IEEE 2006 Custom Intergrated Circuits Conference (CICC) Inductor- and Transformer-based Integrated RF Oscillators: A Comparative Study Harish Krishnaswamy and Hossein Hashemi Electrical Engineering - Electrophysics University of Southern California, Los Angeles, CA-90089, Email: [email protected], [email protected] Abstract- Prior publications claim that transformer-based . resonators achieve improvements in quality factor (Q), which c e L 4 L 2- translates to better phase noise in oscillators. This paper combines rigorous analysis with on-chip practical considerations for various Im Im types of on-chip transformers to demonstrate the importance /2 =-21il I4 2 of the resonator topology for Q-enhancement. We show that - r 1R' Re for a fixed silicon chip area, transformer-based resonators do =2in Q= Qind Q= not exhibit superior performance compared to inductor-based - IT F2LE-C designs. Prototype oscillators are implemented at 5 GHz in a (a) (b) (C) 0.18,um CMOS process to validate these claims. Index Terms integrated circuits, CMOSFET oscillators,phase primaryFig. 1. and(a)secondary.A transformer-based(b) An alternativeresonatortransformer-basedwith in-phase currentsresonatorinwiththe noise, transformers, resonators, Q factor. out-of-phase primary and secondary currents. (c) An inductor-based resonator. All Q values assume k = 1. I. INTRODUCTION II. CIRCUIT THEORETIC ANALYSIS Recently, attention has been paid to the problem of design- ing high quality factor (Q) transformer-based resonators for The energy-based definition relates Q to the ratio of the low phase-noise integrated oscillators [1],[2]. The magnetic resonator stored energy (Etotai) to the resonator power loss coupling between the transformer windings can potentially (Pi0..) as given by increase the stored energy in the resonator, leading to higher Q. Such publications argue that transformer-based resonators Etota( achieve an improvement factor of 1 +-k in Q over the traditional Q x inductor-based resonator, where k is the coupling coefficient of 088o the two-winding transformer employed. In this paper, we will At resonance, the magnetic stored energy (Em) equals the demonstrate a design strategy for on-chip inductor-based res- electric stored energy (e). This magnetic stored energy, for onators that have similar or better Q compared to transformer- resonators composed of lumped elements, is partly comprised based topologies, given a silicon area constraint. of the energy stored in the self inductance of various inductors In section II, we show that transformer-based resonator and partly the energy stored in the mutual inductance of Q strongly depends on the specific topology; both Q en- various coupled pairs as given by hancement and reduction are possible. In section III , it is demonstrated that, due to on-chip issues and for given area N N N constraints, resonators based on planar transformers (like the L 2 H Frlan [4] or Shibata [3] transformers or the Rabjohn balun Etotal = 2Em = :K Ln + , j l/mnI7nIncos(0m.) (2) [5]) can offer no Q-improvement over single-inductor-based n=1 m=ln=l resonators. Section IV demonstrates that stacked transformer- where Ln and In are the self inductance and current magnitude based resonators exhibit inferior Q-performance compared to (rms) of the nth inductor, respectively, and Mmn and 0mn are single-spiral-based resonators, and that single spirals stacked the mutual inductance and current phase difference of the mth over multiple layers can achieve Q-improvement, depending and nth inductors, respectively. In the resonator depicted in on the interconnect structure of the process, thus eliminat- Fig. l(a), the currents in the coupled inductors are in-phase ing the need for true transformer-based resonator topologies. (assuming low loss and k 1). Hence, the mutual magnetic Section V presents the measurement results of prototype stored energy is positive and results in an increase in the oscillators, implemented at 5 GHz, and section VI concludes stored energy and hence the Q compared to the inductor-based the paper. resonator of Fig. 1(c). However, in the resonator depicted in 1-4244-0076-7/06/$20.00 0C2006 IEEE P-45-1 381 OD,ingje OD C2 30 - OD= 150um. S=5um, W=5um. n=2 Iii._IIIS_i_~~~~~~~~~~~~~25- OD=250LIKnS=10u1m.W=5um,n-4 1|* );E H]{ I 4wC ]°25gX 2015 kfrnIRE 0.620.620 63kbalunkIRl,-SS=0.57 ~ ~~~~~GOw_ CLLW-NI 20 kfia baue=05 Cig ;x;Csl sXiS Icsl 4;u 10° L R C R IAoxC ixls w .oSpiral R si Rs'1jjTl2GP L ~~~~~kCp1(A1 *Frian -~~~~~~~~~~~~~~ ~~~~~~0 RSl X I j -- Rsl2t I si2R 0 10 20 30 (a) (b) IC) Frequency in GHz Fig. 2. (a) Spiral inductor layout and physical model. (b) Frlan transformer Fig. 3. Comparison between the resonator Qs of 3 Frlan transformers, baluns layout and physical model. (c) Rabjohn balun layout and physical model. and the corresponding