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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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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 <ω< (4) C1 L 2 C1 L 1 L 2 where Re(μ) is negative and Re(ε) is positive as dispersion diagram displays in Fig. 2(b), indicating that magnetic plasma is formed such that the propagating wave becomes evanescent wave and hence results in reflecting standing wave between the host line and the SRR. As such, SRR loaded T-line can form a high-Q resonator. 3) CSRR T-Line Integer Order Model: Similarly, for T-line loaded with CSRR [Fig. 2(c)], L 1 comes from T-line, while C1 , C2 , and L 2 come from electric coupling of CSRR on the ground. The calculation μ = (Z / j ω) = L 1 gives a positive real part, while ε = (Y/ j ω) = (C1 (1 − ω2 C2 L 2 )/1 − ω2 (C1 + C2 )L 2 ). When working in second quadrant, as shown in Fig. 1, the frequency range is given by 1 1 <ω< (5) (C1 + C2 )L 2 C2 L 2 where Re(μ) is positive and Re(ε) is negative as dispersion diagram shows in Fig. 2(c). In this scenario, electric plasma is formed by inducing the transmission waves along host T-line into evanescent waves. Similarly, CSRR loaded T-line can also be used to form a high-Q resonator. Both SRR and CSRR loaded T-lines are resonant-type metamaterial T-lines, which can provide a high-Q resonance with narrow bandwidth.

Z (ω) = ω

αL



Le

j αL π 2

.

Here, parallel L and C components are footnoted by ‘ p’, and serial L and C components are marked by footnote ‘s’, as shown in Fig. 2(d). For example, αC p gives the fractionalorder of parallel C p . R0 and G 0 measure the constant serial impedance and parallel conductance in the unit cell. From (8), real parts of impedance Z and admittance Y can be further given. At mm-wave√ frequency region, propagation constant γ = α + jβ = Z Y can be demonstrated with expressions of impedance Z and admittance Y as    jα π jα π  α Ls L  e Ls αCs C  e Cs  2 2 ω + 1/ω s s 

 γ = (9) j αCp π j αL p π  α  α  Cp L p × ω C p e 2 + 1/ω L p e 2 . From (9), the phase constant β expressed by the fractional-order model with αC and α L relative to the frequency-dependent dispersion loss becomes     αCs +α Ls   αCp +α L p    1− ω × 1− ωω  ωS P  (10) β = S (ω) ωα L p +αCs × L P × C S

(7)

C. Fractional-Order SRR T-Line Model

According to the fractional calculus of electrical components [15], [16], admittance and impedance of the fractional-order capacitor and inductor become 

As discussed in Section II, Fig. 2, after substituting the fractional-order capacitor and inductor expressions into the integer order model for CRLH T-line unit cell. The characteristic impedance (Z 0 ) of CRLH T-line unit-cell in the fractional-order expression can be derived as   π j αCs π  R + ωα Ls L  e j α Ls 2 + 1/ωαCs Cs e 2  0 s . (8) Z0 =  j αCp π j αL p π G 0 + ωαCp C p e 2 + 1/ωα L p L p e 2

(6)

A. Fractional-Order Capacitance and Inductance Models

j αC π 2

B. Fractional-Order CRLH T-Line Model

where ωs = 1/(L s × Cs )1/2 , ωp = 1/(L p × C p )1/2 , and S(ω) is the sign-function corresponding to the CRLH T-line operating frequency. When it is below balanced resonance frequency, S(ω) becomes negative and vice versa. This equation reveals an important property of CRLH T-line that illustrates its dispersion diagram of phase constant with the operation frequency. As such, one can have a compact fractional-order equivalent circuit to model distributed dispersion loss, and nonquasistatic effects for the CRLH T-line.

III. F RACTIONAL -O RDER M ETAMATERIAL T-L INE M ODEL

Y  (ω) = ωαC C  e

inside L and Cs. Given these loss descriptions in the fractional-order model, the distributed dispersion loss and nonquasistatic are characterized in frequency-dependent terms with much less number of RLGC components compared with the integer order model.

