ECEN 514, Sprng 13 Specal Topcs: Acte Mcrowae Crcuts and MMICs Zoya Popoc, Unersty of Colorado, Boulder LECTURE 4 BROADBAND AMPLIFIERS L4.1. INTRODUCTION The challenge n desgnng a broadband mcrowae amplfer s the fact that the nput mpedance at lower frequences s practcally an open crcut, and at hgher frequences predomnantly capacte and can be almost a short. Ths makes broadband matchng dffcult. For example, the TrQunt dece we used for the project has an nput mpedance that s practcally an open crcut at.1ghz, s almost purely capacte at 1GHz and ab 35+j6 at 5GHz (the package nductance starts domnatng at the hgher frequences). It s clear that desgnng an mpedance matchng crcut that can coer ths frequency range s a dffcult task. In ths lecture, we cuss possble approaches for small-sgnal amplfers, but the challenge for power amplfers s smlar. An example extreme nput and put mpedance of a LDMOS base-staton power dece s shown n Fg.L4.1, ndcatng sub-ohm alues for both nput and put mpedances. The dece was used to desgn of a Wdeband Code Dson Multple Access (W CDMA) base staton PA, operatng at the.11-.17ghz range. The expected put power s 7W (CW) wth gan of 1 db. The transstor operates at 8V dran supply, wth maxmal dran oltage of 66V and maxmal dran current of 11 A. The hgh power transstor conssts of two 4 parallel fnger cells, resultng n a ery low nput and put mpedances. Internal pre-matchng s done on the de to ncrease the mpedance to a slghtly hgher leel seen n the fgure. Ths dece cannot be matched oer a broad bandwdth wth sacrfcng put power and gan. Fgure L4.1. Input and put mpedance of a LDMOS power dece at GHz. Measured source (left) and load (rght) mpedance contours of the constant put power (dashed) and gan (sold) for the ACPR=-45 dbc at.11ghz. 5-ohm charts are shown as nsets for easer orentaton. Impedances for the maxmum put power (x) and maxmum gan (+) are also shown. Selected target mpedances (black crcle) are : ZS = (8.5 + j) and ZL = (1.5 j3.5) at.11 GHz. 1
There are seeral ways to desgn a broadband nput match to an amplfer, each has ts drawbacks and adantages: (1) broadband non-unform mpedance matchng network desgn; () balanced amplfer; (3) resste feedback amplfer; (4) trbuted and (5) traelng-wae amplfer. The frst type s based on desgnng person-compensaton or pre-person networks and results n ery large mpedance matchng networks whch typcally hae substantal loss. If we hae tme, we wll talk ab these nonunform transmsson lne matchng crcuts. L4.. BALANCED AMPLIFIERS A common approach to the problem of broadband amplfer desgn s a balanced amplfer confguraton shown n Fgure L4.. It conssts of a par of 3-dB couplers. For example, f the couplers are deal 9 hybr (such as a branch lne coupler), the scatterng matrx for the balanced amplfer can be wrtten as: INPUT Matchng network Matchng network 5 5 3-dB coupler Acte dece 3-dB coupler OUTPUT Fgure L4.. Balanced amplfer confguraton usng drectonal couplers.. 1 1 ( s11 s11)/ j( s1 s1)/ S= ( 1 1. js1 s1 )/ ( s s )/ and f the two amplfers are dentcal, the scatterng matrx becomes: S= js 1 js 1 Ths means that, as long as the amplfer crcuts are dentcal, they can be whateer we wsh, and the amplfer stll has nput and put matchng. The two amplfers can nddually be tuned for gan, nose or flatness of frequency response. Another common balanced amplfer uses Wlknson combner/dders nstead of the branch-lne couplers. In ths case, quarter-wae sectons n the two lnes prode a 18 degree phase dfference
between the two waes reflected from the nputs of the amplfers, and the reflectons are cancelled. The bandwdth of the amplfer s obously lmted by the bandwdth of the drectonal coupler or Wlknson spltter, both of whch rely on quarter-wae sectons for proper operaton. Therefore, a hybrd s not the best choce (t has ab 15% bandwdth). Instead, most commonly used s a Lange coupler based on coupled lne sectons, whch can hae a bandwdth of octaes. It s also possble to desgn broadband mult-secton branch lne and Wlknson combners (oer decade bandwdth). We wll talk more ab coupled-lne couplers n the next lecture. Balanced amplfers deally hae the same gan and twce the put power as compared to the sngle amplfer. When the sgnal becomes large, each of the transstors recees only half the power, so balanced amplfers can handle more power wth less sgnal torton. Howeer, twce the nput sgnal s requred, and two tmes more DC power. An addtonal adantage s the sze of the crcut and the fact that a large part of the real-estate s taken by passe crcuts. Ths s ery costly n MMIC mplementatons. An mportant factor n balanced amplfer desgn s the ampltude and phase msmatch between the coupler put ports as a functon of frequency, as well as the senstty of ths msmatch to load mpedance aratons. In a practcal desgn, ths should be erfed n smulaton pror to fabrcaton. L4.3. RESISTIVE FEEDBACK AMPLIFIERS Resste feedback can also be used for desgnng a broadband amplfer. The effect of a feedback resstor between the gate and dran of a MESFET s to lower the nput and put mpedance and to broaden the gan cure. The drawback s resste couplng between the bas crcuts, as well as oerall lower gan than for reactely matched amplfers. By obserng the approxmate crcut model for the MESFET wth normalzed resstance alues (to 5), Fgure L4.4, the equatons for the current and oltage n the nput crcut are found to be: n gmn n rf n r 1 Solng for the nput mpedance by elmnatng, we obtan: Z n n n rf 1 1 gm r 1 3
