MMIC GaAs Isolators and Quasi-Circulators With Co-Designed RF Filtering Functionality

This paper reports on the RF design and practical development of GaAs MMIC multi-functional RF isolators and quasi-circulators with embedded filtering functionality. They are based on cascaded arrays of non-reciprocal resonators (NRRs), passive resonators, and impedance inverters. A unique transistor-based architecture is used for the realization of the NRR that exhibits an one-pole type bandpass response in the forward direction and RF signal cancellation in the reversed one. By controlling the number and type of resonators within cascaded resonator arrays, different levels of gain, out-of-band selectivity and in-band isolation can be obtained. The operating principles of the multi-functional isolator/filtering and quasi-circulator/filtering concepts are presented through synthesized and linear circuit-simulated examples. Practical design aspects using a commercially available GaAs MMIC process are also discussed. For proof-of-concept demonstration purposes, four prototypes were designed and experimentally validated at X-band. They include: i) a NRR, ii) a two-resonator based frequency selective isolator (FSI), iii) a five-resonator based FSI, and iv) a two-pole/two-TZ frequency selective quasi-circulator (FSQC).

Considering the aforementioned limitations, this manuscript discusses for the first time the design and practical development of a new class of fully-integrated frequency-selective isolators (FSIs) and quasi-circulators (FSQCs) within an MMIC integration platform alongside their coupled-resonator-based modeling. These new multi-functional devices aim to decrease the size of the RF transceiver through: i) the co-design of BPFs and isolators/circulators and ii) their integration in a MMIC platform. The proposed concept is designed to operate at X-band and implemented on a commercially available GaAs MMIC process. It is based on cascading non-reciprocal resonators (NRRs) with either passive microwave resonators and/or a transmission zero (TZ) generation cell. Therefore, the devised FSI/FSQC can be designed for various transfer functions with varying levels of IS and frequency selectivity depending on the type and the number of resonators that are incorporated in the topology. A detailed design methodology using coupled-resonator-based filter design techniques is uniquely demonstrated in this work for MMIC-based FSIs and FSQCs allowing for modular and scalable design that can be tailored to high order filtering transfer functions.
The content of this paper is organized as follows. Section II, discusses the operating principles and practical implementation in a MMIC GaAs process of the NRR and the FSI/FSQC. In Section III, the experimental testing of the GaAs prototypes at X-band is presented. They include: a NRR, a two-resonator FSI, a five-resonator FSI, and a two-pole/two-TZ FSQC. Lastly, the main contributions of the paper are summarized in Section IV.

II. DESIGN PRINCIPLES
This section discusses the RF design and operating principles of the fully-integrated FSI/FSQC concept. It starts by introducing the NRR concept and its practical implementation using a commercially available GaAs MMIC process and continues with its use in the FSI/FSQC through synthesized and circuit-based examples.

A. NON-RECIPROCAL RESONATOR
The circuit details of the NRR are provided in Fig. 1. It comprises two main parallel RF signal paths: i) a transistor-based path shaped by resistors and capacitors and ii) a capacitivelyloaded transmission line (TL). The transistor-based path is designed to have gain in the forward direction and isolation in the reverse direction as seen in Fig. 1(b). The capacitivelyloaded TL is added in parallel to counterbalance the phase of To illustrate the operating principles of the NRR, the overall design process is presented by first specifying the transistor, which is set in a common source configuration, (i.e., looking into the gate and the drain of the transistor in Fig. 1(a)) and its bias point so that the NRR can exhibit gain at the design frequency. It should be noticed that its gain and IS are affected by the bias point [see Fig. 2].
In order to create the transistor-based path, resistors and capacitors are placed at the gate and drain of the transistor. The resistors facilitate a non-reciprocal response that maintains gain at the design frequency and unconditional stability (stability factor k >1 and auxiliary stability factor B1 >0) over the entire frequency range. The capacitors are added to provide control over the frequency at which the maximum gain, the maximum IS and the best matching for both the input and output ports occurs. As seen in Fig. 1(b), the transistor-based path exhibits a positive phase response in the  forward direction, which is approximately 64°at the design frequency. When the TL with equal but opposite phase of the transistor-based path is added in parallel, the circuit in Fig. 1(a) results in a resonance at the design frequency [see Fig. 1(c)] as also discussed in [42]. For this particular NRR, the TL was capacitively-loaded to reduce the overall size of the transmission line.
To better demonstrate how some of the components in the transistor-based path affect the overall performance of the NRR, some design studies are considered and are provided in Figs. 3 and 4. As it can be seen in Fig. 3(a), R GS primarily affects the unconditional stability of the NRR; in particular, when R GS is decreased to 30 , the conditions k>1 and B1>0 are no longer satisfied. The gate and drain capacitances (C G and C D ) were also altered to see how their values affect the  overall stability of the NRR and are provided in Fig. 4. As it can be seen, the stability (i.e., k) is slightly affected by C G .
A layout for the circuit showing all of the individual components in Fig. 1(a) is provided in Fig. 5. This implementation uses a capacitively-loaded TL for compactness and has a blocking capacitor in the path to prevent bias leakage. In order to properly bias the gate and the drain of the transistor, high impedance inductors were utilized. The inductors were used to conserve space and do not add significant loss to the overall system. The circuit-simulated S-parameters for the NRR, when biased at V D = 2V, V G = 0.8V, are provided in Fig. 1(c), resulting in 1.0 dB of gain and 24.9 dB of IS at 8.9 GHz. It is worth noting that the fractional bandwidth (FBW), which is 30.6% for this case, is predetermined by the design parameters of the NRR and can't be altered.

