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ATIA

COMMUNICATION SYSTEMANALYSIS FOR IHTWEIHROVING LUNAR VEHICLE61 SPC-4

SPACE SYSTEMS

DEFNS 5YSTEM DEARMT - SANTA AM, CAMMORIA

COMMUNICATION SYSTEMS ANALYSIS

FOR LIGHTWEIGHT ROVING LUNAR VEHICLE

G. L. Dunn

2 November 1961

61 SPC-4

Space Systems Operation ,

GENERAL ELECTRIC COMPANY a,Defense Systems Department

Santa Barbara, California

TABLE OF CONTENTS

Page

Introduction-----------------------------

Conclusions-------------------------------

Report #I, PCM -PS-------------------3

Report 02, PCM- FM------------------ U1

Report *3, FM------------------------- a

Appendix ISIN Ratio in an FM System- ------------- 37

61 SPC-4

INTRODUCTION

This TIS summarizes the results of the analysis carried

out in three separate reports contained herein. The three reports

are entitled "Communication Requirements" '' Nos. I through 3

respectively and are reproduced in this TIS in their original form.

All three reports analyze transmitter power require-

ments in terms of data rate for the same system parameters. The

system parameters were obtained from a scrutiny of JPL Research

Summaries, listed in the references throughout the report.

61 SPC-4

CONCLUSIONS

Reference to figure 1 of report #1, figure 2 of report #2

and figure 3 of report #3 indicates that transmitter powers of 15,

16, and 5.5 watts respectively are required for the same data rate.

Thei r,:slts are tabulated below for ease of comparison. The

results are based on the utilization of a 89" receiving antenna.

Table A

Minimum Transmitter PowerRequirements

85' Receiving Antenna

Modulation System Data Rate Transmitter PowerWatts' dbw

FM 5x10 5 elements 5.5 7.4per/sec(- 1 .5x106

bits/ ec)

PCM - PS 1.5x1.06 bits/sec 15 11.75

PCM - FM 1.5x106 bits/sec 16 12

tla

61 SPC-4

Where the analysis wasn based on the utilization of & 250'

D.SIW receiving antenna. the minimum transmitter power require-

ments for each of the three modulation schemes are tabulated

below.

Table B

Minimum Transmitter Power Requi rementb25,0' Receiving Antenna

Modulation Transmitter PowerScheme Data Rate MilDtts db

rM 5x10 5 elements/Dec 370 25.?(2 1.5Sx10 5 bits/usc)

PCM * FM 1.5SKI0 6 bit@/ sec 940 Z9.75

PCM - PS 1. SKI06 bit*/ sec 1000 30

LZ

61 SPC-4

COMMUNICATION REQUIREMENTS

REPORT # 1PCM - PS

Preliminary Transmitter R. F. Power Requirements

The' purpose of this report is to determine the transmitterpower requirements as a function of data transmission rate for theProspector moon-to-earth TV link.

The analysis that follows is based on the utilisation of PCM-PS modulation at an r. f. carrier frequencyof Z250 mc.

The ground based receiver station will utilize the DSITequipment.

The transmitter power requirements utilizing FM and PCM-FM will be made the subject of later reports.

Video Input

The video input will be obtained from the output terminals ofan image orthicon camera located aboard the "tank". The maid-mum data rate assumed is 1. 5 x 106 bits/sec. i. e., 1000 verticallines, 500 horizontal lines and 8 levels of grey,

Video Output

The video output from the communications system will con-sist of a train of binary pulses that will have a digit error of I in105.

System Parameters

Path distance moon-to-earth 2. 5 x 105 statute miles

Carrier frequency 2250 mc.

Noise temperature Tg nf moon (Ref. 1) 1300K

Diameter of receiving antenna (Ref. 2) 85 ft.

3

1 61 SPC-4

IGain of receiving antenna (Ref. 2), Gr 50 db

INoise temperature, Tr receivingantenna (Ref. 2) 50OK

Receiving antenna feed and couplinglosses Lr (Ref. 2) 0.4 db

Low noise maser amplifier effectivetempe.r ture, Te (Ref. 3) 30 0 K

Transmitting antenna dia. (parabolic) 4 ft.

