94 2 16 018I MIlllll!llllllll - DTIC94 2 16 018I MIlllll!llllllll94-05149 NSWCDD/TR-93/249 SOLID-STATE, ACTIVE-PHASED ARRAYS-SOME ASPECTS OF RECEIVER DESIGN BY JOSEPH D. HARROP SHIP

AD-A275 893NSWCDD/TR-93,249 Imlhih|iII

SOLID-STATE, ACTIVE-PHASED ARRAYS-SOME ASPECTS OF RECEIVER DESIGN

BY JOSEPH D. HARROP E LETESHIP DEFENSE SYSTEMS DEPARTMENT E

FEBR4UARY 1994

Approved for public release; distribution is unlimited,

"�"a NAVAL SURFACE WARFARE CENTERDAHLGREN DIVISIONDahigren. Virginia 22448-5000

94-0514994 2 16 018I MIlllll!llllllll

NSWCDD/TR-93/249

SOLID-STATE, ACTIVE-PHASED ARRAYS-SOME ASPECTS OF RECEIVER DESIGN

BY JOSEPH D. HARROP

SHIP DEFENSE SYSTEMS DEPARTMENT

FEBRUARY 1994

Approved for public release; distribution is unlimited.

NAVAL SURFACE WARFARE CENTER

DAHLGREN DIVISION

Dahigren, Virginia 22448-5000

NSWCDD/TR-93/249

FOREWORD

Although solid-state receiver technology has been used for many years, much of theNavy's use of solid-state transmitter technology has been limited to communication equipmentor other uses requiring relatively low power, low frequency, or both. The uses have expandedto the point that it has now become necessary to address some of the issues and trade offsinvolved in the design of transmit/receive modules so that active phased-array characteristics canbe fully understood.

The analytical work performed here investigates the general relationship among thesystem-noise figure, third-order intercept, and dynamic range of active antenna array receivers.That relationship can be used to analyze the performance of, and understand the requirementsfor, active phased-array radar receivers.

This report analyzes the dynamic range and third-order intercept requirements of phased-array receivers and the effect on noise figure of adding receiver attenuation to implementweighting (taper) of the array elements. However, additional analysis is needed to develop areliable and accurate design tool.

This report has been reviewed by Stuart A. Koch, James I. Miller, Richard Giorgis,Charles E. Spooner, John Cavanaugh, and Tom Hitt.

Approv y

OMAS C. PENDERGRAFT, HeadShip Defense Systems Department

Aaooaajon FeorI D R TA.B&I

LI%'1Rmeed 0

• Dist" Spec laIL/o

ei/ii 'W I•

NSWCDD/TR-93/249

ABSTRACT

The Navy's use of solid-state transmitter technology has been limited to communicationequipment or other uses requiring relatively low power, low frequency, or both. It has nowbecome necessary to address some of the issues and trade offs involved in the design oftransmit/receive modules so that active phased-array characteristics can be fully understood.

The analytical work performed here determines the general relationship among thesystem-noise figure, third-order intercept, and dynamic range of active antenna array receivers.This report analyzes the dynamic range and third-order intercept requirements of phased-amryreceivers and the effect on noise figure of adding receiver attenuation to implement weighting(taper) of the array elements.

iii/iv

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CONTENTS

Page

IN TRO DU CTIO N ...................................................................... 1

DYNAMIC RANGE AND THIRD-ORDER INTERCEPT ................................... 2

ARRAY-NOISE FIGURE CONSIDERATIONS ............................................ 9LIN EA R TA PE R ................................................................ 11COSINE-SQUARED-ON-A-PEDESTAL TAPER ................................... 12

RESULTS AND CONSIDERATIONS ................................................... 15

R E FE R E N C E S ........................................................................ 17

APPENDIXES

A-SYSTEM-NOISE FIGURE CALCULATION .................................... A-1B-THIRD-ORDER INTERCEPT ................................................. B-1C-R E SU LTS ................................................................... C -ID-TAPER-WEIGHTING EFFECTS .............................................. D-1

D ISTRIB U TIO N ..................................................................... (1)

ILLUSTRATIONS

Figure Pape

1 SIGNAL AND THIRD-ORDER INTERCEPT CURVES .......................... 3

2 LIN EAR TAPER ........................................................... 11

3 COSINE-SQUARED-ON-A-PEDESTAL TAPER .............................. 13

v/vi

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INTRODUCTION

Although solid-state receiver technology has been used for many years, much of themilitary's, specifically the Navy's, use of solid-state transmitter technology has been limited tocommunication equipment or other uses requiring relatively power, low frequency, or both.With improvements in device power versus frequency, solid-state devices have entered thetraditionally held realms of tube technologies; i.e., radar transmitters; e.g., AN/SPS-40 solid-state transmitter replacement, AN/TPS-59 transmitter, and others. Along with these newdevices, new approaches to old problems have emerged, specifically, the implementation ofactive element phased-array radars. In addition to moving the transmitting device to the arrayface, came locating the receiver front ends at the array face, reducing receive losses, and makingthe receiver an integral part of the transmit/receive (TR) modules. These receivers' outputs arethen combined in subarray groupings or individually to form the composite receiver output.Some of the issues and trade offs involved in the design of these TR modules must be addressedso active phased-array characteristics can be fully understood.

The analytical work performed here determines the general relationship among thesystem-noise figure, third-order intercept, and dynamic range of active antenna-array receivers.That relationship can then be used to analyze the performance of, and to understand and developthe requirements for, active phased-array radar receivers. These parameters are particularlyuseful for their ability to provide insight into a radar's potential performance in clutterenvironments.

The system-noise figure is a measure of a receiver's sensitivity or minimum detectablesignal level. In its simplest form, it represents the noise level in the receiver that a signal mustexceed to become detectable. The third-order intercept point is used as a receiver/amplifierfigure of merit that represents the level of intermodulation distortion created by two interferingsignals at the input to the receiver/amplifier. Under certain in-band signal interferenceconditions, intermodulation products appear in the passbands of the receiver's clutter rejectionfilters. The third-order intercept point affects the ability of the radar to reject that clutter. Ingeneral, good noise-figure and third-order intercept point performance presents conflictingrequirements to the radar system designer. When noise figure is improved, the third-orderintercept point is degraded and vice versa. The dynamic range of a receiver is a measure of itsability to achieve a high third-order intercept point and at the same time achieve a low noisefigure.

Many others1.2.3 have done similar work that contributed to an understanding of thesubject. This work originally began as confirmation and extension of work by J.B. Hoffman ofTechnology Service Corporation.' However, what makes this work unique is the inclusion ofreceiver attenuator losses combined with bearnformer network (array manifold) characteristicsto determine their effect on array performance. As discussed in Appendix A, the gain of the

Inm •mmmmmma m mml m

NSWCDD/TR-93/249

beamformer is different for signal and noise. The gain for the signal is 1 per channel, while thegain for noise is i/GB, where G. is the beamformer gain (see Appendix A), because the signalvoltages are added coherently (in phase) while the noise voltages are added noncoherently(random phase). It is concluded that, under certain circumstances, these parameters can effectthe system-noise figure in such a way as to have a determinable effect on third-order intercept,dynamic range, and overall array-noise figure. As a check of this work, the equations developedhere were used to reevaluate the test case designs offered in Mr. Hoffman's study.' The noisefigure analysis of Appendix A is a direct result of using that study's module configuration andwas used to check the match between this and that study.

This report is presented in four parts with four appendixes. Part I is the introduction andPart 2 is the analysis of the dynamic range and third-order intercept requirements of phased-array receivers. Part 3 is an analysis of the effect on noise figure of adding receiver attenuationto implement weighting (taper) of the array elements. Part 4 attempts to tie Parts 2 and 3together in a general sense. It is essentially the results of the effort, but it is clear that additionalanalyses must be done to develop a reliable and accurate design tool. It is hoped that this workcan be useful in pointing the way to future needs and efforts. Appendixes A and B develop thenoise-figure and third-order intercept expressions, respectively, used to generate the results ofAppendix C. The results of Parts I and 2 was also applied to the test designs mentioned aboveand shown in Appendix C. Appendix D demonstrates the effect on noise figure of adding eitherlinear or cosine-squared-on-a-pedestal taper to an array antenna.

DYNAMIC RANGE AND THIRD-ORDER INTERCEPT

The third-order intercept characteristics of an amplifier are shown in Figure 1. Thesignal and third-order gain curves are clearly labeled. Their intersection is the third-orderintercept point-the point that the third-order intermodulation products of two equal and closelyspaced (in frequency) input signals would intersect the signal-gain curve if no gain compressionoccurred. The graph axes are labeled Output Power (dBm) and Output Signal Power (dBm).Because of this, the signal gain curve has a gain of 1 and the third-order intercept gain curvehas a slope of 3. All inputs are given in terms of the output power resulting from them. Onthis graph, the dynamic range would be the difference between P,)., and PO.dst. This assumesthat it is desirable to keep the distortion output (POAdS) equal to the noise-output level of thesystem at that point-a fact that will be a key factor later in the discussion.

NSWCDD/TR-93/249

50

Third

zder

"•40 Dr.

40 - ignal

P0, ip

Po.Max

20 -- _

A

010

00

0 10 20 +40

Pin'.x .4. GS pi,'lp +Gol

Output Signal Power (dBm)

FIGURE 1. SIGNAL AND THIRD-ORDER INTERCEPT CURVES

We will now develop an expression for the input-intercept point, Pii, the output-interceptpoint referenced to the input of amplifier chain. The first step is to write an expression for theslope of each curve.

BC

P.p-PIMPo,s,-P o~max

P ,jP+Gs-(P,.• +G5s)

-1

I3

NSWCDD/TR-93/249

and:

Am2

P. O+GS(Pjý+G 5 )

=3

where:

Gs = system gain

Pi nu= maximum input power producing distortion

(Pod) equal with noise level

p,, = input intercept point

PojP = output intercept point

Po = maximum signal output, corresponding with P,,

occurs when Pod equals noise level

P,,& = distortion (third order) output signal

These combine to yield:

m= Po_ -Pom_ 1

m 2 Poip-PodU 3

which reduces to yield:

Podt = 3*Po -2*PoO

4

NSWCDD/TR-93/249

But:

P,==(P 1 ,m+GS) * Mi

= (Px.+Gs) * 1

and finally:

PoA = 3*P ,m=+3*Gs-2 *Po4, (1)

Since we want the maximum output distortion not to exceed the output noise level to obtainmaximum dynamic range, then:

PoA =NLo = NLi +G.

where:

NLo = system output noise levelNL, = system input noise levelG= system noise gain

= system signal gain-beamformer gainGB = beamformer gain

= Gs-Gn

Similarly:

PoF0 , = (P,.,,,+G)* l

5

NSWCDD/TR-93/249

Substituting these into Equation (1) gives:

NLi+G" = 3*P,,• +3*G,-2*P4, ,-2*G,

which finally reduces to:

3*Pi•.•-NLi+GB (2)

Next, we need to determine the relationship between Pi.,. and dynamic range so it canbe substituted into Equation (2). Looking at dynamic range at the output of the beamformer,DRo.b, from Figure 1:

DROb = ',o.- Po-4 (3)

Earlier we stated that to have maximum dynamic range requires the output distortion be nogreater than the output noise level, we can write:

Po, = NLo

where:

NL° = NLi+Gn

Combining yields:

Pod = NLi+Gn (4)

Also from Figure 1:

Po= = P, G, (5)

6

NSWCDD/TR-93/249

Combining Equations (4) and (5), and noting that:

G. = G,-Gg

yields:

DR.,b = Pi.mi+G,-(NLi+G)

= Pim,•+G,-NLi-G,+GB (6)

DRo.b = Pix=-NLj+Gg

and we can rearrange Equation 6 to show:

Piu = DRo.b +NLi-GB (7)

The final steps are as follows: First we substitute Pi., in the form of Equation 7, intoEquation 2 and solve for DRo.b:

3*DRo.,+3*NLi-3*G -NLi+GB

which reduces to:

DRo.b = 2 -(pj, _NL+G) (8)

7

NSWCDD/TR-93/249

This s the dynamic -'ýge out of the beamformer network. To determine the dynamic range ofeach individual moduie, the beamformer gain is subtracted from DRob.

