TECHNICAL FEATURE

THEORY AND PROPOSEDMETHOD FOR DETERMININGLARGE-SIGNAL RETURN LossOR "HOT S22" FOR POWERAMPLIFIERS

Power amplifiers (PA) are a critical func-tional block in today's wireless commu-nications. They are found in every cell

phone, cordless phone, RF remote control-ler, etc. Any application requiring the wirelesstransmission of analog or digital signals will re-quire a PA. In wireless equipment, the PAs areusually placed as close as possible to the anten-na to minimize RF losses, maximize power ef-ficiency and maximize battery life. RF systemsengineers need to determine the PA return lossunder actual output power drive levels. Thisso-called "Hot S22" is needed to calculate themismatch loss at the antenna interface and todetermine the actual wireless system transmitpower (a key requirement for regulatory bod-ies, such as the FCC).

The verification of a PA output return losshas proven to be a problematic and challengingendeavor when the PA is delivering high outputpower. High power PAs will inadvertently heatup as the output power levels are increased.

Under high output power con-ditions, the power transistor'sparameters may significantlychange as temperature andbias conditions change.' There-fore, the PA output return lossmay be substantially differentwhen operated under low out-put power versus high output

--P REFLECTED z,

-=.A. Fig. 1 Power transmission from sourceto load.

92

power. Most PA suppliers will only publish re-turn loss values under small-signal conditions.These values should be checked against actualhigh power conditions when conducting sys-tems transmit power budgets. A number of testequipment suppliers have "off-the-shelf' testhardware for measuring the return loss of highpower units,2,3 but these solutions are usuallyvery expensive, and may not justify the invest-ment for engineers conducting only occasionalhigh power tests.

This article outlines a simple and cost -effec-tive solution for determining the return loss ofa high power PA. A test procedure is outlined,based on a mathematical approach, to deter-mine the PA large- (or small-) signal return lossby measuring the insertion phase variation ofthe PA at specific VSWRs, using an inexpensiveand simple test arrangement.

PA REFLECTION COEFFICIENTAny RF test configuration can be expressed

by a source impedance ZL, and a characteristicimpedance (Zo), as shown in Figure 1. If theload impedance is equal to the source charac-teristic impedance then the reflected traveling

PATRICK NARAINE ANDCHANDRA MOHANSkyworks Solutions Inc., Woburn, MA

MICROWAVE JOURNAL. JUNE 2009

TECHNICAL FEATURE

wave does not exist (as is the case fora matched load). However, when ZL isnot equal to the PA output impedanceZo, then the traveling wave V betweenthe PA to the load contains two com-ponents: one is traveling in the +z di-rection and the other traveling in the-z direction.V=V+e--YZ+V_e+-Yz (1)

The traveling wave in the +z di-rection is the incident power, and thetraveling wave on the -z direction isthe reflected power.Vinc=V+e--Y.Z (2)Vref= V_e+-Y.Z (3)where 'Y is the propagation constant.

Now replace the source with anactual PA and the load with a phasetuner, which rotates the phase by 2'ITradians and causes, in theory, full re-flection back to the PA, as illustratedin Figure 2. The reflection coefficientis determined to be the ratio betweenthe reflected and the incident vectoras follows:

r L = IrL I·ej9

V ejOlot+(9+cjl)rL=------

V jOlot+cjl+e

I'PA = IrPAI·ej'PV' jOlot+(9+cjl+'P)r = ----'+_e _

PA V_ejOlot+(9+cjl)

where:<I> is the shifted phase caused by

thePAe is the phase angle of the reflec-

tion coefficient I'L'I' is the phase angle of the reflec-

tion coefficient I'PAThe summing vector, V, in the

coupled port contains three vectorsthat are directed from three differentpaths, that is:

=

V1=Vinc' CF (6)

V2=Vinc' rPA' rC CF (7)V3=Vinc' rC CF . DR (8)

where CF is the bidirectional cou-pling factor and DR is the directivityfor the bidirectional coupler.V=V1+V2+V3 (9)V=CF'V+eiwot+<!>+

CF·f PA'rL'V+eiwot+<!>+CF·DRT L'V+eiwot+<!> (10)Using directional couplers with

DR > 20 dB, ensures that V3 is muchsmaller than V2, that is:V2»V3Vinc' fpA' fL· CF»Vinc·fL· CF· DRf PA»DR (ll)

It is recommended that the direc-tivity for the bidirectional couplershould be higher than the PA returnloss by 15 dB. This will ensure that thevector V3 will remain negligible.

