Multi-functional microwave and millimeter wave circuits are essential components of next generation communication systems. Since emerging applications require multi-functional RF front ends, there is a pressing need for power dividers/combiners capable of accommodating these advancements [1, 2]. One promising approach for miniaturizing the RF front-end and enhancing functionality involves combining the power divider, tunable filter, and isolator functions into a single circuit. Circulators and isolators are widely used in measurement, communication, and radar systems [3]. However, conventional circulators and isolators are mainly designed using a ferrite magnetic material [4], which is expensive, bulky, and incompatible with integrated circuit (IC) design.

In recent years, the spatio-temporal modulation (STM) technique has been widely used to design non-reciprocal circuits without the use of magnetic materials. Non-reciprocal bandpass filters (NR-BPFs) that integrate functionalities of isolators and filters using time-modulated resonators have been explored [5–13]. The STM concept has also been utilized to design non-reciprocal power dividers (i.e., |S₂₁| ≠ |S₁₂| and |S₃₁| ≠ |S₁₃|) by employing a combination of static and time-modulated resonators [14, 15]. In [16, 17], non-reciprocal filtering power dividers (NR-FPDs) with tunable frequencies were presented.

However, these designs require at least six time-modulated resonators. The aforementioned NR-BPFs and power dividers have achieved excellent reverse isolation only at the center frequency (f₀). In [6, 10–12], an NR-BPFs yielded reverse isolation values of up to 40 dB at f₀, however, the 20 dB reverse isolation bandwidth was very narrow. Similarly, NR-FPDs with improved isolation bandwidth have been presented in [16, 17]. However, the 20 dB isolation bandwidth of these NR-FPDs was in the range of 23–50 MHz.

This paper presents the design of a microstrip line NR-FPD that offers frequency tunable characteristics with ultrawide bandwidth isolator functionality. The proposed design features an equal and unequal power division ratio (PDR) with low transmission insertion loss (IL) and ultrawide high isolation in the backward direction. To achieve deep understanding of the proposed multi-functional NR-FPD’s non-reciprocity behavior, the analytical spectral scattering parameters (S-parameters) of the microstrip line NR-FPD were derived. As a proof of concept, an equal PDR NR-FPD with ultrawide reverse isolation bandwidth and tunable frequency functionality was designed, fabricated, and measured.

For the experimental proof-of-concept, an NR-FPD with an equal PDR (k₂ = 1) was designed and fabricated. The NR-FPD prototype was fabricated using a Taconic substrate with a thickness of h = 0.787 mm and a dielectric constant of ɛ_r = 2.2. The proposed NR-FPD was designed with a fractional bandwidth of 6% and a passband return of 26.10 dB in the static state. The design objective was to obtain minimum IL and ultrawide high isolation in the backward direction while tuning the frequency from 1.60 GHz to 2 GHz. The time-modulated resonator was implemented by using transmission terminated with SMV1233-079LF varactor diode developed by Skyworks Inc. [19].

Fig. 7 shows the overall circuit implementation of the proposed NR-FPD. J-inverters, namely J_s1 and J₄₅, were implemented using series transmission (W_a, L_a) and a coupled line (W₁, L₁, g₁). Similarly, coupling between the second and third resonators (J₁₂) and between the third and fourth resonators (J₃₄) was implemented using a short-circuited transmission (W_g, L_g). Additionally, the coupling between the second and third resonators was implemented using a coupled line (W₄, L₁, g₂). Quarter-wavelength transmissions (W_p, L_p) were utilized for implementing J-inverters J₅₆ and J₅₇. In addition, another quarter-wavelength TLs (W₀, L₀) were employed to implement J-inverters J₆₇ and J₇₈. The DC-bias voltage and the progressive phase shift sinusoidal modulation signal were applied to the varactor diode through transmission (TL_bias: W₅ and L₅), as shown in Fig. 7. The simulation results were obtained using the ANSYS high frequency structure simulator and Keysight Advanced System Design (ADS). The equivalent circuit model of the SMV1233-079LF varactor diode provided by manufacture was used in harmonic balance simulation. For the measurement, the DC-bias voltage and sinusoidal modulation signals were supplied to the NR-FPD circuit using 33622A Keysight arbitrary wave generators, where the DC-bias voltage and phase shift of the modulation signals could be easily controlled.

The frequency response of the fabricated prototype was characterized by measuring the S-parameter results. Fig. 8 shows the measurement setup for the NR-FPD. The comparison between the simulation and experimental S-parameters of NR-FPD is depicted in Fig. 9. As shown in the figures, the experimentally characterized S-parameters were well aligned with the simulations. The measured S-parameters results are summarized in Table 3.

Although Fig. 9 depicts the S-parameters of the fabricated NR-FPD at three tunable frequency states (A, B, and C) only, it should be noted that the frequency response of the fabricated NR-FPD was altered between 1.620 GHz and 1.950 GHz by varying the bias voltage of the varactor diode. The measurement results show that the passband input return loss (|S₁₁|) remained higher than 12 dB, output return losses (|S₂₂| and |S₃₃|) were better than 15 dB and reverse ISO exceeded 19 dB. The transmission loss remained in the range of 4.31–5.41 dB (excluding the inherent 3.01 dB power division). These transmission losses occurred due to the parasitic resistance of varactor diodes. The parasitic resistance of the varactor diode increased at lower DC-bias voltages, causing the forward loss to increase slightly, while the frequency was tuned toward a lower frequency. The measurement also showed that the isolation of the two output ports (i.e., (|S₃₂|) was higher than 16 dB at the passband center frequencies. Due to cross-coupling resulting from the progressive phase shifted sinusoidal modulation signal, transmission zeros (TZs) appeared in the forward direction of transmission, as shown in Fig. 9. When resonators were modulated with the progressive phase shift sinusoidal signal, IM products were generated. As a result, the RF power signal was distributed among the IM products, and transversal propagation of the RF signal occurred not only through the fundamental frequency, but also through non-adjacent resonators at harmonic frequencies. This phenomenon led to the generation of TZs.

To investigate the cause of the forward transmission IL, we performed a simulation of the NR-FPD using the SPICE model of SMV 1233-079LF varactor diode from Skyworks Inc. The results shown in Fig. 10 indicate that the forward transmission IL was mainly due to the parasitic resistance (R_s) of the varactor diode. As the value of R_s increased, the forward transmission IL also increased. Therefore, the IL can be reduced if a varactor diode with lower parasitic resistance (high Q-factor varactor diode) is used.

Table 4 compares the performance of the proposed NR-FPD with those described in previously published works [14–17]. Notably, these previously reported NR-FPDs [14–17] exhibited a high reverse ISO only at the center frequency and the 20-dB isolation bandwidth remained between 5 and 96 MHz. In contrast, this paper proposes an NR-FPD with frequency tunability and an ultrawide high reverse ISO bandwidth. The experimental results show that attenuation exceeded 20 dB in the reverse direction for all operating frequency ranges.

This paper proposes a novel design of a multi-functional NR-FPD that combines the functions of a tunable bandpass filter, a power divider with an arbitrary PDR, and an isolator into one circuit. The achievement of an ultrawide high reverse isolation bandwidth was facilitated by properly selecting the modulation parameters of the time-modulated resonators. Moreover, the proposed NR-FPD features a low transmission IL in the forward direction and ultrawide high reverse isolation bandwidth in the backward direction, with tunable frequency functionalities. To validate the performance experimentally, a prototype of the NR-FPD was designed. The results show that the measured S-parameters had excellent agreement with the simulation.