The Design and Analysis of Non-Uniform Down-Sized Differential Distributed Amplifiers

Transcription

1 The Desin and Analysis of Non-Uniform Down-Sized Differential Distributed Amplifiers Ahmad Yazdi and ayam Heydari Department of EECS University of California, Irvine Irvine, CA Abstrat In this paper the desin and analysis of a novel non-uniform fully differential distributed amplifier is presented. The ainbandwidth produt of the proposed amplifier desined in a 0.8µm standard CMOS proess reahes a reord level of GHz. roved by both the analytial models and the HSICE simulations, down-sizin the devie and indutor sizes of eah stae with respet to the preedin stae in a distributed amplifier will result in a better ain-bandwidth produt. A omprehensive analytial study is arried out to predit the behavior of the amplifier. HSICE simulations verify the superior performane of the proposed non-uniform distributed amplifier ompared to its onventional ounterpart in terms of a better ain-bandwidth produt and a flat frequeny response.. Introdution The inreasin trend in wireless/wire-line ommuniation market for hih data-rate appliations, partiularly the analo/rf front-end, is pushin the interated iruits to operate in multi-iahertz bandwidth. The distributed amplifier is known to be a ood andidate for ultra broadband amplifier desin. A distributed amplifier trades delay with bandwidth and, is therefore apable of ahievin muh hiher bandwidth than lumped arhitetures []. The distributed amplifier onept was first proposed by erival [] as an attempt to resolve the usual ain-bandwidth onstraint in resonant amplifier. Ginzton [] in 948 exploited this idea with thermioni devies and introdued the term, distributed amplifier. Sine then, there have been tremendous efforts to inorporate the distributed onept in various tehnoloies to ahieve wide bandwidths. Distributed amplifiers employ a topoloy in whih indutors or transmission lines (T-lines) separate the ain staes, yet the output urrents from individual staes ombine in additive fashion. From another perspetive, the parasiti apaitanes of the ain staes beome a part of the eletrial parameters of atual (or artifiial) transmission lines, whih results in hiher bandwidth [3]-[7]. One of primary soures of performane deradation in any distributed amplifier is the existene of non-zero indutive loss and output resistane of the ain staes that in turn derease ain and bandwidth. The indutive loss inreases with frequeny due to the skin effet phenomenon [3], whih exaerbates the ain attenuation in hih frequenies. As a onsequene, the series loss of the indutors and output resistane of transistors ditate the bandwidth of distributed amplifiers. In this paper a non-uniform down-sized fully differential distributed amplifier has been introdued. It is shown that down-sizin both the transistor size of eah onstituent stae and the indutor size of eah artifiial line toward the load results in a better ain-bandwidth produt ompared to a onventional uniform CMOS differential distributed amplifier. The key advantae of usin the differential topoloy is its immunity to ommon-mode environmental noise (e.., power/round noise and substrate noise) due to the on-hip interonnets, bond wires, and pakae parasitis. The superior noise performane of the proposed differential arhiteture ompared to the sinle-ended iruit [8] is ahieved at the expense of more power dissipation and larer hip area. This paper is oranized as follows: Setion disusses the onventional fully differential distributed amplifier. It also enompasses a detailed analysis of the ain of the onventional iruit as well as key parameters in the bandwidth alulation of the onventional iruit. Setion 3 disusses the proposed non-uniform fully differential distributed amplifier. Setion 4 inludes the simulation results for both the onventional and proposed differential distributed amplifiers. The simulations have been arried in a 0.8µm CMOS proess provided by the Jazz Semiondutor, In. The simulation results are based on the Jazz devie model for the indutor, apaitor, and resistor. Finally, the onlusion is provided in Setion 5.. Conventional Distributed Amplifier The iruit shemati of a onventional CMOS differential distributed amplifier is shown in Fi.. [6]. In this paper the ain-bandwidth produt refers to both the voltae-ain as well as the power-ain /04 $ IEEE

