Synthesis of Rational Transfer and Admittance Matrices with Active RC Common-Ground Networks Containing Unity-Gain Voltage Amplifiers

Necessary and sufficient conditions exist, which show that only a subset of all rational matrices can be realized as the transfer or admittance matrix of a common-ground network of resistors, inductors, capacitors, and grounded unity-gain voltage amplifiers (VGUGAs). This paper shows that by eliminating the ground constraint on the amplifiers (VUGAs) one can realize any rational transfer or admittance matrix with a common-ground RC :VUGA network. The synthesis is based upon a simple circuit whose transfer function is the ratio of two independent admittances. This is used with one capacitor and one resistor to form a differentiator. The differentiators are cascaded to form an admittance polynomial whose coefficients are determined by products. Transfer functions are realized by forming ratios of these polynomial admittances. The synthesis procedure results in selecting component values by inspection and permits tuning the circuits with the resistors.