Synthesis of low‐sensitivity second‐order real digital filters using complex two‐port adapters

If complex coefficients are used in the realization of the real‐coefficient transfer function, the degree of freedom in the circuit construction is enhanced. This creates a possibility that a lower‐sensitivity filter can be realized than in the traditional low‐sensitivity filter using the real coefficients. This paper discusses a method to construct the second‐order real‐coefficient IIR filter using the complex two‐port adapter. First, by using the complex two‐port adapter, a method for circuit construction is proposed where the second‐order bandpass, lowpass, high‐pass, and asymmetrical bandstop transfer functions are realized. The proposed circuit can be realized with fewer number of multipliers than the conventional circuits using complex coefficients. Then a method is shown which selects the complex two‐port adapter according to the value of the real part of the coefficient of the complex multiplier. By this selection method, the circuit with the lowest sensitivity in regard to the real part can be realized without increasing the computational complexity for the circuit. Furthermore, a method is considered to reduce the sensitivity also for the imaginary part of the complex multiplier coefficient. Finally, using a simple example, it is verified that the circuit obtained by the proposed construction method has the low sensitivity.