B. NRR MODELING USING COUPLING ROUTING DIAGRAMS
Since the NRR creates a single pole type of transfer function in the forward direction and a TZ in the reverse one, it can be represented by the coupling routing diagram (CRD) and FIGURE 6. CRD and synthesized response for the NRR in Fig. 1(a) using the coupling element values in Table 1. Fig. 6 its synthesized response in Fig. 6. In particular, the transistorbased path is represented by the couplings between nodes 1, 2, 3 and 4 (i.e., M 12 , M 23 , M 32 , and M 34 ) while the capacitively loaded TL-based path is represented by the coupling between nodes 1 and 4 (i.e., M 14 ). It should be noted that different coupling element values are used for the coupling between nodes 2 and 3 in order to generate the desired non-reciprocal S-parameters. The coupling element values have been calculated using the design method in [42] and are summarized in Table 1. Specifically, the coupling between nodes 1 and 2 and 3 and 4 are set arbitrarily to 1. Next, the couplings between nodes 2 and 3 (M 23 Table 1 and circuit-simulated response of the NRR in Fig. 1(a).

TABLE 1. M-and R-Matrix Element Values for the CRD in
Finally, the coupling between nodes 1 and 4 (M 14 ) is obtained using the normalized admittance of the capacitivelyloaded TL. Since the phase of the capacitively-loaded TL is not exactly 90°at the design frequency, the R-matrix values for node 1, 4 R 11 and R 44 are found using (4), where Y TL11 and Y TL22 are the admittance of the input and output ports of TL-based path, respectively. Having specified the M-and the R-matrix element values of the NRR, its S-parameters can be calculated by (5)-(7).
A comparison of the CRD-synthesized response and the circuit-simulated response are provided in Fig. 7. As it can be seen, the CRD lines up well with the circuit-simulated response at the design frequency, thus validating the proposed CRD model. The variances between the CRD response and the circuit-simulated response outside of the design frequency are due to the CRD only being applicable to a single frequency.

C. FREQUENCY SELECTIVE ISOLATOR
In order to create a frequency selective isolator (FSI), the NRR can be cascaded through impedance inverters (i.e., quarterwavelength long TLs at f cen ) with alternative resonator types to achieve different types of transfer functions. In particular, when the NRR is cascaded with additional NRRs, the order of the FSI, its gain, and IS are increased. If the NRR is combined with passive microwave resonators, the frequency selectivity of the FSI is increased, however the gain and IS levels are the same as in the NRR case when using ideal (i.e., lossless) passive resonators. Examples of these characteristics are provided in the CRD-synthesized examples of a two-resonator FSI in Fig. 8 and a five-resonator FSI in Fig. 9.  Specifically, the two-resonator FSI in Fig. 8 is comprised of two NRRs that are coupled through an impedance inverter (M 45 ) equal to 1. In addition, a comparison of the CRDsynthesized response and the circuit-simulated response is provided in Fig. 8(b). Similar to the NRR, the variance in the two responses is due to the CRD only being applicable to a single frequency. The block diagram and CRD-synthesized response for the five-resonator FSI is presented in Fig. 9   An example demonstrating this operating principle for the two-resonator FSI is shown in Fig. 10. As it can be seen, as the coupling value of the impedance inverter connecting the two FSIs (M 45 ) is decreased, the BW of the FSI is decreased. A comparison between the NRR, two-resonator FSI, and the five-resonator FSI, is provided in Table 2 and Fig. 11. The two-resonator FSI and the five-resonator FSI have comparable gain and isolation levels due to having two NRRs present in the filter topology, however the frequency selectivity of the five-resonator FSI is higher. While a finite number of examples have been demonstrated, a wide range of transfer functions could be implemented by altering the number of the NRRs and the passive resonators in the filter topology. Furthermore, it is worth noting that while stability has only