Here, C  is the fractional capacitance with order αC and αC ∈ (0, 1] is the fractional-order relating to the loss of capacitor. L  is the fractional inductance with order α L and α L ∈ (0, 1] is the fractional-order relating to the loss of inductor. When α L or αsC = 1, there exist frequency-dependent losses in real part of the fractional-order capacitance/inductance expressions. The physical meaning of α L and αC is defined as the strength of dispersion losses

As denoted in SRR’s integer order model, after taking the fractional-order impact into account, the permittivity μ and permeability ε can be simply measured by μ=

(α −1)  L 1e ω L1

ε=ω

(αC −1)  p

j (α L −1)π 1 2

C pe

(11)

.

(12)

j (αC p −1)π 2

− j (αC +1)π 1 2

ω−(αC1 +1) e + C1

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Given by (11) and (12), permittivity (εr ) and permeability (μr ), represented by capacitors and inductors inside model, will change in a fractional-order manner regards to the operating frequency. The SRR operating condition can be affected in a fractional-order fashion that is verified by the comparison results in the Section IV. D. Fractional-Order CSRR T-Line Model Similarly, as recorded by CSRR’s integer order model, the fractional-order model for CSRR in forms of the permittivity (μ) and permeability (ε) can be simply derived as μ = ω(α L 1 −1) L  1 e ε=ω

(αC −1) 1

C1 e

j (α L −1)π 1 2 j (αC −1)π 1 2

(13) +

ω

−(α L 2 +1)

− j (α L +1)π 2 2

e L 2

.

(14)

The two symmetrical expressions of μ and ε by the fractional-model models for SRR and CSRR are presented in this section. After introducing the fractional-order model, permittivity (εr ) and permeability (μr ) derived from the capacitor and inductance related to frequency behave in the frequency-dependent fractional-order fashions that can accurately and compactly model the coupling effects from metamaterial loads.

Fig. 3. Fractional-order metamaterial T-line modeling parameters extraction flow. TABLE I C OMPARISON OF D IFFERENT RLGC M ODELS AT mm-WAVE R EGION

E. Metamaterial T-Line Fractional-Order Model Extraction The fractional-order model parameter extraction flow for metamaterial T-line at the mm-wave frequency region is shown in Fig. 3. The extraction begins with the measurement S-parameter obtained from a vector network analyzer (VNA) [17]. The measurement S-parameter is converted into transfer matrix (T matrix), and after that errors introduced from the testing pads and connected T-lines are deembedded by open-thru approach [18]. Next, the parameter extractions are classified into two categories: for CRLH T-line, propagation constant γ and characteristic impedance Z 0 are calculated from deembedded T-matrix according to [19]. Afterward, multisets of functions for Z 0 and γ can be sampled within measured frequency intervals within MATLAB such that parameters in the fractional-order model to describe a CRLH T-line unit cell can be figured out. As for SRR and CSRR T-lines, μ and ε expressions are utilized to extract ten fractional-order model parameters as given by (11)–(14). Fractional parameters can be calculated by solving multifrequencies matrixes similar to the approach for extracting the CRLH T-line fractional-order model. F. Comparison With Other RLGC Modeling Works RLGC models at mm-wave region are well explored recently for its SPICE-compatible property for timedomain simulations [20]. The proposed modeling is more compact owing to the fractional-order capacitor and inductors in (6) and (7) that show frequency-dependent impendence; while in the conventional methods with RLGC ladders [21] usually requires lots of stages to obtain an accurate approximation. Therefore, with the fractional-order,

