Amplifier Gain Worksheet - Maple Programming Help

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Amplifier Gain Worksheet

Introduction

In this application, we will plot the gain of the following amplifier circuit, for both the ideal and non-ideal response.

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Parameters

 > $\mathrm{R__1}≔1000:$
 > $\mathrm{C__1}≔{10}^{-7}:$
 > $\mathrm{R__In}≔1000:$
 > $\mathrm{C__3}≔4.7\cdot {10}^{-8}:$
 > $\mathrm{R__2}≔1000:$
 > $\mathrm{C__2}≔4.70\cdot {10}^{-7}:$
 > $\mathrm{R__f}≔{10}^{102}:$

Amplifier bandwidth factors:

 > $\mathrm{GBP}≔{10}^{6}:$
 > $\mathrm{LPF}≔300:$

Support Function

 > $\mathrm{ll}≔\left(\mathrm{Z1},\mathrm{Z2}\right)\to \frac{\mathrm{Z1}\cdot \mathrm{Z2}}{\mathrm{Z1}+\mathrm{Z2}}:$

Transfer functions

 > $\mathrm{Z__1}≔\mathrm{R__1}+\frac{1}{\mathrm{s}\cdot \mathrm{C__1}}:$
 > $\mathrm{Z__2}≔\mathrm{R__2}+\frac{1}{\mathrm{s}\cdot \mathrm{C__2}}:$
 > $\mathrm{Z__In}≔\mathrm{ll}\left(\mathrm{R__In},\mathrm{Z__1}\right):$
 > $\mathrm{factor}\left(\mathrm{Z__In}\right)$
 $\frac{{500}{}\left({s}{+}{10000}\right)}{{s}{+}{5000}}$ (4.1)
 > $\mathrm{Z__fb}≔\mathrm{ll}\left(\mathrm{R__f},\mathrm{ll}\left(\mathrm{Z__2},\frac{1}{\mathrm{s}\cdot \mathrm{C__3}}\right)\right):\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}$

Ideal amplifier gain:

 > $\mathrm{G__EAideal}≔\mathrm{factor}\left(\frac{\mathrm{Z__fb}}{\mathrm{Z__In}}\right)$
 $\mathrm{G__EAideal}{≔}\frac{{42553.19148}{}\left({s}{+}{2127.659574}\right){}\left({s}{+}{5000.}\right)}{\left({s}{+}{1.934235977}{}{{10}}^{{-96}}\right){}\left({s}{+}{23404.25531}\right){}\left({s}{+}{10000.}\right)}$ (4.2)

Non-ideal op-amp effects: Finite open loop gain

 > $\mathrm{β}≔\frac{1}{1+\mathrm{G__EAideal}}:\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}$

Finite open loop gain

 > $\mathrm{A__vo}≔\frac{\mathrm{GBP}}{\mathrm{LPF}}\cdot \frac{1}{\left(1+\frac{\mathrm{s}}{2\cdot \mathrm{π}\cdot \mathrm{LPF}}\right)\cdot \left(1+\frac{\mathrm{s}}{2\cdot \mathrm{π}\cdot \mathrm{GBP}}\right)}$
 $\mathrm{A__vo}{≔}\frac{{10000}}{{3}{}\left({1}{+}\frac{{s}}{{600}{}{\mathrm{\pi }}}\right){}\left({1}{+}\frac{{s}}{{2000000}{}{\mathrm{\pi }}}\right)}$ (4.3)
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 $\frac{{4000000000000}{}{{\mathrm{\pi }}}^{{2}}}{\left({600}{}{\mathrm{\pi }}{+}{s}\right){}\left({2000000}{}{\mathrm{\pi }}{+}{s}\right)}$ (4.4)

Non-ideal error amplifier gain:

 > $\mathrm{G__EA}≔\mathrm{simplify}\left(\mathrm{G__EAideal}\cdot \frac{1}{1+\frac{1}{\mathrm{A__vo}\cdot \mathrm{β}}}\right)$
 $\mathrm{G__EA}{≔}\frac{{1.787162409}{}{{10}}^{{25}}{+}{1.679932664}{}{{10}}^{{18}}{}{{s}}^{{2}}{+}{1.197398814}{}{{10}}^{{22}}{}{s}}{{5.36148722210544}{}{{10}}^{{21}}{+}{{s}}^{{5}}{+}{6.36102770911571}{}{{10}}^{{6}}{}{{s}}^{{4}}{+}{3.99681963841567}{}{{10}}^{{13}}{}{{s}}^{{3}}{+}{1.32302446297123}{}{{10}}^{{18}}{}{{s}}^{{2}}{+}{9.24883894862041}{}{{10}}^{{21}}{}{s}}$ (4.5)

Analysis

 > $\mathrm{sys1}≔\mathrm{TransferFunction}\left(\mathrm{G__EA}\right):$
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 > $\mathrm{display}\left(\mathrm{p1},\mathrm{p2}\right)$
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