Operational AmplifiersOp Amps – a useful building block

K. El-Ayat

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2Figure 2.2 The op amp shown connected to dc power supplies.

Op Amp: A DC coupled high Gain differential Amplifier

Many useful applications

An Op Amp produces an output voltage that is much larger than the difference between its two inputs (very high gain)

-ve

+ve

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Figure 2.3 Equivalent circuit of the ideal op amp.

An Ideal Op Amp

Vout= A(v2-v1)

Differential input stage amplified

• Infinite input impedance• Zero Output impedance• Infinite open-loop gain A• Infinite bandwidth

• Op amps are DC (direct coupled) • Usually used with external

components R, C, …

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Figure 2.6 Analysis of the inverting configuration. The circled numbers indicate the order of the analysis steps.

Inverting Op Amp - AnalysisTerminal 2 (+ve input) ground

RF (or R2) connected to terminal 1 (-ve)

Negative feedbackSince open loop gain A very highThen v1-v2= vo/ A = 0v1 = v2 = gnd

VO = - (R2 / R1) * Vi

i1 = i2 & Gain G = - R2 / R1

G (closed loop) gain

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Figure E2.6

Op Amp – Class Analysis ExampleFind all I, v, gain

v1 =

i1 =i2 =

vo = iL =io =

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Figure 2.10 A weighted summer.

An Op Amp Application; Weighted Summing Circuit

vo = - [(Rf / R1) * v1 + (Rf / R2) * v2 +….+ (Rf / Rn) * vn]

in = ?i = ?

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Figure 2.11 A weighted summer capable of implementing summing coefficients of both signs.

vo= v1(Ra/R1)(Rc/Rb) + v2(Ra/R2)(Rc/Rb) –v3(Rc/R3) –v4 (Rc/R4)

Two Op Amp comnibation Summing Circuit , with both signsCan calculate in 2 steps

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Figure 2.12 The noninverting configuration.

Non inverting Op AmpApplication

Use +ve Op Amp input

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Figure 2.13 Analysis of the non-inverting circuit. The sequence of the steps in the analysis is indicated by the circled numbers.

Non-inverting Op Amp: Analysis

vo = vi + (vi/R1)*R2

vo = vi(1 + R2/R1)G = 1 + R2/R1

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Figure 2.14 (a) The unity-gain buffer or voltage follower amplifier. (b) Its equivalent circuit model.

Unity Gain Op AmpVoltage follower - unity gain; high current gainBuffer stage between processors - switches

G = 1 + 0 /R1; R2 0

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Figure E2.9

Op Amp problem – find vo

Assume x is voltage at both Amp inputs –ve, & +ve

x = 3/5 (v1-v2) + v2 ; resistor dividerI = x / 1 = (vo- x) / 9vo = 10 xv o= 10 *[ 3/5 (v1-v2) + v2 ] = 6 v1 + 4 v2 ANS.

I

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Figure E2.13

Another Op Amp problem – Should be able to analyze

vo =

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Figure 2.16 A difference amplifier.

Can use as a difference Op Amp

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Figure 2.23 Frequency response of an amplifier with a nominal gain of +10 V/V.

Frequency response of Op AmpGain = +10

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Figure 2.22 Open-loop gain of a typical general-purpose internally compensated op amp.

Open-loop gain of Op AmpGain declines rapidly with freq

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Figure 9.1 The basic two-stage CMOS op-amp configuration.

Two-stage CMOS Op Amp - fyi

17Figure 9.4 Typical frequency response of the two-stage op amp.

Frequency Response of CMOS Op Amp fyi

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Figure 2.37 The inverting configuration with general impedances in the feedback and the feed-in paths.

Inverting Op AmpApplication to Impedances