State space representation for log domain filtering synthesis

New method for the state space representation of filters based on the companion form technique has been proposed. It is useful for synthesis of log domain filters. For state space representation of a log domain filter, it is very important to have almost equal coefficients of the state space equations since these coefficients are proportional to currents or voltages of the designed device. The method allows selection of two arbitrary parameters (α, β) to adjust these coefficients. By using this technique, more balanced state space equations can be obtained. This method offers an option to obtain desired adjustable coefficients. It is particularly useful for synthesizing high order log domain circuits using state space methods. The proposed method is applied to second and fifth order log domain filter designs to show the application. Simulation results demonstrated that different system equations which are determined by the proposed method affect the performance of the filter.