2 in / / L / M M M M / M N M N L L L / L / L / L / M M M N / Z d L / C L / L L L in / L / BIAS out Fi.. Conventional CMOS differential distributed amplifier equivalent half iruit of the The ate-soure and drain-bulk parasiti apaitanes alon with the inter-stae indutors form uniform Liruits. The Liruits virtually behave as transmission lines [4], [6], [9]. The input sinal differentially applies to the ate lines, as depited in Fi.. Sine the ate lines are idential, sinals arrivin at the ates of eah differential pair have a 80- deree phase differene. Similarly, knowin the fat that drain lines are also idential, the sinals in the drain lines have a 80-deree phase differene. Havin identially mathed differential pairs allows us to employ the half iruit tehnique [0]. The equivalent half iruit is shown in Fi.. The differential voltae travelin alon the ate lines exites eah individual differential ain stae (.f. Fi. ). The sinal at the input of eah differential stae is amplified by that ell. The amplified sinal at the differential output of eah ain stae then propaates toward the load. The differential input sinal travelin alon the ate lines will be attenuated due to the non-zero indutor losses. Consequently, ain staes loated at the far-end of the iruit will reeive the sinal with smaller voltae amplitudes. The equivalent smallsinal model of the ate and drain lines of equivalent half iruit are shown in Fi.. For the drain lines, drain-soure resistanes of transistors as well as series resistanes of indutors are the dominant ontributors to the loss. As for the Z d out / ate lines, the indutor series resistane is the only ontributor to the loss. L / / L L / / in Fi.. The iruit models for Gate line, and drain line Eah LC line is terminated by its harateristi impedane (defined as sqrt(l/c)). From Fi., the urrent delivered to the load is [3]: θ N d N k θ I O me ( ) d () ke k where, k is the voltae aross Cs of the k th transistor and N is the total number of staes. θ d is defined as: θ d A d jφ d where A d and φ d are the attenuation and phase-shift of eah interstae Liruit in the drain line, respetively. k is expressed in terms of the input voltae and ate line propaation onstant as follows [3]: (k ) θ 0.5 in e () k ( ) where, similar to the drain line, θajφ. is the utoff frequeny of the ate line. The input power, the power delivered to the load, and voltae ain for the iruit of Fi., under a mathed termination, are derived as follows: A v out in 0.5 in in Re 0 Z0 out m ( R 0d { Z } (3) IO Re{ Zout} (4) R 0 [ ( ) sinh[0.5n ( A )] / d A )] e sinh[0.5( A d N ( Ad A ) / A )] where, R 0d, Re{Z 0d, }. From Eq. (5), it is observed that the bandwidth is defined by ate and drain line attenuations and the number of staes. The ate and drain attenuations, A and A d, are frequeny dependent. This frequeny dependene affets the flatness of the manitude response of the ain. The ate and drain attenuation per setion are: A Re ( jl R )( G jc ) (6) C s C s C s R0 L / / L R 0d m s C db m 4 s { } d d d ds db L / / C db Z d (5) /04 $ IEEE

3 { ( jl R jc } A Re ) (7) s To study the variations of the ate and drain attenuations with frequeny, (6) and (7) are rewritten as follows: G ds 4 (8) Ad Re 4( ) L d j ( ) L d Gds Q Q A 4 Re 4( ) ( ) j (9) Q where Q is the quality fator of eah inter-stae indutor and /sqrt(lc) is the utoff frequeny of the line. Indiated in Fi. 3 is the ate and drain attenuations versus frequeny for different utoff frequenies and onstant.g ds. As an important observation, whih is also seen from Fi. 3, the frequeny dependene of the both the ate and the drain line attenuations is redued as the utoff frequeny of the line inreases. To inrease the ain-bandwidth produt of the onventional distributed amplifier, we should first study the mehanisms that affet the ain and bandwidth of the onventional iruit. For the uniform distributed amplifiers in whih all ain staes are idential, the ontribution of eah ain stae to the overall output ain is the same. More preisely, the voltae waveform at the load termination is the superposition of the voltae waveforms propaatin throuh different staes. This implies that for the speial ase of idential ate and drain lines, the voltae ain assoiated with eah sinal path, inludin ain stae, from the input to the output terminal of the amplifier is the same. On the other hand, the ain of eah stae is linearly proportional to the transondutane ( m ) of eah stae. For the fixed biasin point, the transondutane of eah stae is linearly proportional to the sizin of the transistors of that stae. Consequently, for the fixed bias point sizin of the transistors in linearly affets the over ain. The bandwidth of the distributed amplifier is set by the frequeny variation of the line s attenuation. From Eq. (5), the attenuation of the line exponentially inreases the slope of the frequeny roll-off of the manitude response, whih approximately auses an exponential derease in the bandwidth. Furthermore, the frequeny dependeny of the ate and drain line attenuations is diminished by inreasin the line ut-off frequeny. The ut-off frequeny of eah line depends on the size of the indutors and apaitors of that line. The parasiti apaitanes of the transistors in the distributed amplifier of Fi. are dominant omponents of the line s apaitanes. Therefore, hanin the transistor sizes of onstituent staes will vary the ain and bandwidth of the amplifier. The above observation provides the main idea behind the proposed non-uniform distributed amplifier to ahieve a better ain-bandwidth produt. Fi. 3. The ate and drain attenuation versus frequeny for the 0.4nH and G ds 70µmho 3. roposed Non-Uniform Fully Differential Distributed Amplifier The proposed non-uniform differential distributed amplifier is depited in Fi. 4. As was disussed in the previous setion, the attenuation of the drain and ate lines exponentially effets the bandwidth of the iruit. In the proposed shemati, eah stae toward load termination is proressively down-sized with a salin fator of K. This obviously auses m, C db, C s, and G ds of eah transistor to beome /K th of those of the transistor that belons to the previous stae. The inter-stae indutor of eah stae is also saled down to be /K th of the previous stae. Similar to the onventional iruit, sinals in the ate lines have a 80- deree phase differene. Similarly, sinals in the drain lines also have a 80-deree phase differene. One aain, identially mathed differential pairs in eah stae allow us to employ the half iruit tehnique [0] /04 $ IEEE