ITransmitting antenna gain, Gt based on55% efficiency 27 db

I Transmitter/antenna coupling andmatching losses (assumed), Lt 0. 6 db

Circular polarization losses, Lp 3 dbAnalysis

I The system noise temperature T. of the receiving system

is given by: (Ref. 4)

I = IT1 + Tr] + [Lr -1] T, +[Te Lr (1)where To = Z900 K

I Hence, we obtain T@

- [130 + 50]+[I.l -1] Z90 +[30x1. l]

U a 242 ° K

The noise power Pn per cycle of post detection bandwidth is

SPn 2KTs = 1.38 x10 2 3 xZ.42x10 2 x2

= 6. 68 x I0-21 watts/cps

i - -202 dbw (2)

For a digit error of 10- 5 we require a post detection S/N of13 db (Ref. 5). The post detection bandwidth here is assuud tobe equal to the data rate. If we let this bandwidth be Bn , then thenoise power will be PBn a 2 KTaBn watts (3). Then for a data

I rate of 1.5 x 106 bit@/sec. we obtain from (2) and (3).

III

61 SPC-4

PBn = -202 + 10 log1 1.5 x 106= -140.725 dbw

Since there is no modulation gain in a PCM-PS system, then thereceived signal input power Pr. required for a 13 db output S/N is

Pr = PBn + 13 db (4)

= -140.25 + 13 = -127.25 dbw

The received signal input power Pr is given by

Pr = Pt - Lt + Gt -0( + Gr - Lr - Lp (5)

Where Pt is transmitter power level (ref to 1 watt)

CX is the free space losm between isotropic antennas and isgiven by

a = 37 + 20 log f (mc) + 20 log d (miles)

for f = 2250 mc and d = 2.5 x 105 miles

we obtain a = 212 dbThe transmitter power required Pt is from (5)

Pt = Pr + Lt +C( + Lr + Lp . Gt -Gr

and for the 1. 5 x 106 bit/sec data we get

Pt = -127. 25 + 0.6 + 212 + 0.4 + 3 - 27 - 50.

= 11. 75 dbw = 15 watts

Values of Pt required for data rates between 5 x 104 and 1.5 x 106bits/sec are tabulated in Table 1. The results of Table I areplotted In Figure 1.

Case for Z50 Foot Antenna at DSIF

If the 250'dish is utilized at the DSIF site, the system para-meters are changed as follows: (Ref. 2)

Receiving antenpa gain Gr increased to 61 db.

Receiving antenna noise temperature Ta, reduced to 150 K.

The system noise temperature T, is reduced by 350 K to242-35 a 2070 K and the thermal noise power per cycle of band-width is reduced from -202 dbw to -202 - 10 log242 a ZOL.7 dbw.

5

61 SPC-4

The noise NBn in a 1.5 mc bandwidth becomes -4140.25 + 0.7)say -141 dbw and the received signal power required, Pr a

-141 + 13 = -128 dbw.

The system transmission gain, however, is increased by 11db due to the higher receiving antenna gain. The net result isthat the transmitter power requirements are reduced by 11 + 0.7= 11.7 db.

Transmitter power requirements as a function of data rateutilizing the 250 ft. DSIF antenna, are tabulated in Table IL

The results of Table II are plotted in Figure 2.

References

I . G. E. Co., DED presentation "Techniques Applicable toLunar Landing". Feb. 10, 1960. Page 27, Chart 6-1

2. JPL Technical Memo 33-27, Feb. 13, 1961. Page 22

3. JPL Research Summary 36-7, Vol. 1, Feb. 15, 1961.Page 78

4. H. I. Ewen, "A Thermodynamic Analysis of MaserSystems". Microwave J. Vol. 2, Pages 41-46,March 1959.

5. H. N. Putschi, "Evaluation and Development of a PCM-PSRadio Telemetry System". G. E. Co., TIS R59ELS34,May 7, 1959. Figure 16

6. Reference Data for Radio Engineers, IT.TL, 4th edition.Page 751

6

61 SPC-4

ed ~~ ~ I IAmIAm m(A ~ 1-4 04 IA N 4 -1

z R

in

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wo 0

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7

61 SPC-4

0 w n N w0 I

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61 SPC-4

IH U I I H fill In 114, 1111MMIUM.1111HUHHH11111J.1 If Lill 11Figur I

Transmitter Power vs. Data Rate

NRZ, PCM-PS Systemf M' 5T Path distance Z. 5 x 10 miles (moon-earth)851 Receiving Antenna ...

41 Transmitting Antenna

4 System noise temperature Z4Z*K

Digit error rate I x 10.......... ... ...

........ ..... .................... .... .......... .... .......... ................ ............................. .....

... ........... ..... .........................

... ........................... ...... ...... ................... ......