DR. =2 *(Pi ip-NLI)- 1 *GB (9)3 =3

This equation allows one to determine the dynamic range and third-order intercept requirementsfor the array modules. Note also that this expression relates dynamic range to noise figurethrough NLi.

Since:

NLi 1=O*log(K*To*B*FsA)

then:

DR. = ,(P- -10*log(K* To*B*FsA)--ý) (10)3 2

and:

DR.b 2 * (PiP,- 10* log(K* To* B* FsA)+GB) (11)

also:

GB = DRobm-DR.

These equations demonstrate that the dynamic range, noise figure, third-order interceptpoint, and the beamformer gain are all tied together and need to be considered mutually. Bymanipulating the terms of these equations, proposed designs can be evaluated and modified tooptimize the various parameters.

8

NSWCDD/TR-93/249

Consider, for example, the need for a system dynamic range of 85 dB, a noise figure of2 dB, and a bandwidth of 40 MHz. Then Equation 11 would indicate that an input third-orderintercept of -5.45 dBm is needed if the array has 5,000 elements (GB=37 dB). Equation 10shows that the array module needs only 48 dBm of dynamic range to satisfy these requirements.A further reduction in required module dynamic range could be achieved by increasing thenumber of array modules. By going to a narrower bandwidth system (i.e., 4MHz) the interceptpoint is correspondingly reduced to -15.45 dBm.

Therefore, array and waveform designs need to be closely matched to the receiver designto obtain optimum performance. Soft parameters (i.e., noise figure and third-order interceptpoint) can and should be traded off to help meet overall system requirements. Harderparameters (i.e., number of array elements and bandwidth) are more difficult to trade off whenconsidering overall radar design.

ARRAY-NOISE FIGURE CONSIDERATIONS

It was mentioned earlier that array attenuation, used to adjust taper on receive, can havean effect on overall array noise figure. See the equations in Appendix A. Usually when taperis applied, a taper loss is suffered. This is a loss in signal-to-noise ratio because of theattenuation of the signal and is considered an acceptable trade off to achieve improved antennabeam-shape performance. There is, however, an additional phenomenon that can occur that hasthe effect of raising the noise figure of the receiver elements that have the taper attenuationapplied to them. These are concentrated on the periphery of the array. This raises the overallarray noise figure of the array which, in effect, lowers the signal-to-noise ratio even further.

This effect can be demonstratea by considering two basic types of taper, linear andcosine-squared-on-a-pedestal. The reasons for considering these tapers are that they arerelatively simple to analyze and the cosine-squared-on-a-pedestal taper can be related to other,more complex tapers.4 To begin with, we need to develop an expression for the noise figureas a function of module attenuation. To do this, go to Appendix A and retrieve the expressionfor noise figure for that example. Other examples will be slightly different, depending onreceiver design. From Appendix A:

i -GB

Lm*LB*(-- -)+(Lm*LB*FR-1)FSA = FG+LRIFI+ ) B

G1 GI*G 2 GI*G2*G3

9

NSWCDD/TR-93/249

This can be reduced to:

LR,(F 2-lI) LR,(F 3- t) LRFSA = FA+LR*Fl+ + -1 __Lit

GI.*G2 G1*G2*G3

i-G 8LR*Ls*( GB )+LR*L,*FR

G* G2*G3

It is evident that the first part of this equation is independent of module loss and the second partis a term multiplied by module loss. If we now assume that module loss is a function of positionon the array, and assuming a circular array, this equation can be reduced and rewritten in theform of a simple first-order equation:

Fs, = FAA+L.(r,O)*FBB

and this will be integrated over the surface of the array to get a total noise figure. The integralhas to be multiplied by the density (modules per unit area) and then divided by the number ofelements to get back to the average effective noise figure for the modules. This is:

F1 = GB * f* 2 foR(FA+Lm(r,O)*FBB) *r*drdO

- 2f fRdrd,. FBB 2. RAA *r d0 ' *f+ fo r*L,(r,@)drdO

10

NSWCDD/TR-93/249

The number of modules is equal to the beamformer gain (GB). At this point, it is convenientto note that the taper will be applied only in the radial direction so that L. is a function of onlyr and not 0. Solving the first double integration and making the appropriate substitutions resultin the following simplification:

F = *f r*Lm(r)dr (12)F1 A A+R 2 0

Equation 12 provides the basis for the analyses that follows. As stated earlier, bothlinear and cosine-squared-on-a-pedestal tapers will be considered in the analysis. The term (L.)will be developed for each case and applied to Equation 12 to develop an appropriate expressionfor each taper.

LINEAR TAPER

Linear taper is represented in Figure 2. Remembering that the module loss is a functiononly of radial distance, Equation 13 can be written directly from Figure 2 as:

Lr) m, - )*r+1 (13)R

X= max

0

3.-

0 R

Radial Distance From Center of Array

FIGURE 2. LINEAR TAPER

11

NSWCDD/TR-93/249

This assumes that the attenuation at the center of the array is zero (i.e., I(0)= 1) and that itincreases linearly to a maximum at the array edge. Putting Equation 13 into Equation 12 gives:

1F , 2: [ )f r+ rJdrdOSAR2 0 0 R

and solving the "rdrdO" term results in:

F,, r2,1rLs Lm -1F1 -= F +Fs+ * f,2--f, R J L R 1 )*r 2 drd@

Solving this last equation is relatively simple and results in Equation 14:

SA = F +FBB*( 3" )1 (14)3 )

This result is very simple, but it should be remembered that FAA and FBB are somewhat morecomplicated. Appendix D provides examples using receiver design data from Reference 1.

A result of this analysis is that, for good receiver design, unless the taper is very severe(i.e., greater than 20 dB or so), the term FAA dominates, and there is little effect on overall noisefigure. This stems from the fact that the noise figure is primarily determined by the first stagesof amplification in a good design. If, however, there is less isolation in the amplifier chain, thiseffect could become noticeable and cause difficulties for lower weighting values as demonstratedin the third example of Appendix D. Also linear taper is not a normal taper to use. It doesserve as a useful example however.

COSINE-SQUARED-ON-A-PEDESTAL TAPER

Cosine-squared-on-a-pedestal taper is represented in Figure 3. Equation 15 can bewritten directly from Figure 3 as:

Lm(,)= I +(Lm,mx-I)*cos 2(71 *(I- r) (15)2 R

12

NSWCDD/TR-93/249

Lam, ma•c

0

1

0 R

Radial Distance From Center of Array

FIGURE 3. COSINE-SQUARED-ON-A-PEDESTAL TAPER

Before substituting Equation 15 into Equation 12, it would be helpful to reduce Equation 15 toa simpler, more easily integrable form. First, make the substitution:

cos2a 1 I*(i+cos(2*, ))2

which, when substituted into Equation 15, results in:

L.(r) = + (LMm-21) + (LMj- 1) *cos( 71 *(I-R))[+ 2 2R

Simplifying this equation and making the substitution:

cos(a-13) = cos(a)*cos(1P)+sin(a)*sin(P)

results in:

LO CosL( (16)2 2 R

13

NSWCDD/TR-93/249

Putting this expression for L... into Equation 12, repeated here for clarity, results in Equa-tion 17 below.

2*FB .. ( 1.FIsA= FAA+ R2-• o (12)

F1 FMFSA AA1 (17)

+ 2*f R r*( EJA *cos(')JdrdS(7R 2 2 R

Equation 17 can be solved and ultimately simplifies to its final form of:

F1 = F1 +F2a,[l+(Lxaz-1),(1+2SA AA(18)

2 C2

Equation 2-7 is also dominated by the FA term and for weighting functions like Hamming(equivalent to cos2 with L,., = 1/.08 = 12.5 or w 11 dB attenuation), the effect of increasingperipheral module noise figure is negligible compared to the system-noise figure, assuming goodreceiver design. However, for low, sidelobe Taylor weighting, which is closely matched tocosine-squared-on-a-pedestal up to about -42 dB sidelobes4 , the maximum weighting can be 30to 50 dB. Because of this similarity, it is assumed that this weighting should give results similarto Taylor weighting up to approximately 35-dB edge attenuation or so. In any event, cosine-squared-on-a-pedestal should be a good demonstrator of the concept. As with the linear taperexample, Appendix D contains calculated examples of this effect. Again, much depends on theamount of isolation in the amplifier chain. The first example shown in Appendix D is veryinsensitive to weighting while the last example is highly sensitive to weighting.

An additional observation that helps to build confidence in cosine-squared-on-a-pedestal'susefulness for exploring more complex weighting structures is the fact that, in each example,the linear and cosine-squared-on-a-pedestal weightings give results that are virtually identical.

14

NSWCDD/TR-93/249

This seems to support the hypothesis that, noting the increased complexity of cosine-squared-on-a-pedestal weighting over linear weighting, even more complex weightings (i.e., Taylorweighting) would show similar results to those shown here.

RESULTS AND CONSIDERATIONS

As stated in the introduction, this work was originally initiated as a confirmation andextension of the work by J.B. Hoffman of Technology Service Corporation' since circumstancesprevented the proper review cycles before its delivery. The approach taken has been to showenough details of the calculations so the reader can follow the logic of the developments withoutstumbling over leaps in mathematical reasoning. It was also intended to highlight -'therprocesses occurring in this area of active-array receiver design.

In his work, Mr. Hoffman developed an expression for noise figure that turns out to bea good approximation that overlooked some of the beamformer network effects, which resultedin inaccurate noise-figure calculations as the module losses are increased. Since one of hisconclusions was to operate the modules with approximately 30-dB attenuation, to achieve anacceptable third-order intercept, the effect of this inaccuracy begins to appear. However,comparing the analyses (refer to Appendix C and Reference 1) tends to show slightly lower noisefigures at high module losses for the expressions developed here which, in itself, tends to benefithis suggestion.

However, the high module losses suggested by Mr. Hoffman are somewhat disconcerting.If you look at the dynamic range for each case, it becomes apparent that the highest dynamicrange occurs between 25- and 30-dB module loss for most cases. Since, as indicated in theintroduction, dynamic range is a measure of a receiver's ability to satisfy both good noise-figureand good third-order intercept point, this result seems to support Mr. Hoffman's suggestion.The results of Parts 2 and 3 also tend to track Mr. Hoffman's results, in terms of calculations,except he stops short in two areas. First, if antenna tapering on receive is desired, that taperis added directly to the module loss he already suggests using. This could result in modulelosses of 60- to 70-dB on receive and, according to the curves in Appendix C, dynamic rangewould suffer greatly. These kinds of losses seem excessive on a per-module basis. Second (andclosely related to the first), Mr. Hoffman uses a 12-dB noise figure as a system benchmarkbecause other low sidelobe systems have similar noise figures because of heavy tapering.However, since the system-noise figure is allowed to grow to this 12-dB level by the inclusionof module losses for the purpose of achieving acceptable third-order intercepts, adding theadditional heavy taper losses will only increase the noise figure more and, as mentioned above,could actually push the receiver into a lower dynamic range situation because of the downwardcurve to the dynamic range at higher losses. The engineer is left with the question of whetherit is better to compromise third-order intercept by putting in only attenuation to accomplishtapering or put in both taper and module attenuation or a compromise between the two.

