Electronically tunable filtering networks: theory, analysis and simulation

A parallel four-port tunable conductance-susceptance network model is proposed for use in tunable filtering networks, with emphasis on its modelling, sensitivity minimising and computer simulation. In contrast with the design of tunable transfer functions in the complex domain, we synthesise a four-port linear and controllable conductance network in the real domain, which is easier to implement with CMOS transconductance elements. The basic building blocks and general forms of the conductance matrix and structure for biquad filtering networks (BFN) are given. The redefined port parameters, equivalent port short-circuit resistance, equivalent port open-circuit resistance and equivalent transfer coefficients are given and used for the analysis of network sensitivity. Theoretical analysis and preliminary simulation results show that the minimum sensitivity condition can be obtained for BFN when the two time constants at two energy-storage ports are equal. It also shows that the ω and Q parameters in biquad filtering networks and the weights in some neural networks are tunable by changing the gate signals, and the input impedance of the network is very large as there is no backward-feed connection to input port. Because the construction is based on CMOS elements, the realisation can be readily integrated. This method can also be used to design a tunable-weight network in some neural networks, since a transconductance element can be easily used as a weight between any two neurons