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Theory

The transfer function H(s) from input Vin to output Vout can be expressed as a product

\begin{displaymath}H(s) = \frac{V_{out}(s)}{V_{in}(s)} = H_1(s) H_2(s) = (1 + \frac{R_2}{R_1})\frac{s}{s+ 1/(RC)}
\end{displaymath}

where

\begin{displaymath}H_1(s) = \frac{V_+(s)}{V_{in}(s)} = \frac{s}{s+ 1/(RC)}
\end{displaymath}

is the transfer function from Vin to V+ and

\begin{displaymath}H_2(s) = \frac{V_{out}(s)}{V_{+}(s)} = 1 + \frac{R_2}{R_1}
\end{displaymath}

is the transfer function from V+ to Vout.

The cut-off frequency or 3dB point is

\begin{displaymath}\omega_{c} = 1/(RC) \ \ {\rm rad/sec}
\end{displaymath}

which gives $f_{c} = \omega_{c}/(2\pi)$ Hz and the pass-band gain is $(1 + \frac{R_2}{R_1})$.

Verify all of these assertions and calculations.


ANU Engineering - ENGN2211