Abstract :
This paper presents a synthesis procedure for active RC 2-port networks designed to have specified voltage transfer functions. This is thought to be novel. The basis of the n-port synthesis as applied to RC networks is outlined, with emphasis on the realisation from the y-parameter matrix. The synthesis procedure is then developed from the general expression for the voltage transfer function of the 2-port network, to enable the y parameters to be chosen. The network is synthetised as a 3-port one, and the two input ports are supplied from the same driving source, so giving a 2-port network. This is illustrated by an example having a ripple response in the pass band and a transmission zero in the stop band. It is shown that the frequency at which the transmission zero occurs is dependent upon the ratio of the voltages at two of the ports; hence this frequency can be adjusted, without alteration of the component values in the main filter, by simple adjustment of a potentiometer at one port. General expressions are given for the y parameters for this voltage transfer function. In any active-RC synthesis, it is important to consider the sensitivity of the network response to errors in the transfer characteristic k of the negative-impedance convertor (n.i.c.). It is shown that, for the synthesis presented, this sensitivity depends upon an apparently arbitrary polynomial chosen during the procedure. An optimum polynomial is derived, which minimises the effect of errors in the n.i.c. transfer characteristic. The synthetised circuit is shown before and after its simplification by Bartlett´s bisection theorem. Computed and experimental results are given for a simple example.
