Theory and Proposed Method for Determining Large Signal Return Loss or Hot S22 for Power Amplifiers Using Phase Information

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1 Thory and Proposd Mthod for Dtrmining arg Signal Rturn oss or Hot S for Powr Amplifirs Using Phas Information Patrick Narain and Chandra Mohan (Skyworks Solutions, Inc.) Introduction: Powr amplifirs (s) ar a critical functional block in today s wirlss communications. Thy ar found in vry cll phon, cordlss phon, RF rmot controllr, tc. Any application rquiring th wirlss transmission of analog or digital signals will rquir a. Th s ar usually placd as clos as possibl to th antnna in wirlss quipmnt to minimiz RF losss, imiz powr fficincy and imiz battry lif. RF systms nginrs nd to dtrmin th rturn loss undr actual output powr driv lvls. This so-calld Hot S is ndd to calculat mismatch loss at th antnna intrfac, and to dtrmin th actual wirlss systm transmit powr (a ky rquirmnt for rgulatory bodis,.g. FCC). Th vrification of output rturn loss has provn to b a problmatic and challnging ndavor whn th is dlivring high output powr. High powr s will inadvrtntly hat up as th output powr lvls ar incrasd. Undr high output powr conditions, th powr transistors paramtrs may significantly chang as tmpratur and bias conditions chang [1]. Thrfor, th output rturn loss may b substantially diffrnt whn opratd undr low output powr vs. high output powr. Most supplirs will only publish rturn loss valus for small signal conditions. Ths valus should b chckd against actual high powr conditions whn conducting systms transmit powr budgts. A numbr of tst quipmnt supplirs hav off-thshlf tst hardwar for masuring th rturn loss of high powr units [-3], but ths solutions ar usually vry xpnsiv, and may not justify invstmnt for nginrs conducting only occasional high powr tsts. This papr outlins a simpl and cost-ffctiv solution for dtrmining th rturn loss of a high powr. A tst procdur is outlind basd on a mathmatical approach to dtrmin th larg (or small) signal rturn loss by masuring th insrtion phas variation of th at spcific SWRs using an inxpnsiv and simpl tst arrangmnt. 1

2 1. Rflction Cofficint: Any RF tst configuration can b xprssd by a sourc impdanc (Z ), and charactristic impdanc ( z 0 ) as shown in Figur 1. Pincidnt Z0 Prflctd Z oad Sourc Figur 1: Powr transmission from sourc to load If th load impdanc is qual to th sourc charactristic impdanc thn th rflctd travling wav dos not xist (i.. as is th cas for matchd load). Howvr, whn Z is not qual to th output impdanc, z 0, thn th travling wav btwn th to th load contains two componnts: on is travling in z dirction and th othr travling in th z dirction. γ z γz Th travling wav in z dirction is th incidnt powr, and th travling wav on th -z dirction is th rflctd powr. inc rf γ z γ z Whr γ is th propagation constant. Now lt us rplac th sourc with an actual and th load with a phas tunr, which rotats th phas π radians, and causs in thory full rflction back to th as illustratd in Figur.

3 inc rf Phas Tunr 1 3 Match oad Figur : in a mismatch systm Th rflction cofficint is dtrmind to b th ratio btwn th rflctd to th incidnt vctor as follows: jθ t ( θ φ 0 ) t φ 0 jψ ' t ( θ φ ψ ) 0 t ( θ φ ) φ is th shiftd phas causd by th θ is th phas angl of th rflction cofficint ψ is th phas angl of th rflction cofficint Th summing vctor,, in th coupling port contains thr vctors which ar dirctd from thr diffrnt paths. i.. 1 inc CF 0 3 inc inc CF CF DR Whr CF is th bidirctional coupling factor and DR is th dirctivity for th bidirctional couplr. CF 1 3 0t φ jw0t φ jw t φ CF CF DR 0 3

4 Using dirctional couplrs with DR > 0dB, nsurs 3 is much smallr than, i.. >> 3 inc CF >> inc CF DR DR >> It is rcommndd that th dirctivity for th bidirctional couplr should b highr than th rturn loss by 15dB. This will nsur vctor 3 will rmain ngligibl. Dirctivity R. 15dB If 3 is ngligibl, thn vctor can b rducd to: 1 j t φ CF (1 ω 0 j( θ ψ ) ) Total ' t ( θ φ ψ 0 ) t φ 0 CF( 0t φ ' 0t ( θ φ ψ ) ) Th summing vctor as illustratd in Figur 3, contains vctor 1 which rprsnt th incidnt wav and vctor which rprsnts th rflctd wav. θ ψ 0 1 tφ ' 0t ( φ θ ψ ) φ ϕ Figur 3: Th rflctd wav vctor is rotating π radians across th incidnt wav vctor according to th phas tunr position. 4

