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Miniaturization of Filters

IP.com Disclosure Number: IPCOM000091075D
Original Publication Date: 1969-Oct-01
Included in the Prior Art Database: 2005-Mar-05
Document File: 2 page(s) / 24K

Publishing Venue

IBM

Related People

Riso, V: AUTHOR

Abstract

The miniaturization of active filters can be realized by using an input stage performing a summing operation through feedback loops, with various gain coefficients. This band-pass filter includes integrators S1 and S2 in series, fed through a three-input summing stage sigma. The input signal u is fed to the first input of sigma providing a gain -K1. The output x of sigma is fed to S1 whose output y is fed to S2 providing an output z. The transfer functions of the integrators S1 and S2 are, respectively, - h1/p theta 1 = -1 and h2/p theta 2 = -1 where theta 1 and theta 2 are the time constants of the integrators. Outputs y and z are fed back to the summing amplifier inputs with gains of +K3 and -K2 respectively.

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Miniaturization of Filters

The miniaturization of active filters can be realized by using an input stage performing a summing operation through feedback loops, with various gain coefficients. This band-pass filter includes integrators S1 and S2 in series, fed through a three-input summing stage sigma. The input signal u is fed to the first input of sigma providing a gain -K1. The output x of sigma is fed to S1 whose output y is fed to S2 providing an output z. The transfer functions of the integrators S1 and S2 are, respectively, - h1/p theta 1 = -1 and h2/p theta 2 = -1 where theta 1 and theta 2 are the time constants of the integrators. Outputs y and z are fed back to the summing amplifier inputs with gains of +K3 and -K2 respectively.

Consequently, the following equations can be derived.

y = h1.x

z = h1.h2.x

x = -K1.u+K3.y-K2z

H = y/u = (K1/H2 p theta 2)/>(p/2/theta 1 theta 2/

K2)+(p theta 2K3/K2)+1|. The last equation shows that the filter performs a band-pass function. The characteristic coefficients are Q = (K2/K3 theta 2) x the square root of K2/theta 1 theta 2 and omega(o) = the square root of K2/theta 1 theta 2.

Thus, for low-frequency operation, low value of time constants can be used provided that K2 is chosen less than unity. This condition is satisfied by using adequate values of resistors in the circuits of an operational amplifier used as a summing stage.

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