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Ideal Operational AmplifiersAnalyzing Op Amp Circuits

Common Operational Amplifier CircuitsOther Operational Amplifier Circuits

ElectronicsOperational Amplifiers

Terry Sturtevant

Wilfrid Laurier University

February 17, 2010

Terry Sturtevant Electronics Operational Amplifiers

Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback

Ideal Operational Amplifiers

invertinginput

non-invertinginput

invertinginput

non-invertinginput

output

invertinginput

non-invertinginput

output

Output is proportional to the difference between thenon-inverting and inverting inputs

invertinginput

non-invertinginput

output

Output is proportional to the difference between thenon-inverting and inverting inputs

Active device; requires power to work, even though powerconnections often not shown

Showing power connections

invertinginput

non-invertinginput

output

invertinginput

non-invertinginput

output

V supply+

invertinginput

non-invertinginput

output

V supply+

V supply−

invertinginput

non-invertinginput

output

V supply+

V supply−

Supplies are usually not shown, but must be used.

Operational amplifier supply voltage rules

V supply+ is the positive supply.

V supply− is the negative supply.

In a single supply op amp, the negative supply can be ground.

The output of an op amp can’t go outside the supplyvoltages. In fact, you usually can’t get closer than a volt ortwo from the supplies. These voltage limits are also calledrails.

Single supply op amps are an exception; you usually canusually get within a few millivolts of the negative supply.

When an op amp hits one of the rails, its output can be calledsaturated, or we can say the op amp is in saturation.

The output of an op amp can’t go outside the supplyvoltages.

In fact, you usually can’t get closer than a volt ortwo from the supplies. These voltage limits are also calledrails.

The output of an op amp can’t go outside the supplyvoltages. In fact, you usually can’t get closer than a volt ortwo from the supplies.

These voltage limits are also calledrails.

Equivalent circuit

Operational amplifier equivalent circuit

Rin ≈ ∞Rin ≈ MΩ for real op amps

Rout ≈ 0

Rout ≈ 100Ω for real op amps

Av ≈ ∞Av ≈ 104 → 105 for real op amps

Vout = Av (V+ − V−)

Rin ≈ ∞

Rin ≈ MΩ for real op amps

Rout ≈ 0

Av ≈ ∞

Av ≈ 104 → 105 for real op amps

Rout ≈ 0

Negative feedback

Op amps are rarely used in the open-loop configuration.

Negative feedback

Op amps are rarely used in the open-loop configuration.

They usually use negative feedback.

Negative feedback

β is called the feedback factor, and β ∈ (0, 1)

It is the proportion of the output fed back into the input

If it goes into the inverting input, it is negative feedback

If it goes into the non-inverting input, it is positive feedback

Rin ≈ Rin (1 + βA)

Rout ≈ Rout(1+βA)

gain = 1β ; i.e. the output depends only on the feedback,

not on the op amp characteristics

Negative feedback

You will virtually never use positive feedback!

Note that allof the circuits that follow use negative feedback; (i.e.feedback goes into the non-inverting input.

You will virtually never use positive feedback! Note that allof the circuits that follow use negative feedback;

(i.e.feedback goes into the non-inverting input.

You will virtually never use positive feedback! Note that allof the circuits that follow use negative feedback; (i.e.feedback goes into the non-inverting input.

Terminology

Without feedback is called open loop configuration

With feedback is called closed loop configuration

The gain without feedback is called open loop gain

The gain with feedback is called closed loop gain

Terminology

Analyzing Op Amp Circuits; ideal assumptions with closedloop circuits

No current goes into op amp inputs

Inputs are virtually equal ; i.e. inputs are at the same voltage

Frequency of input signal doesn’t matter

These assumptions only hold if the output is notsaturated! i.e. if the output is not at either of the rails

Instead of thinking of the device as an amplifier, you can thinkthe purpose of the device is to keep the inputs equal

These assumptions only hold if the output is notsaturated!

i.e. if the output is not at either of the rails

Buffer circuitInverting amplifier circuitSumming amplifier circuitNon-inverting amplifier circuitDifferential amplifier circuit

Buffer (or voltage follower)

V− = Vout and V+ = Vin

V− ≈ V+ (virtual equality)

∴ Vout ≈ Vin

Inverting amplifier

VinVout

Many op amp circuits are based on this.

V+ = 0 (ground)

If Rf = Vout − V−

IiRi = V− − Vin

If = Ii (no current into inputs)

∴ Vout−0Rf

= 0−VinRi

∴ Vout = −RfRi

V+ = 0 (ground)

IiRi = V− − Vin

∴ Vout−0Rf

= 0−VinRi

∴ Vout = −RfRi

V+ = 0 (ground)

IiRi = V− − Vin

∴ Vout−0Rf

= 0−VinRi

∴ Vout = −RfRi

V+ = 0 (ground)

IiRi = V− − Vin

∴ Vout−0Rf

= 0−VinRi

∴ Vout = −RfRi

V+ = 0 (ground)

IiRi = V− − Vin

∴ Vout−0Rf

= 0−VinRi

∴ Vout = −RfRi

V+ = 0 (ground)

IiRi = V− − Vin

∴ Vout−0Rf

= 0−VinRi

∴ Vout = −RfRi

V+ = 0 (ground)

IiRi = V− − Vin

∴ Vout−0Rf

= 0−VinRi

∴ Vout = −RfRi

Summing amplifier

Vout = −Rf

+ V2R2

Can be extended to many inputs

Summing amplifier

Vout = −Rf

+ V2R2

)Can be extended to many inputs

Non-inverting amplifier

Vin Vout

Vout =(

1 + RfR1

Differential amplifier

Vout = V1R2R1+R2

(1 + Rf

)− V2

Simplified if Rf = R2 and R1 = R3

∴ Vout = RfR1

(V1 − V2)

If all resistors are equal, Vout = V1 − V2

Vout = V1R2R1+R2

(1 + Rf

)− V2

∴ Vout = RfR1

(V1 − V2)

Vout = V1R2R1+R2

(1 + Rf

)− V2

∴ Vout = RfR1

(V1 − V2)

Vout = V1R2R1+R2

(1 + Rf

)− V2

∴ Vout = RfR1

(V1 − V2)

Integrator

Output is the integral of the input over time

Vout = − 1RC

∫Vindt

Often has a large resistor in parallel with C to avoid saturation

Integrator

Vout = − 1RC

∫Vindt

Integrator

Vout = − 1RC

∫Vindt

Differentiator

Output is the derivative of the input over time

Vout = −RC dVindt

Differentiator

Output is the derivative of the input over time

Vout = −RC dVindt

Logarithmic amplifier

Output is related to the logarithm of the input

Vout ∝ − ln Vin

Logarithmic amplifier

Output is related to the logarithm of the input

Vout ∝ − ln Vin

Exponential amplifier

Output is related to the exponential of the input

Vout ∝ −eVin

Exponential amplifier

Output is related to the exponential of the input

Vout ∝ −eVin

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