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

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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

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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. If k < 1, the fered by modern processes to conserve chip area. The windings Frlan transformer would have a slightly better high frequency 2 are implemented on different metal layers, one above the other Q value (by a factor of 1+k'), bbut its low frequency Q would (Fig 4(b)). This, however, results in an asymmetric structure; degrade below that of the single spiral by the same factor. the self inductances of the windings are similar to first order, Simulations were performed in IE3D, a Method-of-Moments but the series resistance is higher for the lower metal layer, based EM simulator [6], on Frlan transformers with various dimensions and the correspondingly scaled spirals.dimensiosThese aFurther,owntoisrdcdhckesnsadrdilonpcse.stacked structures experience more severe and asym- structures were implemented in the top metal layer, which has metric substrate parasitic effects, due to the greater proximity a thickness of 2 ,utm and a height of 9.77 ,utm above the silicon of the lower metal layer to the substrate. Also, the presence of substrate. Fig. 3 depicts the comparison of the resonator Qs. each winding deteriorates the quality of the other, due to the It can be clearly seen that, in agreement with the preceding proximity effect.3Finally, the achievable coupling coefficients analysis, the Q' of Frlan transformer-based resonator is not ~~~~~~~~~~~~~arelargely a function of the separation between the metal higher compared to that of a spiral-based LC resonator, when layers used (Fig. 5). Due to these mitigating factors, stacked subject to the same effective inductance and area constraint. transformer-based resonators are generally found to exhibit While the preceding analysis assumed a symmetric planar inferior Q as compared to spiral inductor-based resonators. transformer, the conclusion holds good for asymmetric planar The Q of inductors can be improved by strapping multiple transformers as well, such as the balun (Fig. 2(c)). In this case, metal layers together using vias [7]. These multi-layer spirals the primary and secondary windings of the transformer are not are expected to have higher resonator Qs than single-layer identical, and hence the choice of terminal capacitances Ci and spirals because the (low-frequency) series resistance reduces C2 at each winding is not straightforward. Assuming low loss to the parallel combination of the resistances of the upper, and k - 1, it can be shown that lower, and via-metals. The extent of improvement is process 1 dependent, and is governed by the relative quality of the Wr = (8) strapped layers, via thickness and increased substrate effects. /LICI + L2C2 EM simulations were performed on single-layer and double- Deriving the expression for Q and maximizing it with layer spiral inductors and stacked transformers for two differ- respect to C1 and C2 under the constraint that Wr in (8) must ent silicon processes, the results of which are depicted in Fig. remain constant, we obtain 5. In both processes, the stacked transformer exhibits inferior performance when compared to the single-layer spiral. The double-layer spiral outperforms its single-layer counterpart substantially in process A (which is the process used for the This design equation, coupled with (8) to obtain the desired simulations of section III and chip fabrication in section V); frequency of resonance, dictates the choice of Ci and C2 for this is largely due to the substantial via thickness between optimal Q for a given asymmetric transformer. Fig. 3 also the top two metal layers, which greatly reduces the series includes the EM simulated Q for such optimally dg * _1resistance.- In process B, the via thickness is significantly asymmetric tansformer-baed resonatos. In all caes, the pea lower. Further, the closer proximity of the upper layers to the Qs of the single inductor- and balun-based resonators are 3Proximity effect is the phenomenon of current crowding in a conductor within 12% of each other. due to the close proximity of another conductor.

P-45-3 383 Vdd 10000 100000 1000000 10000000 100000000 M3 M4 Vdd NigrWigr-45 M1,2 1.1 pm 0.18pm M3,4 10 2.2pm 0.18pm r F 6 M5,6 2036pm51p M7.8 20 22pm 18pm I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~O -85 M7 M8 Z ea L~~~~~V~~~~ m~~a -105-