FIGURE 13. Conceptual block diagrams for the: (a) One-pole FSQC and (b) the two-pole/two-TZ FSQC. (c) Circuit-simulated S-parameters for the one-pole and the two-pole/two TZ FSQCs. The wilkinson power divider is circled in green and the TZ generation cell is circled in red.
been presented for a single NRR, all of the presented FSIs are unconditionally stable.
In order to practically realize the FSIs using the MMIC platform, the design begins by using the NRR layout in Fig. 5. Afterwards, the impedance inverters are materialized through quarter wavelength long TLs at the design frequency. Since the NRRs require biasing, blocking capacitors are incorporated to prevent leakage to the RF ports. Finally, the passive resonators are realized through shorted quarter-wavelength long stubs to provide low loss and small size. The layout for the five-resonator FSI is provided in Fig. 12.

D. FREQUENCY SELECTIVE QUASI-CIRCULATORS
The NRR concept can also be expanded to the realization of three-port networks, such as frequency selective quasicirculators (FSQCs) as shown in the conceptual diagrams ( Fig. 13(a), (b)) and circuit-simulated responses in Fig. 13(c). The most basic form of the FSQC is shown in Fig. 13(a) and it exhibits a one-pole type transfer function, as demonstrated in Fig. 13(c). The FSQC consists of a Wilkinson power divider at the input port and a NRR (which contributes to one pole per path) at each output port (port 2 and 3) to enable the signal to flow in a single direction and provide IS in the reverse  direction. In order to increase the frequency selectivity and the out-of-band isolation of the FSQC, a TZ generation cell can be placed at the input port as shown in the conceptual diagram in Fig. 13(b) and the circuit simulated response in Fig. 13(c).
The TZ generation cell is comprised of two series LC resonators that are cascaded in parallel for size compactness. In this arrangement, they create two TZs at their respective resonant frequency and a pole at the average of the two resonant frequencies; an example of this is demonstrated in Fig. 14. Various design aspects can be considered, including the resonant frequency and the 3-dB rejection BW of the TZs; these considerations are provided in Fig. 15. In particular, the location of the pole can be altered by changing the 3dB rejection BW of the TZ (see Fig. 15(a)). Furthermore, the location of the pole can be altered by changing the resonant frequency of the TZs to either create a symmetric or an asymmetric response (see Fig. 15(b)).
When comparing the one-pole type FSQC to the twopole/two-TZ type FSQC, the latter demonstrates higher selectivity, while the IS, IL and size are comparable to the one-pole design. The order, IS, and frequency selectivity of the two-pole/two-TZ FSQC could be increased if additional resonator types were added to the design. Examples of this are provided in Fig. 16, where either a passive resonator ( Fig. 16(a)), or a TZ generation cell is added to the input port (see Fig. 16(b)), or additional NRRs are added to the output ports (see Fig. 16(c)).
As it can be seen in Fig. 16(a), the passive resonator increases the frequency selectivity of the FSQC, resulting in a three-pole/two-TZ FSQC, however, the IS and out-of-band response are the same as the two-pole/two-TZ FSQC. When a TZ generation cell is added to the input (Fig. 16(b)), the FQSC exhibits a three-pole/four-TZ response. In this instance, the second TZ generation cell can either be designed symmetrically or asymmetrically. An asymmetrically designed TZ generation cell is provided in Fig. 16(b). When compared to the two-pole/two-TZ FSQC, the out-of-band isolation and frequency selectivity are increased. In order to increase the isolation and frequency selectivity, NRRs can be added to the output ports as seen in the example in Fig. 16(c). In all of these examples, additional inverters had to be placed between the resonators, thus increasing the overall size of the FSQC.
In order to practically realize the FSQCs using the commercially available GaAs process, the layout for the twopole/two-TZ FSQC in Fig. 17 is designed. The NRRs are made using the circuit and CRD described in Section II-A and Section II-B, however they are biased at V D = 2V, V G = 0.85V (P DC = 284.6 mW since two NRRs are used). The Wilkinson power divider is designed using quarter wavelength long TLs at X-band and the TZ generation cell for the twopole/two-TZ FSQC is implemented using lumped elements for size compactness. The quality factor (Q) for the lower and upper TZ are 20.3 and 24.1, respectively.

