A comparative study of single-amplifier filters, fifteen different two-amplifier circuits, and the state-variable three-amplifier configuration is given. The figures-of-merit used are the passive sensitivities, the \omega_0 gain-sensitivity products, the Q gain-sensitivity products, and the \omega_0 and Q deviations due to the amplifiers' limited bandwidth. In addition, practical matters such as input impedance and component spread are considered. Among the circuits considered a particular twoamplifier resonator emerges as the "best" biquadratic section. Some of the interesting results include a unified expression, applicable to a large class of low-sensitivity circuits, for the \omega_0 deviation due to the amplifier's limited frequency response. In this expression, which applies for all active filters which have low \omega_0 active sensitivities, the only configurationdependent quantities are the Q gain-sensitivity products.

Sensitivity and frequency limitations of biquadratic active filters

This letter describes a technique which employs the lowpass properties of transistors to realise a high-Q factor selective amplifier with optimum sensitivity. It requires only resistors as passive elements and transistors as active devices. The realisation of the circuit is optimally insensitive to variations in the gain of transistors and provides for independent adjustment of the amplifier Q factor.

Active bandpass network with only resistors as passive elements

A technique is described for improving the selectivity of a low-sensitivity multi-loop negative feedback active network, which uses one operational amplifier. Voltage amplifiers with positive finite gain are introduced inside the various loops of the network. This simplifies quite considerably the network function and improves the selectivity for a given range of element values while not affecting the low sensitivity of the network. Also, additional low impedance outputs are available which for a particular input make the network suitable for the simultaneous realization of more than one function (with common poles but different zeros). Second and third-order networks are examined in detail and experimental results arc given from their use in the realization of a band-pass and a low-pass filter.

Selectivity enhancement of certain low-sensitivity RC active networks †

Simple feedback concepts are used to synthesize driving impedances, generalized impedance inverters/converters and oscillators using voltage controlled voltage sources and RC elements. They lead to several new circuits. Some of these are suitably modified to obtain high Q active filters with minimum sensitivity.

Active RC Synthesis of Driving Impedances, Generalized Impedance Inverters/Converters, Oscillators and Filters

A second order RC band-pass filter is designed using a current and a voltage amplifier of any finite non-zero gain. The Q-sensitivity either with respect to resistances or with respect to capacitances can be made zero. The networks contain minimum number of passive elements.

Design of a RC Band-pass Filter Using a Voltage and a Current Amplifier of any Finite Non-zero Gain

An active RC circuit is described, which can be used as a second-order bandpass or highpass filter. Its sensitivity is independent of the Q factor and very low.

Y. Bedri

Papers

Active RC bandpass and highpass network