5 Th angl ϕ is th angl btwn th incidnt vctor 1 to th summing vctor and it also dtrmind as th variation in insrtion phas btwn insrtion phas at SWR1:1 to th insrtion phas whn th phas tunr is shiftd within π radians with SWR>1:1. Thr ar two locations on th phas tunr whr th imum and minimum insrtion phas is achivd. At ths two locations, th rflctd vctor is prpndicular π π to th incidnt vctor ( θ ψ or θ ψ ), and th angl ϕ rachs th highst valu, ϕ. φ ϕ φ ϕ Figur 4: ctor diagram for imum and minimum insrtion phas. Maximum or minimum phas variation occurs whr th forward incidnt vctor is prpndicular to th rflctd vctor and th insrtion phas variation is th angl ϕ btwn th forward vctor and th summing vctor. At ths two locations of 90 dgrs insrtion phas, th product of th load and rflction cofficints can b writtn as: π π ( ) ( ) ' 0t φ ' 0t φ Total 0t φ 0t φ Total 0log 0log tanϕ tanϕ 0log 0log 0log tanϕ 5

6 0log 0log tanϕ 0log Sinc th phas tunr has a full rflction thn 1 and th rturn loss (in db) can b xprssd as: _ R. 0log tanϕ ϕ can b found by rotating th phas tunr within π radians and imum insrtion phas can b sarchd using a phas dtctor with a tst stup shown in th Figur 5. R. RF Bidirctional Couplr Phas Tunr Pinc Phas Dtctor Prf Figur 5: Tst st up for masuring imum insrtion phas 6

7 . rflction cofficint with dtrmind mismatch load: In practic, s ar spcifid ovr a limitd SWR rang. Th can b damagd or unstabl with a load SWR abov what has bn spcifid by th vndor. Thrfor, th sam analysis will b givn whn th load phas tunr is connctd to th through an attnuator in ordr to limit th SWR which will rflct on th. inc rf Att Phas Tunr Phas Dtctor 1 Match oad Figur 6: Tst st up for masuring imum insrtion phas with limitd SWR 1 CF tanϕ ( ) 0 t φ ( ) ' 0 t ( θ φ ψ Att ) ' 0t ( θ φ ψ ) ( Att) ( Att) 0t φ tanϕ ( Att) tanϕ _ R. 0log 0 log( ( Att) Sinc th phas tunr has a full rflction, 1 and th rturn loss can b xprssd as: ) 7

8 tanϕ _ R. 0log 0log( ( Att) or: 0log(tanϕ ) _ R. ( db) Att( db) ) If th rturn loss is high and th attnuator usd btwn th to th phas tunr is high, thn th phas angl ϕ maz may b small and difficult to masur in ordr to hav accurat rsults. Thrfor, it is suggstd to us a small attnuator (.g. 1 db to 3 db) btwn th and th phas tunr. 3. Tst Mthod: Stp 1: Connct th as illustratd in Figur 7 using a 50 Ohms load at th output of a bidirctional couplr (additional attnuation can b connctd in front of th phas dtctor whnvr it is dsird to masur rturn loss for vry high powr ). R. RF Phas Dtctor Bidirctional Couplr Match oad Match oad Figur 7: Tst Stup for matchd load. Masur th insrtion phas at th various frquncis of intrst using small signal or larg signal input powr. Th insrtion phas with 50 ohms load will b th rfrnc insrtion phas bfor loading th with diffrnt SWRs. In Tabl 1 blow, w show th masurd valu for a high powr ( Watts) 350 MHz to 470 MHz Skyworks th SKY A photo of th mountd in its tst fixtur is shown in Figur 1. 8