III. EXPERIMENTAL VALIDATION
To evaluate the validity of the FSI/FSQC concepts, four prototypes were designed, manufactured, and measured at X-band using the WIN Semiconductor MMIC GaAs process, which consists of three metal layers (Metal 1, Metal 2, and ground), using circuit and full-wave electromagnetic (EM) analysis in AWR, Cadence. They include: i) a non-reciprocal resonator, ii) a two-resonator FSI, iii) a five-resonator FSI, and iv) a two-pole/two-TZ FSQC.

A. NON-RECIPROCAL RESONATOR
The NRR was designed using as a basis the circuit in Fig. 1 and the layout in Fig. 5, as shown in in Fig. 18. It was designed to enable gain (8-finger pHEMT transistor biased at V DD = 2V, and V G = 0.8V) in the forward direction and a TZ in the reverse direction at the operating frequency. The transistor-based path, including the lumped elements at the gate and the drain are circled in blue, while the TL connecting the gate and the drain is comprised of a distributed TL that is capacitively-loaded. A blocking capacitor is added to the TL to prevent biasing leakage and the bias lines include high-inductance inductors for size compactness.
When biased at V DD = 2V and V G = 0.8V, the device is turned on and provides a non-reciprocal response. A comparison between the EM-simulated and RF-measured S-parameters is provided in Fig. 19(a). As it can be seen, the measurements are in fair agreement. While the NRR was designed to have 1.2 dB of gain and 25.5 dB of IS, the  Fig. 18. (a) Before process variation is considered. (b) After process variation is considered. measurements result in IL of 0.2 dB and IS of 14.8 dB. The variation between the simulated and measured results are due to the variances in the MMIC process. When altering the lumped element values up to 5%, the measured results line up well with the simulated response thus successfully validating the proposed concept; this is provided in Fig. 19(b). The measured results are summarized as follows: f cen = 8.8 GHz, 36.2% FBW, |S 21 | = -0.2 dB, maximum in-band IS = 14.9 dB, and minimum in-band IS = 8.9 dB. IS is defined by |S 21 |-|S 12 | (i.e., directivity). Fig. 20 provides the NRR performance in terms of P 1dB and IIP 3 /OIP 3 which are summarized as follows: P 1dB = 15.5 dBm, IIP 3 = 18.4 dBm, and OIP 3 = 18.1 dBm.

B. TWO-RESONATOR FSI
To validate the two-resonator FSI in Fig. 8, a prototype was designed, manufactured and measured. It is comprised of two NRRs that are coupled through a quarter-wavelength-long TL. A photograph of the prototype is provided in Fig. 21 with the NRR circled in blue. Unlike the NRR prototype in Fig. 18, the two-resonator FSI has different biasing. The biasing combines the two gates together and the two drains together through TLs (added on a different metal layer), thus requiring a single bias point for the gates and a single bias point for the drains. The TLs are high impedance quarter-wavelength long at f cen .
Considering the variances in the manufacturing process, a comparison of the EM-simulated results and RF-measured Sparameters for the two-resonator FSI prototype is provided in Fig. 22. The RF-measured performance for the prototype is summarized as follows: f cen = 8.9 GHz, 18.7% FBW, |S 21 | = +0.3 dB, maximum in-band IS = 31.7 dB, and minimum inband IS = 25.1 dB. Furthermore, as shown in Fig. 23 the tworesonator FSI exhibits P 1dB = 10.2 dBm, IIP 3 = 17.3 dBm, and OIP 3 = 17.2 dBm.

C. FIVE-RESONATOR FSI
To further increase the order and frequency selectivity of the FSI, a five-resonator prototype was designed, manufactured, and measured at X-band. As shown in Fig. 24, it is based   on the circuit schematic in Fig. 9, with two NRRs (circled in yellow) and three passive resonators (circled in cyan). Quarter-wavelength-long TLs were used for the inverters and the passive resonators were shorted 90°stubs. A comparison of the simulated and measured results is provided in Fig. 25 showing good agreement, thus validating the proposed concept. The FSI performance is summarized as follows: f cen = 8.6 GHz, 15.6% FBW, |S 21 | = -1.9 dB, maximum in-band IS = 30.6 dB, minimum in-band IS = 26.6 dB, P 1dB = 18.0 dBm, IIP 3 = 20.4 dBm, and OIP 3 = 17.2 dBm.

