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an es ee |
| | | |
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| | f | |

|
G. L | | | ie J
“200. -160. -120. -80. -40. 0. 40. 80. 120. 160. 200.

FREQUENCY SEPARATION (AF) IN NH7.

Figure C-15.

FDR for Category 4 Transmitter Vs. Category B Receiver.

|
200.

at [7 | 71 1 14
i j | | | | i '
H i
a0. } : i; __|
t T j {
ia ae ———
| | [-—~ | ae | |
60. T T } |
( | H |
| | | |
#0 a 7 1
| |
| | / | |
| i i | | | j |
20. | 7 VW + ; {
y | | |
| i
0. | u i
-200. -160. -120. -80. -40. Qo. 49. 60. 120. 60.
FREQUENCY SEPARATION (4F) IN MHZ.

Figure C-16.

PDR for Category 4 Transmitter Vs. Category C Receiver.

Cc-14


Where P(fF) = transmitter relative power density (normalized)
to be < 1)
G@®) = relative receiver selectivity (normalized
to be > 1)
oF = frequency separation (transmitter minus

receiver frequency)

Absolute transmitter power and receiver sensitivity does not
enter into the caluclation because FDR depends only on the
shape of the victim receiver IF selectivity and undesired
signal emission spectrum.

Since the undesired signal emission spectrum and victim
receiver selectivity curves are usually given in dB units,
a more practical form of equation C-2 in dB is:

[Pap (F)-Ggp (F+AF) 1/10
OFR;, = 10 log [ ar EQ. C-3

Pap F) Gap FI /210,
-10 log 10
Where

Pap (F) = emission spectrum,in dB

Sap)

selectivity curve, in dB

The On-Tuned-Rejection (OTR) factor is derived in
Reference 30, In summary, the OTR factor can be obtained
by considering the Laplace transforms of a single pulse of
amplitude "A" and width T:

SINGLE sin TFT
LL = At —e- IFT EQ. C-4
PULSE TFT

Where the Laplace transform parameter, S, has been replaced by
j2mF. The phase given by the exponential factor indicates

that when: the receiver bandwidth B, is less than the emission
bandwidth Bp = 1/t, the phase variation over the receiver band-
width is small. This means that the voltage must be summed
first and then squared instead of summing the square of the

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FREQUENCY SEPARATION (AF) IN MHZ.

Figure C-7.

FDR for

Category 1 Transmitter Vs. Category C Receiver

190.

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FREQUENCY SEPARATIGN (AF) IN MHZ-

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c-10

FDR for Category 2 Transmitter Vs. Category A Receiver.


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voltages as many documents imply. For a relatively constant
emission spectrum over the IF pass band, the received peak
power is therefore proportional to the ratio of the receiver
to transmitter bandwidths and the OTR factor in dB is given by:

20 log BL/B, BL <B,
OTR “| 10% he oe EQ. C-5
0 BB
Where
BR = receiver 3 dB bandwidth
By = emission 3 dB bandwidth

OFRCAL Program and its Validation

A computer program called OFRCAL (Reference 29) was
employed to evaluate equation C-3 numerically by the trapezoidal
method. Input to the program consisted of amplitude (dB) and
frequency data point pairs of the undesired signal emission
spectrum and victim receiver IF selectivity curves.

The OFRCAL program accuracy was validated by experiment.
This involved using the measured IF selectivity (Figure C-2)
of the RSMS spectrum Analyzer and the measured emission
spectrum output (Figure C-3) of a RF pulse generator as inputs
to the OFRCAL routine. The FDR curve computed by the routine
was then compared with the measured FDR curve as shown in
Figure C-4. The measured FDR was obtained by using the RF
pulse generator as an input source to the RSMS spectrum
analyzer and tuning the spectrum analyzer across the RF pulse
emission spectrum. The measured and computed FDR curves
agreed within 2 dB of each other at all AF frequencies.

