This document describes a filter circuit with components R = 5.1 kOhm, C = 2 OhmF, and an ideal op amp. It is a first order filter. It is an all-pass filter with constant magnitude. The linear DC gain is 1. The linear infinite frequency gain is 1. The gain in dB when f = 1 kHz and the phase shift in degrees when f = 14 kHz are requested. The complex transfer function T(s) = V0(s)/V1(s) is derived in terms of s, R, and C.

1. The component value for the filter shown below are R = 5.1 kOhm C- 2OhmF and the op amp
may be considered to be ideal. What is the order of the filter? What type of filter is it? What is
the linear de gain? What is the linear infinite frequency gain? What is the gain dB when f = 1
kHZ? What is the phase shift in degrees when f = 14kHz? Derive the complex transfer function
T(s) = V0(s)/Y1(s). Express the answer in terms of the symbols s, R, and C (not the numerical
values.)
Solution
LET V be the input terminal of the opAmp gain
Vi - iR = V
V -Vo = iR
Vi + Vo = 2V......................(1)
other equation we have
V = sCR/(1+sCR) Vi
Vi + Vo = 2sCR/(1+sCR) Vi
Vo= sCR-1/(sCR +1) Vi
Vo/Vi = sCR-1/(sCR +1)
order 1
all pass filter(const magnitude)
dc gain =1