4 in / / L / in / / C L / L / L / (W/L) M M / / M (W/L) L / /K L /K /K /K /K (W/L)/K M M M (W/L)/K /K N / /K /K L /K /K L /K N L / L /K L /K /K N /K N /K N M n (W/L)/K N L /K L L /K N L /K N /K /K N /K N (W/L)/K N M N M N /K N L /K N L /K N Z d L /K N Z d out out / utoff frequenies. The ut-off frequenies of the T-setions alon the lines are doubled, as the sinal travels toward the load. Substitutin Eq. () in (0) and usin equations (3) and (4), we have: ( ( ) N θd θ n θ Nθd K N ( m n ) K i i K i n i ( ) K A 0.5( R0 dr0 ) n e ( n) ( ) K () L /K m- /K m- C s /K m- L /K m /K m C s /K m L /K m /K m C s /K m L /K m /K m C s /K m The ain amplitude Z Z i Z i Z i Z versus i i Z i frequeny for the onventional distributed amplifier and proposed nonuniform distributed amplifier are shown in Fis. 6 and, respetively. /K m /K m C ds /K m C /K m /K m ds /K m ( G ds /K m m /K m )m/ G ( m /K m ds /K m )m/ Fi. 4. The iruit shemati of the proposed N-stae nonuniform down-sized differential distributed amplifier with a salin fator of K, and the equivalent half iruit model of Fi. 4 shows the equivalent half iruit model of proposed non-uniform differential distributed amplifier. Fi. 5 shows the small-sinal models of the ate and drain lines for the equivalent half iruit model of the non-uniform distributed amplifier. Startin from Eq. () while aountin for the non-uniform harateristis of the proposed iruit, the output urrent for the salin fator K is alulated as follows: N θ d θ d ( ) n i K i n K N θ d m n I out e e ( n ) n K (0) Similarly, startin from Eq. (), k for the proposed iruit of Fi. 4 is obtained as follows: n ( i ) IN K i K n e () ( ( / ) ) where, θ and θ d is propaation onstant of the first T-setion of the ate line and drain lines, respetively. N is the number of staes and is the utoff frequeny of the first T-setion of the ate line. We assume that T-setions of the ate and drain lines assoiated with the same stae have idential θ n θ Z i Z i Z i Fi. 5. Small sinal model of the ate line for the proposed non-uniform distributed amplifier Small sinal model of the drain line for the proposed non-uniform distributed amplifier This simulation is arried out under the assumption that the utoff frequenies of the drain and ate lines for onventional distributed amplifier are idential. This utoff frequeny is set equal to the utoff frequeny of the first T-setions of the ate and drain lines in the proposed non-uniform distributed amplifier. In our experiment, the W/L-ratio of transistors in the onventional iruit is equal to W/L-ratio of the first transistor M and M in Fi. 4. M and M have the larest W/L-ratio in the non-uniform distributed amplifier. Therefore, the transondutane, m, of transistors in the onventional iruit is idential to the transondutane of the first transistor in non-uniform ounterpart. Clearly, the proposed iruit has a superior ain-bandwidth produt ompared to the onventional one. Althouh the ain is halved, but the bandwidth beomes at least 0 times larer. The overshoot in the frequeny response is readily explained usin Eq. (5) and (). As mentioned above, the utoff frequeny of eah T- setion is K times smaller than the previous setion. Therefore, as the sinals travels down the lines toward the Z i /04 $ IEEE