It is felt that more thought needs to be given to the specific requirements of the particularsystem being evaluated. The design of an individual stand-alone receiver would have to satisfy

15

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different requirements than that of a receiver that is to be part of an array of receivers on anactive-array radar antenna, which is the stated ultimate subject of this effort. By looking at thefigures in Appendix C, one can see there are approaches that could be used. Cases 1 through4 are good examples of designs with low noise figures and reasonable dynamic ranges at lowmodule loss. Cases I through 10 also show good noise figure with slightly better dynamicrange, and third-order intercept point, at low module loss, except that the dynamic range startsto turn down at somewhat lower module losses than for cases 1 through 4. In cases 29 and 30,even higher dynamic ranges are seen at low module loss, except that noise figure is somewhatmore compromised than before. The remainder of the cases show variations of these results thatcould possibly be taken advantage of, depending on system requirements. For example, ifsmaller dynamic ranges can be tolerated, operating at lower module losses could be traded forbetter sensitivity by selecting lower noise figures. The requirements may allow operating atlower, more reasonable noise figures with lower third-order intercept points so antenna taperscan be tolerated without excessive noise-figure growth and, in fact, improved dynamic range forthose receivers with the added taper. Perhaps something entirely different, like range- andazimuth-sensitive attenuator control [similar to sensitivity time control (STC)], could beimplemented to control intermodulation distortion from strong interference signals that arelocalized. In some cases, operation at high module losses may satisfy a given set ofrequirements but should not be considered the only method.

Another effect highlighted, but not studied in depth here, is the effect of weighting taperon the overall system dynamic range. The addition of attenuation to the receivers studied hereshow that, for most designs considered, the dynamic range is more sensitive than noise figure.However, the sensitivity is generally to increase dynamic range, up to - 30 dB attenuatorvalues, where it begins to decrease rapidly. This is considered a benefit rather than a problem.It also provides an additional parameter to adjust, or take advantage of, in the design of active-array receivers, as seen above. It is suggested that an analysis similar to the noise-figureanalysis here be done to better characterize this effect.

Another striking observation is that the two weighting tapers used-linear and cosine-squared-on-a-pedestal-gave almost identical results for the three examples shown. As statedearlier, this observation helps to build confidence in cosine-squared-on-a-pedestal's usefulnessfor exploring more complex weighting structures. This seems to support the earlier hypothesisand assumption that, noting the increased complexity of cosine-squared-on-a-pedestal over linearweighting, even more complex weightings (i.e., Taylor weighting) would show results similarto those shown here-at least those resulting from the use of the cosine-squared-on-a-pedestalas a suitable approximation to more complex weightings.

Another possibly useful analysis would be the study of the unequal-input, signal-interceptpoint or multiple signal-generated interference. It would be very difficult to describe a realisticsignal environment, but perhaps a simple set of signals could provide useful information. Thepotential benefits to clutter analysis would be extremely useful.

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REFERENCES

1. Hoffman, J.B., Preliminary Results of Active Array Noise Figure/Third Order InterceptTradeoff Analysis, Technology Service Corporation, Silver Spring, MD, 11 December1991.

2. Collier, Don, "Optimizing LNA's for Use in Phased Arrays," Microwave Systems News,April 1990, pp 37-44.

3. Hayward, W.H., Introduction to Radio Frequency Design, Prentice-Hall, Inc., 1982,pp 202-232 and 367-371.

4. Skolnik, Merril, Radar Handbook, Second Edition, McGraw-Hill Publishing Company,New York, NY, 1990, pp 10.30 - 10.33.

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APPENDIX A

SYSTEM-NOISE FIGURE CALCULATION

A-1

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APPENDIX A NOMENCLATURE

HEMT High-electron mobility transistor

HBT Heterojunction bipolar transistor

MSFET Metal semiconductor field-effect transistor

A-2

NSWCDD/TR-93/249

This appendix develops an expression for the equivalent system noise figure for an activephased-array radar. This work, along with Appendix B, was used for comparison to workperformed in Hoffman's work;A1 those results are shown in Appendix C.

The confusing factors for this analysis are what effect that receiver module losses (in theform of taper and fixed attenuation to optimize third-order intercept) and beamformer effects,have on the array noise figure. Assume the generalized receiver chain of Figure A-i.