Computed FDR's for Radar-to-Radar Interference Predictions

The computed FDR curves used in the Los Angeles and San
Francisco area radar-to-radar interference investigations are
presented in Figures C-5 through C-16. The FDR curves are
computed for combinations of the emission spectrum categories
listed in Table B-2 and the receiver IF bandwidth categories
listed in Table C-l.

The OFRCAL routine used to compute the FDR performs the
integration relative to the receiver tuned frequency.


measurements in the Los Angeles and San Francisco area indicate
that radars are not always operated exactly at their assigned
frequency. The error contribution to FDR predictions due to
the uncertainty of frequency separation between transmitter
(interferer) and receiver (victim) can be significant for
frequency separations less than 10 MHz.


FOR IN DB

100. T | |
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| |
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“200. -160. -120. -80. -40. 0. 40. €0. 120. 169. 200

In DG

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Figure C-5.

FREQUENCY SEPARATION (AF)

IN MHZ. |

FDR for Category 1 Transmitter Vs. Category A Receiver

pay

i
|
!

| eens ee

ir
oO
a

40. 60. 120. 15C.
TON (OF) IN Maz.

Figure C-6. FDR for Category 1 Transmitter Vs. Category B Receiver.


APPENDIX C

FREQUENCY-DEPENDENT-REJECTION

INTRODUCTION

The Frequency-Dependent-Rejection (FDR) model accounts
for the energy coupling loss of an undesired signal ina
victim receiver due to Off-Frequency Rejection (OFR) and
On-Tune Rejection (OTR) of the undesired signal, and is
therefore a necessary component in predicting radar-to-radar
interference levels. The factors which affect the FDR of a
victim radar are the undesired signal emission spectrum,
victim receiver IF selectivity characteristics, and the
frequency separation between the interfering and victim radar.
This appendix discusses the techniques used to model the
radar IF selectivity, and presents the method and program
used to compute the FDR factor. FDR curves computed from the
modeled IF selectivities and emission spectrums, and used in
Los Angeles and San Francisco area investigations are also
presented.

IF SELECTIVITY

Since the victim receiver frequency selectivity is the
principal means by which the receiver discriminates agains
undesired signals, it is an important input parameter to the
FDR program.

Receiver spurious responses must also be considered when
determining the FDR of a victim radar to an undesired signal.
Spurious responses occur when the undesired signal is at a
frequency such that it mixes with the local oscillator to
produce an output at the receiver IF frequency. Since most
radars have mixers, only image responses were investigated.
The local oscillator frequency of most radars are tuned to
30 MHz above the receiver RF tuned frequencies in order to
obtain an IF frequency of 30 MHz. An RF undesired signal
that is 30 MHz above the local oscillator frequency (60 MHz
above RF receiver center tuned frequency) will also be down-
converted to the 30 MHz IF frequency. Modern radars normally
employ an image-rejection mixer or a notch filter at the
radar input to suppress image responses. The image response
of the AN/CPN+4 and AN/MPN-13 radars are generally only 15 dB
down from their center-tuned response, the ASR-4, 5 and 6
47 dB down, and the remainder of the radars greater than 50 dB
down. Reduced FDR due to receiver image response was not
incorporated in the FDR model, but was considered in an
independent FDR calculation.

c-1


IN 0B

FOR

FOR IN 08

|
i

0.
-200. -160.

Figure C-ll.

-120. -80. -40. Cc. 40.
FREQUENCY SEPARATION (AF)

BO. 120.
IN MHZ.

160. 200.

FDR for Category 3 Transmitter Vs. Category A Receiver.

100.
H | |
|
|
80. />— i
scat
oe | | sand
[—~N f= | |
60. y
40. 4
20. } y
O.
-200. -160. -120. -80. -40. 0. 40. 80. 120. 160. 200.
FREQUENCY SEPARATION (AF) IN MHZ.

Figure C-12.

FDR for Category 3 Transmitter Vs. Category B Receiver.