Directivity> PA R.L + 15 dBIf V3 is negligible, then the vector

V can be reduced to:V=V1+V2 (12)V=CF-Y +eiWot+<!>(1+IfPAI·lfd' ei(o+ljJ)(13)

(4) r Total= r PA . r L =v jOlot+(9+cjl+'P)

+e

(5)V=CF(V +eiwot+hV~eiwot+(a+<!>+ljJ))(15)

The summing vector V, as illustrat-ed in Figure 3, contains the vector Vi-which represents the incident waveand the vector V2' which representsthe reflected wave.

The angle 'P is the angle betweenthe incident vector VI to the sum-ming vector V and is also determinedas the variation in PA insertion phasebetween the PA insertion phase atVSWR=l:1 to the PA insertion phasewhen the phase tuner is shifted with-

in 2'IT radians withVSWR> 1.

There are two lo-cations on the phasetuner where themaximum and mini-mum PA insertionphase is achieved.At these two loca-tions, the reflectedvector is perpen-dicular to theincident vector.••• Fig. 2 PA in a mismatch system.

94

.••• Fig. 3 The reflected wave vector isrotating 211" radians across the incident wavevector.

······f························ •.

(14)

.••• Fig. 4 Vector diagram for maximum andminimum insertion.

n n(S+'P=-orS+'P=--)2 2and the angle 'P reaches the highest val-ue, 'PMAX>as shown in Figure 4. Atthese two locations of 90° insertionphase, the product of the load and PAreflection coefficients can be written as:

, jWot+(<!>-~)V e 2

+ = tanV jWot+<!> 'Pmax

+e(16)

-2010glf Totall=-2010gtan'Pmax (17)

-2010glf PAI-20l0glf tl=-2010g tan'Pmax (18)

-2010glf PAI=-2010gtan'Pmax+2010glf d (19)

Since the phase tuner has a full reflec-tion then CL = 1and the PA return loss(in dB) can be expressed as:PA_R.L=-2010g tan'Pmax (20)

'PMAXcan be found by rotating the

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TECHNICAL FEATURE

phase tuner within 21f radians andthe maximum insertion phase can besearched using a phase detector withthe test setup shown in Figure 5.

PA REFLECTION COEFFICIENTWITH A DETERMINED MISMATCHLOAD

In practice: PAs are specified overa limited VSWR range. The PA canbe damaged or unstable with a loadVSWR above what has been specifiedby the vendor.

Therefore, the same analysis willbe given when the load phase tuner isconnected to the PA through an atten-uator in order to limit the VSWR thatwill reflect on the PA (see Figure 6).V=V1+V2 (21)V=CF'(V+ eiWot+<I>+

(Att)2·V~ eiwot+(9+<I>+t\ll) (22)

V' jWot+(9+<I>+t\lltan 'P = (Att)2 . ---'...+_e _

max V jWot+<I>+e

(23)

I' _ tan'PmaxFA - (Att)2 -I'L

PA_RL = -20 log TFA =

-20 log ( tan 'Pmax 1(Att)2 . r L

Since the phase tuner has a full re-flection, I'L ~ i- the PA return loss canbe expressed as:

(24)

(25)

TEST METHODStep 1:

Connect the PA ••. Fig. 6 Test setup for measuring maximum insertion phase withlimited VSWR.as illustrated in Fig-

ure 7 using a 50 n load at the outputof a bidirectional coupler (additionalattenuation can be connected in frontof the phase detector whenever it isdesired to measure the return loss fora very high power PA).

Measure the insertion phase at thevarious frequencies of interest us-ing small-signal or large-signal inputpower. The insertion phase with a 50n load will be the reference insertionphase before loading the PA with dif-ferent VSWRs.

PA_RL = -20logr FA =

-20 log (tan 'Pmax)(Attl

or-2010g(tan'PmaJJ=PA_RL(dB)+2·Att(dB) (27)

If the PA return loss is high and theattenuator used between the PA to thephase tuner is high, then the phaseangle 'PMAXmay besmall and difficultto measure in orderto have accurate re-sults. Therefore, itis suggested to usea small attenuator(1 to 3 dB) betweenthe PA and thephase tuner.

PAR.L

(26)PHASETUNER

••. Fig. 5 Test setup for measuring maximuminsertion phase.

Vref

PAR.~

••. Fig. 7 Test setup for matched load.

TECHNICAL FEATURE

In Table 1, the measured value fora high power (2 W), 350 to 470 MHz,Skyworks' PA (SKY65141), is shown.

Step 2:Disconnect the 50 n load at the

output of the bidirectional couplerand connect a l.5 dB pad in orderto present the PA with a VSWR = 6.Place a phase tuner after the fixed at-tenuator pad. The phase tuner mustbe capable of continuously varyingthe insertion phase ,------------------------------------------,from 0 to 360°. The TABLE 11test setup is illus-trated in Figure 8.Adjust the phasetuner in order tofind the highestand lowest insertionphase and calculateat each frequencywhat the maximum 350phase variation is, 1-4-1-0-------+-62-.-3-------+-75---------+--6.-7---------i

compared to the in-sertion phase at 50 470n, as indicated in L- ..I.- ---I.. .l..- ---'

Table 2. Note thatthe attenuator value is selected to bewithin the specified PA load VSWRrange. The total output insertion lossshould be measured at each maximuminsertion phase location on the phasetuner in order for the return loss to becalculated accurately.