F FFA

3 --

~~~~~~~~- 1G_,3G i , " -

3 GF F, F2 F, B~

FR

FIGURE A-I. GENERALIZED ARRAY-RECEIVER CHAIN

As a first step, we must calculate the equivalent noise figure (F') at the input of onechannel of the beamformer network. To better illustrate this, refer to Figure A-2. The loss (LB)of the beamformer acts on both the signal (Si) and the noise (Ni) inputs equally. However, thegain of the beamformer is different for signals and noise. The signal gain is I per channel whilethe noise gain is 1/G5 per channel since the signal adds coherently (in phase) and the noise addsincoherently (random phase).

A-1 Hoffman, J.B., Preliminary Results of Active Array Noise Figure/Third Order Intercept Tradeoff Analysis,

Technology Service Corporation, Silver Spring, MD, 11 December 1991.

A-3

NSWCDD/TR-93/249

S. F b8, - G.I/G .

N, G.-G.

2 -~ r L

G. -N

NGi F

R

FIGURE A-2. TYPICAL BEAMFORMER

In addition, more noise is added in the beamformer because of beamformer losses. Sincethe definition of noise figure is the ratio of input signal-to-noise (S/N) to output S/N, we canfollow the signal and noise through the beamformer and write the following equations:

So, b -LB

and:

Ni + K*TeB*B

LB* GB GB*LB

A-4

NSWCDD/TR-93/249

where:

Sob = signal at output of beamformer

No, b = noise a t ou tpu t of beamformer

Si = beamforiner (circuit) input signal

NO = beamformer (circuit) input noise

LB = beamformer loss

GB = beamformer (array) gain

K = Boltzmann1 s Constant

B = system-noise bandwidth

TeB = effective passive beamformer temperature

It should be noted that the effective passive-device temperature (Tea) has been defined at theinput of the beamformer so that it is effected by the beamformer loss and gain the same as theinput noise (N1) from previous stages. Continuing to the output of the receiver stage, the outputsignal and noise become:

or Si*GRLB

and:

NOr =GR*( N.+ K* TeB*B eRNo~r G _*( __ G + L * ) +GR*K*Te *B

LB* GB LB*GB

where:

Sor = signal at receiver output

Nor = noise at receiver output

GR = receiver gain

TeR = effective receiver noise temperature

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and, again, Tt is defined at the input to the receiver and is the contribution to the output noisepower from the receiver. Since definition of the noise figure (F) is the input S/N divided bythe output S/N, then:

S.

(Si *GR)[LB

N1 K* TeB*BGR*( LB*G K + +K*TeR*B)

LB* G B LB*GB

where:

Fi = total equivalent noise figure at input of beamformer,

translated receiver with beamformer noise figures

Reducing yields:

Fi = Ni+K*ToB*B+GB*LB*K*TeR*BNi *GB

Continuing:

Fi _ 1i,[ Ni+K*TeB*B K*TeR*BF B N= +GB*LB *( N. IGB Ni Ni (A- 1)

_ 1 Ni+K*TeB*B K*TeR*B+Ni N_))GB Ni Ni Ni

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At this time, it should again be noted that the general definition of noise figure is the input S/Nratio divided by the output S/N ratio, or:

Sin

F- Ni n

SoUtNout

Si" (A-2)Nin

Sin*GN i n * G+NAe*G

N1 n +NAe

where:

NAe = equivalent added noise referenced at input of device

The noise added in the attenuator (L) is:

NAe K*TeB*B

where:

TeB = To* (LB-I)

Applying these results to Equation (A-2) yields:

F Ni+K*To*B* (LB-I)Ni

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and:

Ni* (FB-1) = K* To*B* (LB-1)

= NI* (L -1)

which reduces to:

FB = LB

therefore:

LB Ni+K*TeB*BNj

Similarly:

FR = Ni+K* TeR*BNI

Substituting these last two equations into Equation (A-i) yields:

F' = -1 [LB+GB*LB* (FR-1)]GB A- 3

= L-.•+LB,*(FR-I)

CB

Applying conventional rules about translating noise figures through cascaded stages yields:

F -1 F3 -1 F-FSA = FA+LR* [F1+ 2 G+-___+ F 1

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where, referring to Figure A-i:

FSA = system noise figure defined at antenna terminals

FA = antenna temperature

F, = first amplifier input noise figure

F2 = second amplifier input noise figure

F3 = third amplifier input noise figure

G, = first amplifier gain

G2 = second amplifier gain

G3 = third amplifier gain

Fii = total noise figure at point shown on Figure A-i,

Fi translated through module loss

and:

FiX = Lm*F i

Making these substitutions gives:

FL*L 8 +Lm*LB* (FR-1) -1F2-1 F•-1 GB

FSA = FA+LR* [Fl+ 2 ++ýG G1 *+GBG, G * G2 G,*G2*G3

which ultimately reduces to:

( 1-GBFsA = FA+LR [F+ F2-1 + F3-1 *L* )+(L*L*FR-) (A-4)

GI. GFL*G2 G G* G2G*G3

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APPENDIX B

THIRD-ORDER INTERCEPT7

B-1

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APPENDIX B NOMENCLATURE




B-2

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This appendix derives general expression for the third-order intercept (TOI) of a typicalamplifier chain with attenuators and a beamformer network that could be found in active arrayreceivers. This work, along with Appendix A, was used for comparison to work performed byHoffman.'B" The results are shown in Appendix C.

Each amplifier of a chain has associated with it a TOI referenced to either the input orthe output and different by the gain of the amplifier. The intent here is to determine themaximum overall chain TOI, given its interdependence on the individual amplifier TOIs. FromCollier's work," 2 the general form of total TOI is given for a two-node cascade by:

1 1 -2

where:

ITx = total TO! at point X

IxI = output TO! of first node referenced at point X

I x = output TO! of node two referenced at point X

The example given in Reference B-2 showed quite clearly how Equation (B-i) is applied.However, the method of handling passive components, such as attenuators, was not shown.Referring to Figure B-I, the example is modified to include these effects. The TOls shown areoutput TOls.

A B C D

AR Amp 2

G -10 dB L-5 dB G -10 dB

I -15 dBm I -15 dBm

FIGURE B-1. EXAMPLE PORTION OF A TYPICALAMPLIFIER CHAIN

*-I Hoffman, J.B., Preliminary Results of Active Array Noise Figure/Third Order Intercept Tradeoff Analysis,

Technology Service Corporation, Silver Spring, MD, I 1 December 1991

- Collier, Don, "Optimizing LNA's for Use in Phased Arrays," Microwave Systems News, April 1990,pp 37-44.

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A key simplifying assumption is that all passive components (not components such as limiters)considered can be thought of as having an infinite TOI. While this is not strictly true, it is avalid and useful assumption in this case and for the signal levels considered here. Goingforward through the chain, at point C the contribution from the left of C can be written:

Tc = T 1 + 1 -

IC I C+I -Tc 1 1 ' -

L

= 12T I O G 2

where:

ITC= total TOI at point C

Ic = total TOIs before C, referenced at C

Ic = total TOIs after C, referenced at C

I, = output TOI of first amplifier

= 15 dBm

12 = output TOI of second amplifier

= 15 dBm

G2 = gain of amplifier two

= 10 dB

IA = attenuator output TOI

= 00

L = attenuator loss

=5dB

The definitions of parameters relative to the subscripts and superscripts are consistant andmaintained from this point on. That is, I, and I'2 are the reflection of the output TOIs of

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amplifiers one and two to the point X. Refer to Figure B-I for the definitions for these generalexamples. Substituting values for the parameters yields:

C _-( I I Y)" 31.62*.31623 *0

1 +0)_l10

10 M

10 dBM

C 31.62rW 10

= 3.162 mw

= 5.0 dBm

Combining terms and solving for the total TOI at point C yields:

'Tc I1 + 1

I• + I )-It

10 3.162

= 2.4024 mw

= 3.81 dBm

If we wanted, we could translate this to point D, yielding:

T'T= ITc*G2

= 2.4024* 10

= 24.024 mw

= 13.81 dBm

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Checking this result by using another approach, we can determine each component ofTOI by translating them through the losses and gains to have at point D:

IT" I +!I)-I' I1 12

L

100 31.62

= 24.02 mw

= 13.81 dBm

which is the same results using both approaches.

To determine the chain input TOI point, we can translate this 13.81 dBm back throughthe chain, thus:

ITA = (13.81 dBm) - G2+L-G1

= -1.19 dBm

This can also be checked by doing the original analysis going backward:

IT= 1 1)

I, 1 2 *L

G2

+

31.62 31.62*3.16210

= .13-1

= 7.59630 mw

= 8.80602 dBm

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ITA = 8.80669 dBm-G,

= 8.80669-10

= -1.19331 dBm

or by using the formula:

IT, =~ 1 + 1' -

A 12*L

GI Gi*G 2

1 + 1 -I

3.1623 100100

- .75975 mw

- -1.19331 dBm

which confirms the results.

These examples show that it does not matter where the relation is applied in the chainas long as the gains and losses are adequately accounted for. Each of the individual TOIs canbe referred/translated to the point of interest separately and combined using the formula at thatpoint of interest.

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Applying this technique to the same receiver chain used in Appendix A (reproduced inFigure B-2 with appropriate labels) the individual TOIs (defined at the antenna terminals) are:

S = IR*LR*Lm*LgGR*GG*G 3*G2*GI

S 13* LR3 G3,*G2,Gl

S• _I 2 *LR

G2*G1

ISA _ 1 R

iI

FIGURE B-2. REPRESENTATIVE RECEIVER DESIGN, THE Is ARE OUTPUT TOIs

Combining these components yields the total system TOI referenced to the antenna terminals:

= ( IR*LR*Lmn*L B I 3*LR + I 2*LR I,*LR)- (B-2)GR*GB *G3*G2 *Gl G3*G2 *G, G2 *G, G,

It is easiest to determine each component of Equation (B-2) in dBm, then convert to mwto do the sum. It is concluded that the gain (GB) of the beamformer can be used because thewhole array would be functioning to reach TOI for the off-array receiver amplifier. Each arraymodule is assumed to provide the same signal level to the beamformer. In practice, this maynot be true; receiver weighting (taper) may result in different characteristics. Also, differentplacement of the attenuator (Lm) would yield different results, although mostly for noise figure.

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"APENDIX C

RESULTS

C-1

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APPENDIX C NOMENCLATURE




C-2

