Biquadratic Allpass Phase-Compensating System Design Utilizing Bilinear Error

A new method is proposed for the design of a biquadratic (biquad) allpass phase-compensating system whose stability-margin satisfies an arbitrarily preset stability criterion. The design technique utilizes both the generalized stability-triangle (GST) and the bilinear (BL) phase-error function of the all-pass biquad system, which are derived by the author. Based on the GST condition, it is shown that the original coefficients of the allpass biquad system can be converted into the functions of other two new variables, while the two variables have no limits (bounds) on their values to satisfy the GST condition. That is, arbitrary values of the two new variables can meet the GST condition. Based on the above variable conversions, the design technique further employs a nonlinear optimization method to find the optimum values of the two variables to approximate a prescribed ideal phase. Thanks to the variable conversitions, the resulting values of the two variables never violate the GST condition. As a result, the resulting biquad allpas system not only can always satisfy a prescribed stability margin, but also can best approximate a given ideal phase in the minimax sense. To demonstrate the guaranteed stability margin as well as the system accuracy, a biquad system design example is included.