IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 62, NO. 9, SEPTEMBER 2015. Characterization of CMOS Metamaterial. Transmissi
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IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 62, NO. 9, SEPTEMBER 2015
Characterization of CMOS Metamaterial Transmission Line by Compact Fractional-Order Equivalent Circuit Model Chang Yang, Student Member, IEEE, Hao Yu, Senior Member, IEEE, Yang Shang, Student Member, IEEE, and Wei Fei, Student Member, IEEE Abstract— In this paper, a compact fractional-order equivalent circuit model is developed to characterize three types of metamaterial transmission lines (T-lines): 1) composite right-/left-handed transmission line T-line; 2) split ring resonator T-line; and 3) complimentary split ring resonator T-line, all designed in 65-nm CMOS process at millimeter-wave frequency region. With the consideration of frequency-dependent dispersion loss and nonquasistatic effect, the proposed fractional-order equivalent circuit model can compactly characterize the measured results with good agreement up to 325 GHz. Index Terms— CMOS on-chip metamaterial transmission lines (T-lines), fractional-order equivalent circuit model.
I. I NTRODUCTION
W
Fig. 1. Characterization of four types of T-lines: RH T-line, CRLH T-line, SRR T-line, and CSRR T-line.
Manuscript received March 24, 2015; revised June 5, 2015; accepted July 15, 2015. Date of publication August 3, 2015; date of current version August 19, 2015. This work was supported in part by the Ministry of Education, Singapore, under Grant TIER-1 RG26/10 and in part by the National Research Foundation–Prime Ministers’ Office, Singapore, under Grant 2010NRF-POC001-001. The review of this paper was arranged by Editor M. S. Bakir. C. Yang and H. Yu are with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (e-mail:
[email protected];
[email protected]). Y. Shang is with ADVANTEST Corporation, Singapore (e-mail:
[email protected]). W. Fei is with Hisilicon (Singapore) Pte. Ltd., Singapore (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TED.2015.2458931
only achieve a positive phase shift, the CRLH T-line can realize zero phase shift or nonlinear negative phase shift in compact size with low loss [3], which is applied in power combining network [5], leaky wave antenna with broadside radiation pattern [6], and wide-tuning-range VCO [7]. Fig. 2(b) and (c) shows the dispersion diagram of SRR T-line and CSRR T-line, respectively. Both the SRR T-line and the CSRR T-line can be characterized as resonant-type metamaterial T-lines to generate high-Q resonation for oscillators used in high-sensitivity super-regenerative receivers [8], [9]. However, the prevailing modeling technique is not accurate and compact enough for CMOS metamaterial-based T-lines at mm-wave frequency region. Conventionally, T-line structures are modeled by an integer order RLGC model [10], [11]. As shown in Fig. 2(a)–(c), skin effect can be denoted as R and the loss due to dielectric can be described by G. The integer order model RLGC model is, however, insufficient to describe the T-line characteristics in the mm-wave frequency region. First, the loss term in T-line is difficult to model the distributed dispersion loss and nonquasistatic effects [12], which require a large number of RLGC components to fit the whole mm-wave frequency region [13], [14]; second, the metamaterial T-line has more complex coupling structures such as the metamaterial load onto the host T-line. Recently, the fractional-order model has been found as one promising candidate for compact modeling of T-lines at the mm-wave frequency region. It has been
ITH the advanced scaling of CMOS process, more novel structures with unconventional properties are developed for both active and passive devices in the CMOS millimeter-wave (mm-wave) IC design [1], [2]. For example, metamaterial based transmission lines (T-lines) have shown great advantages in zero-phase coupling and high-quality resonation within compact area, which are utilized in the CMOS mm-wave IC designs of power amplifier, voltage-controlled oscillator (VCO), and antenna [3]–[5]. Fig. 1 explains the unconventional properties of metamaterial-based T-lines in terms of permittivity (εr ) and permeability (μr ). In addition to the conventional right-handed (RH) T-line, there are three types of on-chip metamaterial T-line: 1) composite right/left-handed (CRLH) T-line; 2) split ring resonator (SRR) T-line; and 3) complimentary split ring resonator (CSRR) T-line. Fig. 2(a) shows the dispersion diagram of CRLH T-line. Compared with the conventional T-line which can
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YANG et al.: CHARACTERIZATION OF CMOS METAMATERIAL T-LINE
Fig. 2. Three types of CMOS on-chip metamaterial T-lines unit-cells (middle)with the corresponding dispersion diagrams (left), integer order and fractional-order models (right).
