electronics operational ampliﬁer basicsdenethor.wlu.ca/pc320/lectures/opampbasicbeam.pdfideal...

Ideal Operational AmplifiersAnalyzing Op Amp Circuits

Common Operational Amplifier CircuitsOp amp circuit input resistance

ElectronicsOperational Amplifier Basics

Terry Sturtevant

Wilfrid Laurier University

October 4, 2016

Terry Sturtevant Electronics Operational Amplifier Basics



Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback

Ideal Operational Amplifiers






invertinginput






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






V supply+ is the positive supply.

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






V supply+ is the positive supply.V supply− is the negative supply.

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






V supply+ is the positive supply.V supply− is the negative supply.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.When an op amp hits one of the rails, its output can be calledsaturated, or we can say the op amp is in saturation.






V supply+ is the positive supply.V supply− is the negative supply.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.When an op amp hits one of the rails, its output can be calledsaturated, or we can say the op amp is in saturation.






V supply+ is the positive supply.V supply− is the negative supply.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.

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






V supply+ is the positive supply.V supply− is the negative supply.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.When an op amp hits one of the rails, its output can be calledsaturated, or we can say the op amp is in saturation.





In a dual supply op amp, typically the positive and negativesupplies are similar, such as ±12V .

In a single supply op amp, often the negative supply isground.→ Single supply op amps are an exception to the previousrule; you usually can usually get within a few millivolts of thenegative supply.





In a dual supply op amp, typically the positive and negativesupplies are similar, such as ±12V .In a single supply op amp, often the negative supply isground.

→ Single supply op amps are an exception to the previousrule; you usually can usually get within a few millivolts of thenegative supply.





In a dual supply op amp, typically the positive and negativesupplies are similar, such as ±12V .In a single supply op amp, often the negative supply isground.→ Single supply op amps are an exception to the previousrule; you usually can usually get within a few millivolts of thenegative supply.





Equivalent circuit

Vin*

@R

Vout





Operational amplifier equivalent circuit

Rin ≈ ∞→ Rin ≈ MΩ for real op ampsRout ≈ 0→ Rout ≈ 100Ω for real op ampsAv ≈ ∞→ Av ≈ 104 → 105 for real op ampsVout = Av (V+ − V−)






Rin ≈ ∞

→ Rin ≈ MΩ for real op ampsRout ≈ 0→ Rout ≈ 100Ω for real op ampsAv ≈ ∞→ Av ≈ 104 → 105 for real op ampsVout = Av (V+ − V−)






Rin ≈ ∞→ Rin ≈ MΩ for real op amps

Rout ≈ 0→ Rout ≈ 100Ω for real op ampsAv ≈ ∞→ Av ≈ 104 → 105 for real op ampsVout = Av (V+ − V−)






Rin ≈ ∞→ Rin ≈ MΩ for real op ampsRout ≈ 0

→ Rout ≈ 100Ω for real op ampsAv ≈ ∞→ Av ≈ 104 → 105 for real op ampsVout = Av (V+ − V−)






Rin ≈ ∞→ Rin ≈ MΩ for real op ampsRout ≈ 0→ Rout ≈ 100Ω for real op amps

Av ≈ ∞→ Av ≈ 104 → 105 for real op ampsVout = Av (V+ − V−)






Rin ≈ ∞→ Rin ≈ MΩ for real op ampsRout ≈ 0→ Rout ≈ 100Ω for real op ampsAv ≈ ∞

→ Av ≈ 104 → 105 for real op ampsVout = Av (V+ − V−)






Rin ≈ ∞→ Rin ≈ MΩ for real op ampsRout ≈ 0→ Rout ≈ 100Ω for real op ampsAv ≈ ∞→ Av ≈ 104 → 105 for real op amps

Vout = Av (V+ − V−)






Rin ≈ ∞→ Rin ≈ MΩ for real op ampsRout ≈ 0→ Rout ≈ 100Ω for real op ampsAv ≈ ∞→ Av ≈ 104 → 105 for real op ampsVout = Av (V+ − V−)





Negative feedback





Negative feedback

Vin





Negative feedback

Vin

Vout





Negative feedback

Vin

β

Vout





Negative feedback

Vin

β

Vout

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





Negative feedback

Vin

β

Vout

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 positivefeedbackRin ≈ 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

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 positivefeedbackRin ≈ Rin (1 + βA)Rout ≈ Rout

(1+βA)







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 positivefeedbackRin ≈ Rin (1 + βA)Rout ≈ Rout

(1+βA)







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 positivefeedbackRin ≈ Rin (1 + βA)Rout ≈ Rout

(1+βA)







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 positivefeedback

Rin ≈ Rin (1 + βA)Rout ≈ Rout

(1+βA)







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 positivefeedbackRin ≈ Rin (1 + βA)

Rout ≈ Rout(1+βA)







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 positivefeedbackRin ≈ Rin (1 + βA)Rout ≈ Rout

(1+βA)







You will virtually never use positive feedback!