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This appendix presents the result of applying the noise figure, third-order intercept, anddynamic-range equations that were developed in this effort to the parameters used in Reference1 with an antenna contribution (FA) of 0.53416 as determined using the approach utilized inAppendix D. The difference is that the starting noise figure was read as 2.77 dB at that timeversus 2.75 dB in Appendix D. This explains why this number is different, although onlyslightly, from that used in Appendix D. For each result, the parameters will be restated first,as taken from Reference C-i, along with the page number in Reference C-1 that corresponds tothe presented case. The graphed results will then be presented in Figures C-I through C-6. Thereader must compare these results with those of Reference C-I; however, three examples ofHoffman'scresults (see the following text) are shown for immediate comparison.

In general, the results of the two analyses agree very closely. The noise-figure resultsat low-module loss agree quite closely. Any errors, with the exception of case 28, are thoughtto be because of initial inaccuracy in reading the noise-figure graphs to calculate the effects ofantenna temperature. See the introduction above, page C-56, and Appendix D. At high-moduleloss (40 dB) the differences vary from =0.5 to --2.5 dB difference. These are still smalldifferences because of the similarity in the equations used. The noise figures shown here areall smaller because of the negative term arising from the effects of beamformer gain. Therefore,the noise figures presented here are somewhat better (at high-module loss) than in the originalanalysis.

Third-order intercepts are virtually identical in Reference C-1 and here because it isbelieved that the same equations were used. For this reason, little can be said except that theoriginal work has been confirmed in this area. It should be mentioned that this third-order effectis a result of two input signals of equal magnitude. A complete analysis should also look at themore likely events of nonequal magnitude signal interference and greater-than-two signalinterference cases. A thorough analysis would be very difficult and is beyond the scope of thisanalysis.

Finally, dynamic-range questions arise concerning active, phased-array antennas. Theanalysis of Reference C-I did not address dynamic-range questions. The curves presented here,showing dynamic range, show considerable dependance on module loss, as one would expect.The dynamic range can typically change - 13 dB or more for a module loss from 0 to 30 dB.An analysis of system-dynamic range versus antenna-weighting taper (similar to the noise-figureversus taper analysis presented here earlier) should be undertaken. Antenna taper would causethe outer elements to experience increased dynamic range, in most cases considered here up toa 30-dB weight. Because the dynamic range increases, this may not be an issue; but if time hadpermitted, that analysis would have been done. Cases 1, 4, and 7 of Hoffman'sCI results areshown for comparison and are shown immediately after those cases as presented here.

C-i Hoffman, J.B., Preliminary Results of Active Array Noise Figure/Third Order Intercept Tradeoff Analysis,

Technology Service Corporation, Silver Spring, MD, 11 December 1991.

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Case 1: HEMT 3-Stage Configuration. F, = 0.8 dB, G = 15 dB, TOI.= 28 dBm, Lý = 0.5 dB, LA = 3 dB, GB = 40 AB, F= 4 dB:G = 10 dB, TOIR = 55 dBm, Reference Page 27.

4.9

4.8

4.7

4.6 -

4.5 - __ _ _S 4.4

am 4.3

' ~ 4.2 - _ _ _ _

4.1

3.9

S3.83.7

3.6

w 3.5

-4 4

0 3.33.2

3.1 /

3- _

2.9 -_

2.8 -2.7

0 10 20 30 40

MODULE LOSS (dB)

Figure C-lA. Case 1, HEMT 3-Stage Noise Figure, ReferencePage 27.

C-4

NSWCDD/TR-93/249

-16

S-02-18

'M -29S-20_ -21 -

E- -22 --23

O -24

P4 -25 -w -26

E -25

0: -32 /___-37-38

MIODULE LOSS (dB)Figure C-lB. Case 1, HEMT 3-Stage Third Order Intercept,Reference Page 27.

-29

79 -32__ ___ ___ ___

78

0 76 - 30 40

'.- 757 - /_________ ___ ______ ___

S79

768

75

0z 73__ _ __ _ _ _ _

70 -___ ___ ___

69 ___

68 -___ ___ ____ ___

67 -___ ___ ____ ___

66

650 1o 20 30 40

MODULE LOSS (dB)

Figure C-IC. Case 1, HEMT 3-Stage Dynamic Range,Reference Page 27.

C-5

NSWCDD/TR-93/249

5.0

5.6 -

5.4 -

5.2 -

"-" 5

* 4.8

S4.4

o 4.2

S. 4

r 3.8 -

i-s 3.6

03.4

3.2 -

3

2.8 .. __._ _

2.6H0 10 20 30 40

MODULE LOSS (dB)

Figure C-ID. Hoffman'sc- Results, Case 1, HEMT 3-StageNoise Figure, Reference Page 27, Shown For Comparison.

-16

0 -18 - - - -I

-19 -

V -20 -~' -21 -______

S-22 - 7/--S-23

• -25

-26 -

-27- -28 -

-29

S-30S-31o -32 -

-33-34 -

I -35-36

E 37 _ 3-38 - ___ ___ ______ ___ __ _

0 10 20 30 40

MODULE LOSS (dB)

Figure C-1E. Hoffman'scOIResults, Case 1, HENT 3-StageThird-Order Intercept, Reference Page 27, Shown ForComparison.

C-6

NSWCDD/TR-93/249

Case 2: HEMT 3-Stage Configuration. F1 = 0.8 dB, G, = 15 dB, TOI0= 28 dBm, t = 1 dB, LA = 3 dB, GB = 40 dB, FR = 4 dB, Ge= 10 dB, TOIR = 55 dBm, Reference Page 28.

5352

5-

4 4948-----"•47-__

S464 75

44

S43

• 4-

39

3 8

37

z 3 53432 33 23 1. ____ ___ ______0 10 20 30 40

MODULE LOSS (dB)

Figure C-2A. Case 2, HEMT 3-Stage Noise Figure, ReferencePage 28.

C-7

NSWCDD/TR-93/249

-16

• -18M -19

• -20 ,,-21

C1 -22

W -23 /U -24 '-'

W -25E- -26-,

-27 _

-28-29

-30-31

-32 /

-33--34

S-35 _

S-36--37

0 t0 20 30 40

MODULE LOSS (dB)

Figure C-2B. Case 2, HENT 3-Stage Third-Order Intercept,Reference Page 28.

so

79 -

78 -. ___ __________

r 77 ,

75 -

. 74 -z 73-

72-

0 71-

70-

< 69- _6

>- 68 -___

67 -

66 - ___ ______ ______

650 10 20 30 40

MODULE LOSS (dB)

Figure C-2C. Case 2, HEIT 3-Stage Dynamic Range,Reference Page 28.

C-8

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Case 3: HEMT 3-Stage Configuration. Fi = 0.8 dB, G, = 15 dB, TOIi- 28 dBm, L. = 2 dB, LA - 3 dB, GB = 40 dB, FR = 4 dB, G,= 10 dB, TOI, = 55 dBm, Reference Page 29.

62

6

m1,-~58 -/__ __

S 56 - _ ___

54

In4 4/

• 46. -

f-4 4. 4 ____

0Z 4 2

3.8 - 10 10 20 30 40

MODULE LOSS (dB)Figure C-3A. Case 3, HEMT 3-Stage Noise Figure, ReferencePage 29.

C-9

NSWCDD/TR-93/249

-16

-17 ___ __ _

- -18-20 ___ __ _

r -22o -23

-24E-. -25S-26 _

-27•1 -28 _ __

• -29I -300 -31 / .....

C -32 //

4 -33

= -34E- -35

-360 10 20 30 40

MODULE LOSS (dB)Figure C-3B. Case 3, HEMT 3-Stage Third-Order Intercept,Reference Page 29.

so

78 -

77 /

I~ 75 -/ '74 74

'< 73 _

- 71 -

370Z>. 69 /

S 68

6766 '

0 10 20 30 40

MODULE LOSS (dB)

Figure C-3C. Case 3, HEMT 3-Stage Dynamic Range,Reference Page 29.

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Case 4: MESFET 3-Stage Configuration. F1 = 1.1 dB, G% - 11 dB,TOi = 33 dBm, I - 0.5 dB, LA - 3 dB, Go = 40 dB, Fit 4dB, Gt = 10 dB, IIt = 55 dBm, Reference Page 30.

14

13 -

' 12 /

101-

S 9

05-_

4- _

3 - -0 10 20 30 40

MIODUJLE LOSS (dB)

Figure C-4A. Case 4, HESFET 3-Stage Noise Figure,Reference Page 30.

c-11

NSWCDD/TR-93/249

S0

LU -t2 ____ ___

-4

S-14

E -16

i -1_

-20

-22__ __ _

-26 ___ __ _

0 to 20 30 40

NODULE LOSS (dB)

Figure C-4B. Case 4, HESFET 3-Stage Third- OrderIntercept, Reference Page 30.

8988 - ___ ___ ______________

87 - ___ ______

86 - _ , ___"*• 85 - /__ ___ ___ ___

84 / \~83z 82'< 81

80

•9 79

78

'• 77

71

75

0 80 20 30 40

MODULE LOSS (dB)

Figure C-4C. Case 4, MESFET 3-Stage Dynamic Range,Reference Page 30.

C-12

NSWCDD/TR-93/249

16

15

M 13-

'S 11

C-4 9 -

t8

S7

z __ _ __

4 -

3 L------0 10 20 30 40

HODULE LOSS (dB)

Figure C-4D. Hoffman'sclResults, Case 4, MESFET 3-StageNoise Figure, Reference Page 30, Shown For Comparison.

S-2 -- '__ _

E-, -46

p-8

• -10

S-12-14

-16 -//

'Z4 -20 _

- -22 -___E, -24E - -4 - /__ ___

-260 t0 20 30 40

MODULE LOSS (dB)

Figure C-4E. Hoffman'scResults, Case 4, MESFET 3-StageThird Order Intercept, Reference Page 30, Shown ForComparison.

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Case 5: MESFET 3-Stage Configuration. F1 = 1.1 dB, G1 = 11dB,TOIi = 33 dBm, L = 1.0 dB, LA = 3 dB, Go = 40 dB, Fi= 4dB, G = 10 dB, TOIR = 55 dBm, Reference Page 31.

14

13 - - - __ ___

w 10

9

0

4 j '

0 10 20 30 40

MODULE LOSS (dB)

Figure C-5A. Case 5, MESFET 3-Stage Noise Figure,Reference Page 31.

C-14

NSWCDD/TR-93/249

2 -_

0 0

E -2

- t

W -i6M -12

S20-22

E- -24

-26

0 10 20 30 40

NIODULE LOSS (dB)

Figure C-5B. Case 5, MESFET 3-Stage Third- OrderIntercept, Reference Page 31.

89

88

87 -

' 85- " 84

w 83 _

z 82

S 80

S 77

?> 6 -S75

730 10 20 30 40

MODULE LOSS (dB)Figure C-5C. Case 5, MESFET 3-Stage Dynamic Range,Reference Page 31.

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Case 6: MESFET 3-Stage Configuration. F, = 1.1 dB, Gi = 11 dB,TOIi = 33 dBm, Iý = 2.0 dB, LA = 3 dB, GB = 40 dB, FR =4dB, GR = 10 dB, TOIR =55 dBm, Reference Page 32.

15

14 -

1-' 3 - __ ___

12-

11-

00

S 9

7 710 A/

4- p__ ___ __,__

0 10 20 30 40

MODULE LOSS (dB)


C-16

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2 -2..__ --.--

-4

P4. -6 ___ _ __

Eý -10 ___ ___ __ _z"- -12

04 -14w/

g -16

S-20F-1

-22 /

-24

0 10 20 30 40

MODULE LOSS (dB)

Figure C-6B. Case6, MESFET 3-Stage Third-Order Intercept,Reference Page 32.

89

88

87 - ___ ___

86

85 --

84 ___

83 /

328.

[-791S 78

S77S 76S 75

74

73 0 to 20 30 40

MODULE LOSS (dB)

Figure C-6C. MESFET 3-Stage Dynamic Range, Reference Page32.

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Case 7: HEMT/HBT 2-Stage Configuration. Fl = 0.8 dB, F = 4 dB,GI = 15 dB, G2 = 12 dB, TOII = 28 dBm, TOI 2 45 6Bm, L =0.5 dB, LA = 3 dB, Ge = 40 dB, FR = 4 dB, GR = 10 dB, TOIR- 55 dBm, Reference Page 33.

zo

19

M2 16 -

15

13

ý_D 12

0--__ 10

9 /U3 7 ,0 6Z 5-_ __ _

0 10 20 30 40

MODULE LOSS (dB)

Figure C-7A. Case 7, HE14T/HBT 2-Stage Noise Figure,Reference Page 33.

C-18

NSWCDD/TR-93/249

12 /

S 10-

V 6

M.. -2

Z -4 /__

E_ 4

E - 0-6 ___

I -8-

I -16

-20

0 10 20 30 40

MODULE LOSS (dB)

Figure C-7B. Case 7, HEMT/HBT 2-Stage Third-OrderIntercept, Reference Page 33.

93

92

90 - _ _ _ _

Tj 89--__ _

88 -

87• 86S 85

84 /S 83

S 82< 81

S80 /S 79

78

77L0 10 20 30 40

MODULE LOSS (dB)

Figure C-7C. Case 7, HEMT/HBT 2-Stage Dynamic Range,Reference Page 33.

C-19

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22 -.-

20 - ...... /

, 17

15 - ___ ___ ___

14 -S13 -

12-

10 - ___

o 6z s- ___

3-

0 10 20 30 40

MODULE LOSS (dB)

Figure C-7D. Hoffman' sc'Results, Case 7, HEMT/HBT 2-StageNoise Figure, Reference Page 33, Shown For Comparison.

1412

10-,

8

-6E 0-

a /

-2-_

E- -2 /

