Class 12 > Unit # 22:Solid State of Electronics > Operational Amplifier & Comparator

Operational Amplifier, Ideal Characteristics, and Op-Amp as a Comparator - Talha's Physics Academy

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Operational Amplifier, Ideal Characteristics, and Op-Amp as a Comparator

Operational Amplifier & Characteristics of an Ideal Op-Amp

"An operational amplifier (commonly known as an op-amp) is a high-gain, direct-coupled electronic voltage amplifier with differential inputs and, usually, a single-ended output."

Its primary function is to amplify the difference between two input voltages while rejecting any signals common to both. Originally designed to perform mathematical operations in analog computers (such as addition, subtraction, integration, and differentiation), op-amps are now fundamental building blocks in modern linear and signal-processing circuits.

Fig: Circuit diagram illustrating an operational amplifier.

Characteristics of an Ideal Op-Amp

An ideal operational amplifier is a theoretical model used to simplify circuit analysis. It possesses perfect electrical characteristics, which serve as a benchmark for real-world devices:

  1. Infinite Open-Loop Voltage Gain ($G_o$): It amplifies the differential input signal by an infinite factor, meaning even an infinitesimally small input voltage difference can produce a maximum output.
  2. Infinite Input Impedance: The resistance between the two input terminals is infinite. Consequently, it draws zero current from the signal source, preventing any loading effects on preceding stages.
  3. Zero Output Impedance: It behaves as a perfect voltage source with zero internal resistance. This allows it to drive any load current without dropping its output voltage.
  4. Infinite Bandwidth: It can amplify signals of any frequency, from DC to infinitely high frequencies, with equal gain and zero time delay.
  5. Zero Common-Mode Gain: It completely rejects any signal or noise that is identical and simultaneous on both input terminals. Its Common-Mode Rejection Ratio (CMRR) is infinite.
  6. Zero Offset Voltage: When the voltage difference between the two inputs is exactly zero, the output voltage is precisely zero.
  7. Infinite Slew Rate: The output voltage can change instantaneously in response to an instantaneous change at the input, meaning there is no distortion or propagation delay.
  8. Zero Noise: The ideal op-amp does not generate any internal electrical noise, ensuring a perfectly clean output signal.

Working of Op-Amp as a Comparator

The op-amp is connected to two power supplies. One battery of $9\text{ V}$ is connected between the zero-volt line and the $+9\text{ V}$ positive supply terminal of the op-amp, and the other between the zero-volt line and the negative power supply terminal. The output voltage is given by:

$$V_{\text{out}} = G_o (V^+ - V^-)$$

where $G_o$ is the open-loop voltage gain. Notice that all of these voltages are measured with reference to the zero-volt line, which is often connected to earth.

Suppose that $G_o = 10^5$ and that $V^+ = 0.15\text{ V}$ and $V^- = 0.10\text{ V}$. Then the equation becomes:

$$V_{\text{out}} = 10^5 (0.15 - 0.10) = 10^5 \times 0.05 = 5000\text{ V}$$

Certainly, this is physically impossible because it exceeds the power supply limits. The op-amp is therefore saturated and $V_{\text{out}}$ will be close to one of the power supply voltages, in this case $9\text{ V}$ because $V^+$ is bigger than $V^-$.

Operating Rules as a Comparator

  • (i) If $V^+$ is slightly greater in magnitude than $V^-$, then $V_{\text{out}}$ will have a magnitude equal to the positive power supply voltage ($+9\text{ V}$).
  • (ii) If $V^+$ is slightly smaller in magnitude than $V^-$, then $V_{\text{out}}$ will have a magnitude equal to the negative power supply voltage.

The op-amp is serving as a comparator, comparing $V^+$ and $V^-$. If these voltages are slightly different, the output voltage immediately indicates which one is larger.

Fig: Circuit diagram illustrating an operational amplifier acting as a voltage comparator.

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