D. TWO POLE/TWO-TZ FSQC
The NRR concept was further expanded to the realization of FSQCs as shown in the photo in Fig. 26(a). It is based on the two-pole/two-TZ FSQC design in Fig. 13 and is comprised of a Wilkinson power divider, two NRRs (circled in blue), and a TZ generation cell (circled in black). Its performance is provided in Fig. 26(b) and is summarized as follows: f cen   While not all of the S-parameters are provided, the measured results line up well with the simulated results, thus successfully validating the concept. Its out-of-band performance can be improved by increasing the filter order, i.e., by adding passive resonators or NRRs. Its measured non-linear performance parameters are provided in Fig. 27 and summarized as follows: P 1dB >18 dBm, IIP 3 = 25.2 dBm, and OIP 3 = 20.5 dBm. It is worth noting that the P 1dB is higher than 18 dBm, however our equipment was unable to measure at a higher input power level.

E. COMPARISON WITH THE STATE-OF-ART
A comparison of the proposed MMIC FSIs with other stateof-the-art (SOA) FSIs and IC-based isolators is provided in Table 3. When compared to other GaAs MMIC FSIs [43], the FSI concept has been validated for higher order transfer functions (5 poles vs. 3 poles in [43]) while it exhibits comparable IS. Overall, this work proves to be more modular and scalable to higher order transfer functions, different levels of gain and IS by incorporating different resonator types (i.e., passive resonators, NRRs, and TZ generation cells). When compared to STM-based FSIs, the devised FSIs have been demonstrated at a significantly higher frequencies (8.8 GHz versus <1.2 GHz in [32], [33], [34], [35], [36], [37]). Furthermore, they have lower IL (<2 dB versus 3.7 dB in [32]), and higher order transfer functions. While the transistor-based FSIs in [42] provide higher gain and IS, they are significantly larger in size and operate at a lower operating frequency. Moreover, when compared to the other integrated isolator components in [16], [17], [18], [19], they exhibit comparable IS and IL, however the proposed approach combines the functions of the RF isolator and BPF into a single component, thus reducing the overall size of the device. When compared to the transistorbased isolator in [19], the proposed approach provides better linearity (18.4 vs. 0.7 dBm). When directly compared to the GaAs integrated FSIs or isolators, the proposed approach provides better performance with respect to IL and the number of resonators and TZs incorporated into its design.
A comparison of the proposed MMIC FSQC with SOA FSQCs and active circulators is provided Table 4. As it can be seen, there are only two demonstrations of co-designed FSQCs [31], [44]. The proposed topology results in a significantly smaller size (0.094λ by 0.084λ vs. 0.48λ by 0.34λ in [44]) and higher operating frequency than the FSQCs in [31] and [44]. The proposed FSQC results in better matching at the RF ports than the active circulators reported in [23], [24], [25], [28]. In relation to the quasi-circulator in [16], the devised FSQC results in better IS levels (>16 dB). When looking at the P 1dB , this approach provides the best performance (P 1dB >18 dBm vs. <−2.1 dBm in [25], [29], and [30]). In addition, the proposed FSQC provides higher IIP 3 (25.2 dBm vs 1.2 in [29]). When compared to the circulators in [45], [46], [47],  [48], the proposed approach operates at a higher frequency (8.7 GHz vs <3.2 GHz) and incorporates filtering capabilities. Whereas the configurations in [45], [46], [47], [48], may demonstrate a somewhat frequency dependent response, their selectivity is poor and doesn't really makes them comparable to what is expected by a filter. None of these designs can be scaled to high order BPF response which is a major contribution of this work. As such, when using the approaches in [45], [46], [47], [48], the RF front-end would exhibit larger physical size as it would require to cascade additional filters in each branch of the RF circulator. The proposed FSQC has better P 1dB than the design in [47] and better IIP 3 than the design in [45], [46]. Furthermore, the FSQC presented in this work results in better IS than the design in [46]. Lastly, this is the first demonstration of a fully-integrated frequency selective circulator with more than two poles.

IV. CONCLUSION
This manuscript presented the operating principles and practical implementation aspects of a new class of multi-functional MMIC RF components that exhibit the combined function of a BPF and an RF isolator/circulator. The proposed FSIs are based on cascading in series NRRs with passive resonators to increase the frequency selectivity of the RF component. The operating principles of the FSI concept and its extension to high order transfer functions were uniquely presented through circuit-based and CRD-synthesized examples allowing for the scalability of the proposed concept to high order and advanced transfer functions. The proposed FSQC is based on the combination of a Wilkinson power divider, a TZ generation cell, and NRRs to create a two-pole/two-TZ non-reciprocal transfer function. For proof-of-concept validation purposes, four prototypes were designed and measured at X-band using the WIN Semiconductor GaAs process. They include: i) a NRR ii) a two-resonator FSI, iii) a five-resonator FSI, and iv) a two-pole/two-TZ FSQC.