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Effect of Quality Factor on Center Frequency Deviation in Miniaturized CMOS Bandpass Filter

In-Ho Kang, Shang-Ming Li and Young Yun

In this letter, the effect of quality factor on center frequency deviation in miniaturized coupled line bandpass filter (BPF) with diagonally end-shorted at their opposite sides and lumped capacitors is theoretically analyzed. The miniaturized BPF of a two-stage structure with two types of quality factors in standard CMOS process was designed and manufactured at 5.5 GHz. The die area of BPF was 1.44 × 0.41 mm 2 . The measured center frequency of BPF with a quality factor of 4.9 was deviated from 5.5 GHz to 4.7GHz. The one with 14.8 was shifted to 5GHz. The theoretical and measured results validate that quality factor influences the center frequency shift of BPF. Keywords: center frequency shifts, quality factor, shunt resonator, substrate loss, bandpass filter, CMOS.

I. Introduction

Bandpass filters are essential components in wireless communication circuits. RF transceiver development has been moving toward single-chip implementation, eliminating the discrete elements. Many BPFs have been published by CMOS technology, which has emerged as a viable system-on-a-chip technology that enables the full integration of RF integrated circuits. However, these filters have suffered from inherent losses with silicon substrate and low quality factor [1], [2], [3]. The miniaturized bandpass filter using diagonally end-shorted at their opposite sides and lumped capacitors showed more promise and a relatively higher quality factor than filters with the spiral inductors. [4]. However, the center frequencies of these filters are inclined to shift to the lower frequency. The greater difference in the center frequency of these filters between simulation and measurement in CMOS fabrication has not been analyzed until now. In this letter, miniaturized coupled line BPF with a two-stage structure by standard silicon integrated circuits was designed and manufactured at 5.5 GHz. One-layer and six-layer BPFs were implemented for the comparison. The center frequency shifts will be theoretically proven to be caused by transmission losses and quality factors in the lossy distributed inductor of the shunt resonator. These approaches will be verified by the measurements of BPFs with two types of quality factors.

II. Technology Description

A highly-miniaturized BPF can be implemented using a shunt resonator and a section of high-impedance transmission line [5], and the structure is shown in Fig. 1. For the ideal BPF, we can set the conductivity of the substrate to zero and transmission line to lossless. Z c , C1 and θ in Fig. 1 are the characteristic impedance of the shortened transmission line, the lumped capacitor, and the electrical length of the shortened line defined in Hitota’s size reduction method [6].

Sponsorshipandauthorinformationcomehereafteracceptance. Thisdocumentispreparedintheregularorspecial-issuepaperformat.

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C0 and L0 are the capacitor and the inductor for the resonance. The resonator in Fig. 1 has a resonance frequency as follows:

The resonator in Fig. 2 (b) has the following Y admittance:

wr =

where wo is the center frequency.

1 = w0 L0C0

(1)

Y=

1 + R2 + jwL0

1 1 + R1 jwC0

(2)

However, the substrate’s loss effect is actually too severe to be ignored as the silicon substrate is inherently lossy and the electrical field tends to leak into it. Although the exact equivalent circuit of the distributed inductor is complicated, we assume that the inductor loss is mainly due to the series resistance R2 , as shown in Fig. 2 (a), the equivalent circuit of the resonator, because the resistance R p1 , R p 2 of the parallel part does not change the resonant frequency of shunt resonance. Fig. 2 (b) is the simplified circuit of Fig. 2 (a) for modeling the resonance frequency deviation. For the MIM capacitor, an equivalent series resistance R1 exists in the MIM circuit model and a maximum Q of about 80 was reported [7].

=

jwC0 (1 jwR1C0 ) R2 jwL0 + 2 2 2 R2 + ( wL0 ) 1 + ( wR1C0 )

The imaginary part of equation (2) equals to zero for resonance,

jwL0 jwC0 + =0 2 R + ( wL0 ) 1 + ( wR1C0 )2

2 2

(3)

The resonance frequency is derived from equation (3)

1 wr =

Co 2 R2 Lo

LoCo ( R1Co ) 2

(4)

L0

L0

From equation (4), the resonance frequency of the circuit in Fig. 2 (b) using the quality factors is expressed as follows:

1

Fig.1. Ahighly-miniaturizedBPF

wr = w0

1 2 QL

1 1 2 QC

(5)

C0

where QL is the quality factor of the distributed inductor ,

QL =

w0 L0 R2

(6)

QC is the quality factor of the MIM capacitor ,

(a)

QC =

C0

L0 R2

1 w0 R1C0

(7)

R1

The corresponding operating resonance frequency wr in equation (5) will be smaller than the center frequency wo of the lossless circuit. In Fig. 3, the logarithm of w

w0

(b)

Fig.2. Equivalentcircuit oftheresonator

versus QL factor is plotted. Three kinds of

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curves are showed at QC =40, 60, and 80, respectively. As QC increases, as shown in Fig 3, log w increases. This trend is to be notable as not to

w0

be expected. When QC is equal to QL in Fig. 3, wr becomes wo and

log w is zero. w0

log

w -0.5 w0 -1.0

-1.5 -2.0 -2.5 -3.0 -3.5 -4.0 -4.5 -5.0 0 5 10 15 20 25 30 35 40 45 50

Fig.4. Photographofthefabricatedbandpassfilter.