the proposed model is featured with compact size to model the frequency-dependent effects, such as dispersion loss and nonquasistatic effects. The key features of different models are listed in Table I. The comparison results show that the fractional-order model is very compact yet precise at wideband of mm-wave region to model dispersion losses in complex structures like metamaterial T-lines. IV. M ETAMATERIAL T-L INE M EASUREMENT AND C HARACTERIZATION BY F RACTIONAL -O RDER M ODEL Based on the descriptions of metamaterial T-line realization in CMOS as discussed Section II, three types of metamaterial T-lines: 1) CRLH T-line; 2) SRR T-line; and 3) CSRR T-line are fabricated in 65-nm CMOS technology. In order to meet the design requirements, CRLH T-line is characterized up to 325 GHz for 280 GHz antenna design, and SRR/CSRR T-line is characterized up to 110 GHz for 100 GHz oscillator designs, respectively. They are all characterized by Agilent PNA-X (N5247A) on probe station (CASCADE Microtech Elite-300). Note that in higher frequency range measurement for the CRLH T-line, VNA extender (VDI WR3.4-VNAX) is adopted to shift the measurement range up to 325 GHz. Testing setup is shown

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Fig. 4. (a) Measurement setup of on-wafer testing for S-parameter up to 325 GHz. (b) Open-thru deembedding structures and chip micrograph of fabricated metamaterial T-lines. (c) CMOS CRLH T-line. (d) CMOS CSRR T-line (top) and CMOS SRR T-line (bottom). TABLE II M ODELING PARAMETERS OF F RACTIONAL -O RDER RLGC M ODEL FOR M ATEMATERIAL T-L INES

in Fig. 4(a) and all testing pads and traces are deembedded (open, thru) from both sides with recursive modeling shown in Fig. 4(b). All fractional-order model parameters are extracted as the extraction flow in Section III and are listed in Table II. The fractional-order model is introduced to characterize metamaterial T-lines through dispersion diagrams compared with the integer order model simulation results by curving fitting. A. Measurement Results of CRLH T-Line The 13-unit cell CRLH T-line is fabricated in Globalfoundary 65-nm process with a die area of 145 μm × 660 μm excluding the RF pads, as shown in Fig. 4(a). Two waveguide GSG probes with 50-m pitch are

Fig. 5. Characterization of transmission type metamaterial T-line−CRLH T-line by the fractional-order model and the integer order model. (a) Magnitude of S21 in dB. (b) Phase of S21 in degree. (c) Absolute value of extracted characteristic impendence Z 0 . (d) Extracted phase constant β.

used for the S-parameter measurement from 220 to 325 GHz. To verify the two types of RLGC models, 13 identical modeled unit cells are concatenated together to simulate the proposed CRLH T-line structure. Comparisons of S-parameters are made between the measurement, the integer order model, and the fractional-order results of the CRLH T-line, as shown in Fig. 5. From the S21 comparison results, the fractional-order model results of the CRLH T-line agree well with the measurement results at the frequency range of 220–325 GHz. From the perspective of characteristic impedance Z 0 , the fractional-order model fits well with the measurement result at zero phase shift region from 280 GHz, also a smaller error of Z 0 at low-frequency region compared with the integer order fitting result. The average accuracy improvement of 78.8% is obtained by the fractional-order model when compared with the integer order counterpart results of Z 0 . In terms of phase constant β, one can observe that zero phase shift frequency shift (or error) of 21 GHz by the integral order model. According to the CRLH T-line physical property, that means to simulate the zero phase shift frequency, the fractional-order model can achieve much smaller error of 17 GHz than that of β from the integer order model. B. Measurement Results of SRR T-Line The proposed differential SRR T-line unit cell was fabricated in STM 65-nm CMOS process with 7-metal-layer. Fig. 4(d) shows the chip photo. The core area is 140 × 150 μm excluding pads. One fractional-order modeled unit-cell is introduced to characterize the SRR T-line measurement results. As shown in Fig. 6(a) and (b), the measured S21 agree with the fractional-order model simulation results in phase and magnitude very closely. The stopping band frequency is also validated by the fractional-order model compared with the