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

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

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

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

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.




Analyzing Op Amp Circuits; ideal assumptions with closedloop circuits

No current goes into op amp inputsInputs are virtually equal ; i.e. inputs are at the same voltageFrequency of input signal doesn’t matterThese assumptions only hold if the output is notsaturated!→ i.e. if the output is not at either of the railsInstead of thinking of the device as an amplifier, you can thinkthe purpose of the device is to keep the inputs equal





No current goes into op amp inputs

Inputs are virtually equal ; i.e. inputs are at the same voltageFrequency of input signal doesn’t matterThese assumptions only hold if the output is notsaturated!→ i.e. if the output is not at either of the railsInstead of thinking of the device as an amplifier, you can thinkthe purpose of the device is to keep the inputs equal





No current goes into op amp inputsInputs are virtually equal ; i.e. inputs are at the same voltage

Frequency of input signal doesn’t matterThese assumptions only hold if the output is notsaturated!→ i.e. if the output is not at either of the railsInstead of thinking of the device as an amplifier, you can thinkthe purpose of the device is to keep the inputs equal





No current goes into op amp inputsInputs are virtually equal ; i.e. inputs are at the same voltageFrequency 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 railsInstead of thinking of the device as an amplifier, you can thinkthe purpose of the device is to keep the inputs equal





No current goes into op amp inputsInputs are virtually equal ; i.e. inputs are at the same voltageFrequency of input signal doesn’t matterThese assumptions only hold if the output is notsaturated!

→ i.e. if the output is not at either of the railsInstead of thinking of the device as an amplifier, you can thinkthe purpose of the device is to keep the inputs equal





No current goes into op amp inputsInputs are virtually equal ; i.e. inputs are at the same voltageFrequency of input signal doesn’t matterThese 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





No current goes into op amp inputsInputs are virtually equal ; i.e. inputs are at the same voltageFrequency of input signal doesn’t matterThese assumptions only hold if the output is notsaturated!→ i.e. if the output is not at either of the railsInstead of thinking of the device as an amplifier, you can thinkthe purpose of the device is to keep the inputs equal




Buffer circuitInverting amplifier circuit

Buffer (or voltage follower)






Vin






Vin

Vout






Vin

Vout

V− = Vout and V+ = Vin






Vin

Vout


V− ≈ V+ (virtual equality)






Vin

Vout


V− ≈ V+ (virtual equality)∴ Vout ≈ Vin





6V

4V6V

4V

Here’s a simulation.





12V

-12V12V

-12V

With a large amplitude signal, you can see the rails.





12V

11.1V

This is a closer look at the positive rail.





-12V

-11.1V

This is a closer look at the negative rail.





Inverting amplifier

VinVout

RfRi

If-

Ii-

Many op amp circuits are based on this.





V+ = 0 (ground)

If Rf = Vout − V−

Ii Ri = V− − Vin

V− ≈ V+ (virtual equality)If = Ii (no current into inputs)∴ Vout−0

Rf= 0−Vin

Ri

∴ Vout = −RfRi

Vin





V+ = 0 (ground)If Rf = Vout − V−



Rf= 0−Vin

Ri

∴ Vout = −RfRi

Vin







V− ≈ V+ (virtual equality)

If = Ii (no current into inputs)∴ Vout−0

Rf= 0−Vin

Ri

∴ Vout = −RfRi

Vin







V− ≈ V+ (virtual equality)If = Ii (no current into inputs)

∴ Vout−0Rf

= 0−VinRi

∴ Vout = −RfRi

Vin








Rf= 0−Vin

Ri

∴ Vout = −RfRi

Vin




Op amp circuit input resistance





Even though the input resistance of an op amp is very large, theinput resistance of an op amp circuit may not be.






Vin






Vin

I ≈ 0-






Vin

I ≈ 0-

For the buffer circuit, since the signal goes directly into an op ampinput, then the input resistance is very large.




For a circuit like the inverting amplifier, the input signal doesn’t godirectly into the op amp input.





VinVout

RfRi

If-

Ii-





VinVout

RfRi

If-

Ii-

V+ ≈ V− = 0@@I AAAAK





Vin

Ri

Ii ?

It looks more like this.





Vin

Ri

Ii ? Ii = VinRi

It looks more like this.





Vin

Ri

Ii ? Ii = VinRi

It looks more like this.The effective input resistance is Ri .


electronics operational ampliﬁer basicsdenethor.wlu.ca/pc320/lectures/opampbasicbeam.pdfideal...

Documents