......... ... .. .. ..... .......... .......

ni

...... . .... .... ... ...... ..................... .... ....... ...ri t

IL4

IL

IL

IL j 1 6 ... . ......

T ... ..... ... .11 X. ....... ....

4- . ....... ...

.2U... ........

JLL

........... ... .I

HIT

0.8 fft fl. if15 14 13 1 a I 1 10 9 a 7 6 5 4 3 a

TRANSMITTER POWER Watts

61 SPC-4

- Figure 2

~L. -, NRZ, PCM-PS SystemL:.Path distance 2. 5 x 10 miles I

it

.4 -I flI4' Transmitting Antenna

;':IL iiSystem noise temperature 27K- .Q4W~-L. Digit error rate I x 10

IIk

IVA i II

.9L1'Ile " L -,.

1011 llJ if I1' I

~ ~' ~ I itit

TT t7 __ i

1000 500 0 10Transmitter Power Milliwatta

61 SPC-4

COMMUNICATION REQUIREMENTS

REPORT #2PCM - FM

Preliminary Transmitter RF Power Requirements

This report discusses the transmitter power requirements

as a function of data rate for the Prospector moon-earth T. V. link,

The analysis that follows is based on the ufilisation of a

PcM-FM modulation system at a carrier frequency of 2250 mc.

The ground based receiver station will utilise DSIF equipment.

8ystev& Parameters

Path distance moon-earth 2. 5 x 105 statute miles

Carrier frequency - 2250 mc

Noise temperatuie Tg of moon (1) 130" K

Gain of 85' receiving antenna (2) Gr 50 db

Noise temperature, Tr of 85' receiving

antenna (2) 50" K

Gain of 250' receiving antenna, (2) Gr 61 db

Noise temperature Tr of 250' receiving

antenna (2 ) ISO K

Receiving antenna feed and coupling

losses, Lir (2) 0.4 db

Circular polarization losses, Lp 3 db

Gain of 4' diameter transmittingantenna, Gr 27 db

11

61 SPC-4

Transmitting antenna coupling and other

losses (assumed) .6 db

Maseramplifier effective temperatures (3)

To 300 K

Analysis

The system noise temperature To is given by (4)

To = [Tg+Tr] +[Lr- To + [ .LJ (1)

where To a 290" K

and for the 85' antenna system we obtain

To a 242* K

For the 250' antenna system we get To z 207 K.

The thermal noise Pn in the I. F. bandwidth, BIF

is

Pn KT BI ()

u 1.38 x 10-23 TUBIF

for the 85' antenna system we get

Pn a 3. 34 x 10 -21 watts/cycle w -205 dbw/cps

and for the 250' antenna system we get

Pn w -205. 7 dbw/cps

The post detection output SIN of a FM system is given by (ee Ap-

pendix I)

8/Ndb 101 0 10 log10 v J + 20 10010 + +

5 -3 (3)

Where Pr is the received signal power

Pn is the thermal noise power in the 1. F. bandwidth

12

61 SPC-4

BIF is the I. F. bandwidth

Bv is the post detection bandwidth

A F is the peak deviation of the r. f. carrier

fm is the highest modulating frequency ( = By)The +5 db term is the triangular noise spectrum improvement fee

tor, characteristic of a F. M. discriminator.

The -3 db term is the efficiency correction factor for imperfect

limiting.

The ratio ( fm ) is the modulation index of the system.

F. M. Improvement Threshold

Equation (3) is only valid provided that the signal level in

the 1.F. amplifier is above the improvement threshold of the re-

ceiver. T" e improvement threshold is defined as the signal level

where the peak signal is equal to or greater than the peak noise.

Since the input noise is assumed to be "white noise" it has a Gaussian

distribution. Reference to Figure I shows that for 99. 9% of the time

the peak to RMS voltage factor does not exceed approximately 10 db.

We therefore define the improvement threshold as the "10 db thresh-

old". The received signal power required

PR %4 4. Pa I0 db (4)

I. r. Bandwidth

The I. F. bandwidth, BIF. is given by (5)

BI = 2 (AF+ B) ()

Equation (5) states that the 1. F. bandwidth required is twice the sum

13

61 SPC-4

of the peak deviation and the video bandwidth. It should be noted

that doppler shift and frequency drift is neglected.

Video Bandwidth

In order to make a fair comparison between the PCM-PS

system discussed in Report #I. and a PCM-FM system we will as-

sum. that the video bandwidth Bv for the FM case is the same as

for the PS case, . ., Bv equal to the data rate.