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Fig. 6. Characterization of resonant-type metamaterial T-line. SRR T-line and CSRR T-line by the fractional-order model and the integer order model. Magnitudes of S21 in dB (a) SRR T-line and (e) CSRR T-line. Phases of S21 in degree (b) SRR T-line and (f) CSRR T-line. Absolute values of extracted permeability μ (c) SRR T-line and (g) CSRR T-line. Absolute values of extracted permittivity ε (d) SRR T-line and (h) CSRR T-line.

integer order model with a 4 GHz discrepancy. Besides, the extracted effective ε and μ, which reflect the metamaterial SRR T-line property, have good alignment between the measurement and the fractional-order model. However, the error in stopping-band frequency is about 5 GHz drawn from the integer order model. The stopping band is precisely characterized by the fractional-order model over integer order model which is crustal to the SRR T-line based design. C. Measurement Results of CSRR T-Line The proposed CSRR T-line is also fabricated in the same STM 65-nm CMOS process with SRR T-line. The die photo is shown in Fig. 4(d) with the area of 0.022 mm2 without pads. One fractional-order modeled unit cell is introduced to characterize CSRR T-line properties. As shown in Fig. 6(e) and (f), the measured S21 in phase and magnitude agree nicely with the fractional-order model results. For the stopping band frequency simulation, results from the fractional-order model coincide to measurement results while a misalignment of 6 GHz is observed from the integer order model fitting results. As for ε and μ simulation results, the errors are enlarged to about 10 GHz, which means the fractional-order model can characterize the physical property of the CSRR T-line much precisely over the integer order model. D. Scalability of the Fractional-Order Model for Metamaterial T-Line The scalability of the proposed fractional-order model is also explored by comparing the EM simulation results of two-port larger scale metamaterial T-lines. As shown in Fig. 7(a), we increase the number of CRLH unit cells to 15, SRR/CSRR unit cells to 4. The related S-parameters are obtained from the EM simulation, from which, one can follow

Fig. 7. (a) Scaled structures of three types of metamaterial T-lines. Comparison results between their EM simulation and fractional-order model results. Magnitudes of S21 in dB (b) 4 unit cell SRR T-line and (c) 4 unit cell CSRR T-line. (d) Phase constant (β) of 15 unit cell CRLH T-line.

the same parameter extraction flow in Fig. 3 to obtain a scaled fractional-order model results. The comparison results between the scaled fractional-order model and the EM simulation results are shown in Fig. 7(b)–(d). One can observe that the scaled fractional-order model results can match well with the EM simulation results up to 325 GHz with demonstrated scalability. V. C ONCLUSION Metamaterial T-line is one of the most emerging passive devices for the CMOS mm-wave IC design with the need

