Tunable Absorptive Dual Notch Filters Using A Stub-Loaded Coupled Line with An Inductor

Article information

J. Electromagn. Eng. Sci. 2024;24(6):545-555

Publication date (electronic) : 2024 November 30

doi : https://doi.org/10.26866/jees.2024.6.r.260

Young-Ho Cho ¹

, Cheolsoo Park ²^,

, Sang-Won Yun ³

¹Department of Electrical and Communication Engineering, Daelim University College, Anyang, Korea

²Department of Computer Engineering, Kwangwoon University, Seoul, Korea

³Department of Electronics, Sogang University, Seoul, Korea

^*Corresponding Author: Cheolsoo Park (e-mail: parkcheolsoo@kw.ac.kr)

Received 2023 March 17; Revised 2023 August 16; Accepted 2024 May 12.

Abstract

This paper presents tunable absorptive dual-notch filters using a stub-loaded coupled line with an inductor. The two-pole Butterworth filter function is modified to attain absorptive responses at a notch frequency. In addition, a stub-loaded coupled line with an inductor is employed to obtain dual-band bandstop responses, the required coupling coefficients, and quality factors based on the modified Butterworth function at two notch frequencies. In the proposed filter, tunable absorptive dual-notch responses are accomplished without using auxiliary circuits, such as an impedance matching network. The two resonant frequencies and the quality factors of the resonators are independently controlled by adjusting the three loading capacitances of the resonator. Three types of filters are designed and then built on a substrate with ɛ_r = 3.42 and h = 30 mils. The first filter (Filter A) attained a return loss of 11.2–17.1 dB/10.5–24.4 dB at 0.76–0.98 GHz/1.05–1.28 GHz. The measured return loss of the second filter (Filter B) was 12.5–14.8 dB/10.2–12.3 dB at 0.84–1.08 GHz/1.35–1.59 GHz. For Filter C, equipped with a 4-pole response achieved through the cascade connection of two 2-pole filters (Filter B), a return loss of 11.2–15.1 dB/14.2–27.3 dB was obtained at 0.9–1.1 GHz/1.38–1.63 GHz. The application areas of the proposed filters include cognitive radios and carrier aggregation systems requiring two transmit frequencies.

Keywords: Absorptive Filter; Bandstop Filter; Dual Notch; Independent Control; Tunable Filter

I. Introduction

Cognitive radios equipped with dynamic frequency-agile front-end receivers can be employed to improve spectrum efficiency [1–3]. Tunable bandstop filters are essential components for these systems, since they help suppress out-of-band interference signals arising from the large number of potential transmitters in a wide operating frequency range [4]. While a number of tunable bandstop filters have been proposed in the literature [5–9], cognitive radio receivers may be damaged by the reflected signal at notch frequency. To address this issue, tunable multiband absorptive bandstop filters can be used.

Notably, various absorptive bandstop filters that absorb the unwanted reflected signal at notch frequencies have been extensively studied [10–21]. For instance, absorptive filter design theories suitable for lumped-element filters were introduced in [10–12], while [13–21] reported several design methods for distributed absorptive bandstop filters. However, since the filter proposed in [13] was designed based on a balanced configuration using a 3-dB coupler, it resulted in a large size and additional insertion loss. Meanwhile, the absorptive distributed filters in [14, 15] were constructed using coupling matrices and routing diagrams to obtain tunable filters or dual-band filters.

In this context, it should be noted that these design methods resulted in a large size due to the requirement for auxiliary circuits. Even in the case of absorptive bandstop filters realized using impedance matching circuits [16–19], the filter size increased due to the presence of additional circuits. Although the authors of [20–23] designed distributed absorptive filters by transforming the lumped filter topology, it is a difficult approach to implement for tunable filters or dual-band filters due to the complicated filter configuration. Notably, good reflectionless bandstop filters were achieved in [24] based on coupling diagrams. Furthermore, the dual-notch filters in [25] and the tunable filters in [26] were designed based on the filter configurations in [19]. Nonetheless, while several dual-band or tunable absorptive filters have been investigated in the literature [27–30], absorptive bandstop filters with both frequency-tunability and dual-band notch characteristics need to be investigated further for implementation in multi-band cognitive radio receivers.

