Experimental characterization of coupling effects ... - IEEE Xplore

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 45, NO. 3, AUGUST 2003

Experimental Characterization of Coupling Effects Between Two On-Chip Neighboring Square Inductors Wen-Yan Yin, S. J. Pan, L. W. Li, and Y. B. Gan Abstract—Comprehensive experimental results on the coupling effects between two on-chip symmetric and asymmetric neighboring inductors on GaAs substrates are presented in this paper. These pairs of inductors are fabricated with the same track width, turn number, and spacing. Based on the parameters measured using de-embedding technique, we show the effects of edge distance between these two neighboring inductors on the return and transfer losses, and self-resonance frequency. Certain ways to reduce the transfer loss are explored. Index Terms—Coupling, inductance, on-chip neighboring inductors, Q factor, return and transfer losses.

I. INTRODUCTION Spiral inductors are commonly used in monolithic microwave integrated circuits (MMIC) and silicon radio frequency integrated circuits (RFIC). In the past few years, a large amount of experimental and theoretical work has been done on investigating electromagnetic characteristics of microwave spiral inductors in both silicon [1] and GaAs technologies [2]–[4]. Usually, both MMIC and RFIC designs need to incorporate several spiral inductors on the same substrate. Since these structures are physically large, substrate coupling can cause a serious problem in the overall performance. Therefore, it is very important to model and predict various on-chip electromagnetic coupling effects, in particular the coupling between two neighboring spiral inductors [5], [6]. In this paper, on-chip pairs of (a)symmetric inductors on GaAs substrates are tested. For pairs of (a)symmetric planar inductors, the turn numbers are N = 4, the gold alloy track width is W = 12 m, track spacing is S = 4 m, and different edge distances between them is D = 10, 30, and 50 m, respectively. To evaluate the coupling effects between these pairs of inductors, a single square inductor on GaAs substrate with the same turn number N , track width W , and track spacing S , is also tested on GaAs substrate. In our measurement, the S parameters are measured using standard Cascade 9000 analytical RF probe from 1 to 20 GHz. To remove the pad parasitics from the measured S parameters, the de-embedding technique is also employed. Based on the measured S parameters, a complete understanding on the coupling effects between two neighboring spiral inductors has been obtained. II. GEOMETRIES Fig. 1(a) and (b) shows the top views of two pairs of (a)symmetric neighboring inductors with the same turn number N = 4, track width W = 12 m, track spacing S = 4 m, and edge distance D = 30 m. For each inductor in Fig. 1(a) and (b), the inner empty area Ae is 60 2 2 60 m , and the trace length Le is 1780 m. For comparison, Fig. 1(c) show the top view of a single square inductor with same values of N , W , and Ae as two neighboring cases. A summary of the edge distance parameter for all samples is also shown in Table I. The GaAs substrate thickness is Sd = 100 m, and its relative permittivity is 12.9 with a loss tangent of 0.0065. Manuscript received April 19, 2002; revised April 15, 2003. W. Y. Yin and Y. B. Gan are with the Temasek Laboratories, National University of Singapore, Singapore 119260 (e-mail: [email protected]). S. J. Pan and L. W. Li are with the Department of Electrical and Computer Engineering, National University of Singapore, Singapore 119260. Digital Object Identifier 10.1109/TEMC.2003.815597

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III. CIRCUIT MODEL FOR SINGLE INDUCTOR Fig. 2(a) shows the equivalent circuit model of an on-chip single inductor [7]. Based on this model, we can obtain the simulated S parameters by importing the model into software IC-CAP [8]. In addition, a single-equivalent circuit model for two neighboring spiral inductors can be developed, but is only applicable for very low operating frequency range [5]. In comparison to the model used by Bahl [2]–[4], the low loss of GaAs substrate is also considered in Fig. 2(a) to ensure high simulation accuracy. Here, a combination of resistors R1 and R2 (R1 : DC resistance of the trace, and R2 : resistance due to skin effect and eddy current excitation), and inductors L1 and L2 (L1 L2 ; and L1 is the main inductance) is connected to simulate the variation of the resistance with frequency, while Cp is the effective total capacitance across the inductor. The capacitance and resistance of the GaAs substrate, in the input and output ports, are modeled by fC10 ; R10 g and fC20; R20 g, respectively. The simplified model for two neighboring inductors is shown in Fig. 2(b), where the coupling is represented by the mutual inductance M . Its effect can be measured by the transfer loss S21 . In our case, the lower S21 value is desired. Several approaches may be considered to extract all the device parameters in Fig. 2(a). The parameter extraction here refers to the procedure based on the model-specific algorithms to obtain the parameters directly from measured data. This is performed using the software IC-CAP. On the other hand, we can derive the device parameters from the Y or Z parameters, converted from the measured 2-port S parameters of the inductors through the RF probes. For example, the total inductance ( L1 + L2 , since R1 R2 ) in Fig. 2 can be determined by [1] 1

