Conventional design approaches for microstrip filters involve complex mathematical computations and exhaustive parameter tuning, which require a substantial investment of time and intellectual resources. In this letter, we present an inverse design model based on conditional deep convolutional (CDC) generative adversarial network (GAN) to significantly simplify the design process of dual-band microstrip filters. The circuit structure of the filters consists of two fixed feedlines and a square patch with irregular notches that is formed by 32 $\times$ 32 pixels. By establishing the relationship between the pixelated patterns and their corresponding ${S}$ -parameters, the inverse design problem of the filters is converted and simplified to the inverse design problem of the pixelated patterns. It is addressed by an inverse design model based on GAN that is constructed with three convolutional neural networks (CNNs). When feeding a set of customized ${S}$ -parameters into the inverse design model, a series of special pixelated patterns are generated with the assistance of the GAN in about 11 min. Four design examples of dual-band filters with center frequencies located in ${S}$ / ${C}$ -band and ${C}$ / $L$ -band, respectively, are provided to validate the effectiveness of the inverse design model. The simulated ${S}$ -parameters of the inversely designed filters are in good agreement with the customized ones. Two practical examples of dual-band microstrip filters operating at 3 and 5 GHz are presented to further demonstrate the feasibility of the proposed inverse design method.

In this paper, a novel inverse design model, constructed using a generative adversarial network (GAN), is proposed for a varactor-based microstrip tunable lowpass filter (TLPF). Transfer learning algorithm is utilized to simplify the training process of the constructed model. The planar resonant circuits of the TLPFs are represented as pixelated patterns and tunable characteristics are achieved by the tunable capacitance of the varactors. The GAN-based model incorporates multiple simulators that are constructed using convolutional neural networks (CNNs) to predict the outcomes under various tuning conditions. In this way, the relationship between these patterns and the corresponding EM behaviors is established under different tuning voltages applied to the varactors. To significantly reduce the training time and the number of samples required by the extra simulators, an effective solution based on transfer learning is proposed by expanding a single CNN of a well-trained simulator to a series of CNNs of similar simulators with a common architecture. Utilizing the inverse design model, four TLPFs with different customized tuning ranges within 5 to 10 GHz are designed with an efficient process. The training of the model requires approximately 201 min, while the inference time for each design is 12.5 min. The simulation results of the designed TLPFs are in good agreement with the customized ones. Circuit prototypes combining these TLPFs and two additional rejection cells were fabricated and the measurement results show that a 17 dB rejection level is achieved over a wide stopband up to 28 GHz.

This letter proposes a directivity-compensated wideband coupled-line-based microstrip coupler that incorporates capacitive-loading patches and reflectionless amplitude equalizers. Three tiny rectangular patches, which are loaded symmetrically in-between the coupled lines, compensate for the directivity deterioration caused by substrate inhomogeneity in the microstrip coupler. Two reflectionless amplitude equalizers based on resistor-loaded open-ended microstrip line lossy resonators are cascaded at the coupling port and the isolation port, respectively, are utilized to improve the flatness of the coupling coefficient and the isolation without deteriorating the directivity of the coupler. Apart from the amplitude modification in $S$ -parameters, the phase variations introduced during the design process are also analyzed. A prototype of a 20-dB microstrip directional coupler with its working frequency centered at 4.3 GHz was designed and fabricated. Measurement results demonstrate that the fractional bandwidth of the coupling coefficient with its flatness better than $\pm$ 0.5 dB is as high as 137%. Measured directivity ranges from 17.5 to 36.0 dB across 1.36–7.25 GHz, demonstrating the effectiveness of the proposed design.

This article presents a generative model for the inverse design of dual-band filters based on a type of modified complementary split-ring resonator (CSRR). It consists of a series of convolutional neural networks that incorporate the conditional deep convolutional generative adversarial network (GAN) technique. The filters are designed by etching the modified CSRRs on the surface of substrate-integrated waveguides. This design allows us to achieve two passbands with a compact size. In this GAN-based generative model, the CSRRs are represented as two-dimensional matrices. Each matrix corresponds to a training sample of the designed filter, and its S-parameters are extracted through an HFSS simulation. Both the matrices and the S-parameters are fed into the model as the training datasets. Different CSRRs with various sizes are employed for a wider applicable frequency band. Normalized matrices and normalized S-parameters are utilized to simplify the complex generative model resulting from the variations in CSRR sizes. The effectiveness of the generative model is validated through four design examples of dual-band filters, with their center frequencies located within 5 to 18 GHz. The inference time for each design is approximately 18.5 min. The measurement results of the fabricated filters are in good agreement with the simulation ones.

Absorptive bandpass filters (ABPFs) are highly attractive in modern microwave communication systems due to their ability to internally absorb the harmful stopband RF-power reflections. This paper reports an approach to designing quasi-elliptic ABPFs with ultra-wide reflectionless range, enhanced selectivity, and compact size. The method is realized based on a fourth-order quasi-elliptic absorptive lowpass filter (ALPF) prototype with a simplified structure. This ALPF prototype exhibits both good impedance-matching over the whole normalized frequency domain and an adjustable transmission zero close to the passband. By applying an equivalent impedance transformer model, a coupled-line-based ABPF scheme is devised from the ALPF prototype, which eliminates conventional dispersive transmission line inverters, resulting in an ultra-wide reflectionless range and a compact size. Closed-form equations are derived to support the filter synthesis. A 2.45 GHz microstrip ABPF with 30% fractional bandwidth is designed for verification. The measured minimum in-band insertion loss is 0.83 dB and the reflectionless range of return loss better than 10 dB is from DC to 12.88 GHz. Both the upper and lower stopband suppression exceed 20 dB, with the upper stopband extending up to 6.80 GHz. The upper and lower out-of-band roll-off rates are 93.9 and 121.4 dB/GHz, respectively. The overall circuit size is 0.12 λ_g².