In this paper, tunable absorptive dual-notch filters using a stub-loaded coupled line with an inductor are presented. The proposed filter is designed by modifying the two-pole Butterworth filter function. The reflection characteristics at the notch frequency are enhanced by the controlling poles in the transfer function to obtain an absorptive bandstop filter by adjusting coupling coefficients and resonator quality factors (Qs) as conventional filter designs. Notably, since the proposed absorptive filter is realized by adjusting the coupling coefficients and the resonator Q, auxiliary circuits are not required for impedance matching or for the absorption of the reflected signal. The resonator Qs required for the absorptive responses are obtained using finite Q varactors without the need for additional resistors. In addition, a stub-loaded coupled line with an inductor is employed to satisfy the required coupling coefficients, while the resonator Qs are extracted through the modified Butterworth transfer function. When two notch frequencies are tuned, the coupling coefficients and resonator Qs for both low- and high-band notch frequencies can be independently controlled to achieve absorptive responses at two notch frequencies.

In this study, three filters were designed—Filters A and B exhibit two-pole responses, while Filter C is a 4-pole filter. Filter A showed two notch frequency tuning ranges of 0.76–0.98 GHz and 1.05–1.28 GHz, and Filter B was designed for noncontiguous notch frequencies of 0.84–1.08 GHz and 1.35–1.59 GHz.

The two notch frequency tuning ranges of the proposed filter were freely designed using Filter A, which shows continuous notch frequency, and Filter B, which exhibits noncontiguous notch frequency. Filter C, with frequency tuning ranges of 0.9–1.1 GHz and 1.38–1.63 GHz, was achieved as a 4-pole filter.

II. Filter Design

1. Absorptive Bandstop Filter Transfer Function

The transfer functions of an ideal second-order Butterworth bandstop filter can be expressed as follows:

(1) S21=s(s+β)s2+2s+α

and

(2) S11=γs2+2s+α,

where α = 1, β = 0, and γ = 1 [31].

As shown in Fig. 1, when the imaginary values of the poles decrease, α and γ change from 1 to 0.5 and from 1 to 0, respectively, as noted in Table 1. The values of α, β, and γ are extracted using the method introduced in [29]. When the imaginary part of the poles is zero, γ and S₁₁ in (2) also become zero (see Table 1). Consequently, a perfect absorptive bandstop response is obtained.

Fig. 1

Pole locations for the Butterworth filter transfer function.

Table 1

Values of transfer functions

The transfer functions in (1) and (2) can be synthesized using the conventional ladder network method, as depicted in Fig. 2(a). The filter parameters are listed in Table 2 [29]. The input signal is transferred to an output port through J_T but removed at the resonant frequency obtained by J₀₁, G₁, and C₁, thus achieving a bandstop response. The filter bandwidth is controlled, and a reflectionless response is achieved by J₁₂ extracted using (1) and (2) [4]. Notably, the filter in Fig. 2(a) is simulated based on the parameters noted in Table 2 (Fig. 2(b)).

Fig. 2

(a) Bandstop filter network resulting from Eqs. (1) and (2), and (b) its calculated frequency responses.

Table 2

Parameters of the bandstop filter in Fig. 2(a)

When α = 0.5 (the poles are located on the real axis), S₁₁ < − 78 dB is attained at the center frequency. In the case of α = 0.5, β = 0.707, and γ = 0, S₁₁ should appear as the perfect reflectionless response, but S₁₁ < −78 dB was obtained. On rounding off the extracted values (J₀₁, J_T, J₁₂, C₁, and G₁) to their fourth decimal place, some errors occurred in the simulation, thus not completely reaching −∞ dB. Thus, an excellent absorptive bandstop response is obtained at the notch frequency. However, when embarking on filter design, it should be considered that the bandwidth in the case of α = 0.5 is narrower than that of a typical Butterworth filter (α = 1.0). Moreover, while the S₁₁ response is enhanced to form a reflectionless response as well as a two-pole response, the S₂₁ response of the two-pole filter degrades to that of a one-pole filter. The proposed tunable absorptive dual-band bandstop filters are designed maintaining the parameters (J₀₁ = 1.414, J_T = 1, J₁₂ = 1, C₁ = 2.828, and G₁ = 1) pertaining to α = 0.5.