In Fig. 5, the simulated and measured results of the circuit with onelayer and six-layer coupled lines are plotted. The QL of the BPF were found to be 4.9 and 14.8 for the one-layer and six-layer filters, respectively. The QL factor of the six-layer BPF circuit was better than that of the one-layer circuit. The dotted line was electromagnetically simulated by HFSS (Ansoft). The measured center frequency of the one-layer coupled lines BPF was deviated from 5.5 GHz to 4.7 GHz with 0.8 GHz shift as shown in Fig. 5 (a), whereas in Fig. 4 (b), the measured center frequency of the six-layer circuit moved from 5.5 GHz to 5 GHz with 0.5 GHz shift. Both of them have the center frequency shifting to the lower frequency after fabrication. According to the simulation and measured results, the higher the QL factor, the less the center frequency shifts.

Qc=40 Qc=60 Qc=80

QL factor

Fig.3. The logarithmof w

w0

versustheQL factor

III. Results

Insertion Loss and Return Loss [dB]

0 -5 -10 -15 -20 -25 -30 -35 -40 -45 -50 -55 -60 -65 -70 0 1 2 3 4 5 6 7 8 9 10 Simulated S11 Simulated S21 Measured S11 Measured S21

To verify the approaches, two kinds of cascade miniaturized coupled line BPFs with one and six layers were considered. First, a one-stage bandpass filter was designed at 5.5 GHz. For the BPF with one layer, a coupled line of 70 electrical length was used. The coupled line width was 20 m, the transmission line length was 570 m and the separation between the two coupled lines of 140 m was used to provide input/output impedance matching the system impedance Z0 = 50 . The six-layer filter also had a 20 m line width, 570 m line length, and 140 m coupled line separation. Then, two similar one-stage filters with one and six layers were cascaded, respectively. This technology is well explained by [4]. The conductivity of the coupled lines is assumed by 2.4×107 Siemens m and the substrate is lossless for the simulation process. These filters were fabricated using Magnachips 0.18 m process with 10 cm bulk silicon substrate and aluminum metal layers. The total die area, including the ground plane surrounding the integrated BPF, was 1440 m × 410 m. A photograph of the layout is shown in Fig. 4.

Frequency [GHz]

(a)

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0 -5

-10 -15 -20 -25 -30 -35 -40 -45 -50 -55 -60 -65 -70 0 1 2 3 4 5 6 7 8 9 10

Simulated S11 Simulated S21 Measured S11 Measured S21

Filters Implemented Using RF Silicon Integrated Circuits,” EuMC, 2009. [5] I. Kang, S. Shan, X. Wang, Y Yun, J. Kim, C. Park, “A . miniaturized GaAs MMIC filter for the 5GHz band,” Microwave Journal, vol. 50, pp. 88–94, Nov. 2007. [6] T. Hirota, A. Minakawa, and M. Muraguchi, “ Reduced size branch line and rat race hybrids for uniplanar MMIC’s,” IEEE Trans. Microwave Theory Tech., vol. 38, no.3, pp. 270-275, 1990. [7] J. N. Burghartz, M. Soyuer, K. A. Jenkins, “Microwave inductors and capacitors in standard multilevel interconnect silicon technology”, IEEE Microwave Theory and Technologies, vol. 44, No 1, pp. 100-104, Jan. 1996.

Frequency [GHz]

(b) Fig.5. Simulatedandmeasuredresultsofthecircuitwithone-layercoupledlines(a)andsix-layer coupled lines(b).

IV Conclusions .

In this paper, the greater difference between simulation and measurement of the miniaturized bandpass filter using diagonally endshorted at their opposite sides and lumped capacitors in CMOS fabrication has been analyzed. The filters have suffered from inherent losses with silicon substrate and conductor losses. These losses are inclined to cause the center frequency to shift to the lower frequency. It is theoretically proven that the center frequency shifts are mainly caused by transmission losses and quality factors in the lossy distributed inductor of shunt resonator of the coupled lines BPF.

Acknowledgement

This work was supported by the Ministry of Education, Science & Technology (MEST) and the National Research Foundation of Korea (NRF) and IC Design Education Center (IDEC).

References

[1] T. Soorapanth and S. S. Wong, “A 0dB IL ± 30MHz bandpass filter utilizing Q enhanced spiral inductors in standard CMOS”, IEEE J. Solid-State Circuits, vol. 37, No. 5, pp. 579-586, May 2002. [2] B. Georgescu, I. G Finvers, and F. Ghannouchi, “2 GHz Q . enhancement active filter with low passband distortion and high dynamic range”, IEEE J. Solid-State Circuits, vol. 41, No. 9, pp. 20292039, Sept. 2006. [3 ] A. N. Mohieldin, E. S. Sinencio, and J. S. Martinez, “ A 2.7 V 1.8 GHz fourth order tunable LC bandpass filter based on emulation of magnetically coupled resonators”, IEEE J. Solid-State Circuits, vol. 38, No. 7 pp. 1172-1181, July 2003. [4] I. Kang, H. Zhang, Y Yun, P. Tasker,J. Benedikt, A. Porch, “High . Quality Factor Extraction of Miniaturized Coupled Line Bandpass

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Insertion Loss and Return Loss [dB]

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