5 load terminal, the utoff frequeny beomes K times larer and attenuation beomes K times smaller from eah stae to the next stae. These phenomena result in an approximately exponential improvement in bandwidth for the proposed iruit ompared to the onventional distributed amplifier usin same number of staes. However, the ain of eah stae is dereasin almost linearly from eah stae to the next. As a result, the ain-bandwidth produt for the proposed nonuniform distributed amplifier ompared to the onventional distributed amplifier is larely enhaned. The HSICE simulations iven in the next setion onfirm these observations. Fi. 6. Gain vs. frequeny for the onventional and proposed distributed amplifier. The m 33 mmho and 303 GHz 4. Simulation Results The HSICE simulation is arried out on the iruits desined in a 0.8µm standard CMOS proess, whih is provided by Jazz semiondutor In. Fi. 7 shows a omparison between the voltae ains of two 3-stae onventional amplifiers and the proposed 3-stae amplifier versus frequeny. The salin fator K is hosen to be. This salin fator is taken as an example to show that the proposed amplifier ahieves better ain-bandwidth produt ompared to the onventional amplifier. K is not, however, the optimum salin fator. Both onventional and proposed amplifiers have the same harateristi impedane of 50Ω. The load is assumed to be 00Ω. The utoff frequeny of the onventional amplifiers is the same as the first stae of the proposed amplifier. The onventional amplifier whih is omprised of transistors with the W/L-ratio and tail urrent ( ) equal to those of the first stae of the proposed amplifier has the larest ain and smallest bandwidth. Similarly, the onventional amplifier onsistin of transistors with W/L-ratio and tail urrent ( ) equal to those of the last stae exhibits the smallest ain and the larest bandwidth. Fi. 7 shows the voltae frequeny response of the two onventional amplifier and the proposed non-uniform distributed amplifier. The proposed amplifier has the salin fator of with the first stae havin (W/L)00µm/0.8µm and tail urrent of 8mA. One onventional differential distributed amplifier has (W/L)00µm/0.8µm tail urrent of 8mA. The other one has (W/L)50µm/0.8µm and tail urrent of ma As observed in Fi. 7, the ain of the proposed amplifier exhibits a flat frequeny response with a muh smaller overshoot than the onventional amplifiers. The voltae-ainbandwidth produt for the onventional amplifier with (W/L)00 µm/0.8 µm and the tail urrent of 8mA is 0.45 GHz. The voltae-ain-bandwidth produt for the onventional amplifier with (W/L)50 µm/0.8 µm and the tail urrent of ma is.45 GHz. However, the voltae-ainbandwidth produt for the proposed amplifier is GHz. Fi. 8 depits the power ain versus frequeny for the same amplifier as in the Fi. 7. The bandwidth-power-ain-produt is inreased, and for the same reason mentioned above, the power ain of the non-uniform differential distributed amplifier is more flat in the pass-band and the frequeny overshoot is redued. 5. Conlusion In this paper the desin of a new non-uniform differential distributed amplifier was presented. The effet of proressive down-sizin of the devie and indutor sizes on the ainbandwidth produt of the distributed amplifier was studied. The iruit was desin and simulated in a 0.8µm CMOS proess. HSICE simulations on both the proposed nonuniform distributed amplifier and the onventional iruit verified a onsiderable enhanement in the ain-bandwidth produt. Fi. 7. The voltae ain vs. frequeny for the proposed amplifier and two onventional amplifiers /04 $ IEEE

6 [0] B. Razavi, Desin of Analo CMOS Interated Ciruits, MGraw-Hill, 00. Fi. 8 ower ain vs. frequeny of proposed amplifier and two onventional amplifiers. Aknowledement The authors would like to thank Jazz Semiondutor, In., Newport Beah, CA for providin the devie and simulation data, and in partiular, Maro Raanelli, aul Colestok for their help and support. 6. Referenes [] E.L.Ginzton, W.R.Hewlett, J.H.Jasber, and J.D.Noe Distributed amplifiation, ro, IRE, vol.36, pp Au 948. [] W. S. erival Thermoni valve iruits British atent Jan [3] J.B.Beyer, S.N.rasad, R.C.Beker, J.E.Nordman, G.K.Hohenwarter MESFET Distributed Amplifier Desin Guide lines IEEE Mirowave Theory and Tehniques, Transations ol.3 No.3, Marh 984 pp [4] T.Y.Won, Fundamentals of Distributed Amplifiation, Norwood, MA: Arteh House In, 993 [5] H. Wu, A. Hajimiri, Silion-Based Distributed oltae- Controlled Osillators, IEEE J. Solid States Ciruits, vol. 36, No. 3, Marh 00. [6] H. T. Ahn, D. J. Allstot, A GHz Fully Differential CMOS Distributed Amplifier, IEEE J. Solid States Ciruits, vol. 37, No. 8, Auust 00. [7] B. M. Ballweber, R. Gupta, D. J. Allstot, A Fully Interated GHz CMOS Distributed Amplifier, IEEE Transation on Solid- State Ciruits, vol. 35, No., February 000 pp [8] A.Yazdi and.heydari,, A Novel Non-Uniform Distributed Amplifier, to appear in IEEE International Symposium on Ciruits and Systems, May 004. [9] K.B.Nilas, R.D.Remba, R.R.ereira and B.D.Cantos, The delinin drain line lenths iruit-a omputer derived desin onept applied to a -6.5 GHz distributed amplifier IEEE Transations Mirowave Theory and, Tehniques vol 34, pp April /04 $ IEEE