2. Stub-Loaded Coupled Line with an Inductor

A stub-loaded coupled line with an inductor is proposed to realize a dual-stopband response that satisfies the coupling coefficient between two resonators (J₁₂) and resonator Q shown in Table 2.

Two stub-loaded resonator pairs drawn from [7] are coupled in the manner illustrated in Fig. 3(a). The resonator satisfies the resonant frequency and the resonator Q generated through C₁ and G₁. The strong current part (Y_e12, Y_o12, and θ₁₂) in the resonator is arranged to obtain the magnetic coupling of J₁₂, since J_T and J₁₂ have the same sign as magnetic coupling [31]. Furthermore, an inductor is placed at the strongest current part in the resonator to control for the magnetic coupling in the high-band.

Fig. 3

(a) Proposed stub-loaded coupled line with an inductor, and (b) its calculated low- and high-band coupling coefficients (k_L and k_H, respectively).

The coupling coefficients (k) for the low- and high-stopband frequencies are calculated as k=Y_T12/(ϑY_T12/ϑω) using (3)–(4), as mentioned below. Notably, (3) and (8) pertain to the Y-parameters for the schematic shown in Fig. 3(a), following [32]. The related equations are as follows:

(3) YT11=jωCL1-jYL cot θL-YL2 csc2 θL (-jYL cot θL+YC11)(YC12+jYL cot θL-YC11)(YC12-jYL cot θL+YC11)

and

(4) YT12=--YL2YC12 csc2 θL(YC12+jYL cot θL-YC11)(YC12-jYL cot θL+YC11),

which is

(5) YC12=-j2(Yo12-Ye12) cot θ12-j2(Ye122 csc2 θ122Ye12 cot θ12-Ye122 csc2 θ12jYin3+Ye cot θ12+jYin2+2ωL12-Yo122 csc2 θ122Yo12 cot θ12-Yo122 csc2 θ12jYin3+Yo12 cot θ12+jYin2)

(6) YC11=-j2(Yo12+Ye12) cot θ12j2Ye122 csc2 θ122Ye12 cot θ12-Ye122 csc2 θ12jYin3+Ye12 cot θ12+jYin2+2ωL12+j2Yo2 csc2 θ122Yo12 cot θ12-Yo122 csc2 θ12jYin3+Yo12 cot θ12+jYin2

(7) Yin3=jYLωCL2+(jωCL2RL2+1)YLtanθLYL(jωCL2RL2+1)-ωCL2tanθL,

and

(8) Yin2=jYHωCH+(jωCHRH+1)YH tan θHjωCHYH (RH+1jωCH)-ωCH tan θH.

Fig. 3(b) presents the low- and high-band coupling coefficients (k_L and k_H), calculated based on (3) and (4) at 0.9 GHz and 1.1 GHz, with Z_H (= 1/Y_H) = 42 Ω, R_L1 = R_H = R_L2 = 0.7 Ω, C_L1 = 3.9 pF, C_H = 2.32 pF, C_L2 = 7.24 pF, θ_L = 25°, θ_H = 40°, θ₁₂ = 25° at 0.9 GHz, Z_e12 (=1/Y_e12) = 26 Ω, and Z_o12 (=1/Y_o12) = 24.7 Ω. Notably, Z_L (= 1/Y_L) was varied as 30–35 Ω, and L₁₂ was selected as 20, 28, and 35 nH. Fig. 3(b) shows that k_L decreases as Z_L increases, but L₁₂ has only minimal effects on k_L. In contrast, a higher Z_L results in an increased k_H. Furthermore, when L₁₂ increases, k_H declines. As a result, since L₁₂ mostly affects k_H, k_H and k_L can be independently controlled.

