Section 13

Amplifiers and op-amps

v_o=A(v_+-v_-)

Computes Open-loop equation from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Ideal infinite gain

A\to\infty

Computes Ideal infinite gain from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Virtual short

v_+\approx v_-

Computes Virtual short from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Inverting amplifier

viz

v_o=-\frac{R_f}{R_{\mathrm{in}}}v_{\mathrm{in}}

The inverting amp uses the virtual short: Vo=−(Rf/Rin) Vin with v+≈v− at ground.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Non-inverting amplifier

viz

v_o=\left(1+\frac{R_f}{R_g}\right)v_{\mathrm{in}}

The non-inverting amp has gain 1+Rf/Rg with input on v+ and a virtual short.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Voltage follower

viz

v_o=v_{\mathrm{in}}

The follower is a non-inverting amp with gain 1: Vo=Vin.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Inverting summer

v_o=-R_f\sum_k\frac{v_k}{R_k}

Computes Inverting summer from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Differential amplifier

v_o=\frac{R_2}{R_1}(v_2-v_1)

Computes Differential amplifier from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Inverting integrator

viz

v_o(t)=-\frac{1}{RC}\int v_{\mathrm{in}}(t)\,dt

The integrator produces a ramp Vo=−(1/RC)∫Vin dt with negative feedback.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Inverting differentiator

v_o(t)=-RC\frac{dv_{\mathrm{in}}}{dt}

Computes Inverting differentiator from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Open-loop comparator

v_o=\begin{cases}+V_{\mathrm{sat}}&v_+>v_-\\-V_{\mathrm{sat}}&v_+<v_-\end{cases}

Computes Open-loop comparator from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Op-amp saturation

|v_o|\le V_{\mathrm{sat}}

Computes Op-amp saturation from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Common-mode rejection

\mathrm{CMRR}=20\log_{10}\left|\frac{A_d}{A_c}\right|

Computes Common-mode rejection from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Ideal input impedance

R_{\mathrm{in}}\to\infty

Computes Ideal input impedance from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Section 13

Amplifiers and op-amps

Open-loop equation

v_o=A(v_+-v_-)

Computes Open-loop equation from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Ideal infinite gain

A\to\infty

Computes Ideal infinite gain from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Virtual short

v_+\approx v_-

Computes Virtual short from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Inverting amplifier

viz

v_o=-\frac{R_f}{R_{\mathrm{in}}}v_{\mathrm{in}}

The inverting amp uses the virtual short: Vo=−(Rf/Rin) Vin with v+≈v− at ground.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Non-inverting amplifier

viz

v_o=\left(1+\frac{R_f}{R_g}\right)v_{\mathrm{in}}

The non-inverting amp has gain 1+Rf/Rg with input on v+ and a virtual short.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Voltage follower

viz

v_o=v_{\mathrm{in}}

The follower is a non-inverting amp with gain 1: Vo=Vin.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Inverting summer

v_o=-R_f\sum_k\frac{v_k}{R_k}

Computes Inverting summer from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Differential amplifier

v_o=\frac{R_2}{R_1}(v_2-v_1)

Computes Differential amplifier from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Inverting integrator

viz

v_o(t)=-\frac{1}{RC}\int v_{\mathrm{in}}(t)\,dt

The integrator produces a ramp Vo=−(1/RC)∫Vin dt with negative feedback.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Inverting differentiator

v_o(t)=-RC\frac{dv_{\mathrm{in}}}{dt}

Computes Inverting differentiator from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Open-loop comparator

v_o=\begin{cases}+V_{\mathrm{sat}}&v_+>v_-\\-V_{\mathrm{sat}}&v_+<v_-\end{cases}

Computes Open-loop comparator from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Op-amp saturation

|v_o|\le V_{\mathrm{sat}}

Computes Op-amp saturation from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Common-mode rejection

\mathrm{CMRR}=20\log_{10}\left|\frac{A_d}{A_c}\right|

Computes Common-mode rejection from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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Ideal input impedance

R_{\mathrm{in}}\to\infty

Computes Ideal input impedance from the circuit model and the stated conditions.

Ideal op-amp with negative feedback except comparator; |Vo| < Vsat.

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