X -Band MMIC-Based Tunable Quasi-Absorptive Bandstop Filter

—This letter reports on the design and experimental testing of a new class of tunable monolithic microwave integrated circuit (MMIC)-based quasi-absorptive bandstop ﬁlters (ABSFs). An asynchronous tuning method is used to improve the design robustness and obtain an ultrahigh stopband attenuation over a wide tuning range. RF tuning is facilitated by GaAs pHEMT varactors. The proposed ﬁlter conﬁguration exhibits the following unique features: 1) ultrahigh stopband rejection ( > 70 dB) despite using low quality factor lumped element (LE) resonators; 2) miniaturized footprint enabled by the GaAs MMIC process and the use of LE-based impedance inverter elements; and 3) frequency agility. An X -band ﬁlter prototype was manufactured using a commercially available GaAs process. It exhibits a high isolation notch whose center frequency can be tuned between 8.7 and 10.5 GHz while having > 40-dB attenuation and a maximum attenuation of 73.6 dB.


I. INTRODUCTION
T HE unprecedented growth of wireless communication systems is posing an increasing demand for highly selective bandstop filters (BSFs) to mitigate interference without perturbating the frequency bands of interest. Moreover, BSFs with frequency reconfigurability are highly desired in emerging applications such as in cognitive radio transceivers to optimally use the available spectrum [1]. Conventionally, BSFs with high selectivity and low passband insertion loss (IL) are realized by reflective BSF-type configurations [2]. Nevertheless, the stopband rejection for such filters is limited by the unloaded quality factor (Q u ) of their constituent resonators, e.g., 30 dB in the BSF configuration in [2].
To overcome the aforementioned challenges and increase the stopband rejection, absorptive bandstop filters (ABSFs) have been increasingly investigated as interference suppression alternatives [3]. By superpositioning out-of-phase RF signals from two in-parallel cascaded signal paths, a theoretically infinite rejection can be achieved in the output of these filters. Alternative ABSF topologies have been proposed to date using microstrip transmission line-based resonators [ [5], [6], [7], [8], acoustic wave resonators [9], lumped element (LE) components [10], substrate integrated coaxial (SIC) cavities [11], [12], multilayer CPW configurations [13], and thin-film integrated devices [14]. The use of transmission line and CPW-based configurations results in large circuit volumes due to using large resonators (λ 0 /2 at the design frequency). Although LE-based configurations exhibit compact circuit size, their operation is limited to frequencies as high as 2 GHz [10]. Monolithic microwave integrated circuit (MMIC)-based implementation schemes enable the realization of highly miniaturized LE components and are potentially suitable for high-frequency operation. However, MMIC-based BSFs are currently underdeveloped. A small number of active BSFs have been proposed to date [16], [17], [18]. Nevertheless, the active elements used in these circuits significantly increase their power consumption. MMIC ABSFs have also been reported [19], [20], [21], [22]. However, they are based on frequency static configurations and exhibit low rejection levels (maximum 35 dB for single chip).
Taking into consideration the aforementioned limitations, this letter reports on the design and practical validation of an X-band GaAs pHEMT-based frequency reconfigurable quasi-ABSF with the following unique characteristics: 1) ultrahigh stopband rejection (>70 dB) despite being based on low-Q u LE resonators; 2) miniaturized filter size enabled by MMIC integration and the use of LE-based impedance inverters and transmission lines; and 3) wide frequency tuning at X-band.

II. THEORETICAL FOUNDATIONS
The coupling routing diagram (CRD) of an ABSF configuration is shown in Fig. 1(a). It is comprised of two resonating nodes [2 and 3 in Fig. 1(a)] and three coupling elements. The resonators are coupled to the source and load (1 and 4) via the external coupling elements m e1 and m e2 and are coupled to each other with the inter-resonator coupling element m 1 . The source and load are coupled with an internode coupling element m sl = 1 that can be represented by a transmission line of length θ (θ = 90 • at = 0) and impedance Z 0 , where Z 0 is the system reference impedance.

A. ABSF Design Considerations
A fully absorptive behavior is obtained when the following conditions are satisfied for the CRD coefficients [4]: where Q u is the unloaded quality factor of the resonating nodes. Furthermore, the sign of m sl needs to be equal to  the sign of m 1 . As shown in Fig. 1(b), the filter response exhibits an infinite attenuation and zero reflection at the design frequency ( = 0) despite its resonators having finite Q u . However, when the resonators are synchronously tuned away from the center frequency, the transmission line length θ (source-to-load coupling) is no longer 90 • and causes the attenuation to be finite (−55 dB), as shown in Fig. 1(b). The attenuation at = 0 can be increased by asynchronously tuning the resonators, as shown in Fig. 1(c). As discussed in [7], the use of asynchronously tuning introduces an additional design degree of freedom to satisfy the requirement of infinite attenuation so that it can be maintained over a wide frequency range. However, the input reflection becomes finite, i.e., the filter response is quasi-absorptive. Fig. 2(a) shows the filter response for different Q u s. While the coupling element values are specified using (1). As it can be seen, lower Q u s increase the stopband bandwidth (BW). In order for infinite attenuation to be obtained, high precision is required in the coupling element values that are a function of Q u . The resonators' Q u is usually hard to be predicted for a new integration process and for each distinct resonator design. As such, manufacturing tolerances are expected to cause discrepancies on the coupling values. Fig. 2(b) shows the synthesized response when m e1 and m e2 are increased from their optimal values [obtained by (1)] by a small amount. For example, for the case of Q u = 20, attenuation is reduced to 18 dB when m e1 and m e2 are larger than the optimal  value by 0.005. Therefore, alternative design methods need to be developed to achieve high attenuation in practical filter implementations.