In theory 'PMAX= 'PMIN' thereforethe following equation is valid:

MEASURED MAXIMUM AND MINIMUM INSERTION PHASEWITHVSWR=6

TABLE IINSERTION PHASE WITH VSWR=1 FOR

A SKYWORKS PA

350 171.4

410 71.2

-30.5470

157.1 179.9 12.2

'Pmax - 'Pmin2 = 'Pmax - 'P50n =

'P50n - 'Pmin

However, in practice 'PMAX and'PMIN may not be equal since the phasetuner may not be ideal and symmet-ric. Therefore, the insertion phase atVSWR = 1 ('Pson) is subtracted fromthe absolute value for the maximumphase variation (<!>-'PMAXor <!>+'PMAX)'

The return loss of the PA is calculat-ed according to the following formula:

PA_RL = _2010g[tan'P~ax 1 (29)(Att)

where 8MAXis in degrees and Att isthe measured attenuation from the PAoutput to the phase tuner input.

TEST RESULTSThe theoretical analysis shown in

-42 -26.2 8.6

PAR.L VSWR = 6:1

••. Fig. 8 Test setup for mismatched load.

(28) the above sections was verified usinga high power 2 W SMT PA from Sky-works (SKY65141). The PA was testedover its entire operating frequencyrange, 350 to 470 MHz. The actualreturn loss measurement was madewith a network analyzer at small inputsignal and the results are given in Fig-ure 9.

The measurement results are com-pared to the calculated return loss us-ing the proposed phase measurementprocedures outlined in the above sec-tions.

The new test procedure was doneusing different load VSWRs to dem-onstrate that the return loss mea-surements are repeatable at differentVSWRs. The return loss obtainedusing the new proposed phase tech-nique is shown in Figures 10 and 11.

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TECHNICAL FEATURE

-8

-10!-12- -14N

~ -16

~1"\,',.. '7~

~~ Vr-, r

mlFREQ= 350.0 MH.dB (5(2,2)) = -9.964m2FREQ= 410.0 MH.dB (5(2,2)) = -15.617m3FREQ= 470.0 MH.dB (5(2,2)) = -13.559

-18

-20340 360 380 400 420 440 460 480

FREQUENCY(MH.)

A Fig. 9 Return loss measured at low power.

VSWR = 6:1 VSWR = 16:1 rlVSWR = 3.5:1 NA_MEASUREMENT

~~ .-" ...•~

20 360 400 440 480FREQUENCY (MH.)

-8-10

liD -12"a-:::.-14~ -16

-18-20

3

A Fig. 10 Calculated PA return loss at Pin= -30dBm.

A Fig. 12 Photo of high power PA(SKY65141) mounted in its test fixture.

The same method was used to calcu-late the FA return loss using higher in-put signal with VSWR = 3.5. A photoof the FA mounted in its test fixture isshown in Figure 12.

CONCLUSIONA FA return loss is a parameter,

which can vary depending on the FAoutput power, the FA bias current,etc. Therefore, the FA return lossunder high output power conditionsshould be measured and not be as-sumed to be the same as the returnloss measured under small-signaloutput power conditions. The FA

..•...<, -...•. V-

20 360 400 440 480

-8-10

liD -12~-;;--14.;:-16

-18-20

3FREQUENCY (MHz)

A Fig. 11 Calculated return loss Pin =-4 dBm and VSWR = 3.5. .

return loss can be calculated fromthe phase between the summing(incident and reflected vectors) tothe incident vector, which is mea-sured with a matched-load.

This article demonstrates that the"hot" FA return loss can be accuratelycalculated by measuring the maxi-mum insertion phase variation at anygiven VSWR, and at any given inputdrive level. The proposed return lossmeasurement technique can be im-plemented using low cost test compo-nents, eliminating the need for costlynetwork analyzers .•

References1. L. Liou, J. Ebel and C. Huang,

"Thermal Effects on the Charac-teristics of AlGaAs/GaAs Hetero-junction Bipolar Transistors Us-ing Two-dimensional NumericalSimulation," IEEE Transactionson Electron Devices, Vol. 40, No.1, January 1993, pp. 35-40.

2. "Recommendations for TestingHigh-power Amplifiers," AgilentApplication Note 1408-10.

3. "Hot S22 and Hot K-factor Mea-surements," Anritsu ApplicationNote AN1141 0-00295.

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