Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
ElectronicsOperational Amplifier Basics
Terry Sturtevant
Wilfrid Laurier University
September 3, 2014
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Ideal Operational Amplifiers
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Ideal Operational Amplifiers
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Ideal Operational Amplifiers
invertinginput
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Ideal Operational Amplifiers
invertinginput
non-invertinginput
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Ideal Operational Amplifiers
invertinginput
non-invertinginput
output
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Ideal Operational Amplifiers
invertinginput
non-invertinginput
output
Output is proportional to the difference between thenon-inverting and inverting inputs
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Ideal Operational Amplifiers
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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Showing power connections
invertinginput
non-invertinginput
output
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Showing power connections
invertinginput
non-invertinginput
output
V supply+
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Showing power connections
invertinginput
non-invertinginput
output
V supply+
V supply−
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Showing power connections
invertinginput
non-invertinginput
output
V supply+
V supply−
Supplies are usually not shown, but must be used.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Equivalent circuit
Vin*
@R
Vout
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Equivalent circuit
Vin*
@R
Vout
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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−)
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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−)
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Operational amplifier equivalent circuit
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−)
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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−)
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Operational amplifier equivalent circuit
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−)
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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−)
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Operational amplifier equivalent circuit
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−)
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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−)
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Negative feedback
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Negative feedback
Vin
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Negative feedback
Vin
Vout
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Negative feedback
Vin
β
Vout
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Negative feedback
Vin
β
Vout
Op amps are rarely used in the open-loop configuration.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
Negative feedback
Vin
β
Vout
Op amps are rarely used in the open-loop configuration.→ They usually use negative feedback.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative 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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative 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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative 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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative 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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative 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 positivefeedback
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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative 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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative 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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative 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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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. )
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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. )
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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. )
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Basic Schematic SymbolShowing power connectionsOperational amplifier supply voltage rulesEquivalent circuitNegative feedback
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.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
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 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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
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 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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
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 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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
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 rails
Instead of thinking of the device as an amplifier, you can thinkthe purpose of the device is to keep the inputs equal
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Buffer circuitInverting amplifier circuit
Buffer (or voltage follower)
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Buffer circuitInverting amplifier circuit
Buffer (or voltage follower)
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Buffer circuitInverting amplifier circuit
Buffer (or voltage follower)
Vin
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Buffer circuitInverting amplifier circuit
Buffer (or voltage follower)
Vin
Vout
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Buffer circuitInverting amplifier circuit
Buffer (or voltage follower)
Vin
Vout
V− = Vout and V+ = Vin
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Buffer circuitInverting amplifier circuit
Buffer (or voltage follower)
Vin
Vout
V− = Vout and V+ = Vin
V− ≈ V+ (virtual equality)
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Buffer circuitInverting amplifier circuit
Buffer (or voltage follower)
Vin
Vout
V− = Vout and V+ = Vin
V− ≈ V+ (virtual equality)∴ Vout ≈ Vin
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Buffer circuitInverting amplifier circuit
6V
4V6V
4V
Here’s a simulation.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Buffer circuitInverting amplifier circuit
12V
-12V12V
-12V
With a large amplitude signal, you can see the rails.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Buffer circuitInverting amplifier circuit
12V
11.1V
This is a closer look at the positive rail.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Buffer circuitInverting amplifier circuit
-12V
-11.1V
This is a closer look at the negative rail.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Buffer circuitInverting amplifier circuit
Inverting amplifier
VinVout
RfRi
If-
Ii-
Many op amp circuits are based on this.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Buffer circuitInverting amplifier circuit
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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Buffer circuitInverting amplifier circuit
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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Buffer circuitInverting amplifier circuit
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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Buffer circuitInverting amplifier circuit
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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Buffer circuitInverting amplifier circuit
V+ = 0 (ground)If Rf = Vout − V−
Ii Ri = V− − Vin
V− ≈ V+ (virtual equality)If = Ii (no current into inputs)
∴ Vout−0Rf
= 0−VinRi
∴ Vout = −RfRi
Vin
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Buffer circuitInverting amplifier circuit
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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Buffer circuitInverting amplifier circuit
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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
Op amp circuit input resistance
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
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.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
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
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
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
I ≈ 0-
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
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
I ≈ 0-
For the buffer circuit, since the signal goes directly into an op ampinput, then the input resistance is very large.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
For a circuit like the inverting amplifier, the input signal doesn’t godirectly into the op amp input.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
For a circuit like the inverting amplifier, the input signal doesn’t godirectly into the op amp input.
VinVout
RfRi
If-
Ii-
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
For a circuit like the inverting amplifier, the input signal doesn’t godirectly into the op amp input.
VinVout
RfRi
If-
Ii-
V+ ≈ V− = 0@@I AAAAK
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
For a circuit like the inverting amplifier, the input signal doesn’t godirectly into the op amp input.
Vin
Ri
Ii ?
It looks more like this.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
For a circuit like the inverting amplifier, the input signal doesn’t godirectly into the op amp input.
Vin
Ri
Ii ? Ii = VinRi
It looks more like this.
Terry Sturtevant Electronics Operational Amplifier Basics
Ideal Operational AmplifiersAnalyzing Op Amp Circuits
Common Operational Amplifier CircuitsOp amp circuit input resistance
For a circuit like the inverting amplifier, the input signal doesn’t godirectly into the op amp input.
Vin
Ri
Ii ? Ii = VinRi
It looks more like this.The effective input resistance is Ri .
Terry Sturtevant Electronics Operational Amplifier Basics