used to calibrate capacitor (C) and inductor (L) components in the conventional RLGC T-line model at high-frequency region [12], [15]. By properly deciding the values of fractional-order parameters, one can build compact equivalent circuit model for any T-lines to fit within a wideband frequency region. In this paper, we have developed a fractional-order RLGC model for the metamaterial T-lines at the mm-wave frequency region with the following advantages. First, the fractional-order RLGC model of CRLH T-line can have compact description of distributed dispersion components to add in. Second, the fractional-order RLGC model can precisely model the coupling effect in the resonant-type metamaterial (SRR/CSRR) Tlines. The proposed factional-ordered RLGC model is verified with S-parameter measurement results (up to 325 GHz) for the metamaterial T-lines fabricated in 65-nm CMOS. Compared with the conventional integer order RLGC model, the proposed fractional-order RLGC model demonstrates the improved accuracy in compact form of equivalent circuit models. Unique properties of the metamaterial T-lines can be efficiently characterized, including εr and μr for CSRR/SRR T-lines, and characteristic impedance (Z 0 ) and β for CRLH Tlines, which are important for the CMOS mm-wave IC designs. II. CMOS M ETAMATERIAL T RANSMISSION L INE A. Metamaterial T-Line in CMOS To design a metamaterial T-line in the standard CMOS process, the first thing to be considered is propagation and ohmic loss. As such, the top-most metal layer is exclusively employed as signal layer for the maximum distance to the
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bottom ground layer M1 for terminal pad, T-lines, inductors, and other high-Q passives to improve the transmission efficiency. In the CMOS process, SiO2 is filled between the top layer and the ground layer with dielectric constant of 3.9. For the CRLH T-line design in CMOS, as shown in Fig. 2(a), where Cs comes from interdigital capacitors, L p comes from long metal stripe connected to ground through vias, while both L s and C p come from parasitic as well as lossy elements (R, G) with integer order. The capacitor Cs is fabricated by interdigital capacitor with the finest metal pinch according to design rules delivering largest capacitance with smallest layout overhead. Inductor L p is derived from microstrip lines connected to the ground layer by via bars (bunch of merged via bars) which can reduce ohmic losses. The ground layer deployed by lower most metal layer serves as a shielding to decay the substrate loss through the ground. For SRR/CSRR T-line design in CMOS, one needs to consider two perspectives: 1) compact size and 2) tight coupling strength. Thus, differential SRR/DSRR T-lines are proposed as shown in Fig. 2(c). The two loaded CSRR/SRR unit cells are excited by the axial magnetic field generated by the host T-line. As the differential, host line generates coherent exciting magnetic field with a bidirectional and superimposed manner, which can further enhance the Q-factor and reduce the loss. Thus, a stronger coupling between the host T-line and the SRR/CSRR load can be achieved with larger mutual capacitance and mutual inductance. Similarly, floating metal serves as shielding ground to minimize the substrate loss. B. Metamaterial T-Line Integer Order Model 1) CRLH T-Line Integer Order Model: Fig. 2(a) shows realization of CRLH T-line, where Cs comes from interdigital capacitors, L p comes from long metal stripe connected to ground through a via, while both L s and C p come from parasitic as well as lossy elements (R, G) with integer order. One important property of the CRLH T-line is its phase constant varies from negative to positive as the working frequency increases. According to T-line theory, the propagation constant (γ ) and characteristic impedance (Z 0 ) can be calculated as γ =α + jβ = Z s × Y p 2 2 ω ω − 1 × − 1 ωs ωp = − (1) ω2 × L p × Cs 2 ω −1 ωs Lp Z0 = Zs ÷ Yp = (2) × 2 Cs ω −1 ωp where ωs and ω p are resonant frequencies for serial and parallel resonators, respectively. In addition, α and β are attenuation constant and phase constant, respectively. Under a balanced condition: ωs = ω p , phase velocity (v p ) can be simplified as ω2B L p Cs ω (3) vp = =
2 β 1 − ωB ω
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IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 62, NO. 9, SEPTEMBER 2015
when ω < ω p , suggesting LH region with a negative phase shift obtained; when ω > ω p , suggesting RH region with a positive phase shift obtained. In between, there is a zero phase shift region, as shown in Fig. 2(a). 2) SRR T-Line Integer Order Model: For T-line loaded with SRR [Fig. 2(b)], L 1 and C2 come from T-line, while C1 and L 2 come from magnetic coupling of SRR on both sides of T-line. The calculation ε = (Y/ j ω) = C P gives a positive real part, while μ = (Z / j ω) = (L 1 + L 2 − ω2 C1 L 1 L 2 )/(1 − ω2 C1 L 2 ). As a result, the frist and fourth quadrants in Fig. 1 can be covered. For example, the fourth quadrant can be obtained when 1 L1 + L2
