Double conversion method for synthesis of inverse filters

A novel method for the inverse filter synthesis of the same type from an original filter is presented. The proposed procedure utilizes a double conversion, frequency inversion and swapping the transfer and reflection functions, which are commonly used for lowpass to highpass filter transformation. Due to the use of double conversions, the resulting filter always has the same type as the original filter. Using this procedure, the available general Chebyshev synthesis method can be used to synthesize inverse Chebyshev and elliptic filters. As an illustration, the coupling matrix of a third-order inverse Chebyshev bandpass filter is synthesized using the presented method. Then the original filter and its inverse filter are fabricated using microstrip technology. The measured and simulated filter results are shown to be in good agreement.