A pole‐zero pairing strategy for minimum‐gain‐sensitivity nth‐order biquadratic filter cascades

In attempting to use the pole‐zero assignment for gain sensitivity minimization in biquadratic filter cascades, a new expression for the total gain error is derived. In this result the logarithmic gain slope appears as a weighting factor to a second term depending on the structure and the parameter or component inaccuracies. On the basis of this partitioning, a pairing method for minimum gain sensitivity is developed which uses the ‘modified bottleneck algorithm’. Additional investigations finally show that minimum gain sensitivity and optimum dynamic range lead to similar constraints which can be achieved simultaneously in most applications.