Im

L=

Y

(1)

!

where the short-circuit input admittance Y11 represents the combination of R1 , R2 , Cp , L1 , L2 , R10 , and C10 , while the Q factor is computed by

Q=

Im[Zin ]

(2)

Re[Zin ]

and

Zin = 50

1

0

S

0S

(1+S

S

)

S 0S S 1+ (1+S )

(3)

:

In (2), Re[Zin ] and Im[Zin ] represent the input resistance and reactance of an inductor, respectively. The self-resonant frequency (fres ) of an inductor can be found by setting Im[Zin ] = 0 [2]–[4], i.e., the inductive reactance and parasitic capacitive reactance are equal [4]. Upon knowing the values of fW; S; Le g for an on-chip inductor, its inductance L and resistance R can be evaluated by some empirical formula, for instance [7]

L(nH ) = where a, b, c, d, and inductor layouts.

(W

a

(cLe ) + S )b

( (

) )

(4)

e are all fitting coefficients, depending on the

IV. EXPERIMENTAL RESULTS AND DISCUSSIONS The measured data of single or pairs of inductors should be corrected by the standard de-embedding technique to remove the pad parasitics

0018-9375/03$17.00 © 2003 IEEE

558


(a)

(b)

(c) Fig. 1. Top view of two pairs of on-chip (a)symmetric and a single-square spiral inductors. (a) Two symmetric inductors. (b) Two asymmetric inductors. (c) Single inductor with = 4, and = 2033 m(right: enlarged without pads).

(a) Fig. 2.

(b)

Models of a single and two neighboring spiral inductors: (a) single case and; (b) two neighboring case.

from the measured S parameters. The pad de-embedding was accurately performed by subtracting the Y parameters of the “open” pad pattern from that of the single inductors, as well as the two neighboring inductors, i.e., 1) measure the S parameters of the open pads (Spad ); 2) convert Spad into the Y parameters (Ypad ); 3) measure the S parameters of the inductor together with pads (Smea ); 4) convert Smea into the Y parameters (Ymea ); 5) subtract the Ypad from Ymea to obtain the Y parameters; and 6) convert the Y parameters to S parameters. The simulated S - parameters for a single inductor in Fig. 1(c) are obtained using software IC-CAP with SPICE algorithm. The simulation errors can be computed by (mea) N Spq 0 Spq(sim) 1 pq ) es = N (mea) m i=1 Spq (

(5)

where Nm (= 201) is the number of frequency points measured, while (mea) sim (pq = 11, 12, 21, and 22) are the measured and simSpq and Spq (11) ulated S parameters, respectively. The simulated errors for both es

Fig. 3.

Calculated

factor as a function of frequency for one single inductor.

and es are less than 2.2% from 1 to 20 GHz. Further, the extracted data for the main devices in Fig. 1(c) are found to be Cp = 20 fF , (21)


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TABLE I SIX PAIRS OF (A) SYMMETRIC INDUCTORS WITH DIFFERENT EDGE DISTANCES, INCLUDING A SINGLE GEOMETRY

where D denotes edge distance; type A, asymmetric case; and type S, symmetric case.

