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Gain of an Ideal and Non-Ideal Amplifier

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Amplifier Gain

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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restart; with(DynamicSystems); with(plots)

Parameters

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NULL

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R__1 := 1000

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C__1 := 10^(-7)

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R__In := 1000

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C__3 := 4.7*10^(-8)

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R__2 := 1000

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C__2 := 4.70*10^(-7)

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R__f := 10^102


Amplifier bandwidth factors

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GBP := 10^6

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LPF := 300

Support Function

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ll := proc (Z1, Z2) options operator, arrow; Z1*Z2/(Z1+Z2) end proc

 

Transfer functions

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Z__1 := R__1+1/(s*C__1)

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Z__2 := R__2+1/(s*C__2)

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Z__In := ll(R__In, Z__1)

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factor(Z__In)

500*(s+10000)/(s+5000)

(4.1)
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Z__fb := ll(R__f, ll(Z__2, 1/(s*C__3)))

Ideal Amplifier GainNULL

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G__EAideal := factor(Z__fb/Z__In)

42553.19148*(s+2127.659574)*(s+5000.)/((s+0.1934235977e-95)*(s+23404.25531)*(s+10000.))

(4.2)

 

Nonideal Op-Amp effects: Finite open loop gain

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beta := 1/(1+G__EAideal)

Finite open loop gain

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A__vo := GBP/(LPF*(1+s/(2*Pi*LPF))*(1+s/(2*Pi*GBP)))

(10000/3)/((1+(1/600)*s/Pi)*(1+(1/2000000)*s/Pi))

(4.3)
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simplify((10000/3)/((1+(1/600)*s/Pi)*(1+(1/2000000)*s/Pi)), 'size')

4000000000000*Pi^2/((600*Pi+s)*(2000000*Pi+s))

(4.4)

Nonideal error amplifier gain

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G__EA := simplify(G__EAideal/(1+1/(A__vo*beta)))

42553.19148*(s+5000.)*(s+2127.659574)/(1.012406241*s^3+33512.60113*s^2+234275827.3*s+135808057.8+0.1611267141e-6*s^4+0.253302959e-13*s^5)

(4.5)

Analysis

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with(DynamicSystems)

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sys1 := TransferFunction(G__EA)

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sys2 := TransferFunction(G__EAideal)

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p1 := PhasePlot(sys1, range = 10 .. 100000, hertz = true, legend = "Non-ideal")

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p2 := PhasePlot(sys2, range = 10 .. 100000, hertz = true, legend = "Ideal", color = black)

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display(p1, p2)

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NULL