Operational Amplifiers (4.1-4.3)Dr. HolbertApril 3, 2006

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Op AmpsOp Amp is short for operational amplifier.An operational amplifier is modeled as a voltage controlled voltage source.An operational amplifier has a very high input impedance and a very high gain.

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Use of Op AmpsOp amps can be configured in many different ways using resistors and other components.Most configurations use feedback.

ECE201 Lect-16

Applications of Op AmpsAmplifiers provide gains in voltage or current.Op amps can convert current to voltage.Op amps can provide a buffer between two circuits.Op amps can be used to implement integrators and differentiators.Lowpass and bandpass filters.

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The Op Amp SymbolNon-inverting inputInverting inputGroundHigh SupplyLow SupplyOutput

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The Op Amp Model+Inverting inputNon-inverting inputRinv+v-+A(v+ -v- )vo

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Typical Op AmpThe input resistance Rin is very large (practically infinite).The voltage gain A is very large (practically infinite).

ECE201 Lect-16

Ideal Op AmpThe input resistance is infinite.The gain is infinite.The op amp is in a negative feedback configuration.

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The Basic Inverting Amplifier+Vin+VoutR1R2+

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Consequences of the IdealInfinite input resistance means the current into the inverting input is zero:i- = 0Infinite gain means the difference between v+ and v- is zero:v+ - v- = 0

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Solving the Amplifier CircuitApply KCL at the inverting input:

i1 + i2 + i-=0R1R2i1i-i2

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KCL

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Solve for vout

Amplifier gain:

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RecapThe ideal op-amp model leads to the following conditions:i- = 0 = i+v+ = v-These conditions are used, along with KCL and other analysis techniques, to solve for the output voltage in terms of the input(s).

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Where is the Feedback?+Vin+VoutR1R2+

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ReviewTo solve an op-amp circuit, we usually apply KCL at one or both of the inputs.We then invoke the consequences of the ideal model.The op amp will provide whatever output voltage is necessary to make both input voltages equal.We solve for the op-amp output voltage.

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The Non-Inverting Amplifier+vin+voutR1R2+

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KCL at the Inverting Input+vin+voutR1R2i-i1i2+

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KCL

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Solve for Vout

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A Mixer Circuit+v2+voutR2RfR1v1++

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KCL at the Inverting Input+v2+voutR2RfR1v1i1i2ifi-++

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KCL

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KCL

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Solve for Vout

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Class ExampleLearning Extension E4.1Learning Extension E4.2Learning Extension E4.3

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