Operational Amplifiers - Configurations and Characteristics
What is an Op Amp
An Op Amp is an integrated circuit that can be used to amplify both DC and AC signals. One of the most
common Op Amps available is the LM 741. Inside the Op Amp is a complex electronic circuit. You can
use the Internet to find a picture of the equivalent circuit of the Op Amp. The diagram below shows the
pin numbers for the various terminals of the device. Note that the Op Amp requires plus and minus
voltage sources to power the device.
Op Amp Model
The diagram shows a simplified model of an Op Amp. It consists of 2 inputs – a Non-Inverting input V+
and an Inverting Input V-, an output VOUT, an input resistance RIN, an output voltage source GVIN and an
output resistance ROUT.
The values of these parameters for a LM 741 Op Amp are found in the table below.
Parameter
Input resistance
Output resistance
Open loop gain -G
Value
2 MΩ
75 Ω
100,000
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Open Loop Configuration
The open loop gain was referred to in the model as G but it is also commonly designated as AOL.
This is an extremely large value and makes the Op Amp an impractical amplifier in an Open Loop
configuration. Like β for a bipolar transistor, the value of the open loop gain (AOL) is highly variable from
one device to another of the same type.
Saturation Voltage
The output voltage from an Op Amp circuit can only approach the value of the DC supply voltage(s).
These are referred to as the saturation voltages and represent the maximum output voltage.
VSAT = ± VCC – (1 to 2 V)
so for VCC = ± 12V the maximum outputs voltages are approximately ± (10 to 12) V.
The plus and minus saturation voltages are typically not equal.
Sample Calculation
This calculation illustrates the difficulties with Open Loop mode. Assume AOL = 100,000 and VSAT = ± 10 V
The minimum input voltage that will cause the output to saturate is VIN,min
= ± 10 V/100,000 = ± 100 µV
This is a very small input signal and makes the Op Amp not practical for
larger input signals.
This calculation illustrates one significant conclusion for Op Amps.
The voltage difference between the 2 input terminals is essentially zero.
Closed Loop Configurations
A Closed Loop Op Amp circuit uses negative feedback to improve amplifier performance. Negative
feedback involves connecting a sample of the output voltage back to the Inverting input of the Op Amp
with a resistor network as shown. This feedback voltage is a sample of the output voltage applied 180°
out of phase with the input. The amount of feedback is determined by a voltage divider involving Rf and
Ri. The feedback ratio B = Ri/(Ri + Rf) and represents a value between 0 and 1 (0 and 100%). The
feedback voltage Vfb is the voltage at the Inverting input and is B x VOUT.
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Vfb
The effect of negative feedback is to Reduce and Stabilize the voltage gain of the amplifier.
Inverting Amplifier Configuration
In the Inverting Amplifier configuration the VIN signal is connected to the Inverting Input. Note that there
are differences in the labeling standards for the resistors. Note: the negative sign for the voltage gain
indicates that the input and output waveforms for this amplifier are 180 out of phase.
The closed loop voltage gain of this amplifier
AV,CL = - Rf/RIN
Examples
1. If Rf = 10 kΩ and RIN = 1 kΩ, what are the feedback ratio and the closed loop voltage gain for
the amplifier.
Feedback ratio B = 1 kΩ/( 1 kΩ + 10 kΩ) = 0.091 = 9.1 %
The closed loop voltage gain AV,CL = - 10 kΩ/1 kΩ = - 10
2.
Repeat the calculations for Rf = 100 kΩ and RIN = 2.2 kΩ
Feedback ratio B = 2.2 kΩ/( 2.2 kΩ + 100 kΩ) = 0.02 = 2 %
The closed loop voltage gain AV,CL = - 10 kΩ/1 kΩ = - 45.5
For these 2 examples when the feedback ratio decreased, the voltage gain increased.
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Notice that in both these examples that the closed loop voltage has been reduced considerably from the
value of 100,000 for the open loop gain and that this gain would be very stable from one amplifier
circuit to another because the voltage gain is entirely dependent on the two external resistors and
resistors are very stable electronic components.
Non-Inverting Amplifier Configuration
In the Non-Inverting Amplifier configuration the VIN signal is connected to the Non-Inverting Input. The
input and output signals are now in phase.
The closed loop voltage gain of this amplifier
AV,CL = 1+ R1/R2
Examples
1. If R1 = 15 kΩ and R2 = 1 kΩ, what are the feedback ratio and the closed loop voltage gain for the
amplifier.
Feedback ratio B = 1 kΩ/( 1 kΩ + 15 kΩ) = 0.06 = 6 %
The closed loop voltage gain AV,CL = 1 + 15 kΩ/1 kΩ = 16
2.
