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# High Q Active Filter

IP.com Disclosure Number: IPCOM000074482D
Original Publication Date: 1971-May-01
Included in the Prior Art Database: 2005-Feb-23
Document File: 3 page(s) / 64K

IBM

## Related People

Esteban, DJ: AUTHOR [+2]

## Abstract

One of the problems arising during the implementation of band-pass filters is the difficulty encountered when trying to obtain devices of a small size, the Q coefficient value of which is both high and insensitive to the circuit component variations.

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High Q Active Filter

One of the problems arising during the implementation of band-pass filters is the difficulty encountered when trying to obtain devices of a small size, the Q coefficient value of which is both high and insensitive to the circuit component variations.

Theory shows that active filters enable high-Q values to be obtained with components of a reduced size. But on the other hand the Q of these filters is more sensitive to the component variation than the Q of passive filters. In particular, the Q of the active filters is sensitive to the variations of gain A of the operational amplifier which is used.

It is thus of a particular advantage to be able to build active filters with a high- Q but which are at the same time the least sensitive to the gain A variations as possible. This goal can be attained by the structure of the high-Q active filter.

Mathematical theory shows that characteristics such as central frequency (omegao) and Q of a filter can be simply deduced from the transfer function W(s) of the filter ("s" being the Laplace-Carson variable). In other words, if W(s) = Eout over Ein = alpha s over Beta s//2/ + gamma s + 1 where Eout = output voltage of the filter Ein = input voltage of the filter, and alpha, beta, gamma = parameter functions of the filter components.

Thus, the central frequency and the Q can be derived from these formulaes

(Image Omitted)

Let us thus determine the transfer function of the present filter and we will be able to calculate the condition needed for the Q obtained to have the required qualities, that is to say a minimum sensitivity to the variations of gain A of the amplifiers used.

The circuit shown can be converted into a closed loop comprising two cells, the resp...