Op-amp Circuits
What is Op-amp Circuits?
A high-gain, direct-coupled differential amplifier with a single-ended output, used as a building block in analog circuits.
Key formula / rule: Inverting Amplifier
Key points
- Understand the fundamental characteristics of an ideal and a practical op-amp.
- Analyze basic op-amp configurations like inverting and non-inverting amplifiers.
- Apply the virtual short concept to analyze op-amp circuits.
- Identify and understand the function of op-amp circuits like summers, integrators, and differentiators.
Common exam trap
Assuming ideal op-amp characteristics for all circuits without considering limitations.
Definitions
- Term
Operational Amplifier (Op-Amp)
- Meaning
A high-gain, direct-coupled differential amplifier with a single-ended output, used as a building block in analog circuits.
- Term
Virtual Short
- Meaning
The condition where the voltage difference between the inverting (-) and non-inverting (+) input terminals of an op-amp is approximately zero, due to high open-loop gain and negative feedback.
- Term
Negative Feedback
- Meaning
A configuration where a fraction of the output signal is fed back to the input, typically reducing gain but increasing stability and bandwidth.
- Term
Slew Rate
- Meaning
The maximum rate of change of the output voltage of an op-amp, expressed in V/µs.
- Term
Bandwidth
- Meaning
The range of frequencies over which an amplifier operates effectively, typically defined by the -3dB points.
- Term
Common-Mode Rejection Ratio (CMRR)
- Meaning
A measure of an amplifier's ability to reject signals that are common to both input terminals.
Learning objectives
Understand the fundamental characteristics of an ideal and a practical op-amp.
Analyze basic op-amp configurations like inverting and non-inverting amplifiers.
Apply the virtual short concept to analyze op-amp circuits.
Identify and understand the function of op-amp circuits like summers, integrators, and differentiators.
Recognize the importance of feedback in op-amp circuit design.
Formulae
- Name
Inverting Amplifier
- Note
Output is inverted and amplified by the ratio of feedback resistor to input resistor.
- Expression
Vo = -\frac{Rf}{Rin} Vin
- Name
Non-inverting Amplifier
- Note
Output is amplified by (1 + ratio of feedback resistor to input resistor). Input impedance is very high.
- Expression
Vo = \left(1 + \frac{Rf}{Rin}\right) Vin
- Name
Summing Amplifier (Inverting)
- Note
Output is the negative sum of weighted input voltages.
- Expression
Vo = -Rf \left(\frac{V1}{R1} + \frac{V2}{R2} + \dots + \frac{Vn}{Rn}\right)
- Name
Integrator
- Note
Output voltage is proportional to the integral of the input voltage over time.
- Expression
Vo(t) = -\frac{1}{RinCf} \int Vin(t) dt + Vo(0)
- Name
Differentiator
- Note
Output voltage is proportional to the derivative of the input voltage with respect to time.
- Expression
Vo(t) = -Rf Cin \frac{dVin(t)}{dt}
- Name
Ideal Op-Amp Conditions
- Note
These conditions are assumed for analysis with negative feedback.
- Expression
V+ = V-, I+ = 0, I- = 0
- Name
Virtual Short
- Note
Applies to op-amp circuits with negative feedback operating in the linear region.
- Expression
V+ - V- \≈ 0
Prerequisites
Basic circuit theory (Ohm's Law, Kirchhoff's Laws).
Understanding of transistors (BJT, MOSFET) as building blocks of op-amps.
Concept of voltage and current amplifiers.
Feedback concepts (positive and negative feedback).
Common mistakes
Assuming ideal op-amp characteristics for all circuits without considering limitations.
Incorrectly applying the virtual short concept when positive feedback is dominant or the op-amp is saturated.
Ignoring op-amp limitations like slew rate, bandwidth, and input offset voltage in high-frequency or precision applications.
Errors in circuit analysis due to incorrect application of Kirchhoff's laws or Ohm's law.
Confusing inverting and non-inverting configurations.
Keywords
Op-Amp
Operational Amplifier
Differential Amplifier
Virtual Short
Negative Feedback
Inverting Amplifier
Non-inverting Amplifier
Integrator
Differentiator
Summing Amplifier
Active Filter
Analog Circuits
Practice preview
An inverting operational amplifier circuit has an input resistor R1 = 1 kOhm and a feedback resistor Rf = 10 kOhm. What is the closed-loop voltage gain of this amplifier?…
easy
An ideal operational amplifier is configured as a voltage follower. If the input voltage is 5 V, what is the output voltage?…
medium
An ideal op-amp differentiator circuit has an input resistor R = 10 kOhm and a feedback capacitor C = 0.1 microF. If the input voltage is a ramp V_in(t) = 2t V, what is the output voltage V_out(t)?…
medium