Repeat the calculations for Rf = 120 kΩ and RIN = 3.3 kΩ
Feedback ratio B = 3.3 kΩ/( 3.3 kΩ + 120 kΩ) = 0.027 = 2.7 %
The closed loop voltage gain AV,CL = 1 + 120 kΩ/3.3 kΩ = 37.4
Special case of the Non-Inverting Amplifier – Non Inverting Voltage Follower Amplifier
When the feedback resistor R1 is set to zero – a short circuit and the other resistor R2 is removed then
the voltage gain of this circuit becomes 1. The input and output signals are in phase.
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AV,CL = 1+ R1/R2 = 1+ 0/∞ = 1
Effects of Negative Feedback on RIN and ROUT
Negative feedback as has already been seen affects the voltage gain of closed loop amplifiers but it also
has effects on RIN and ROUT of Op Amp amplifiers.
Non-Inverting Amplifier
Negative feedback improves the values for both RIN and ROUT for the Non-Inverting amplifier - makes RIN
larger and ROUT smaller.
RIN,NonINV = (1 + BAOL)x RIN
ROUT,NonInv = ROUT/(1 + BAOL)
Example
In a previous example the Feedback ratio B was calculated as 0.06.
RIN,NonINV = (1 + 0.06 x 105) x 2 MΩ = 12 GΩ
ROUT,NonInv = 75 Ω/(1 + 0.06 x 105) = 12.4 mΩ
Inverting Amplifier
Negative feedback improves only the value for ROUT for the Non-Inverting amplifier. RIN is small for this
configuration.
RIN,INV = R1
ROUT,INV = ROUT/(1 + BAOL)
In a previous example the Feedback ratio B was calculated as 0.091.
RIN,INV = 1 kΩ
ROUT,INV = 75 Ω/(1 + 0.091 x 100,000) = 8.2 mΩ
Clearly the Inverting amplifier suffers from a low input resistance.
Non Inverting Voltage Follower Amplifier
For the voltage follower amplifier
RIN = (1 + 1 x 100,000) x 2 MΩ = 200 GΩ
ROUT,INV = 75 Ω/(1 + 1 x 100,000) = 0.75 mΩ
An ideal amplifier has an infinite input resistance and a zero output resistance. Clearly the voltage
follower is an excellent approximation to an ideal amplifier.
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Summary Table
Parameter
Non-Inverting Amp
Inverting Amp
Voltage Follower
Voltage gain
Input Resistance
Output Resistance
Voltage gain
Input Resistance
Output Resistance
Voltage gain
Input Resistance
Output Resistance
Expression
1 + Rf/R1
RIN,NonINV = (1 + BAOL)x RIN
ROUT,NonInv = ROUT/(1 + BAOL)
- Rf/R1
R1
ROUT,Inv = ROUT/(1 + BAOL)
1
RIN = (1 + AOL)x RIN
ROUT = ROUT/(1 + AOL)
Typical value
Small to moderate
Very large
Very small
Small to moderate
small
Very small
small
Extremely large
Extremely small
Frequency Response of Op Amp Circuits
Open Loop Mode
The frequency response of the Open loop circuit is shown. Because of internal resistances and
capacitances the Op Amp behaves like a low pass filter with very low corner frequency with a value of 10
Hz. The corner frequency determines the Bandwidth for the circuit. BW = fC – 0 = fC.
In Open loop mode the Op Amp attenuates input signals above the corner frequency with a roll-off rate
of -20 dB/decade like a first order low pass filter.
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Unity Gain Frequency
The Unity Gain frequency is the frequency where the voltage gain drops to 1 or 0 dB. For a LM 741 Op
Amp the Unity Gain frequency is 1 MHz.
Closed Loop Frequency Response
As we saw earlier the effect of negative feedback is to reduce and stabilize voltage gain. The diagram
shows the open loop response as well as another graph for the voltage gain for a closed loop circuit with
a closed loop voltage gain called ACL,mid. The voltage gain is significantly less and as a result the corner
frequency fc,CL (and the bandwidth) has been increased.
This allows us to draw the conclusion that as the closed loop voltage gain is decreased the Bandwidth
increases.
Gain-Bandwidth Product
The conclusion from above can be generalized into a result that states that the
Gain-Bandwidth Product = Gain x Bandwidth = Constant value
The Gain-Bandwidth product for a LM 741 Op Amp can be determined as
Recall that the Gain = 1 at the Unity Gain frequency of 1 MHz
Gain-Bandwidth Product = 1 x 1 MHz = 1 MHz
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Examples
What is the gain of a closed loop Op Amp circuit at 50 kHz when the Gain-Bandwidth Product is 1 MHz?
Gain = 1 MHz/50 kHz = 20
What is the Bandwidth of a closed loop Op Amp circuit with a gain of 100 when the Gain-Bandwidth
Product is 1 MHz?
Bandwidth = 1 MHz/100 = 10 kHz
Application Note
Written by David Lloyd
Computer Engineering Program
Humber College
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