Two symmetrical third-order microstrip bandpass filters (BPF) with all mixed coupling coefficients are proposed and analyzed. The first filter is a combline filter with stepped impedance resonators (SIR) closely spaced to each other. This leads to mixed couplings between adjacent resonators. The cross coupling of the end resonators is also mixed K13 = Km13 + Ke13 (MCC). Its magnetic component Km13 is due to a parasitic magnetic coupling between these resonators. To form the electric coupling component Ke13 a thin microstrip line segment was used that connects the resonators through the capacitive gaps. It was found that such a filter has two adjustable transmission zeros (TZ), which can be located both to the right and left of the central frequency f0 of the bandwidth. The second BPF differs from the first in that its central SIR is replaced by a half-wave through-type resonator, which is included in the filter as a two-port circuit. The used half-wave resonator has a U-shape and it works as the admittance inverter, in addition to the resonance phenomenon. This feature leads to a change in the frequency response of the filter. This filter has two adjustable TZs, which are located on both sides of the center frequency f0 of the bandwidth asymmetrically. The direct and inverse problems for the third-order BPF with all mixed couplings are also solved. The solution is based on the conductance matrix [Ỹ] and its minor M31. The direct problem solution makes it possible to determine the TZs of the filter using the given coupling coefficients. In the inverse problem, the filter’s coupling coefficients are determined by the specified TZs. The samples of two experimental filters and measuring frequency responses are presented.

中文翻译：

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具有更高选择性和非对称频率响应的微带 BPF

提出并分析了具有所有混合耦合系数的两个对称三阶微带带通滤波器（BPF）。第一个滤波器是梳状线滤波器，其阶梯阻抗谐振器 (SIR) 彼此间隔很近。这导致相邻谐振器之间的混合耦合。端部谐振器的交叉耦合也是混合 K13 = Km13 + Ke13 (MCC)。它的磁性分量 Km13 是由于这些谐振器之间的寄生磁耦合造成的。为了形成电耦合元件Ke13，使用了一条通过电容间隙连接谐振器的细微带线段。发现这种滤波器具有两个可调传输零点 (TZ)，它们可以位于带宽中心频率 f0 的右侧和左侧。第二个 BPF 与第一个的不同之处在于它的中心 SIR 被一个半波贯通型谐振器代替，它作为双端口电路包含在滤波器中。所用的半波谐振器呈 U 形，除谐振现象外，还起到导纳逆变器的作用。此特征会导致滤波器频率响应发生变化。该滤波器有两个可调 TZ，它们不对称地位于带宽中心频率 f0 的两侧。还求解了所有混合耦合的三阶 BPF 的正反问题。该解决方案基于电导矩阵 [Ỹ] 及其次要 M31。直接问题解决方案可以使用给定的耦合系数来确定滤波器的 TZ。在逆问题中，滤波器的耦合系数由指定的 TZ 决定。给出了两个实验滤波器和测量频率响应的样本。