraded, and hard-mounting provides a satisfac­
8. Thermal time constant
T6�2 min.
9. Vibration sensitivity
ribbon mounts also show promise. The BTL crystal
resonant frequency of this assembly is well above 2000
cis.
Experience with this type of crystal at Hughes Air­
craft Company shows a reduction of two orders of mag­
ilf/fo� 1. SX lO-s peak deviation un­
der stated vibration and shock en­
vironment
10. Thermal sensitivity
ilf/10 � ± 1 X 10-" for
range 79°F ± 18°F
11. Aging
�..fIfo� ± 1 X 10-6 per year after ini­
temperature
nitude in vibration sensitivity compared to the standard
tory thermal time constant. Crystal specifications for a
current system are shown in Table 1.
MEASUREMENTS AND TECHNlQUES
Short term stability requirements for a Doppler radar
have been defined in terms of linewidth and spectrum.
These parameters are measured under both quiescent
tial aging and with storage -6SoF
to +165°F
and vibration environments.
12. ,\1ount
Either 2- or 3-point ribbon mount
with resonances of mount above 3
kc/s
listed below:
13. Case
TO-S transistor case
14. Case seal
Cold-weld in vacuum, after complete
cleaning and bake out. Seal will be
leak tested.
15. Setting tolerances
Typical measurement techniques
In a typical solid-state microwave source, the crystal
are
1) The two-oscillator comparison method employs
two similar microwave sources and a mixer to
translate the combined microwave spectrum of
both to a convenient frequency for measurement.
Vibration measurements are made by exposing one
oscillator to vibration while isolating the other.
Linewidth measurements have been made with a
commercially
QUARTZ CRYSTAL REQUIRE�ENTS
and results
available
low-frequency
discrim­
inator (Laboratory for Electronics Stalo Tester).
Only the IF discriminator unit, which has a video
bandwidth of 10 to 7000 cis, is used. A Collins
is the element which is most sensitive to vibration. It
51J4 receiver or Hewlett-Packard HP-310A wave
has been found empirically that a standard wire-mount
analyzer is used as a low-frequency narrow-band
crystal will not provide the required linewidth and
spectrum analyzer. Block diagrams and typical
spectrum under a typical airborne vibration environ­
test results are shown in Figs. 6 and 7. The data
ment. The reason for this is the sensitivity of the reso­
in Fig. 7 represent the envelope of the multiple
nator to vibration at the internal mount resonant fre­
discrete line spectrum resulting from vibration at
quencies.
a single frequency.
Because of other system requirements, attempts to
2) A micrOl'iave frequency discriminator employing a
reduce vibration sensitivity must not degrade <I.ging or
transmission cavity is used for microwave spec­
temperature characteristics. This rules out presently
trum measurements. This equipment gives the
available "ruggedized" or stiffly mounted crystals in the
same spectrum information as commercially avail­
standard configuration. Aging or temperature perfor­
able test sets without resorting to a critical carrier­
mance of these devices is sacrificed to move the mount
nulling scheme [3]. Typical solid-state local oscil­
resonance above the critical vibration region of 20 to
lator sources do not generally have sufficient out­
2000 cis.
put power to employ carrier nulling to advantage.
Attention has been turned to vibration isolation of
A particular advantage is that no reference oscil­
standard crystal units. The improvement afforded by
lator is required in this system. The phase vs. fre­
isolation is accompanied by an increase in thermal time
quency characteristic of the microwave cavity is
constant of the isolator-crystal system. This results in
used to convert frequency variations to phase varia­
degraded alert times in systems requiring temperature
tions. The phase detector compares cavity input
stabilization before operating.
The use of a ribbon mount as developed by Bell Tele­
phone Laboratories (BTL) appears to satisfy the re-
and output phases to give a voltage proportional
to frequency deviation. Typical data and a block
diagram are shown in Fig. 8.
PROCEEDI :\GS OF THE IEEE
248
20
X-BAND LlNEWIDTH (2M)
CRYSTAL
TYPE
RANDOM
VIBRATION,
(5q's RMS)
QUIESCENT
50 CIS
He-IS
He-IS WITH
ISOLATOR
TO-5
CIS
CIS
50
50
Fig_ 6.
