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## Q. 2.15

Transfer Function—Noninverting Operational Amplifier Circuit

PROBLEM: Find the transfer function, $V_{0}(s)/V_{i}(s)$, for the circuit given in Figure 2.13.

## Verified Solution

We find each of the impedance functions, $Z_{1} (s)$ and $Z_{2} (s)$, and then substitute them into Eq. (2.104).

$\frac{V_{0}(s) }{V_{i}(s)}=\frac{Z_{1} (s)+Z_{2}(s)}{Z_{1} (s)}$

Thus, $Z_{1} (s)=R_{1} +\frac{1}{C_{1} s}$

and

$Z_{2}(s)=\frac{R_{2}(1/C_{2}s ) }{R_{2}+(1/C_{2}s )}$

Substituting Eqs. (2.105) and (2.106) into Eq. (2.104) yields

$\frac{V_{0}(s) }{V_{i}(s)}=\frac{C_{2}C_{1}R_{2}R_{1}s^{2} +(C_{2}R_{2}+C_{1}R_{2} +C_{1} R_{1} )s+1 }{C_{2} C_{1}R_{2} R_{1}s^{2}+(C_{2}R_{2} +C_{1} R_{1} )s+1}$