scaled spirals. Fig. l(b), the currents in the coupled inductors are out-of- 1 INDUCTOR-PLANAR TRANSFORMER COMPARISON phase. Hence, the mutual magnetic energy is negative and Consider a planar Frlan transformer with the following reduces the stored energy and the Q. defining parameters: n (number of turns for each winding), w Consider a resonator with n inductors, each of value L and (conductor width), s (inter-turn spacing) and OD (transformer parasitic series resistance R, and a certain number of lossless outer dimension). The main advantage of the Frlan transformer capacitors. Every inductor pair has a coupling coefficient of is that the two windings are perfectly identical. k. Further, the placement of all inductors in the resonator is Assuming a symmetric resonator topology such as Fig. 1(a), perfectly symmetric. From symmetry, the current through each under the low loss assumption, inductor must be the same I with rms-value I. At resonance, WrL(1 + k) Qf rlani R#R2hwL( (1±k)2 (6) 1 2 rt(rt-1~~~~~~~~~~~~R+ 2Em 2 x [ x - +L kLI2], (3) where L and R are the inductance and the series resistance of Etotal 2 (2 2 each winding, k is the coupling coefficient of the transformer, and R,h is the (frequency dependent) equivalent shunt resis- Ploss n x 12R, (4) tance of the Co, Csi, and Rsi substrate parasitic network lumped at each terminal of each winding. wr is the desired resonant frequency. It must be noted that the inter-winding - wL Q = (1x Etotai (1 + (n7- 1)k). (5) capacitance has no effect on the resonator Q of Fig. l(a). Pboss R Now, for comparison, consider a single spiral with the fol- Hence, an improvement factor of 1 + (nr - 1)k is seen over lowing layout parameters to ensure equal chip area: rningle = a resonator based on a single inductor due to the magnetic n, Wsingle= 2w, Ssingle= 2s, ODsingle = OD. The Q for a coupling between various inductors. It must be noted that, in parallel LC resonator can be written as general, transformer-based resonators are higher-order systems wrLsingle and can exhibit multiple resonance modes; the mode of interest Qsingle R2. +W2L2 (7) is the one with highest impedance magnitude. Rsige 2Rshsingle However, on-chip inductors and transformers exhibit far where Lsingle, Rsingle, and Rsh-single are the corresponding more complicated characteristics than can be captured in a parameters for the spiral inductor. simple L-R series model. Fig. 2 depicts physical layouts and This spiral inductor is constructed to have the same inner lumped equivalent physical models for various types of on-chip and outer dimensions as each winding of the Frlan transformer planar inductors and transformers. Hence, a fair comparison and also has the same number of turns. Since these are the between inductor- and transformer-based resonators requires a factors that dominate the self-inductance, Lsingle - L. Further, consideration of on-chip parasitics and an area and effective the parasitics to the substrate are the same in both cases, except inductance constraint 2. This is tackled in the next two sections. for the fact that they would have to be distributed in parallel across 4 terminals in the case of the Frlan, as opposed to 2 in 11n Fig. 1(a), under the low loss assumption, the current drawn from the the case of the spiral. Hence R8h 2Rsh-sirigle. Finally, at resonator terminals iS negligible, making the resonator symmetric. R sicRha sia 2The inductance of the equivalent second-order parallel RLC circuit that low frequencies, Rsjginge=2,sneteprahswcte approximates the behavior of the resonator at resonance. conductor width as the Frlan. P-45-2 382 30 Process A Process B F=.Top Layer Ind _ |: :ESE Top Layer Ind 25 -- Double-laver Ind El Double-layer Ind _-Stacked Trans Stacked Trans ProcessA ProcessB 20 -o etl 2 m 0.9p _P=l}_=1=Y 15- P2 zEl:20:: T40cnesTic 0 ym Et { a)P2 p1 (b) P24pm22X1 8gRThickness 1 pm 10 -E[Z10a Top Metal IY 281 x 0 Fig. 4. (a) Double-layer spiral layout. (b) Stacked transformer layout. CandSIni) 2.34o152.2010 To eta 9.77 pm 7.8 Height pmn 0~~~~~~~~~~Tosemr056 0.76 0 5 10 15 25 At low frequencies, where series metal loss dominates, Frequencyin GHz25 Qsingle = u RLingie,r Lsingl e and Qfrlian - L(I+kR ) These two values shouldvalusbeshuldbecmparblecomparable, becusethebecause the (11 +- k)) fctorfactor, in Fig. 5. Resonator Q for single- and double-layer spirals and a stacked transformer with OD = 150,umm w = 10,umm s = 10,umm n = 2. the best case of k = 1, offsets the advantage enjoyed by the t w single spiral in Rsingle At high frequencies, where substrate loss dominates, INDUCTOR-STACKED TRANSFORMER COMPARISON IV. lyr QRsh-single and Q l 2Rsh exlicmlile (s92g1e = WrLsingle and Qer1a= wL(1+Hk) Once again, Stacked transformers exploit the multiple metal layers of- when k 1, these two values are the same.