F- -10-6--12 O 20 30

9:ý -14 - ___ ___ ___

-16 -___

E- -18 -

0 t0 20 30 40

NODULE LOSS (dB)

Figure C-7E. Hoffman'sc"Results, Case 7, HEMT/HBT 2-StageThird Order Intercept, Reference Page 33, Shown ForComparison.

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Case 8: HEMT/HBT 2-Stage Configuration. F, = 0.8 dB, F = 4 dB,GI = 15 dB, G = 12 dB, TOI =28 dBm, TOI 45 6Bm, L,=1.0 dB, LA = ý dB, G = 40 dB, FR = 4 dB, GR 10 dB, TOIR= 55 dBm, Reference Page 34.

19 -

18 - ______ ______ ___

17 -

16 -S15 -___ ______

14 -

w13 --

S12-

11-jz. 10

9-

I--4 7 -

0 6 _ _ _ll

6 _ _ _ _ _

4-

0 t0 20 30 40

MODULE LOSS (dB)

Figure C-8A. Case 8, HEMT/HBT 2-Stage Noise Figure,Reference Page 34.

C-21

NSWCDD/TR-93/249

14 -

1 12

1 0

E- -2

.- -6M -6 ___

':• -to0

-12 E

i -14 ,-16 -_ _

-20 __ _

10 20 30 40

MODULE LOSS (dB)

Figure C-8B. Case 8, HEMT/HBT 2-Stage Third- OrderIntercept, Reference Page 34.

93

92 -

91 - Z_' - - -- "

90 - __

" " 89 -

88 , \

87 ____

S86-

85

84 - ___ ___ ___

83

S 82-_ __ _

81-_

>.4 80 - _ _

79 -___ ___

77 -l (0 20 30 40

MODULE LOSS (dB)Figure C-8C. Case 8, HEMT/HBT 2-Stage Dynamic Range,Reference Page 34.

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Case 9: HEMT/HBT 2-Stage Configuration. F, = 0.8 dB, F = 4 dB,GU = 15 dB, G =12 dB. TOI = 28 dBm, TOI,= 45 dBm, IT =2.0 dB, LA = ' dB, G9 L 40 dB, F, 4 dB, Gi 10 dB, TOI.

55 dBm, Reference Page 35.

21

20191817 -___

S 16 ___

~Z13-12-

z2 tU-) 9/

6 _

0 10 20 30 40

MODULE LOSS (dB)Figure C-9A. Case 9, HEMT/HBT 2-Stage Noise Figure,Reference Page 35.

C-23

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14

-~12 _ __

10

E 6.4 4

E-

-4

-6

0 -8oo -10

4 -14 ___ ___ _ __

E- 16 --18 ___ __ _

0 10 20 30 40

NODULE LOSS (dB)


93

92 -

91 -

M 90 -

z 86-_85-

84 8S83- /

8 -

80- /4

S 79

78

770 1o 20 30 40

MODULE LOSS (dB)


C-24

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Case 10: MESFET 2-Stage Configuration. F1 = 1.1 dB, G, = 11 dB,TOIi = 33 dBm, Iý = 1.0 dB, LA = 3 dB, G = 4OdB, FR =4dB, G1 = 10 dB, TOI = 55 dBm, Reference Page 36.

24 _2:3 -____ _____ __

22 - _

20 _

19 -_ _ _

16__ _ __ ___ _17

Sis

= 14 _©13 //t-I 12

10-r• 9 /

S6 _._

3 -

0 10 20 30 40

M[ODULE LOSS (dB)

Figure C-10A Case 10, HESFET 2-Stage Noise Figure.Reference P - 36.

C-25

NSWCDD/TR-93/249

12 - ___ ___ ___ ___ ___ __ _lo

6

0.. 4

w 0Sz

-2H- -2-/

-4-

-6 /

--10

S-10-________ ___

-14

0 10 20 30 40

MODULE LOSS (dB)

Figure C-1OB. Case 10, MESFET 2-Stage Third-OrderIntercept, Reference Page 36.

93

92 -

~N 91 - ______

M

89 N

S85

S84- _

83

82

810 10 20 30 40

MODULE LOSS (dB)


C-26

NSWCDD/TR-93/249

Case 11: MESFET 1-Stage Configuration. Fl = 1.1 dB, G1 = 11 dB,TOIi = 33 dBm, Iý = 1.0 dB, LA = 3 dB, Go = 40 dB, F= 4dB, Go = 10 dB, TOIt = 55 dBm, Reference Page 37.

36

34 -

32 _____

I- 30CQ 20 ./

"26 _

24 /

M 22

201

16

14

rxa 12U-)08

4 ___

20 to 20 30 40

MIODULE LOSS (dB)

Figure C-IIA. Case 11, MESFET 1-Stage Noise Figure,Reference Page 37.

C-27

NSWCDD/TR-93/249

24 -

22 _____

2 20

"186

16 4

I 12

E-~ 10 _ __z/-4 8 ____

'- 4

1z3 -2E - _4

___

0 10 20 30 40

hODULE LOSS (dB)

Figure C-lIB. Case 11, MESFET 1-Stage Third OrderIntercept, Reference Page 37.

94

93 -__

C 92

0 0 0304

'S 91

' 90

r) 88

85

840lO 20 30 40

MODULE LOSS (dB)


C-28

NSWCDD/TR-93/249

Case 12: HEMT 3-Stage Configuration. Fi = 0.8 dB, G. = 15 dB, TOii= 28 dBm, I.R = 0.5 dB, LA = 6 dB, GS = 40 ýB, FR = 4 dB,Gi= 10 dB, TOI, = 55 dBm, Reference Page 38.

0 5

245

4- _

z 3

0 10 20 30 40

IHODULE LOSS (dB)

Figure C-12A. Case 12, HEMT 3-Stage Noise Figure,Reference Page 38.

C-29

NSWCDD/TR-93/249

-16

-17 -

-or -19 -. ,_",-., -20 /

S-21 /_134 -22

u -23 -

E- -2Sz -26

-27

-28 ____ __

-29

0 -30

S-31t -32

-33 -

34 -

-35 0 1 20 30 40

MODULE LOSS (dB)

Figure C-12B. Case 12, HEMT 3-Stage Third -OrderIntercept, Reference Page 38.

80

79 ----

'' 78 -___ ___ ___

77 -_

k-I

76

z 74

C73

ý2 70

9:: 69

68

67LL0 10 20 30 40

MODULE LOSS (dB)Figure C-12C. Case 12, HEMT 3-Stage Dynamic Range,Reference Page 38.

C-30

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Case 13: HEMT 3-Stage Configuration. F, = 0.8 dB, G = 15 dB, TOI,= 28 dBm, L = 1.0 dB, LA * 6 dB, Go = 40 AB, FRt = dB,GR = 10 dB, TOI = 55 dBm, Reference Page 39.

6.5

6

55-

45

3,5-

30 10 20 30 40

MODULE LOSS (dB)


C-31

NSWCDD/TR-93/249

-16

-17

M -19,

a -z0-a /

S-22S -23--24 /S- -20 i ______ ___ ___ ___

E -26

o -27

S-28- _

--31

S-32E - -33

-34

0 10 20 30 40

MODULE LOSS (dB)

Figure C-13B. Case 13, HEMT 3-Stage Third- OrderIntercept, Reference Page 39.

79 -

- 78 -

CQ 77 - ______ ______

76 -

75 _ _ _

S 74

73 -7

[3 72

7-1

S 70

• 69

68 ý

670 10 20 30 40

MODULE LOSS (dB)


C-32

NSWCDD/TR-93/249

Case 14: HENT 3-Stage configuration. F, = 0.8 dB, G. = 15 dB, TOI.= 28 dBm, 1ý = 2.0 dB, LA = 6 dB, G9 = 40 aB, FR 4 dB:Got= 10 dB, TOIR = 55 d~m, Reference Page 40.

7.5

6- 55-__

04

0 0 20 30 40

MIODUILE LOSS (dB)


C-33

NSWCDD/TR-93/249

-15

-16

S-17

E- -20 /.. -21 -___ ___ ___ ___ ___

% -22 -

w -23 -E - 2S-24 -

-25

O -26 -8

* -27 -____

- 28 - _______

-29

S-30; -31

-3Z-33

0 10 20 30 40

MODULE LOSS (dB)

Figure C-14B. Case 14, HEMT 3-Stage Third-OrderIntercept, Reference Page 40.

80

79 -

S78

77 -

76 - ___ ___ ___ ___ ___

75 _ __ _ _

z• __ _ _

S 73-

~372 -

71 __ _ _ _ _

Z 70 __ _

69

68

67

0 10 20 30 40

MODULE LOSS (dB)


C-34

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Case 15: HEMT 3-Stage Configuration. F = 0.8 dB, G = 15 dB, TOIi= 28 dBm, % = 0.5 dB, LA 3 AB, Go = 40 dh, FRt 10 dB,GR = 10 dB, TOIR =45 dBm, Reference Page 41.

10

9.

S 7*r4

• 6

5.

C0 0 3 4

0z 3-

_ _ _

2- ___

010 20 30 40

MODULE LOSS (dB)


C-35

NSWCDD/TR-93/249

-16

• -- -18 __ _

M -20 ____-_

, -22

E- 4 _24

S-26 /

0 -28 _

W -30

Z -32 '

-•34

-36

-380 -40

S-42I -44E- -46 __ _ _ _

-48

0 10 20 30 40

MODULE LOSS (dB)


787776 -

75 - ___ ___ ___

74 - __________

rn ?73

'O 72

71 -

70 - ___

z 69 //• 68

67

66 /

.< 65

Z 64

M 63

62 -

61

60 /59

0 io 20 30 40

MODULE LOSS (dB)


C-36

NSWCDD/TR-93/249

Case 16: HEMT 3-Stage Configuration. F = 0.8 dB, Gi = 15 dB, TOI,= 28 dBm, It = 1.0 dB, LA - 3 cB, GB - 40 dB, FR = 10 dB,Gi = 10 dB, TOIR = 45 dlm, Reference Page 42.

10

S8-

0

U3

0 to 20 30 40

ýIODULE LOSS (dB)


C-37

NSWCDD/TR-93/249

-16

N -18

- 20 __ _

-22 ____

-24 _

S-26 _ .,

o -28

S-30

Z -32 _

- 34

-36

-38

o -40

-42

E -46

-48

0 10 20 30 40

NODULE LOSS (dB)


78

77 -

76 -

M-' 74 -

77372 -71 -/

70z 7'-69 _/

S68-

67

66 - ______________

S65 -

64- 6_Z63-

62 -

61 - /

60 - ______

59 L0 10 20 30 40

MODULE LOSS (dB)

Figure C-16C. Case 16, HEHT 3-Stage Dynamic Range,Reference Page 42.

C-38

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Case 17: HEMT 3-Stage Configuration. F - 0.8 dBI G. - 15 dB, T0I1= 28 dBm, It = 2.0 dB, LA 1 3 AB, GI = 40 dB, FR 10dB,GR = 10 dB, TOIR = 45 dI•, Reference Page 43.

10

S 9

r 6*

z 4 1

3

0 10 20 30 40

NODULE LOSS (dB)Figure C-17A. Case 17, HEMT 3-Stage Noise Figure,Reference Page 43.

C-39

NSWCDD/TR-93/249

-14 _____

S-16 -___

-20 ___ __ _

S-24 ___ _ __

U -26 ___

W -30'-4

- 32 ________

-34_________

9:7 -36 I

0 -38 ___

S-40

-4 -2 _ __

E- -:44 ___ __

-46 ________ ________

0 to 20 30 40

MIODUJLE LOSS (dB)

Figure C-17B. Case 17, HEHT 3-Stage Third- OrderIntercept, Reference Page 43.

78 - ______

77 - __________ ___ ___ ___ ___

76 - _______

M 74 -__ _ __ _

72 - ___ ______ _____ _

70-_

69-

S68-

67 - ___ ___

U 66-

< 64- __

63-_

62- __

60 - __________ ___

0 to 20 30 40

MODULE LOSS (dB)


C-40

NSWCDD/TR-93/249

Case 18: MESFET 3-Stage Configuration. F1 = 1.1 dB, G, = 11 dB,TOI1 = 33 dBm, 1TI 0.5 dB, LA - 3 dB, UG = 40 dB, FR =10dB, G3 = 10 dB, T0 1 = 45 dBm, Reference Page 44.

21 _____

20

19

"Cl: 16 /

S14-m~l

~13_ __

S12-

93 8

0 6 ___

5

3-

0 10 20 30 40

NODULE LOSS (dB)


C-41

NSWCDD/TR-93/249

S-2 /___ ___0-4 /__

S-6 /

E- -_1 -12 /

- -16E - i ____ ___

• -az _ _Z_o /

-202 -24 _

-260

-28

-30 __ _

-32 ___ __ _

E- -34________ ___

-36 __ _

0 10 20 30 40

I4ODULE LOSS (dB)

Figure C-18B. Case 18, MESFET 3-Stage Third--OrderIntercept, Reference Page 44.

8Z

81-____

79-_

'E 78

77 /

76 _

S 75

74 _

73 /

72 - ______

3 71- 7

70-_

> 69

68-

67 - Z

0 10 20 30 40

MODULE LOSS (dB)


C-42

NSWCDD/TR-93/249

Case 19: MESFET 3-Stage Configuration. FP - 1.1 dB, Gi = 11 dB,TOI = 33 dBm, -1. 0 dB, LA - 3 dB, Go - 40 dB, F =10dB, G1 = 10 dB,IPOI 1 - 45 dBi, Reference Page 45.

20 -

19 -

f 18

"U 16 -

15 -

145

12 -P-4 it -

S 9-0410

4

310 20 30 40

tIODULE LOSS (dB)Figure C-19A. Case 19, MESFET 3-Stage Noise Figure,Reference Page 45.

C-43

NSWCDD/TR-93/249

S-2 ___ __ _

. -6 _

-t -0 _

-12 -_o

-14 ____ ____ ____ ___

E-._ _Z -18

-20

S-22S-24C -26 -

-26 ____ ____

-30 -

S-32 -

E- -34

-360 10 20 30 40

11ODULE LOSS (dB)


82

78 - \

77 /

76 /z< 75

1 74 - _

72 --

o< 71

70 /

69

68 -67/0 10 20 30 40

MODULE L055 (dB)Figure C-19C. Case 19, MESFET 3-Stage Dynamic Range,Reference Page 45.

C-44

NSWCDD/TR-93/249

Case 20: MESFET 3-Stage Configuration. F, = 1.1 dB, Gi = 11 dB,TOIi = 33 dBm, LR = 2.0 dB, LA = 3 dB, GB = 40 dB, FR =0dB, Gt = 10 dB, TOIR = 45 dBm, Reference Page 46.

22 //21 - ____ ________ ________

20 _

(- 19

Q 18i"i 17-

16 -

~14 _ _ _ __

t---I 12- __ _

- 8 /0 7

410 20 30 40

MODULE LOSS (dB)


C-45

NSWCDD/TR-93/249

2

- 0 -

t -4 -"* -6 __E-, -e _ _ _

[.3 -tO-14

- -10 6• -14________ ___•- -16 ____ ___

-18 __ _

1:1 -20 _

S-22 _

-24 ____0-26

I -28

-30_ _ _ _ _ _ _ _ _

E- -32 /

-34

G to 20 30 40

MODULE LOSS (dB)

Figure C-20B. Case 20, MESFET 3-Stage Third-OrderIntercept, Reference Page 46.

82

81 -

80 - _______ ______

S 79 - ______

78 .

7? - ___

0 76-

75 75

74 _

t) 7 -

S71- __

70-- _

69

670 10 20 30 40


C-46

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Case 21: HEMT/HBT 2-Stage Configuration. F, = 0.8 dB, F% = 4 dB,G, = 15 dB, G = 12 dB, TOI = 28 dBm, TOI 2 =45 dBm, tý =0.5 dB, LA = 3 dB, G9= 40 cB, Fit 10 dB,G 10 dB, TOIR= 45 dBm, Reference Page 47.

28

26 -

24 ///

222

S20 ///

1 /

14 -_

ý4 12 __ _

U)1'-. a-0Z6

0 10 20 30 40

NODULE LOSS (dB)Figure C-21A. Case 21, HEMT/HBT 2-Stage Noise Figure,Reference Page 47

C-47

NSWCDD/TR-93/249

0-5