2400
300
70
CIS
-2 0
cIS
CIS
W
z
-10
1\
II
, ,
, \
- 80
MEASURED
!z
�
�
wz
��
��
;,: '"
9-
0,-,
-20
KC/S FROM CENTER FREQUENCY
VIBRATION WITHOUT
I ,
,/ I I
-30
-60
I,
/
-40
�
Fig. 8.
ISOLATOR
SINUSOIDAL VIBRATION
-50
./"/
-'
//
/'
"
1\
" I
\
/ "-'
Spectrum measurement with microwave bridge.
6
2x10Z
0
"
",!;i
<to::
W<D
I
./
....... .......
�
-70 �______�__-L�-L�-L__�__
____L-__L-�
-20
-100 -80
-60 -40
20
o
60
80
40
100
KC/S FROM CENTER FREQUENCY
Fig. 7.
\
-100 L.._--'-_�______-'--_-"-_-'-_--'-__L____'
20
40
60
100
-100 -80
- 60
-40
-20
0
80
VIBRATION WITH
,-x
"
I-----'---�
ISOLATOR
I
w;­
'-'0
<D
o
,/1
-60
Two-oscillator linewidth measurement.
HC-18 CRYSTAL
---
I
I
'" I,
QUIESCENT SPECTRUM
::J
0::
W
•
ESTIMATED
-40
<D
o
o
SPECTRUM OF
CRYSTAL-CONTROLLED
MICROWAVE SOU RCE
o
(1.5
O>...J
r<l<t
-6
BFO OUTPUT
'10 OPERATE
IxlO
SHAKE-TABLE
�§
-CJ)
_--..,
<l::>
Z
in
Two-oscillator spectrum measurement.
0
500
test equipment consists of two similar oscillators
phase-locked in a narrow-loop bandvvidth. The
phase detector output is a measure of phase devia­
tions at rates higher than the loop bandwidth.
This system has been used to obtain vibration in­
formation directly at the oscillator frequency with­
out requiring the rest of the system. A block dia­
gram and typical data appear in Fig. 9.
Some techniques presently used to achieve short term
stability under environment have been derived from
considerations reviewed in this paper. These are sum­
marized here:
1) Use is made of the highest oscillator frequency and
drive level consistent with other system require­
ments.
2) Foamed construction is used in all RF circuitry.
3) Crystal vibration isolators are necessary with pres­
ent crystals; replacement vvith ribbon-mount TO-S
crystals is desirable.
COKCLCSION
Short-term frequency stability is a major problem in
a Doppler radar. Because of their effect on range and
resolution, linewidth and spectral purity are the param­
eters used to characterize short term stability for a
Doppler radar.
1500
VIBRATION FREQUENCY,
3) Measurements have been made at the oscillator
frequency with a phase-locked discriminator. The
1000
Fig. 9.
2000
cIs
Phase-locked discriminator measurement of crystal
vibration sensitivity.
'\leasurements
of
linewidth
and
spectrum
under
quiescent and environmental conditions point to the
need for increased understanding of oscillator short-term
instabilities and for improved components such as the
BTL TO-S crystals.
Short-term frequency stability is one of the factors
limiting the capabilities of present-day radars. This
problem \\·ill become even more severe in the future as
greater radar range and resolution are required.
ACKNOWLEDG:-'IENT
The authors are pleased to acknowledge the contribu­
tions, direct and indirect, of G.
O.
D'Nelly, E. V.
Phillips, and W. W. Maguire of Hughes Aircraft Com­
pany, and suggestions by J. A. iVI ullen of Raytheon Co.
and D_ 1- Healey III of Westinghouse Electric Corp.
REFERENCES
[1] :\1. I. Skolnik, Introduction to Radar Systems. ,\,lew York: McGraw­
Hill, 1962.
[2] L. P. Goetz and W. A. Skillman, "Master oscillator requirements
for coherent radar sets," 1964 Proc. Symp. on the Definition and
?vleasurement of Short-Term Frequency Stability.
[3] A. T. \Vhitwell and :-I. \\"illiams, "1'\ new microwave technique
for determining noise spectra at frequencies dose to carrier,"
Microwave I, pp. 27-32, !'>ovember 1959.
[4] \\'. \V. ?vlaguire, "Application of pulsed Doppler radar to airborne
radar Systems," 1958 Proc. Nail. Conj. on Aeronaut. Electronics,
Dayton, Ohio, pp. 291-295.