9 Frquncy (MHz) Insrtion Phas at SWR 1:1 and Pin-4dBm θ 50Ω Tabl 1: Insrtion phas with SWR 1:1 for Skyworks high powr th SKY Stp : Disconnct th 50 ohms load at th output of th bidirctional couplr and connct a 1.5dB pad in ordr to prsnt th a SWR of 6:1. Plac a phas tunr aftr th fixd attnuator pad. Th phas tunr must b capabl of continuously varying th insrtion phas from 0 to 360 dgrs. Th tst stup is illustratd in Figur 8A. R. SWR6:1 RF Bidirctional Couplr db 1.5dB Phas Tunr ϕ min ϕ Match oad Phas Dtctor Figur 8A: Tst Stup for mismatchd load. Figur 8B: ctor Diagram at th coupling port whnφ 0. Adjust th phas tunr in ordr to find th highst and lowst insrtion phas and calculat at ach frquncy what th imum phas variation is compard to th insrtion phas at 50 Ohms as indicatd in Tabl. Not, th attnuator valu is slctd to b within th spcifid load SWR rang. Th total output insrtion loss should b masurd at ach imum insrtion phas location on th phas tunr in ordr for th rturn loss to b calculatd accuratly. 9

10 Frquncy (MHz) Minimum Insrtion Phas φ ϕ ) ( Maximum Insrtion Phas φ ϕ ) ( Maximum Insrtion Phas ariation ϕ Tabl : Masurd imum and minimum insrtion phas with SWR 6:1 at various pass band frquncis. In thory ϕ ϕ min, thrfor th following quation is valid: ϕ ϕ min ϕ ϕ50ω ϕ50ω ϕ min Howvr, in practic ϕ and ϕ min may not b qual sinc th phas tunr may not b idal and symmtric. Thrfor, th insrtion phas at SWR 1:1 ( ϕ 50Ω ) is subtractd from th absolut valu for th imum phas variation ( φ ϕ or φ ϕ ). Th rturn loss of th is calculatd according to th following formula: tanϕ R. 0 log[ ( Att) _ ] Whr θ is in dgrs and Att is th masurd attnuation from th output to th phas tunr input. 10

11 4. Tst Rsults: Th thortical analysis shown in th abov sctions was vrifid using a high powr Watts SMT from Skyworks -- th SKY Th was tstd ovr its ntir oprating frquncy rang to 470 MHz. Actual rturn loss masurmnt was mad with a small input signal and th rsults ar givn in th following graph: Figur 9: Rturn oss masurmnts at low powr using ntwork analyzr Th masurmnt rsults ar compard to th calculatd rturn loss using th proposd phas masurmnt procdurs outlind in th abov sctions. Th nw tst procdur was don using diffrnt load SWRs to dmonstrat th rturn loss masurmnt is rpatabl at diffrnt SWR. Th rturn loss obtaind using th nw proposd phas tchniqu is shown in Figurs 10 and

12 -8-10 Rturn oss at Pin-30dBm SWR6:1 SWR16:1 SWR3.5:1 NA_Masurmnt -1 db Frq (MHz) Figur 10: Rturn oss Calculation with diffrnt SWRs vrsus ntwork analyzr masurmnt. Th sam mthod was usd to calculat th rturn loss using highr input signal with SWR 3.5:1. -8 Rturn oss at Pin-4dBm db Frq (MHz) Figur 11: Rturn oss Calculation with high input driv lvl 1

13 Figur 1: Photo of th High Powr (SKY65141) mountd in its Tst Fixtur 13

14 Conclusions: rturn loss is a paramtr which can vary dpnding on th output powr, bias currnt, tc. Thrfor, th rturn loss undr high output powr condition should b masurd, and not b assumd to b th sam as th rturn loss masurd undr small signal output powr condition. Th rturn loss can b calculatd from th phas btwn th summing (incidnt and rflctd vctors) to th incidnt vctor which is masurd with a matchd-load. This papr dmonstrats that hot rturn loss calculation can b accuratly calculatd by masuring th imum insrtion phas variation at any givn SWR, and at any givn input driv lvl. Th proposd rturn loss masurmnt tchniqu can b implmntd using low cost tst componnts, liminating th nd for costly ntwork analyzrs. REFERENCES [1]. iou, J.Ebl, and C. Huang, Thrmal Effcts on th Charactristics of AlGaAs/GaAs htrojunction bipolar transistors using two-dimnsional numrical simulation, IEEE Trans. Elctron Dvics, vol. 40. pp , [] Rcommndations for Tsting High-Powr Amplifirs, Agilnt Application Not [3] Hot S and Hot K-Factor Masurmnts. Anritsu Application Not AN

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