(a)

(b)

(c)

(d)

Fig. 4. Measured and for two neighboring spiral inductors with a single spiral inductor on GaAs substrates corresponding to = respectively. (a) Phase of return loss ; (b) phase of transfer loss ; (c) magnitude of return loss ; and (d) magnitude of return loss

R1 = 0:05 , R2 = 5:9 , L1 = 2 nH , L2 = 0:31 nH , C10 = 33:8 fF , and C20 = 110:78 fF . Hence, the total inductance is about L 2:31 nH . Fig. 3 depicts the calculated Q factor from the measured S parameters. This curve is smoothened using polynomial fitting technique. From Fig. 3, it is found that the maximum Q-factor and resonance frequency for this inductor are about 32.5 and 17 GHz, respectively. These values are typical for an inductor on GaAs substrate with N = 4, W = 12 m and S = 4 m. Fig. 4(a)–(d) depicts the return loss S11 and the transfer loss S21 as a function of frequency, for three edge distances (D = 10, 30, and 50 m), respectively. For comparison purposes, the case of a single spiral inductor is also included here. From a detailed analysis of the measured results, some observations can be made. 1) For a pair of symmetric or asymmetric inductors, the magnitude and phase of S11 , and the phase of S21 are not sensitive to variation in the edge distance, as shown in Fig. 4(a)–(c). Very little change is observed as D is increased from 10 m to 30 m and 50 m.

10, 30, and 50 m, .

2) There also exists very little difference in S11 between symmetric and asymmetric structures, as shown in Fig. 4(a) and (c). 3) jS21 j is very sensitive to variation in the edge distance D , as shown in Fig. 4(d). The magnitude of S21 increases with D for both symmetric and asymmetric structures. As Howard et al. [5] have pointed out, a spiral inductor in free space is a magnetic dipole with H field proportional to (1=D)3 . By taking into account the negative magnetic image of the spiral inductor due to the ground plane, the jS21 j is approximately proportional to (1=D)5 . 4) Generally speaking, in the case of symmetric pairs jS21 j is more sensitive to variation in frequency than that of the asymmetric pair [Fig. 4(d)]. jS21 j for symmetric pairs is normally lower than that of the asymmetric pairs. 5) At f 9:0 GHz, jS21 j for the symmetric pairs, as shown in Fig. 4(d), reaches the minimum for the case of D = 10 m, which is the smallest edge distance. It should be emphasized that for a single spiral inductor, we need to enhance the forward energy transfer S21 and reduce the return loss

560


(a)

(b)

(c) Fig. 5. Frequency dependence of the input impedance for six sets of two neighboring spiral inductors. (a)

= 10 m; (b)

= 30 m; (c)

= 50 m.

TABLE II EVALUATED RESONANCE FREQUENCY FOR SIX PAIRS OF (A)SYMMETRIC INDUCTORS, INCLUDING A SINGLE CASE

S11 . For two neighboring spiral inductors not used as a transformer, we need to reduce the transfer loss S21 between them. With respect to the magnitude and the phase of S21 in Fig. 4, there are significant differences between the single and two neighboring cases. This is due mainly to the hybrid effects of their separation D and relative orientation. Fig. 5(a)–(c) depicts the frequency dependence of the input impedance of six pairs of inductors. In Fig. 5(a)–(c), the self-resonance can take place at certain frequency, and can be evaluated by Im[Zin ] = 0. From Fig. 5(a), it is found that fres at D = 10 m for the symmetric pair is higher than that of the asymmetric pair, while for D = 30 and 50 m, each fres , as shown in Table II, is lower than that of the asymmetric pairs.

V. CONCLUSION An extensive experimental study on on-chip single and neighboring spiral inductors are performed in this paper, so as to explore ways to reduce the coupling between inductors used in MM(RF)IC designs. For practical applications, two spiral inductors are designed with symmetric and asymmetric patterns, respectively. Based on the S parameters measured using the de-embedding technique, the effects of edge distances between these two inductors on the return and transfer losses, as well as self-resonance, are clearly demonstrated. In order to save the on-chip area occupied by neighboring passive devices, we need to decrease the edge distance between them. However, the decrease in edge


distance may increase the coupling effect. When using two spiral inductors, their edge distance limit and relative orientation should be chosen appropriately to meet certain requirements.