The proposed filter was designed based on the circuit illustrated in Fig. 3(a) to control for coupling coefficients and obtain absorptive notch responses at two frequencies.

The stub-loaded resonator in Fig. 3(a) is expected to satisfy the resonator Q through G₁ = 1 S and C₁ = 2.828 F, listed in Table 2. Notably, when the two notch frequencies were 0.9 GHz and 1.1 GHz, with the fractional bandwidth being 0.03, the low- and high-notch frequency Qs were 94.2 and 77.1, respectively [33].

Fig. 4 presents the results of the simulated resonator Q with regard to the parameters considered for the calculated results in Fig. 3(b). Low-frequency Q (Q_L) is controlled using C_L1 and C_L2. It is evident that Q_L increases with an increase in C_L1 or C_L2. Furthermore, when C_L1 and C_L2 are 3.9 pF and 7.24 pF, respectively, the Q_L is 94.2. Since C_L1 and C_L2 were asymmetrically tuned, Q_L was obtained as the required value. It is also observed that high-frequency Q (Q_H) increases as C_L1 or C_H increases. When C_L1 and C_H are 3.9 pF and 2.32 pF, respectively, the Q_H is 77.1. Therefore, Q_L and Q_H can be independently controlled using C_L1, C_L2, and C_H, while Q_H is predominantly controlled using C_H.

Fig. 4

Q of the stub-loaded resonator at low- and high-resonant frequencies.

In bandstop filters, J_T is typically realized as a quarter-wavelength transmission line. However, when a capacitor-typed J-inverter (C₀₁) is applied for J₀₁, an additional capacitor for J_T is required to absorb the −C₀₁ of J₀₁ [34]. Therefore, a capacitor-loaded transmission line, depicted in Fig. 5, was employed.

Fig. 5

Quarter-wavelength transmission line and capacitor-loaded transmission line.

The design equations were extracted based on the ABCD parameters of the two transmission-line inverters as follows:

(9) ωCT=1ZT12,

(10) ZT12=2ZT,

and

(11) cosθT12=12.

3. Tunable Filter Design

As shown in Fig. 6, the proposed tunable filter configuration is accomplished by implementing the circuits presented in Fig. 3 and 4. J₁₂ and the two resonators (C₁ and G₁) in Fig. 2 are realized as the stub-loaded coupled line with an inductor in Fig. 3. Furthermore, J_T is achieved using the transmission line loaded with two capacitors shown in Fig. 5. A capacitor-typed J-inverter (C_D01 and D₀₁) is used for J₀₁ (=ω₀C₀₁). −C₀₁ is absorbed into C_T in Fig. 5 and C_L1 in Fig. 3.

Fig. 6

Proposed filter configuration.

Filter A was designed at f₁ = 0.9 GHz and f₂ = 1.1 GHz, with fractional bandwidths of 0.03. The coupling coefficients (k_L and k_H) were 0.011, while the low- and high-band resonator Qs (Q_L and Q_H) were 94.2 and 77.1, respectively. The design parameters, calculated based on (3)–(7), were as follows: Z_L (= 1/Y_L) = 33 Ω, Z_H (= 1/Y_H) = 42 Ω, R_L1 = R_H = R_L2 = 0.7 Ω, C_L1 = 3.9 pF, C_H = 2.32 pF, C_L2 = 7.24 pF, L₁₂ = 28 nH, C₀₁ = 0.6 pF, C_T = 1.89 pF, θ_L = 25°, θ_H = 40°, θ₁₂ = 25° at 0.9 GHz, Z_T12 = 70.7 Ω, θ_T12 = 45° at 1 GHz, Z_e12 (=1/Y_e12)= 26 Ω, and, Z_o12 (=1/Y_o12)= 24.7 Ω.