Transmitter power V. data rate is tabulated in Tab'es I and

II for modulation indices of 1 and 2. 4 respectively utilising 85' re-

ceiving antennas. Tables III and IV indicate transmitter power

requirements utilitsing 250' receiving antennas.

The results of Tables I through IV are plotted in .igures

- S respectively.

14

61 SPC-4

References

(1) G. E., D. E. D. Presentation "Techniques Applicable to a

Lunar Landing", February 19, 1960, page 27, Chart 6-1.

(2) J. P. L. Technical Memorandum 33-27, February 13, 1961,

page 22.

(3) J. P. L. Research Summary 36-7, Volume I, February IS,

1961, page 78.

(4) H. I. Ewen, "A Thermodynamic Analysis of Maser Systems"

Microwave J., Volume 3, March 1959, pages 41 - 46.

(5) H. S. Black, "Modulation Theory" D. Van Nostrand Co.,

November 1958, pages 200 - 202.

15

61 SPC-4

0 -

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61 SPC-4

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61 SPC-4

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61 SPC-4

,r -, n tn 0n tn in in

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61 SPC-4

................. . ....... .......

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61 SPC-4

-4 1.11 1 1-1 11 1-1-1-11AL4411- 1144' 1 1 A -9 IJ I t I I I~ 1 :9 4- 1 1 t U I I

Figure 2

-Y Transmitter Power VS Data Rate

4- tr -1 H.-I PCM-FM Mod Index:85' Receiving Antenna

17 -1] 171- 1 T 24V KT -.2

TH I I 11-111111] H] 1 4:111-111 a f 44

tff 1 -1111 t I I I 11-- IIFT

.. 0

-11J I I I :T

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z

M I J - R_ - 1-1 t

it

it

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__--flit J t 1:1I ....... ....TLH ItH - -11. J1111111 - 1_1 1 -11 11 --- --- -IT41 I U14 IJ _11 11-1 _11.11-11H IF -1 -11 A-_ _ _ _ -" -- ............--------W _U I 1.-11: Ill I-Itt

_lttt RU W.4 1t

-4 _t. -. . T4-6 1z 8 4 0 zi

Transmitter power watts

61 SPC-4

I I T FLUL

Figure 3

Transmitter Power vs Data Rate

PCM -FM Mod Index: 2. 441 t 1111 1 U J- 85' Receiving Antenna

To 242* K

-7 7 TILL -1-MILI J- L IT TU i LLL

41TFAll-14 1

ITTT _47 7

It fit T

I

1-1 1 LL HA

7t]

T I

I AA

7:

----------

-----------X

Transmitter power watts

61 SPC-4

11111111 H ILLIA 11 11' 11111 111 1111

J-1 1111-1 11 1 111 11 1 IL Figure 4

Transmitter Power vs Data Rate

I Hill It - PCM- FM Mod Index: I

TH 1 -1 1- 11 11 1 250' Receiving AntennaTs Z07 K

I _1 t I

I L V I H I I I I H I 1H I 1 11 11 111 1I I 'T' 4 1

t .1

I H H_ I I t - -11.1 it I

J-] I I H-111: I I I 'ARM-4-1 HI I if -1 1 1 -1 1 f i l l-

TT-71W - fill 111-1

__ _ .. -11 1': 11 11-11 - , - 1 :1.11 --- -I It HH___Ht- 'I I 1 .1 -1-11-1-1-1- 1 U14TI-1

I' I tJ _11-1

I -tit Jtt_ -ItIN-1 t i -i -1-1-1 -11T-X-111 fl -1$W__ fl t -11 It

TV -T1 I _11 H IT. -4.1 IJI-1 LL -11 -11 11-T fjj- -L--V- A AA 1-11 1

Al I I I I

-1 t t h 11- - till

T) 11 H -1 TH7

T I I t -1

t -1 -tit -1

+EH -

LIA-L

-Ell -

1000 Boo 600 400 200 0

Transmitter Power Milliwatts

61 SPC-4

I! 1 1.11 111 .1 -ij LIA

6. . . . . . . . . . . .