r f n 1(Z ) 1(Z ) r f r n g m n 1 r f + gs - 1 g m n r Fgure L4.4. Smplfed equalent crcuts for nput and put MESFET crcuts n a seres feedback amplfer. For the put crcut, the current and oltage can be expressed as: g 1 r r m gs f (1 r ) f gs where the oltage can be elmnated to ge the expresson for the put mpedance: Z 1 rf 1 gm 1 rf r 1 g m In both cases, the mpedance s reduced and can be controlled by the amount of feedback resstance. R fs R fs Z R fp n Z n gs gmgs R fp n R fp Fgure L4.5. Smplfed crcut for seres-shunt resste feedback amplfer. The aboe smplfed analyss was an example of the more general case of seres-shunt resste feedback shown n Fgure L4.5, where n addton to the seres feedback 4
between gate and dran, there s a parallel feedback resstor placed n the source. The admttance matrx for ths network (for a ery smplfed FET model) can be wrtten as 1 1 R n fs R fs n gm 1 1 1 gmrfp Rfs Rfs The admttance matrx can now be conerted to s-parameters usng the standard conerson formulas:. 1 g 1 mz Z Rfs (1 gmrfp ) Rfs S 1 gmz Z 1 g 1 mz 1 gmrfp R fs Rfs(1 gmrfp) where gmz Z 1. If the desgn attempts to obtan a match at nput and R R (1 g R ) fs fs m fp put,.e. s 11 s, then the resstor alues are related to the transconductance by gmz Z 1 m fp Rfp Rfs Rfs gm 1 g R or. From the aboe equatons, now s 1 and s 1 can be found to be s Z R Z and s fs 1 1 Z Rfs Z. Notce that the gan of the amplfer depen only on the characterstc mpedance and the alue of the seres feedback resstor, not on the dece parameters. Ths means that flat gan oer a frequency range can be obtaned wth feedback. The physcal meanng of the aboe equatons s that the nput VSWR can be unty wth a poste alue of the parallel feedback resstor, f the transconductance of the acte dece s large. Ths s usually not the case n a MESFET, but s the case n a bpolar transstor. For example, f we desre that the amplfer hae s1 1 db, the mnmal transconductance n a 5-ohm system and the alue of the seres feedback resstor are found by settng R fp (ths s the case that was frst cussed wth just the seres feedback): 5
g m,mn 1 s 1 83 ms and Rfs 8. Z Ths s a farly large alue of transconductance. Off course, the standard feedback relaton Rfs Z(1 s1) s ald. When both seres and shunt feedback resstors are used, and the transconductance s large enough, the best nput and put match are obtaned for RfsRfp Z. Ths gnores the phase of s 1, whch can ary rapdly as the frequency ncreases and cause poste feedback through the resstor. Ths can be soled by addng an nductor n the seres feedback branch wth a alue that the amount of feedback decreases after a certan frequency. L4.4. DISTRIBUTED AMPLIFIERS A technque whch achees extremely broadband operaton s the trbuted amplfer, shown n Fgure L4.6. The dea behnd t s that, nstead of tryng to tune the transstor capactances, these capactances are used as part of a lumped-element approxmaton to a transmsson lne. On the nput sde, nductors L g are placed between the gate-to-source capactances C gs of the adjacent transstors, and n that way the famlar lumped-element artfcal transmsson lne wth a characterstc mpedance of Z g Lg / Cgs s formed. Z g s nearly frequency ndependent. The phase elocty of a wae traelng along ths lne s g 1/ LgCgs. Ths transmsson lne can be resstely termnated at the end wth lttle loss of nput sgnal. On the put sde, nductors L d are placed between dran-to-source capactances of the adjacent deces, and a transmsson lne wth a characterstc mpedance Zd Ld / C and phase elocty d 1/ LdC s formed. Ths s an acte transmsson lne and the sgnal bul up along t. The phases of the puts of the nddual transstors wll only be approprate for left-to-rght propagaton, so lttle power wll be lost n the resste termnaton at the left end of the lne. In effect, the two transmsson lnes are coupled lnes wth a couplng coeffcent greater than unty. The nductors L g and L d can be chosen to equalze the phase eloctes of the two coupled lnes. Ths cusson s ald only for a unlateral transstor approxmaton. From ths descrpton of the trbuted amplfers, t appears that an arbtrarly large gan can be acheed by makng a large number of sectons. In the equalent crcut for the transstor, howeer, there are some resstors as well, and ths wll make the transmsson lne lossy. As a result, a lmted number of transstors can be added before the loss oercomes the gan. The frequency cure of the gan as a functon of the number of sectons s shown n Fgure L4.7. It shows that after 5 sectons, there s no apprecable ncrease n gan, whereas the flatness of the gan s reduced. Dstrbuted amplfers hae been reported wth flat gan from 1 to 4GHz, and nto the 1-GHz range. 6
Fgure L4.6. A trbuted MESFET amplfer usng a ery smplfed unlateral FET model. Fgure L4.7. Dependance of the gan ersus frequency as a functon of the number of sectons of a trbuted amplfer (from publshed data). Dstrbuted amplfers are monolthcally ntegrated so that the deces are ery small compared to the guded waelength. In practce, t s dffcult to make good nductors n monolthc crcuts (why?) at hgh mcrowae frequences. Therefore, short sectons of transmsson lnes are used nstead between the stages of a trbuted amplfer. Snce n that case, the artfcal transmsson lne model becomes een more of an approxmaton, these amplfers are often ewed as traelng wae deces. The equalent crcut of a traelng wae amplfer s shown n Fgure L4.8. Fgure L4.8. Crcut of a traelng wae trbuted amplfer. 7