The filter dimensions were as follows: g₁₂ = 3.74 mm, L_C12 = 21.18 mm, W_C12 = 4.4 mm, W_L1 = 3.08 mm, L_L1 = 8.05 mm, L_L2 = 6.73 mm, L_H = 5.92 mm, L_L3 = 13.33 mm, W_H = 2.18 mm, W_T12 = 0.9 mm, and L_T12 = 18.6 mm. Furthermore, Filter C, exhibiting a 4-pole response, was realized through a cascade connection of two Filter Bs.

III . Measurements

1. Filter A

Fig. 7 shows a photo of the fabricated Filter A, as well as the simulated and measured results.

Fig. 7

(a) Fabricated Filter A and (b) the measured and simulated responses (solid line, measurement results; dotted line, simulation results).

The measured rejection levels, as shown in Fig. 7(b), are 29 dB and 33 dB at 0.83 GHz and 1.21 GHz, respectively. The measured return losses are 17.1 dB at 0.83 GHz and 26.2 dB at 1.21 GHz. S₁₁ < −9.8 dB is attained at 0.6–1.4 GHz. Furthermore, since C₀₁, Z_T12, C_T12, and θ_T12 were designed at 1 GHz, a return loss characteristic < −14.6 dB is obtained at frequencies between the two notch frequencies. The measured insertion losses were 0.85 dB, 0.55 dB, and 1.91 dB at 0.7 GHz, 1.0 GHz, and 1.3 GHz, respectively. Notably, since the capacitor-loaded transmission-line inverter features a lowpass-typed structure, the insertion loss increased at higher frequencies. Moreover, when the cut-off frequency for the inverter increased, the outband response was also enhanced. Therefore, ω in (9) was fixed at the high-band center frequency.

Fig. 7(b) confirms that the measurements agree well with the simulations at the two notch frequencies. However, the measured bandwidth was wider than that in the simulated result due to errors in varactor modeling. Notably, the two notch frequencies were independently controlled, as shown in Fig. 8. The low-frequency notch is tuned to 0.76–0.98 GHz, with rejection levels of 25.2–40.1 dB and −10 dB rejection bandwidths of 20–25 MHz (Fig. 7(a)). The return losses for the low and high notch frequencies are 11.2–17.1 dB and 10.5–26.2 dB, respectively. Furthermore, the insertion loss was measured as 0.55–1.1 dB at 200 MHz offset frequency from the low-band notch frequency. Meanwhile, the tuning range for the high-frequency notch is 1.05–1.28 GHz, with rejection levels of 20.5–28.9 dB and −10 dB rejection bandwidths of 28–35 MHz (Fig. 7(b)).

Fig. 8

Measured (a) low-band tuning and (b) high-band tuning for Filter A.

Return losses at the high- and low-frequency notches are 10.5–24.4 dB and 10.1–20.3 dB, respectively. The insertion loss at the 200 MHz offset frequency from the high-band notch frequency was measured to be 0.72–2.12 dB. When the notch frequencies are tuned, absorptive responses are exhibited, and good bandstop characteristics are also accomplished. Notably, one notch was kept fixed, while the other notch frequency was being tuned.

2. Filter B

Filter B is characterized by noncontiguous frequency tuning ranges. Fig. 9(a) shows the photo of the fabricated filter, while the measured and simulated absorptive dual-notch responses are shown in Fig. 9(b).

Fig. 9

(a) Fabricated Filter B, and (b) the measured and simulated responses (solid line, measurement results; dotted line, simulation results).

3. Filter C

Fig. 11(a) shows a photo of the fabricated Filter C. Characterized by a 4-pole response, Filter C was realized by the cascade connection of two Filter Bs.

Fig. 11

(a) Fabricated Filter C, and (b) the measured and simulated responses (solid line, measurement results; dotted line, simulation results).