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to develop compact yet accurate model. To characterize the distributed frequency-dependent dispersion and nonquasistatic effects as well as coupling between host T-line and metamaterial load, a compact fractional-order RLGC model is proposed in this paper. The measured results have confirmed that the proposed fractional-order RLGC model has improved accuracy over the traditional integer order RLGC model at the mm-wave frequency region. For the CRLH T-line characterized from 220 to 325 GHz, the accuracy of the characteristic impedance Z 0 by the fractional-order model is 78.8% improved on average when compared with the conventional integer order model. For the characterized SRR T-line and CSRR T-line from dc to 110 GHz, the fractionalorder model results show negligible stopping band frequency offsets (less than 0.1 GHz) over the integer order model. ACKNOWLEDGMENT The authors would like to thank W.-M. Lim, VIRTUS IC Design Centre of Excellence for their measurement support, and Integrand Software for providing the EM simulation tool EMX. R EFERENCES [1] C. Yue and S. Wong, “Physical modeling of spiral inductors on silicon,” IEEE Trans. Electron Devices, vol. 47, no. 3, pp. 560–568, Mar. 2000. [2] A. Kurokawa, T. Sato, T. Kanamoto, and M. Hashimoto, “Interconnect modeling: A physical design perspective,” IEEE Trans. Electron Devices, vol. 56, no. 9, pp. 1840–1851, Sep. 2009. [3] A. Lai, T. Itoh, and C. Caloz, “Composite right/left-handed transmission line metamaterials,” IEEE Microw. Mag., vol. 5, no. 3, pp. 34–50, Sep. 2004. [4] C.-J. Lee, K. M. Leong, and T. Itoh, “Metamaterial transmission line based bandstop and bandpass filter designs using broadband phase cancellation,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2006, pp. 935–938. [5] A. Dupuy, K. M. Leong, and T. Itoh, “Power combining tunnel diode oscillators using metamaterial transmission line at infinite wavelength frequency,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2006, pp. 751–754. [6] Y. Shang, H. Yu, P. Li, Y. Liang, and C. Yang, “A 280 GHz CMOS on-chip composite right/left handed transmission line based leaky wave antenna with broadside radiation,” in Proc. IEEE IMS, Jun. 2014, pp. 1–3. [7] S. Ma, W. Fei, H. Yu, and J. Ren, “A 75.7 GHz to 102 GHz rotarytraveling-wave VCO by tunable composite right/left hand T-line,” in Proc. IEEE CICC, Sep. 2013, pp. 1–4. [8] Y. Shang, H. Fu, H. Yu, and J. Ren, “A-78 dBm sensitivity superregenerative receiver at 96 GHz with quench-controlled metamaterial oscillator in 65 nm CMOS,” in Proc. IEEE RFIC, Jun. 2013, pp. 447–450. [9] W. Fei, H. Yu, Y. Shang, D. Cai, and J. Ren, “A 96 GHz oscillator by high-Q differential transmission line loaded with complementary split ring resonator in 65 nm CMOS,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 60, no. 3, pp. 127–131, Mar. 2013. [10] J. Bechhoefer, “Kramers–Kronig, bode, and the meaning of zero,” Amer. J. Phys., vol. 79, no. 10, pp. 1053–1059, Sep. 2011. [11] C.-S. Yen, Z. Fazarinc, and R. L. Wheeler, “Time-domain skin-effect model for transient analysis of lossy transmission lines,” Proc. IEEE, vol. 70, no. 7, pp. 750–757, Jul. 1982. [12] Y. Shang, W. Fei, and H. Yu, “A fractional-order RLGC model for terahertz transmission line,” in Proc. IEEE IMS, Jun. 2013, pp. 1–3. [13] X. Huo, P. C. H. Chan, K. J. Chen, and H. C. Luong, “A physical model for on-chip spiral inductors with accurate substrate modeling,” IEEE Trans. Electron Devices, vol. 53, no. 12, pp. 2942–2949, Dec. 2006. [14] J. Chen and J. Liou, “Improved and physics-based model for symmetrical spiral inductors,” IEEE Trans. Electron Devices, vol. 53, no. 6, pp. 1300–1309, Jun. 2006.

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Chang Yang (S’14) received the B.S. degree from Liaoning University, Shenyang, China, in 2008, and the M.S. degree from the University of Electronic Science and Technology of China, Chengdu, China, in 2012. He is currently pursuing the Ph.D. degree with the School of Electrical and Electronics Engineering, Nanyang Technological University, Singapore.

Hao Yu (M’06–SM’13) received the B.S. degree from Fudan University, Shanghai, China, in 1999; and the Ph.D. degree from the Department of Electrical Engineering, University of California at Los Angeles, Los Angeles, CA, USA, in 2007. He has been an Assistant Professor with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, since 2009. His current research interests include 3-D-IC and RF-IC at nanotera scale.

Yang Shang (S’11) received the B.S., M.S., and Ph.D. degrees from Nanyang Technological University, Singapore, in 2005, 2009, and 2015, respectively. He is currently a Senior R&D Engineer with ADVANTEST Corporation, Singapore.

Wei Fei (S’10) received the B.S. and Ph.D. degrees from Nanyang Technological University, Singapore, in 2007 and 2015, respectively. He is currently a Senior Design Engineer with Hisilicon (Singapore) Pte. Ltd., Singapore.