Ml 657n ?BcH(lM ?B/H(10M frn 2d O Fig. 6. (a) circuitM2 diagrams for the single-inductor- and balun-based 5 GHZ -~~~bas425 oscillators. (h) Chip microphotograph of the two oscillators. TABLE I PHASE NOISE PERFORMANCE AND OSCILLATION FREQUENCY OF THE TWO OSCILLATORS FOR A VARIETY OF BIAS CURRENTS. substrate indicates that substrate loss is a more dominant factor ______in inductor Q for this process. As a result, the double-layer mA |dTrans. Trans.z( Md )|ftaGH 1 GHztn ° spiral performs only comparably to the single-layer spiral. 0.6 -116 -116 |-135.3 -136.9 5.12 5.14 |-190 1.00 -117 -116.5 -138.1 -136.9 5.11 5.12 -190 V. MEASUREMENT RESULTS 1.28 -117.5 -118.7 -138.2 -138.4 5.11 5.12 -192 1.50 -118.7 -120 -138.3 -138.4 5.11 5.12 -194 To validate the claims of this paper, two 5 GHz oscillators using spiral- and balun-based resonators were implemented in the standard 0.18,um CMOS process (Fig. 6). The oscillator of 1.8 V. Fig. 7 depicts the measured phase noise of each active core and all other parameters are kept equal, and hence oscillator versus the offset frequency for one bias current while a comparison between their phase noise is a direct indication of Table 1 shows the phase noise at typical offset frequencies for resonator Q. The tank capacitors are implemented using MIM a variety of bias currents and their (common) figure of merit capacitors and the negative-Gm cell is implemented using (FOM = (Af) - 2OloglOf § +H lOlog1OPdc-mW). It is complementary cross-coupled nMOS-pMOS pairs to improve clear that the phase noise performances of both oscillators are phase noise. nMOS open-drain buffers are employed to isolate nearly identical, validating our conclusions. Further, the efforts the oscillators from the measurement setup. to optimize the Q of the transformer- and corresponding- Effective inductance and area constraints of 3 nH and 250 spiral-based resonators have resulted in a FOM that compares were set for both cases. The primary winding of the favorably to recently reported state-of-the-art oscillators. balun was selected to achieve the highest stand-alone Q. EM simulations in IE3D, followed by the fitting of the S- VI. CONCLUSION parameters into the model described in Fig. 2(c), reveal that The possibility of Q-enhancement using transformer-based the model parameters are: L1=3.14 nH, L2=1.64 nH, R1=7.21 resonators is investigated. On-chip issues such as substrate par- Q, R2=5.45 Q and k = 0.79. The optimal values for terminal asitics and area constraints are considered and it is concluded capacitors were selected using (8) and (9). Simulation results that transformers (planar or stacked) an offer no improvement predict an optimal Q of 18.95 when C1=215 fF and C2=255.8 over single spirals, when subject to an area constraint. Proto- fF. The effective inductance at resonance is 2.73 nH. type oscillators, implemented at 5 GHz, validate this claim. The correspondingly scaled spiral inductor was also sim- REFERENCE,S ulated in IE3D, and the resultant S-parameters were fit into inductor The main model [1] Matt Straayer et al., "A Low-Noise Transformer-based 1.7 GHz CMOS the model described in Fig. 2(a). VCO," ISSCC 2002 Dig. of Tech. Papers, vol. 1, pp. 286-287, Feb. 2002. parameters were found to be L=3.1 1 nH and R=6.06 Q. The [2] Donghyun Baek et al., "Analysis on Resonator Coupling and its applica- Q was found to be 18.3 with an effective inductance of 2.66 tion to CMOS Quadrature VCO at 8 GHz," 2003 IEEE Radio Frequency nH. Clearly, the single-inductor-based resonator is found to IntegratedK. ShibataCircuitset al., Symposium,"Microstrp pp.spiral85-88,directionalJune 2003.coupler,"IEEE Trans. perform comparably to the transformer-based resonator, when Microwave Theory Tech., vol. 29, pp. 680-689, July 1981. subject to the same area and effective inductance constraint. [4] E. Frlan et al., "Computer-aided design of square spiral transformers and The chip dimensions are 460 ,um x 600 ,um for each oscilla- [5] inductors,"G. G. Rabjohn,in Proc."MonolithicIEEE MTT-S,microwavepp. 661-664,transformers,"June 1989.M. Eng. thesis, tor. The RF pads were wire-bonded to 50 Q traces on a printed Carleton University, Ottawa, ON, Canada, Apr. 1991. circuit board and connected to the spectrum analyzer using RF [6] IE3D User's Manual, Release 10, Zeland Software Inc. et cables.measuedTheahipphasevarensietyie performancesofe biastmxcu ofs bothatmaroscillatorss y voslltagwere [7] iogy,"ElectronicsM. Soyeur al.,Letters,"Multilevelvol. 31,monolithicno. 5, pp. inductors359-360, Marchin silicon1995.technol-

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