B. Quasi-Absorptive Design
To increase the tuning range of the ABSF and improve its design robustness over manufacturing tolerances, asynchronous tuning can be considered. Fig. 3 shows the filter response using nonideal coupling values and how asynchronous tuning can be used to enhance the filter performance. As shown, when both resonators are synchronously tuned (ideal response in blue), the attention level is reduced to 20 dB when m e1 and m e2 are larger than their optimal value by 0.005 (black trace). By detuning one of the resonators by a small amount, the infinite attenuation performance can be retained (red trace) [7]. It should be noted that the frequency shifts after the asynchronous tuning, which can be compensated by tuning both resonators.
For proof-of-concept validation purposes, a quasi-absorptive tunable ABSF operating at X-band is designed. The circuit schematic is shown in Fig. 4. To further miniaturize the filter, the source-to-load coupling is realized by its T-type equivalent circuit (L 0 , C 0 ) and the inter-resonator coupling is realized by its π-type circuit equivalent. In particular, the external coupling elements m e1 and m e2 are realized using a high-pass π-type equivalent (C e , L e ) and the inter-resonator coupling m 1 is realized using a low-pass π-type equivalent (C 1 , L 1 ). Note that the π equivalent circuits are partially merged with the resonator tank C r and L r to reduce the total number of LE components. A variable capacitor is used in the resonator to tune the frequency.
For the initial design, a center frequency of 9 GHz and Q u of 20 are assumed to calculate the coupling values. It should be noticed that in the practical design, the coupling values (m coefficient) need to be denormalized with respect to the resonator impedance. The denormalized coupling values (k coefficient) are given as follows: where Z r = (L r /C r ) 1/2 is the impedance of the resonator. For the case of Q u = 20, k e1 and k e2 are calculated to be 0.0089, and k 1 = 0.001. After obtaining the coupling value, the LE components can be calculated using (5) and (6) where k i is the denormalized coupling value (k e1, k e2 , and k 1 ).
The final values of the LE components are shown in Fig. 4.

III. EXPERIMENTAL VALIDATION
To experimentally validate the proposed tunable ABSF concept, an X-band prototype was designed and manufactured using the WIN Semiconductor PH1-10 GaAs MMIC process. A photograph of the filter prototype is shown in Fig. 5. The variable capacitor C r is realized using a six-finger pHEMT transistor with its gate connected to the ground. A bias voltage between −0.3 to +0.5 V is applied to tune the filter response, which corresponds to a capacitance tuning between 0.34 and 0.63 pF. The overall footprint of the filter is 1.01 × 1.55 mm.
The measured S-parameters of the filter are plotted in Fig. 6(a) and are summarized as follows: f c tuning between 8.7 and 10.5 GHz with an attenuation of more than 40 dB and passband IL between 1.9 and 2.3 dB. The maximum measured stopband attenuation is 73.6 dB at 9.03 GHz. Fig. 6(b) compares the simulated and measured performance for one tuning state. As it can be seen, a decent agreement is observed, successfully validating the proposed on-chip tunable ABSF concept.
A comparison of the proposed integration concept with state-of-the-art ABSFs is provided in Table I. As shown, the proposed concept is the only MMIC-based frequency-tunable quasi-ABSF with very high stopband attenuation within a wide tuning range. Compared to microstrip or LE-based ABSFs, the GaAs MMIC process used in this work allows for significantly smaller footprint and higher operating frequencies. Enabled by asynchronous tuning, an ultrahigh stopband attenuation (>70 dB) is achieved, which is significantly higher compared  to other static MMIC ABSF designs, e.g., 23.7 dB in [19] and 23.1 dB in [22].

IV. CONCLUSION
This letter reports on the design, manufacturing, and testing of a GaAs MMIC-based quasi-ABSF tunable notch filter with ultrahigh stopband rejection (>70 dB) using low-Q resonators, miniaturized size, and frequency agility. An X-band filter prototype was manufactured using a commercially available GaAs MMIC process. It exhibits a high isolation notch whose center frequency can be tuned between 8.7 and 10.5 GHz while having >40-dB attenuation.

ACKNOWLEDGMENT
The authors would like to thank WIN Semiconductors Corporation, Taoyuan, Taiwan, for providing access to their PIH1-10 process and for manufacturing the monolithic integrated circuit (MMIC) components.