📘 Operational Amplifiers (Op-Amps) – Reviewer
What is an Operational Amplifier?
An Operational Amplifier (Op-Amp) is a high-gain electronic voltage amplifier with a
differential input and, usually, a single-ended output. It is called "operational" because it was
originally designed to perform mathematical operations like addition, subtraction, integration,
and differentiation in analog computers.
Symbol and Terminals
Op-Amps have the following terminals:
Inverting Input (−)
Non-inverting Input (+)
Output (Vout)
Power Supply (+Vcc and −Vee or GND)
+Vcc
|
+ |
Vin →| |→ Vout
- |
-Vee
Ideal Op-Amp Characteristics
1. Infinite Open-Loop Gain
AOL→∞A_{OL} \to \infty
Any small voltage difference between the inputs is amplified infinitely.
2. Infinite Input Impedance
Rin→∞R_{in} \to \infty
No current flows into the input terminals.
3. Zero Output Impedance
Rout=0R_{out} = 0
Output can drive any load without loss.
4. Infinite Bandwidth
Amplifies signals of all frequencies equally.
5. Zero Offset Voltage
Output is zero when both inputs are at the same voltage.
6. Perfect Common Mode Rejection Ratio (CMRR)
Amplifies differential inputs, rejects common signals.
Golden Rules of Ideal Op-Amps (for Negative Feedback)
The voltage between the inverting and non-inverting inputs is zero:
V+=V−V_+ = V_-
The current into both input terminals is zero:
I+=I−=0I_+ = I_- = 0
Common Op-Amp Configurations
1. Inverting Amplifier
Input is applied to the inverting terminal through resistor R1R_1
Feedback resistor RfR_f connects output to inverting input
Non-inverting input is grounded
Gain:
Av=VoutVin=−RfR1A_v = \frac{V_{out}}{V_{in}} = -\frac{R_f}{R_1}
2. Non-Inverting Amplifier
Input is applied to the non-inverting terminal
Feedback and resistor R1R_1 form a voltage divider to the inverting input
Gain:
Av=1+RfR1A_v = 1 + \frac{R_f}{R_1}
3. Voltage Follower (Buffer)
Output is connected directly to the inverting input
Non-inverting input receives the signal
Gain:
Av=1A_v = 1
Used to isolate circuits (high input impedance, low output impedance).
4. Summing Amplifier
Multiple inputs applied through individual resistors to the inverting input
Used to add multiple signals
Output:
Vout=−(RfR1V1+RfR2V2+⋯ )V_{out} = - ( \frac{R_f}{R_1}V_1 + \frac{R_f}{R_2}V_2 + \cdots )
5. Differential Amplifier
Subtracts one input from another
Output:
Vout=RfR1(V2−V1)V_{out} = \frac{R_f}{R_1}(V_2 - V_1)
6. Integrator
Input through resistor RR, feedback is a capacitor CC
Output:
Vout=−1RC∫Vin dtV_{out} = -\frac{1}{RC} \int V_{in} \, dt
7. Differentiator
Input through capacitor CC, feedback is a resistor RR
Output:
Vout=−RCdVindtV_{out} = -RC \frac{dV_{in}}{dt}
Important Op-Amp Parameters
Gain Bandwidth Product (GBW): Product of amplifier gain and bandwidth; constant
for a given op-amp.
Slew Rate: Maximum rate of change of output voltage per unit time (V/µs).
CMRR (Common Mode Rejection Ratio): Ratio of differential gain to common-mode
gain (in dB).
PSRR (Power Supply Rejection Ratio): Ability to reject changes in supply voltage.
Input Offset Voltage: Small voltage needed to make output zero when inputs are equal.
Input Bias Current: Average current into both inputs.
Input Offset Current: Difference in input bias currents.
Applications of Op-Amps
Signal Amplification (audio, instrumentation)
Analog computation (adder, subtractor)
Filters (low-pass, high-pass, band-pass)
Signal conditioning
Oscillators (e.g., Wien Bridge Oscillator)
Converters (voltage-to-current, current-to-voltage)
Analog-to-Digital and Digital-to-Analog interfaces
Practical Considerations
Real op-amps have limited bandwidth and finite gain
Always decouple power supply with bypass capacitors
Avoid large feedback loops to prevent oscillations
Use appropriate compensation to improve stability
Choose op-amps with low offset and high slew rate for precision applications
Common ICs
LM741: General-purpose op-amp
TL081/TL082: JFET input op-amps (low bias current)
LM324: Quad op-amp package
OP07: Low-offset op-amp for precision
