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# Phase Lag Compensator Circuit

IP.com Disclosure Number: IPCOM000045329D
Original Publication Date: 1983-Mar-01
Included in the Prior Art Database: 2005-Feb-06
Document File: 2 page(s) / 31K

IBM

Taub, DM: AUTHOR

## Abstract

The preceding article draws attention to the advantage of using complex conjugate poles and zeros in servo compensator circuits.

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Phase Lag Compensator Circuit

The preceding article draws attention to the advantage of using complex conjugate poles and zeros in servo compensator circuits.

The above figure shows a phase-lag circuit following the same principles. The relationships between the component values are given by the following equations. Writing

C'=C(1) + C(3) and R'=R(1)R(3)/(R(1) + R(3)) the relationships are C(2)/C'=2a the square root of (C(2)R(2)/(C'R'))cos Theta-1

C'R'=1/Omega(0) the square root of (1/a.C'R'))cos theta-1

C(1)=a/2/C'

and

R(3)=R'/(2(1-a)cos Theta) the square root of (C(2)R(2)/(C'R')) where a is the ratio of the radius on which the poles lie to the radius on which the zeros lie, which in this case will be less than
1. Omega(0) and Theta have the same meaning as in the phase-lead circuit, and the amplifier gain is again assumed to be infinite.

Referring to equation (3), tolerance problems can be avoided by choosing the ratio C(2)R(2)/(C'R') high enough to ensure that 2a the square root of (C(2)R(2)/(C'R'))cos Theta is reasonably large compared with 1.

One can regard this circuit as a type of low-pass filter in which, as frequency increases, the gain falls to a finite value instead of zero. Were this acceptable, the circuit has the advantage over a conventional low-pass filter of lower phase- lag in the pass band.

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