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A Time-Domain Microwave Oven Noise Model for the 2.4-GHz Band Yasushi Matsumoto, Morio Takeuchi, Katsumi Fujii, Akira Sugiura, and Yukio Yamanaka

ACKNOWLEDGMENT The authors would like to acknowledge Dr. F. J. Lin and B. L. Ooi for valuable discussions. REFERENCES [1] Y. K. Koutsoyannopoulos and Y. Papananos, “Systematic analysis and modeling of integrated inductors and transformers in RFIC design,” IEEE Trans. Circuits Syst. II, vol. 47, pp. 699–713, Aug. 2000. [2] I. J. Bahl, “Improved quality factor spiral inductors on GaAs substrates,” IEEE Microwave Guided Wave Lett., vol. 9, pp. 398–400, Oct. 1999. , “High current handling capacity multilayer inductors for RF and [3] microwave circuits,” Int J. Radio Freq. Microwave, vol. 10, pp. 139–146, 2000. , “High-performance inductors,” IEEE Trans. Microwave Theory [4] Tech., vol. 49, pp. 654–664, Apr. 2001. [5] G. E. Howard, J. Dai, Y. L. Chow, and M. G. Stubbs, “The power transfer mechanism of MMIC spiral transformers and adjacent spiral inductors,” in Proc. IEEE Microwave Theory Technology Symp., 1989, pp. 1251–1254. [6] M. Werthen, I. Wolff, R. Keller, and W. Bischof, “Investigation of MMIC inductor coupling effects,” in Proc. IEEE Microwave Theory Technology Symp., 1997, pp. 1793–1796. [7] W.-Y. Yin, “Three-Dimensional Spiral Interconnects in MM(RF)ICs,” MMIC Modeling and Packaging Lab., Nat. Univ. of Singapore, Singapore, 2001. [8] Agilent Technologies, Software IC-CAP, Palo Alto, CA, 2000.

Abstract—A time-domain noise model is developed for analyzing the performance degradation of wireless communication systems in the 2.4-GHz band caused by microwave ovens, taking into account the noise generation mechanism and its characteristics. The proposed noise model consists of a series of frequency-modulated tone bursts, which can be realized with a set of FM/AM modulators. It yields a simple and general expression of the noise waveform in terms of six parameters that can be determined from measurements. Band-limited noise waveforms can also be derived from the model via simple approximations. Comparisons of both the waveform and the frequency spectrum are made between actual noises and the proposed model, which clearly demonstrate the validity and usefulness of the model. Index Terms—Bluetooth, electromagnetic noise, industrial, scientific, and medical (ISM) band, noise measurement, wireless LAN.

I. INTRODUCTION Indoor wireless communication systems in the 2.4-GHz band, such as Bluetooth and IEEE 802.11b wireless LAN (WLAN), are becoming widespread. However, this frequency band is allocated to industrial, scientific and medical (ISM) equipment. For example, there are a tremendous number of microwave ovens using this frequency band. Hence, wireless communication systems in this frequency band may suffer from interference caused by the electromagnetic noise of microwave ovens. To analyze the performance degradation of interfered communication links, one of the key issues is the modeling of interfering noise. Many theoretical and experimental studies have modeled microwave oven noises. For example, empirical models were developed using the noise’s amplitude probability distribution (APD) [1], [2]. Middleton’s impulse noise model was also used to evaluate the performance degradation of wireless links with respect to the bit-error rate (BER) [3]. In recent years, stochastic models have been developed considering the fact that actual oven noises have periodic burst envelopes. For instance, intermittent Gaussian noise chopped by periodic pulses was used to study a direct-sequence spread-sequence (DS–SS) system in [4]. Reference [5] proposed a method for producing periodic bursts of random noise having a given Middleton’s class-A APD. These stochastic models are, however, expressed in terms of statistical parameters such as APD, and hence no information is provided on time-domain noise waveforms. This is a drawback because the models cannot be applied directly to the evaluation of short-term BER characteristics of interfered communication systems. Furthermore, it should be noted that an actual microwave oven noise waveform greatly changes with frequency. Therefore, such stochastic models are ineffective in analyzing the BER degradation of an interfered frequency-hopped spread-spectrum (FH-SS) system because different

Manuscript received July 23, 2002; revised March 4, 2003. This work was supported in part by the Japan Society for the Promotion of Science (JSPS) under Grant 14750201. Y. Matsumoto, M. Takeuchi, K. Fujii, and A. Sugiura are with the Research Institute of Electrical Communication, Tohoku University, Sendai 980-8577, Japan (e-mail: [email protected]). Y. Yamanaka is with Yokosuka Radio Communications Research Center, Communications Research Laboratory, Yokosuka, Kanagawa, 239-0847, Japan. Digital Object Identifier 10.1109/TEMC.2003.815514 0018-9375/03$17.00 © 2003 IEEE