C-12


FOR IN O08

IN 08

R

100.

30. T
poe] |

60. 7

coor
|

|
|
0. }
-200. -160. -120. -80. -40. QO. 40. 8C. 120. 160. 200.
FREQUENCY SEPARATION ( F) IN MHZ.

Figure C-9. FDR for Category 2 Transmitter Vs. Category B Receiver.

Fe

10. T T T H
| | | |

eo. | = )
St i
pa | +—4

so. | | ! Cn ware H
N |

a. | i ono
| | |

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: | f i H

i ' \ i i

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oe | ' a ee
-200. -160. -i20. -80. -40. oO. 40. 8G. 120. 160 209

FREQUENCY SEPRRATIGN ( F)} iN MHZ.

Figure C-10. FDR for Category 2 Transmitter vs. Category C Receiver.

C-11


FDR in dB

60

50

40

30

20

10

_
CALCULATED FDR Va
rg
MEASURED FDR If
-10 -8 -6 -4 -2 0 2 4 6
AF IN MHz

Figure C-4. Comparison

of Measured and Calculated FDR

c-8



RELATIVE LEVEL IN dB

85 ; \__ CATEGO!

-100

-120

-140

-O1 ol 1 10 100

Sf IN MHz

Figure C-l1. Modeled Radar Category IF Selectivities


Therefore, the FDR for positive values of AF correspond to
the transmitter being tuned higher than the receiver frequency.

The OTR factor was computed using Equation C-5 to take
into account the category A receiver bandwidth being less
than the category 1 and 2 transmitter emission bandwidths.
The FDR curves that appear in Figures C-5 and C-8 were shifted
up about 6.0 and 2.0 dB, respectively, to take the OTR
factor into account.

Emission Spectrum Effect on FDR

The relative width of the category 1 through 4 emission
spectra are reflected in the FDR curves. The narrowest
emission spectra, associated with category 4 transmitters,
caused the category 4 transmitter FDR curves (Figures C-14
through C-16) to have steeper slopes in the AF = 0 region
than other transmitter category FDR curves (Figures C-5
through C-13). This indicated that the FDR curve is highly
dependent on transmitter emission spectra shape and relatively
independent of IF selectivity curve shape.

SUMMARY OF FDR MODELING

Since FDR is emission spectrum dependent, the error in
FDR predictions are dominated by the error between measured
and modeled emission spectra. FDR curves were computed
using the Ontario ASR-5 and Longbeach ASR-5 radar measured
emission spectra (Figure B-12, B-13), and the measure IF
selectivity of the Los Alamitos AN/CPN-4 radar (Figure C-17).
The resulting FDR curves are shown in Figure C-18 and C-19
superimposed on the corresponding transmitter/receiver
category FDR curves computed from modeled emission spectra
and IF selectivities.

The difference between the FDR curves, FP-FM, were
computed for every 10 MHz. These differences were used to
compute the average absolute difference and standard
deviation indicated in Table C-2, for the -AF and +AF regions
of FDR curves. The agreement of the average absolute error
and standard deviation values for category 2 radars, shown
in Table C-2, agree to within 0.2 dB of those for the
category 2°emission spectrum errors shown in Table B-3. This
confirms that the FDR error approximately equals the emission
spectrum modeling error.

Uncertainty in the exact frequency separation can also
contribute to error in the FDR prediction. Radar frequency

c-15


{ 100
\ 80 FDR BASED ON
|
MODELED DATA
+—_|
) -—+—_| Lt
_— a
} S60 = va
} a TPDR BASED ON
& S MEASURED DATA|
£ Y f
} 40
\
| \
\
\
ae tyr
\ AW]
| ie
q
:
} -200 0-260 -120 -80 40 0 40 80 120 160 200
| FREQUENCY SEPARATION (AF) IN MHz
Figure C-18. PDR for Ontario Transmitter Vs. Los Alamitos Receiver.
}
}
)
{ 100
| 60 FDR BASED ON
—— MODELED DATA
. SS ee eee
) e ~
{ 60 > os
; 5 ; “TO
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= FDR BASED ON
on \ MEASURED DATA
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} \
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i
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0
-200 s1€0 -120 0-80 -40 0 40 80 120 160 209

Figure C-19.

