# Design of a Compact Ultra-Wideband Microstrip Bandpass Filter
## 1 Introduction  
As wireless and satellite communication technologies, radio frequency circuits and communication systems have become increasingly complex, the whole circuits tend to be integrated and miniaturized. The interference between communication systems is becoming more and more serious, while the ultra-wideband (UWB) wireless system has the advantages of high-speed data transmission, strong anti-interference performance and low transmission power. UWB wireless communication has attracted extensive attention, and more and more ultra-wideband filters have been proposed. One of the methods to design a UWB bandpass filter is to use multimode resonators (MMR), and even-odd mode analysis is often used to analyze the transmission characteristics of such filters. In Refs. [1; 2; 3], scholars adopted the design method of multimode resonators and used the characteristics of odd and even resonance modes to determine the center frequency and adjust the passband bandwidth. Combined with different structural designs and material choices, wideband or ultra-wideband passband characteristics can be achieved. An equivalent circuit is an effective method to help analyze the transmission characteristics and resonance modes of an ultra-wideband bandpass filter when designing it. In Refs. [4; 5], the transmission function and frequency characteristics are observed by circuit simulation, and the position changes of the center frequency and transmission zeros are predicted by adjusting the equivalent capacitance and inductance of the microstrip line length. This method has also been reported in many studies. In Ref. [6], the equivalent circuit model is extracted from the topology of the spatial filter under the conditions of tight coupling and loose coupling, which are used to better understand the filtering mechanism andpredict the electromagnetic behavior of the filter. Then the circuit model can be further optimized through simulation and calculation. In Ref. [7], an ultra-wideband bandpass filter is designed based on the coupled branch lines, and the even and odd resonance modes of the filter are analyzed by using the equivalent circuit to suppress the stopband harmonics. At the same time, a wide reconfigurable bandwidth range is realized by variable capacitors. Ref. [8] reported a reconfigurable UWB bandpass filter, which was a cascaded design consisting of a reconfigurable lowpass filter and a reconfigurable highpass filter and had excellent out-of-band suppression. Because of the cascaded structure itself, the ultra-wideband filter designed by this method was relatively large in size, complex in structure and large in insertion loss (IL). In Ref. [9], a bandpass filter with a 3 dB fractional bandwidth (FBW) of 32% was designed by using two quarter-wavelength resonators in a comb-line structure. In Ref. [10], a UWB filter based on a quarter-wavelength stepped impedance resonator was reported. The 3 dB fractional bandwidth is 55%, but the insertion loss is also large. Many new technologies and materials have been developed for the miniaturization design of ultra-wideband filters. [PERSON] et al. proposed an ultra-wideband filter with three-layer structure manufactured by low-temperature co-fired ceramic (LTCC) technology with a fractional bandwidth of 85.2% at the center frequency of 3.2 GHz, and the size of the whole filter was only 5 \(\times\) 4.5 \(\times\) 0.65 mm\({}^{3}\)[11]. An ultra-wideband bandpass filter with a 3 dB fractional bandwidth of 75% with a center frequency of 1.8 GHz was reported in [12]. Thanks to the convenience of low-temperature co-fired ceramic technology, this filter with an eight-layer structure design was only 5.2 \(\times\) 3.6 \(\times\) 1.2 mm\({}^{3}\) in size. By introducing an appropriate coupling structure, a steep transition band was realized, but the in-band reflection was relatively large. In Ref.