The measured rejection levels attained are 20.5 dB and 29.8 dB at 0.98 GHz and 1.53 GHz, respectively. Meanwhile, the measured return losses are 12.5 dB at 0.98 GHz and 18.8 dB at 1.53 GHz, respectively. Furthermore, the insertion loss is 0.75 dB, 0.57 dB, and 2.31 dB at 0.7 GHz, 1.2 GHz, and 1.7 GHz, respectively. Notably, the lowpass-typed structure of the capacitor-loaded transmission-line inverter resulted in outband degradation in the measured S₂₁. Fig. 10 clarifies that the two notch frequencies are independently controlled. The low-frequency notch covers 0.84–1.08 GHz, with rejection levels of 20.5–29.4 dB and −10 dB rejection bandwidths of 22–31 MHz (Fig. 10(a)). The return losses for the low and high notch frequencies are 12.5–14.8 dB and 15.1–24.2 dB, respectively. Meanwhile, the tuning range for the high-frequency notch is 1.35–1.59 GHz, with rejection levels of 20.1–33.4 dB and −10 dB rejection bandwidths of 27–38 MHz (Fig. 10(b)).

Fig. 10

Measured (a) low-band tuning and (b) high-band tuning for Filter B.

Furthermore, return losses for the high- and low-frequency notches are 10.2–12.3 dB and 14.3–24.2 dB. The insertion loss at 200 MHz offset frequency from the notch frequency was measured to be 0.8–2.6 dB.

A transmission line (47° at 1.2 GHz) between the two filters and D_T was implemented for impedance matching. The simulated and measured results are shown in Fig. 11(b). Notably, the electrical length was determined based on (11). To enhance impedance matching at the two notch frequencies, D_T of the capacitor-loaded transmission-line inverter had to be controlled. The measurements agree well with the simulations at two notch frequencies. The measured rejection levels are 44.5 dB and 43.9 dB at 1.0 GHz and 1.45 GHz, respectively. The measured return losses are 15.1 dB at 1.0 GHz and 22.6 dB at 1.45 GHz, respectively. These results indicate enhanced attenuation compared to the two-pole filter, while also accomplishing a good return loss response. S₁₁ < −14.3 dB is obtained at 0.6–1.8 GHz, while the insertion loss is 0.92 dB, 1.25 dB, and 2.61 dB at 0.7 GHz, 1.2 GHz, and 1.6 GHz, respectively. The two notch frequencies are tuned, as shown in Fig. 12.

Fig. 12

Measured (a) low-band tuning and (b) high-band tuning for Filter C.

Fig. 12(a) shows that the low notch frequency tuning range is 0.9–1.1 GHz, with rejection levels of 42.5–45.1 dB and −20 dB rejection bandwidths of 25–48 MHz. Return losses at the low and high notch frequencies are 11.2–15.1 dB and 12.7–22.6 dB, respectively. The insertion loss is 0.88~1.42 dB at 200 MHz offset frequency from the low-band notch frequency. Meanwhile, the high-frequency notch is tuned to 1.38–1.63 GHz, attaining rejection levels of 39.2–58.5 dB and −20 dB rejection bandwidths of 28–58 MHz (Fig. 12(b)). The high- and low-frequency notch return losses are 14.2–27.3 dB and 12.1–18.8 dB, respectively. The insertion loss at 200 MHz offset frequency from the high-band notch frequency was measured to be 0.82–2.72 dB.

4. Comparison with Other Filters

Table 3 summarizes a comparison of the filter proposed in this study with existing tunable distributed absorptive bandstop filters in the literature. Although various reflectionless bandstop filters have been realized by researchers, single stopband characteristics were attained only in [14–16, 26]. Furthermore, although the filters introduced in [25, 30] exhibit dual-band responses, the insertion loss of the filter in [25] is degraded, and auxiliary impedance matching circuits are required to achieve the absorptive response in [30]. In contrast, the proposed design produces dual stopband responses while maintaining a return loss > 10 dB based on a 4-pole filter configuration without the need for any auxiliary impedance matching network.