FREQUENCY SEPARATION (AF) IN MHz

FDR for Long Beach Transmitter Vs.

C-17

Los Alamitos Receiver.


TABLE C-]

RADAR IF BANDWIDTH CATEGORIES

BANDWIDTH
CATEGORY RADAR (MHz)
A AN/APS-20 130
(1.0 MHz BANDWIDTH) | AN/FPS-6 0.8
AN/FPS-90 0.8
AN/MPS-14 9.8
WSR-57* 0.75
B AN/CPN-4 2.25
(2.25 MHz BANDWIDTH AN/MPN-11 2.25
AN/MPN-13,14,15 2.26
AN/MPS-19 3.00
AN/FPN-47 5.0 *ee
c AN/FPN-55 5.0 ***
(5.0 MHz BANDWIDTH)] ASR-4,5,6,7 5.0 ***
WSR-57 ** 4.5

* (4.0 usec pulse width mode)
** (0.5 sec pulse width mode)
*** (MTI Mode Bandwidth)



The selectivity of a receiver is the composite selec-
tivity of all the tuned circuitry in the receiver prior to
detection; however, in a superheterodyne receiver, the
selectivity is determined by the IF stages because the
preceding mixer and RF circuits are relatively broadar band.
This is because the required filter characteristics are
more physically relaizable and less expensive to build at the
lower IF frequency.

IF Selectivity Modeling

The radars in the 2.7 to 2.9 GHz band generally employ a
combination of synchronously-tuned, stagger-tuned triplets,
and stagger-tuned doublet stages of IF amplification. The
frequency response function (Reference 26) for the number and
type of tuned IF stages employed in most radars indicated
that an 80 dB/decade slope beyond the -3 dB points is the
best choice for the IF selectivity model. This fall-off slope
agrees with measured IF selectivities of the 2.7 to 2.9 GHz
band radars that appear in Reference 27. Although some radars
May have a steeper selectivity skirt, this will not signifi-
cantly affect the frequency-dependent-rejection since the
20 and 40 dB/decade fall-off of conventional magnetron emission
spectrum (see emission spectrum modeling equations B-1 through
B-3 in Appendix B) governs the shape of the FDR curve.

To simplify the modeling effort, radars with nearly
identical IF selectivities and bandwidths were grouped into
the categories indicated in Table C-l1. The modeled IF selec-

tivities for the categories listed in the Table are plotted
in Figure cC-l.

FDR_CALCULATIONS

FDR is the sum of attenuation of the undesired signal due
to OFF-Frequency-Rejection (OFR) and the On-Tuned-Rejection
(OTR) in GB.

FDP (dB) = OFR(dB) + OTR(dB) EQ. C-1

Off-Frequency Rejection (OFR) is cefined in Reference 28 as:

je ar
OFR = (F+AP) EQ. C-2

PE) ar
f=


IN 08

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IN 0B

FOR

100. T 3]
80.
a _
| | __
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|
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40. N if
20. |
| | |
40. 80. 120- 160. 200.

QO.
-200. -160. -120. -80. -40. 4d.
FREQUENCY SEPARATION (AF)

Figure C-13.

IN MHZ.

FDR for Category 3 Transmitter Vs. Category C Receiver

100. pas
f | i !
60. ! 5
pol H
| i H
60. | 7 i i 3
| i H '
| | '
40. 5 | H mm
| H !
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ra | | i | |
-200. -160. -120. -80. ; + 40. 809. 120. 169. 2¢
(OF) IN MHZ.

Figure C-14,

c-13

FDR .for Category 4 Transmitter Vs. Category A Receiver.


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