Figure 5

AM IHI Transmitter Power ve Data Rate

PCM-F Md Index: Z. 4250' Receiving AntennaTo Z07 K

6.0 I- q1-i t ! H i 1 1 1 [ f i l l 1 1 1 1 ! 11

- 41-111 lilt T A I III I.A.... A. 1 1:11-1111-1 A-A I I I- ITU I i I I- A It I I I I N I II I-I-A

M1 il. I ...-11: 1111 1. -A I Ht.-............... IIH -t 111 1 t -1

I 11-1 Lt I --H IX 111.. 1 -11 1. - 1 41- - -1111 -11 -1- 1 11:1I Ittl 1 -11 1111 A-] I:-":-M 1--

fl

1.

t

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411t -X:

-=H 11' 41f I --A = Ul114- 1--: 44-441 fl

:11A

44-- ..... ...44- - M

- ---------

r1800 1400 1000 600 200 0 94

Transmitter power - milliwatts

61 SPC-4

COMMUNICATION REQUIREMENTS

REPORT No. 3

F. M.

Preliminary Transmitter RF Power Requirements

The purpose of this report is to determine the transmitter powerrequirements as a function of signalling rate for the Prospectormoon-to-earth TV link.

The analysis that follows is based on a composite video signal fre-quency modulating (FM) an RF carrier.

The carrier frequency assumed is 2250 Mc and the ground-basedreceiver station will utilize the DSIF equipment.

Video Input

The video input signal to the communication transmitter will bederived from the output of the TV camera. The input signal will bea compo site video containing both the video and synchronizer signals.The video signal will be in analog form and the synch signals will bein the form of pulses.

Video Output

The video output from the ground-based communication receiver willbe a single-ended composite video signal.

System Parameters

Path distance moon-to-earth A. $ x 10 statute miles

Carrier frequency 3250 Me

25

61 SPC-4

Noise temperature T of moon( l ) 130*K

Diameter of receiving antenna(2) 85 ft

Gain of receiving antenna { 2} , G 50 db

Noise temperature, T , (2)receiving antenna 50' K

Receiving antenna feed andcoupling losses L 0.4 db

r

Low noise maser amplifiereffective temperature, T (3) 30" K

6

Transmitting antenna dia.(parabolic) 4 ft

Transmitting antenna gain, Gt ,based on 55% efficiency 27 db

Transmitter/antenna couplingand matching losses (assumed),Lt 0.6 db

Circular polarization losses, L 3 dbp

Output SIN

In order to make a fair comparison between FM, PCM-PS andPCM-FM, equal video output S/N ratios will be assumed. In thePCM-PS and PCM-FM cases (see reports I and 2) 8 levels of graywere assumed requiring therefore 3 binaryti ts. The peak-to-plssignal to rms noise voltage therefore was

S/N a aT S (1)

where S = the number of quantum steps

so we obtaine

SIN = 2V- 8 = 27.7 say 30:1 = 30db.

Fror the purpose of analysis in the FM case, let us assume a com-psite block negative video signal with a peak-to -peak white voltage

=-I and black level = 0. 25Vpp pp

26

61 SPC-4

The output S/N therefore taking into account the synch pulses

30=- a 40:1 a 32 db.

Analysis

The output S/N Itin in an FM system is given by MIrmo noise)

PR (AF)( + 2 db (2)

SI W10log 1 0 - P + 20log B' 008BFN BVB

The peak-to-peak signal/rms noise ratio is therefore

P RlI IBlPP/ N a 10 log -+ 20 log + 10 log +2 (3)

PN (kI 2B

where PR a the received signal power

P N = the noise power in the I r amplifier

AF • 2a r a twice the peak deviation of the carrier

B I F the I F bandwidth

BV a the video bandwidth

Zdb represents the difference between the 5 db triangular noisespectrum gain and - 3 db limiter efficiency factor.

The results of the analysis are tabulated on Tables I through IV andplotted in Figures 1 through 4.

27

61 SPC-4

v n N o In NH 04 4 .

zf N & if N

.0 .4

0' F

a In~ N In N

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61 SPC-4

*

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61 SPC-4

z

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61 SPC-4

0 N

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61 SPC-4

-- tI FigurelI

* jil~ f IFM Mod Index: 1

Ii i

itnmt~ owr. at

61 SPC-4

* lb i il Transmitter Power veSignalling Rate

FM Mo ndx I

T1 I'' 1

In 00 1 60 140 110 600 !0T0n.ite Powe i I Jiliwttl.

61 SPC-4

ILI

h T A ;i:1II I.

: :,: .11 ii ;I' l h~h Ili F igur 3 '

TransmitePoe -Wtter Poe34Sliwln a

61 SPC-4

-- ILVI

7-1!