"1 -0

o -5____ ___

•[- -15 ____

-15

o -20 /

•- -25 ___ _ __

E-,-30 ____ ____

O 10 20 30 40

MODULE LOSS (dB)


83

82

80

79 /

78zC 7776

S 7S

74

73

72 --

7110 10 20 30 40

MODULE LOSS (dB)


C-48

NSWCDD/TR-93/249

Case 22: HEMT/HBT 2-Stage Configuration. F, = 0.8 dB, F=4 dB,G, = 15 dB, G = 12 dB, TOI = 28 dBm, T01 2 = 45 %Bm, TI =1.0 dB, LA =3 dB, G, = 40 dB, FR = 10 dB, GR = 10 dB, TOI,= 45 dBm, Reference Page 48.

28

26 /

24 -

L.

' 20 -

ýD16 14 /1"' 14 _____

12

w 10 _ _

0Z 6-

4.

2-

0 ±0 20 3'0 40

MODULE LOSS (dB)


C-49

NSWCDD/TR-93/249

to

M

n 0 _____

-04

-15

0 -zo

• -25

-30

0 10 20 30 40

11ODULE LOSS (dB)


83

82 - ______

Ti 80 - /__ ___ ______ ___ ___a /79

79 - ___ ______ ___ ___

77 __ _ _

76

- 7574

z>_ 73

72

a 10 20 30 40

MODULE LOSS (dB)


C-50

NSWCDD/TR-93/249

Case 23: HEMT/HBT 2-Stage Configuration. F, = 0.8 dB, F2 = 4 dB,G= 15 dB, G = 12 dB, TOI = 28 dBm, TOI 2 = 45 d6m, Ll =2.0 dB, LA = 3 dB, Ge = 40 iB, FR = 10 dB, GR = 10 dB, TOIR= 45 dem, Reference Page 49.

28 -

'' 24- ____ ____

22-zo - __ _is /

016 -

1. 4 /

. 12 /° 0 -

0 10 20 30 40

IIODULE LOSS (dB)


C-51

NSWCDD/TR-93/249

15

w 0 0

U 'I--

0 -5

• 15

-20

E-o-30 ___ __ _

0 tO 10 30 40

MODULE LOSS (dB)


83

82

CN 81 -___

'Tfl eo -- _ _ ___

79 -

78

77 _

u 76

74

73

72

71 -- _ _ _ _ _ _

0 10 20 30 40

MODULE LOSS (dB)

Figure C-23C. Case 23, HENT/HBT 2-Stage Dynamic Range,Reference Page 49.

C-52

NSWCDD/TR-93/249

Case 24: MESFET 2-Stage Configuration. F. = 1.1 dB, Gi = 11 dB,TOI = 33 dBM, 1.0 dB, LA =3 dB, Ge = 40 dB, FR= 10dB, G= 10 dB,TOI. = 45 dBm, Reference Page 50.

32

28t

24

22 -

20 ___ ___

•:i e _ _

16

14 _

12 ___ ___ ___ ___

(108

z 6 _ _ ....

4 ______ _____

2

0 10 20 30 40

NODULE LOSS (dB)Figure C-24A. Case 24, MESFET 2-Stage Noise Figure,Reference Page 50.

C-53

NSWCDD/TR-93/249

15 ______ _____

.5

S 0

z

P4i -to

0 -15

• 20

_25

0 to 20 30 40

MODULE LOSS (dB)


83

82

Z 79

C• 78

Z 76

S 75

74O O20 30 40

MODULE LOSS (dB)


C-54

NSWCDD/TR-93/249

Case 25: MESFET 1-Stage Configuration. F. = 1.1 dB, G, = 11 dB,TOIi = 33 dBm, IL = 1.0 dB, LA = 3 dB, Gi = 4O dB, Fit 10dB, GR = 10 dB, TOIR = 45 dBm, Reference Page 51.

45 -

40 -

35

3o 30 _

0 25

20

0

0 10 20 30 40

NODULE LOSS (dB)


C-55

NSWCDD/TR-93/249

Z5

15 15 _

.13

lo 5

'-4z 5

S -5

-150 1O 20 30 40

MODULE LOSS (dB)

Figure C-25B. Case 25, MESFET 1-Stage Third -OrderIntercept, Reference Page 51.

82.5

82 -f f

S81.

S80.5

80 ____ ___

-79.5

Z 79

78.5

78 0 10 20 30 40

MODULE LOSS (dB)Figure C-25C. Case 25, MESFET 1-Stage Dynamic Range,

erceReference Page 51.

C-56

NSWCDD/TR-93/249

Case 26: HEMT/HBT 2-Stage Configuration. F= 0.8 dB, F = 4 dB,G, = 15 dB, G2 = 12 dB, TOI = 28 dBm, TOI 2 = 35 6Bm, t =0.5 dB, LA =3 dB, G= 40 B, Fi =10 dB, Gt =10 dB, TOIR- 55 dBm, Reference Page 52.

28 -

26 -

24 -

212 __ _

20 - A14 OO

ýL4 2 _ _ _ _ _

Fiur C-6Aas_2,HET/B 2Stg Noise__ Figure,

0Z 6- -_ _ _

0 t0 20 30 40

MODULE LOSS (dB)


C-57

NSWCDD/TR-93/249

6 4M 4.

-z -6-8 _/

M -10 _ __

S-12 ......... ___

E-o /-14

0 -12

20

0 10 20 30 40

NODULE LOSS (dB)


88

87 -

86 - ______ ___ ___ _____ _

w 84 -Z 85

S83-_

82-_

0 80

z>• 79

78

770 10 20 30 40

MODULE LOSS (dB)

Figure C-26C. Case 26, HEMT/HBT 2-Stage Dynamic range,Reference Page 52.

C-58

NSWCDD/TR-93/249

Case 27: HEMT/HBT 2-Stage Configuration. F, = 0.8 dB, F = 4 dB,GI = 15 dB, G2 = 12 dB, TOI = 28 dBm, T012 = 35 Bm, ITOI1.0 dB, LA = 3 dB, GB = 40 dB, F. 10 dB, GR 10 dB, TOI,= 55 dBm, Reference Page 53.

28 -

26 -/c-, 24 /

C-Q 22

20 -__ _

S18- __

0•16 -

S14

12

6 -

4

0 to 2o 30 40

NIODULE LOSS (dB)Figure C-27A. Case 27, HEMT/HBT 2-Stage Noise Figure,Reference Page 53.

C-59

NSWCDD/TR-93/249

6 6

E-0

£E 4 ___ __

-2 -'-4

S-12

U

-14

E -12-0

0 10 20 30 40

MODULE LOSS (dB)


88

w 84

Z 83

82-

< 80

79

78

0 to 20 30 40

MODULE LOSS (dB)


C-60

NSWCDD/TR-93/249

Case 28: HEMT/HBT 2-Stage Configuration. F, = 0.8 dB, F%= 4 dB,G, = 15 dB, G = 12 dB, TOI = 28 dBm, T012 = 35 aBm, =2.0 dB, LA = i dB, Go = 40 dB, FR = 10 dB, GR = 10 dB, TOIR= 55 dBm, Reference Page 54.

Figure C-28A is unique among all the cases in that thebeginning noise figure is significantly different than thatobtained in Reference"', = 1 dB. By varying the parameters, theresults were duplicated using G, = 5 dB vs the 15 dB specified.Possibly this was done in the original text and not caught becauseno review cycle was completed.

28 -//

26O

2, 4 /26- __ _

2 -20 -___

~18-~16 -

14-

12 ___ ___ ___

0 10 20 30 40

IIODULE LOSS (dB)Figure C-28A. Case 28, HEMT/HBT 2-Stage Noise Figure,Reference Page 54.

C-61

NSWCDD/TR-93/249

10

6

04

1 2

• -2 ____ ___ ___

-4

-6

S-0

-18

0 10 20 30 40

MODULE LOSS (dB)


87 - ___ ___ ___

86 - ______

S 84- _ _

z 83

80

Z 83- __82 _ _/_j- 81 ___ ___

.< 80-

79 79

78

770 to 20 30 40

MODULE LOSS (dB)


C-62

NSWCDD/TR-93/249

Case 29: MESFET 2-Stage Configuration. F1 - 2.0 dB, G, = 11 dB,TOI = 33 dBm, It = 1.0 dB, LA = 3 dB, Gg = 40 dB, F1 = 10dB, GR = 10 dB, TOI, = 55 dBm, Reference Page 55.

32 -

30 -//

28 ____

S26

• 24 -

22

_

168

14' 12 -

0 1

0 10 20 30 40

MODULE LOSS (dB)Figure C-29A. Case 29, MESFET 2-Stage Noise Figure,Reference Page 55.

C-63

NSWCDD/TR-93/249

6

12

• 6 /__

-14

E-0

-_12__ __ _ _

0 10 20 30 40

MODULE LOSS (dB)


89

88

87 - ______ ___

86

w 85 -

z 84

0 80

79

780 to 20 30 40

HODULE LOSS (dB)Figure C-29C. Case 29, MESFET 2-Stage Dynamic Range,

Reference Page 55.

C-64

NSWCDD/TR-93/249

Case 30: MESFET 1-Stage Configuration. FV = 2.0 dB, G1 = 11 dB,TOI = 33 dBm, R = 1.0 dB, LA = 3 dB, Ge = 40 dB, Fi 10dB, Ge = 10 dB, rTOIt= 55 dBm, Reference Page 56.

45

40

S35

30-

225

20

I-4 15-

0

0 10 20 30 40

IIODULE LOSS (dB)Figure C-30A. Case 30, MESFET 1-Stage Noise Figure,Reference Page 56.

C-65

NSWCDD/TR-93/249

24 -

S22 _

M 20

101

E 12

a4W o4U

2 /

E-

0 0 20 30 40

NODULE LOSS (dB)Figure C-30B. Case 30, MESFET 1-Stage Third--OrderIntercept, Reference Page 56.

z t

w-6

E 82

0 tO 20 30 40

M1ODULE LOSS (dB)Figure C-30C. Case 30, MESFET 1-Stage Dynaird OrdnerInecpReference Page 56.

866

NSWCDD/TR-93/249

Case 31: HEMT 3-Stage Configuration. F = 2.4 dB, Gi = 15 dB, TOI0=28 dBm, 4 = 0.5 dB, LA = 3 JB, G; = 40 dB, FR =1 dB,GR = 10 dB, TOIR - 55 dBM, Reference Page 57.

10

9 .

7 _

6

0

3

0 10 20 30 40

NIODULE LOSS (dB)


C-67

NSWCDD/TR-93/249

-16 -

-17

-18 _ _,,_ _

S-19 _ __'%1 -20

"-21-22

. -23o -24

-25

E, -26 /z -27

-28

-29

• -30

I -310 -32 /

C -33

-34

E- - _ ____

0 10 20 30 40

MODULE LOSS (dB)

Figure C-31B. Case 31, HEMT 3-Stage Third OrderIntercept, Reference Page 57.

78

77 - ___________

,-- 76 -

M 75 -__ _

- 74

[. 73-73 _

72

771-

70 -

i-- 69 -

67

66-

65

054

0 10 20 30 40

MODULE LOSS (dB)


C-68

NSWCDD/TR-93/249

Case 32: HEMT 3-Stage Configuration. F = 2.4 dB, Gi = 15 dB, TOIi- 28 dBm, Lk = 1.0 dB, LA = 3 dB, G' = 40 dB, Fi=t 1dB,G= 10 dB, TOIR = 55 dBm, Reference Page 58.

I o

8

6 _

4

0 10 20 30 40

MIODULE LOSS (dB)


C-69

NSWCDD/TR-93/249

-16 -

S-18 _

M -19 _

S-20 _

-22 __ _

S-23 ///U -24

w -25 ___ __ _

E-. -26z -27

_- 28-29 __ _

• -30

' -31- 32

Q -33 //

C-. -34

= -35 _E -36

-37

0 10 20 30 40

MODULE LOSS (dB)


79

78 -

,-' 77 - ____--------"

' 76 -

'-, 75 //

[=• 74

S 73 //

72 -

71 -

-70 -

69

S68 - /

67-

66 -

0 10 20 30 40

MODULE LOSS (dB)


C-70

NSWCDD/TR-93/249

Case 33: HEMT 3-Stage Configuration. F = 2.4 dB, Gi = 15 dB, TOI,- 28 dBm, I% = 2.0 dB, LA 3 dB, Go = 40 dB, FR =10 dB,GR = 10 dB, TOI, = 55 dBm, Reference Page 59.

11 ___________

,N 10 _ __

9

S 8

010 20 30 40

NODULE LOSS (dB)

Figure C-33A. Case 33, HENT 3-Stage Noise Figure,Reference Page 59.

C-71

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-15

r -17 _____

S-19

E -26

c4 -24E-' -as

--26 ___ _ __

-2S*a -29

-30

9 -32 _P -33.

S-34-36

0 10 20 30 40

MODULE LOSS (dB)


79

78 -

77 - _-- ---- - _

S76 _ _ _

w 74

0 73_z< 72

t)71 - /___

S769

68 z 68 /

t 67 - _ _

66 - ___ ___ ___ ___

65E

010 20 30 40

MODULE LOSS (dB)Figure C-33C. Case 33, HENT 3-Stage Dynamic Range,Reference Page 59.

C-72

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Case 34: MESFET 3-Stage Configuration. F, = 2.0 dB, G = 11 dB,TOI - 33 dBm, LR = 0.5 dB, LA - 3 dB, Go = 40 dB, FR = 10dB, GR = 10 dB, TOIR - 55 dBm, Reference Page 60.

212019 /1. 8 /1i7

16

15 /14 _

13

~12

10 't 0 04

9.ur _-4._s 3,•SE -taeNos Figre

Ef) 8-" 7

3C70 10 20 30 40

MIODULE LOSS (dB)


C-73

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-M -0 ____

0

M -2

V -4 6

E- -6

-e

C-, ./

-10

E-

z -12

1-4

~x1 -16 ___ ___

-0

-22 _ _ _ _ _ _

260 toDULE 31 40

KODLELOSS (dB)

Figure C-34B. Case 34, MESFET 3-Stage Third -OrderIntercept, Reference Page 60.

83 - 7Z-- _____

0 2

z 80 -__ _

79 -

tj 78 ____ __

>:: 77 _

S 76

7 5

74 _ Z73

0 1o 20 30 40


C-74

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Case 35: MESFET 3-Stage Configuration. F, - 2.0 dB, G1 - 11 dB,TOIi = 33 dBm, 4 - 1.0 dB, LA = 3 dB, GB - 40 dB, F,10dB, GR = 10 dB, T'OIt = 55 dBm, Reference Page 61.

21

20 - ___ ___ __ _

19

m 17 -1_ 6 1

w 5 - ___ __ _

13 -12o

10. 9

0-4

0 10 20 30 40

MODULE LOSS (dB)


C-75

NSWCDD/TR-93/249

m -2 -/

E- -6 _

E-10

-12

0 -20 /

-24

-26

010 20 30 40

MODULE LOSS (dB)


86

85

,s 84 - - ___ ___

83 7Z __________

0 80

? 79

78

S 77

Z 76

75

79

0 10 20 30 40

MODULE LOSS (dB)


C-76

NSWCDD/TR-93/249

Case 36: MESFET 3-Stage Configuration. F- 2.0 dB, G. = 11 dB,TOI - 33 dBm, I - 2.0 dB, LA - 3 dB, G5 B 40A, Fit= 10dB, G3 - 10 dB, TOI, - 55 dBm, Reference Page 62.

2221

20

,-, 19cn 18

~17 _ _ _

16

S145

4-l 12~11 _

10 _

z76 -5

4110 2'0 30 40

M•ODULE LOSS (dB)Figure C-36A. Case 36, MESFET 3-Stage Noise Figure,Reference Page 62.

C-77

5 - ______ _______ _______ ______ ______ ______

NSWCDD/TR-93/249

M -2 -___

-4 _____ ____

E-. 1 ___

20

~-22E- -24___

___ ____

0 10 20 3040

MIODULE LOSS (dB)

Figure C-36B. Case 36, MESFET 3-Stage Third- orderIntercept, Reference Page 62.

86 -___ ___ ___

85 - ______

'' 84 - ___ ___ ___ _ __

0 81 _ _ _

.< 80-

C479-____

U 78 -___ ______

77- __

Z 76- _ __ _

S 75 - ___ ___ _____ _

0 10 20 30 40

MODULE LOSS (dB)


C-78

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APPENDIX D