Table 3

Performance comparison with other filters

IV. Conclusion

In this paper, 2-pole and 4-pole tunable absorptive dual-notch filters are proposed, and a filter transfer function for absorptive bandstop filters is established. A coupled line with a lumped inductor and a finite Q varactor was employed to obtain the absorptive response. Furthermore, a dual-notch response was obtained using stub-loaded resonators loaded with asymmetrical capacitances, thus independently controlling two notch frequencies. Moreover, three different filters were designed and tested. In the future, RF microelectromechanical system switched capacitors may be used to achieve significant improvements in power handling and linearity [35].

Acknowledgments

This research was supported by the Ministry of Science and ICT, Korea, through the Information Technology Research Center support program (No. IITP-2023-RS-2022-00156225) supervised by the Institute for Information & Communications Technology Planning & Evaluation.

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Biography

Young-Ho Cho, https://orcid.org/0000-0002-6277-8534 received his B.Eng. and Ph.D. degrees in electronic engineering from Sogang University, Seoul, South Korea, in 2005 and 2012, respectively. From 2013 to 2014, he was a postdoctoral researcher in the Department of Electrical and Computer Engineering at the University of California at San Diego (UCSD), La Jolla, CA, USA. From 2015 to 2018, he was a senior researcher at the Defense Industry Technology Center (DITC), Agency for Defense Development (ADD), Seoul, South Korea. Currently, he is an assistant professor in the Department of Electrical and Communication Engineering at Daelim University, Anyang, South Korea. His research interests include RF filters, tunable and multiband circuits, antennas, and RF systems.

Cheolsoo Park, https://orcid.org/0000-0001-8042-007X received his B.Eng. degree in electrical engineering from Sogang University, Seoul, South Korea, and his M.Sc. degree from the Department of Biomedical Engineering at Seoul National University, Seoul, South Korea. In 2012, he received his Ph.D. in adaptive nonlinear signal processing from Imperial College London, London, UK. From 2012 to 2013, he was a postdoctoral researcher at the University of California, San Diego. Currently, he is an associate professor in the Department of Computer Engineering at Kwangwoon University, Seoul, South Korea. His research interests lie primarily in the areas of machine learning and adaptive and statistical signal processing, with applications in healthcare, computational neuroscience, and wearable technology.

Sang-Won Yun received his B.Sc. and M.Sc. degrees in electronic engineering from Seoul National University, Seoul, Korea, in 1977 and 1979, respectively. In 1984, he received his Ph.D. degree in electrical engineering from the University of Texas at Austin. Since 1984, he has been a professor in the Department of Electronic Engineering at Sogang University, Seoul, South Korea. From January 1988 to December 1988, he was a visiting professor at the University of Texas at Austin. From 2009 to 2011, he worked for the Korea Communications Commission as a project manager. Dr. Yun was the chairman of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S), Korea Chapter, from 2000 to 2004. He was also president of the Korea Institute of Electromagnetic Engineering and Science (KIEES) in 2008. His research interests include microwave and millimeter-wave devices and circuits.

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Study	Auxiliary circuit	Filter poles	Numbers of bands	Tuning range (GHz)	Return loss (dB)
Gomez-Garcia et al. [14]	Yes	3	Single	1.93	11.3
Psychogiou and Gomez-Garcia [15]	Yes	–	Single	0.18–0.31	>22
Lee and Lee [17]	Yes	2	Single	2.0	<15
Hamzah et al. [25]	No	–	Dual	1.0/2.0	>10
Jachowski [26]	No	2	Single	2.3–2.5	>15
Chang and Lin [29]	Yes	2	Dual	4.8/9.6	>15
Gomez-Garcia et al. [30]	Yes	2	Dual	3.86/4.6	>10
This study	No	2/4	Dual	0.9–1.1/1.4–1.6	>10

Pole	α	β	γ
−0.707 ± j0.707	1.0	0.0	1.0
−0.707 ± j0.447	0.7	0.424	0.440
−0.707 ± j0.316	0.6	0.566	0.268
−0.707	0.5	0.707	0

α	J₀₁	J_T	J₁₂	C₁	G₁
1.0	1	1	1	0.707	0
0.7	1.025	1	1	1.061	0.225
0.6	1.071	1	1	1.351	0.382
0.5	1.414	1	1	2.828	1