* 'I Figure 4

0 11 1I Transmitter Power ve Signallinj RateI, 4 Wi I IFM Mod Index: Z. 4

250' Receiving AntennaTo =207 K

*~~I It i'I

TransmIi tihter Power 11 Milliwatt. lilt

61 SPC-4

REFEREtcEs

1. (3. E. Co. # DED presentation# "Techniques Applicable to

Lunar Landing% rob. 10, 1960. Page 27, Chart 6-1.

8, JPL Technical Memo 33.47, reb. 13. 1961. Page 22.

JPL Research Summary- 36-7, Vol. 1, Web. 15, 1961.Page 78,

4. Mischa Schwarts, 'Information Transmission, Modulation&and Noise*l, McGra-Hill Book Go., 1959, Pages 327-329.

5. Appendix 1, Report No. 2, "Commiutication RequiremftistIg0, L, Dunn, Aug. 18, 1961,

16

61 SPC-4

APPENDIX I

S/N Ratio in an FM System

Assume (1) a carrier with a peak amplitude C (unmodulated), andangular velocity w; and (2) a noise component of peak amplitude Nwith a momentary angular velocity p . This leads to the summationof the two rotating vectors Ce'iwt and NeJPt Now the resultantphase angle can be taken and wt subtracted from it to got the noisecontribution to phase angle, or 0 can be evaluated directly from thediagram.

N

/:R

The first case becomes:

tan*I sinwt +x sinpt

cos wt + a cos pt

whero x -EC

Of tan'l x oin p-w)tOf ~ ~ + x coo (p - W)t()

in either case the expression

fd. d (3)

can be used for the contribution of the noise:

g,$?

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N - c oo p - w)t

IN Nfd _1 (p - W) + (p - W) 'a U(41+ -E N2 + a! coo (P - w)t

C

The first term in the square bracket represents a direct current

which can be ignored. The second term may be calculated to give:

A _(N)(p-w -W) + ) -( . .

tr. [( 3(N3+ 5 N 7 N 9+ (pw) cos (p .w) () -3() + ( ) + 9(-

2 t [ZN 2 N N NSN6a+S 10

4 t )44( 6 N _ a N(pew) 3 (p.w)t [4() -4 ) + 16() . 12() + a.-

+ (p-w)cenwN+ 0()-24g10.UOe

+ (pew)co.S(p-w)t 16) - 644 + -

- (p-w) coo6(paw) [(r) 6- 160() + 3Z N 10

* (p-w) co 7(p-w) t 644) 7 ... } .. )

S.

61 SPC-4

The first terms give added direct current due to the differencefrequency. The main term, if N/C in small, in

NE (p-w con (p-w)t

which shows that a noise component gives an output propo rtional toN/C and proportional to its spacing from the carrier frequency.

Now consider an i-f amplifier in which a signal-to-thermal noisepower ratio of C/N has been calculated. Then by taking an inter-fering signal at a frequency f from the carrier (considering it onenoise component), the power will be n a N/Bif. The ratio of ampli-tude

From 'the analysis above, the interfering carrier will produce an odt-put of

where K is the demodulator transfer constant. Now if the frequencyof the interfering carrier is varied throughout the i-f band, we findthat an output is produced between fl and f2 when the'carrier is ilthe A region and also when it is in the B region., The power percycle in the fl to fZ range from the multiplicity of carriers com-prising the noise in the A region is

SK 2 n f2

B A

O * ,

fl f 2

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The noise power appearing in band fI to f2 is:

2 f22 1 3 3

2 K f2 df = 2 K -

-1

where 2 takes care of both A and B regions.

The signal in the output will be K AF in amplitude, or K rF inpower, so the output signal to noise ratio will be,

K - ( A 3r),2 3 C C Bif 3 r AF2, 1(9 )Eu 3 -3 W M

2K (f a ." 2(f ' fl) '22 + f2f 2 f

Summary

C Bif 3(A F)SINN(rms) 2 (fz .-l) (f 2+ff 2 0)

Since in a wide band modulation system f2 >> fib

SIN (ms) C Bif 3 ((I2)

N zlfz - f (f£2)

If we let f - f I By the video bandwidth, and f2 u t the highest2 1video frequency,

C BifS/N (rms) 3 ! 2(B) f )(

f t

To convert to db we multiply each side of Equation (12) by 10 1o10to obtain:

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8/f+ 10log B + 5 db + 20 lo,10(4!) (13)SIN db a 10 log0 0 10 110 2 Bv

Equation (13) assumes perfect limiting, if we assume a limiterefficiency of 50%. Equation (13) then become@

S/N . 10 1o810 !+ 101011 Bi +20 1010 + 5-3 db (14)

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