TAPER-WEIGHTING EFFECTS

D-1

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APPENDIX D NOMENCLATURE




D-2

NSWCDD/TR-93/249

This appendix computes the magnitude of the effects that array-amplitude weighting onreceive has on overall array-noise figure. The weighting is accomplished by adding attenuationto the receive chain, determined by the taper function, just before the beam-former network.The results are compared to the effects of adding attenuation on all modules equal to themaximum taper weight.

The first step that must be taken is to rewrite the system-noise figure equation.

i-GbLm*LB* ( -•-) + (LM*LB*FR-1)

FSA = FA+LR* [F 1 + (F2-1) (F3-1)Gb

This, as before, can be rewritten:

FsA = FA+LR*Fl+ LR* (F 2 -1) LR* (F 3 -1) LRGi G * G2 G,*G2*G3

(D-l)LR*LB* ( -Gb) +LR*LB*FR

+LM* Gb

GI*G 2 *G3

Again as before, an array with nonuniform attenuation (L.) over the array (as for the case oftaper weighting) could utilize Equation D-1 in the general form:

FSA = FA+Lm(r, 0) *FBB (D-2)

For the cases of linear and cosine-squared-on-a-pedestal and referring to their respectiveEquations (14) and (18) from the body of this report, Equation (D-2) can be rewritten in therespective forms of Equations (D-3) and (-4):

D-3

NSWCDD/TR-93/249

FSA = 1 2*Lmx)3 3 (D-3)

= FA+FBB* (666666667*Lnmax+.3333333333)

and:

FSA =FAA+FBB* 1'+ 1Smxl + - 2 212i

1I2+ 2))(D4FAA+BB* i+ 2) *L.,.ax+ (1- ( 1+2 Z2(D4

2 i 2 ,2 I

= FAA+FBB* [.702642367 *Lmmax+. 297357633]

As evidenced by Equations (D-3) and (-4), the final results for the selected taper factors areremarkably similar. It remains as an exercise for the reader to determine if a true Taylorweighting would also have a similar form. It is hoped that the cosine-squared-on-a-pedestal caseis a reasonable indicator of the more complex weighting functions. The maximum weights forTaylor, etc., functions will generally be larger than the cosine function, which, in turn, wouldbe larger than the linear case presented here. If the cosine function is reasonably similar to themore complex functions, then perhaps applying the larger weights to the cosine case will be areasonable indicator for the magnitude of changecs that would occur in noise figure with the morecomplex weighting functions applied to the array face.

For this example, we must return to Hoffmn's work`D and extract the parameters usedfor one of the configurations listed there. The test case is for a three-stage HEMT module of theconfiguration shown in Appendix A, Figure A-1. Those parameters are:

Gi = Individual Stage Gains = 15 dBFj = Individual Stage Noise Figures = 0.8 dBGb = Beamformer Gain = 40 dBLa= Beamformer Loss = 3.0 dBGR = Off-Array Receiver Gain = 10 dBFR = Off-Array Receiver-Noise Figure = 4.0 dBLR = Premodules Receive Loss = 0.5 dBFA = Antenna-Noise Figure = unknown

It should be noted that the postmodule receive loss has been included in the beamformer loss.Also, note that the antenna-noise figure, related directly to antenna temperature, is unknown.

1-D Hoffman, J.B., Preliminary Results of Active Array Noise Figure/Third Order Intercept Tradeoff Analysis,

Technology Services Corporation, Silver Spring, MD, 11 December 1991.

D-4

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The next step that must be taken is to determine this antenna-noise figure. This will be doneby using the noise-figure results in Reference D-l (with L. = 0) to compute the contributionof FA to FsA.

The curve for noise figure in Reference D-1, with l1, = 0, shows:

FsA - 2.75 dB

= 1.883649089 factor

Substituting the appropriate parameters into Equation (D-1) yields:

FSA = FA+1.356330959+Lm(r,O)*.000107040

= FAA +L,,+L, (r, E) *FBB

And for L., = 0, FSA = 1.883649089, so that:

FA = 1.883649089-1.356330959-.000107040 (D-5)

= .527211090

and:

FAA= FA+1. 3 5 6 3 3 0 9 5 9 (D-6)

= 1.883542049

and:

FBB = .000107040 (D-7)

and finally:

D-5

NSWCDD/TR-93/249

FSA = FAA + FBB * Lm (,) (D-8)

= 1.883542049+.000107040*Lm(r,O)

At this point, it is necessary to digress somewhat and discuss the apparently ambiguousresults for the antenna-noise factor, Equation (D-5). If this value were used to calculate antennatemperature, the results would be a negative noise temperature. Yet, this factor appears to benecessary for the noise-figure equation to support all the data generated in Reference 1. Theexplanation appears to be that the antenna temperature seems to be degraded by a rather highantenna ohmic loss not mentioned in the text of Reference D-1. The loss appears to be greaterthan 3 dB, which corresponds to an antenna temperature of approximately 15 deg K. A loss of5 dB would correspond to an antenna temperature of approximately 200 deg K, which one wouldthink is closer to reality. The results presented in Equation (D-5) are used throughout this workto compute noise figures.

Coming back to the task at hand, Equations (D-8), (-3), and (-4) can now be combinedto determine the effects of attenuation (module loss) for the linear and cosine-squared-on-a-pedestal taper functions. These results were computed for several losses with the results shownin Figure D-1. It is evident that, for the case of this three-stage HEMT module, the effect issignificant only for attenuations greater than approximately 30 dB. How likely is this? ForTaylor weighted antenna designs of up to -55-dB sidelobe levels, the attenuation required doesnot reach more than approximately 25 dB. A Taylor-weighted design for -70-dB sidelobes canreach 40-dB attenuation, but this would be a very stressful design to actually produce. It doesnot seem likely that 40-dB attenuation would be used.

D-6

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S I I I

4 I T

.H

0 5 - .. .

I 4-

3[ -4--- - __

H in isU ~ I EU

2 Ma..u. :-......0 20 40

maximum Module Attenuation (dB)

U Linear t Cos^2-on-Pedistal

FIGURE D-1. RELATION BETWEEN MODULE-NOISE FIGURE AND TAPER-MAXIMUM

ATTENUATION FOR A THREE-STAGE HEMT-MODULE DESIGN

Look at two other cases-a two-stage HEMT/HBT design with the parameters:

G, = It stage gain = 15 dBF1 = lt stage noise figure = 0.8 dBG2 = 2" stage gain = 12 dBF2 = 2nd stage noise figure = 4 dBGb = beamformer gain = 40 dBLB = beamformer loss = 3 dBGR = off-array receiver gain = 10 dBFR = off-array receiver-noise figure = 10.0 dBLR = premodules receive loss = 1.0 dBFA = antenna-noise figure = 0.527211090

and a one-stage MESFET design with the parameters:

G, = 1St stage gain = 11 dBF, = 1• stage noise figure = 1.1 dBGb = beamformer gain 40 dBLB = beamformer loss = 3 dBGR = off-array receiver gain = 10 dBFR = off-array receiver-noise figure = 4.0 dBL = premodules receive loss = 1.0 dBFA = antenna-noise figure = 0.527211090

D-7

NSWCDD/TR-93/249

The resulting equations for these two cases are:

FSA = 2.098449736 + Lm(r,0)*.045107352 (D-9)

and

FSA = 2.049021188 + Lm(r,O)*0.301680955, (D-10)

respectively. The resulting curves are shown in Figures D-2 and -3.

38 -- r7

m 3634,---------- -- -

S 32 _ __ _ - __ --- - --- -

30- - _ _ _ -)4 28 _ _-

260- -_ _ _ ___..... 7- - .. ...- _ - - I22 . . . . .. • 4 4

200 -

.) 18 6_ _ ~ _ _ - - -_

o 14near___Cos 2-- on- 1ed--t--

10

(d a I

0 20 40

Maximum Module Attenuation (dB)

E Linear - Cos^2-on-Pedista1

FIGURE D-2. RELATION BETWEEN MODULE-NOISE FIGURE AND TAPER-MAXIMUMATTENUATION FOR A TWO-STAGE HEMT/HBT-MODULE DESIGN

D-8

NSWCDD/TR-93/249

5 0 - ~ . .. ..... .. . . . . . . .. . .. .

35' 0 -- . .. . . .. .

a)

S320 Air -

04 20o a

150

0 20 40

Maximum Module Attenuation (dB)

U Linear I Cos 2-on-Pedistal

FIGURE D-3. RELATION BETWEEN MODULE-NOISE FIGURE AND TAPER-MAXIMUMATTENUATION FOR A ONE-STAGE MESFET-MODULE DESIGN

These figures show that there are designs with a much higher likelihood of using weightsthat will contribute to the overall noise figure than was evident in the first case. In fact, caremust be exercised to avoid sensitivity to this effect. In both cases (considering a -55-dB sidelobedesign), an attenuator requirement of 20-25 dB would have an extreme effect on overall noisefigure. Clearly, this would be unacceptable in a majority of systems.

As mentioned earlier, if (as Mr. Hoffman suggested) these modules were to be operatedat high-module loss to improve the third-order intercept, the combination of high, overallmodulelosses and taper attenuation would cause the noise figure to become even more extreme.Care must be exercised to produce a good active-array design.

It should be reiterated that these curves are for linear and cosine-squared-on-a-pedestaltapers and not for a Taylor taper. The fact that these two tapers yield almost identical resultsseems to suggest that the curves for more complex tapers would be similar. This is, assumedto infer noise-figure effects when the maximum weights for examples of Taylor-tapered antennasare used with these curves . This is hopefully a reasonably valid assumption even without anysupporting objective analyses.

D-9

NSWCDD/TR-93/249

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I February 1994 Final

4. TITLE AND SUBTITLE S. FUNDING NUMBERS

Solid-State, Active-Phased Arrays-Some Aspects of Receiver Design

6. AUTHOR(S)

Joseph D. Harrop

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION

REPORT NUMBER

Naval Surface Warfare Center (Code F42) NSWCDD/TR-93/249Dahlgren DivisionDahlgren, Virginia 22448-5000

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Approved for public release; distribution is unlimited

13. ABSTRACT (Maximum 200 words)

The Navy's use of solid-state transmitter technology has been limited to communication equipment orother uses requiring relatively lowpower, low frequency, or both. It has now become necessary to addresssome of the issues and tradeoffs involved in the design of transmit/receive modules so that active phased-arraycharacteristics can be fully understood.

The analytical work performed here determines the general relationship among the system noise figure,and third-order intercept requirements of phased-array receivers and the effect on noise figure of addingreceive-attenuation to implement weighting (taper) of the array elements.

14. SUBJECTTERMS 15. NUMBER OF PAGES

system noise figure, signal and third-order intercept curves, phased-array 140receivers, linear taper, cosine-squared-on-a-pedestal taper 16. PRICE CODE

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