This cheat sheet summarizes the most common operational amplifier circuit configurations used in introductory electronics and engineering courses. It is designed as a clean printable reference for recognizing circuits, applying gain formulas, and checking signal behavior. Students need it because op-amp problems often look similar, but small wiring changes create very different equations.
The layout is organized into three color-coded sections: ideal rules and basic amplifiers, signal combining and precision gain, and dynamic circuits and filters.
The core idea is that negative feedback makes the op-amp adjust its output so the input terminals are nearly equal in voltage. Basic amplifiers set gain with resistor ratios, while summing and difference circuits combine or subtract signals in controlled ways. Integrators, differentiators, and active filters use capacitors so the output depends on frequency or time-changing signals.
Always check whether the circuit uses negative feedback, whether the input is connected to the inverting or non-inverting terminal, and whether the output can stay within the supply voltage limits.
Key Facts
- For an ideal op-amp with negative feedback, V+ = V- and the input currents are I+ = I- = 0.
- An inverting amplifier has gain Vout/Vin = -Rf/Rin, so the output is inverted by 180 degrees.
- A non-inverting amplifier has gain Vout/Vin = 1 + Rf/Rg, so the output has the same polarity as the input.
- A voltage follower is a non-inverting amplifier with Rf = 0 and no Rg, giving Vout = Vin and very high input resistance.
- An inverting summing amplifier gives Vout = -Rf(V1/R1 + V2/R2 + ...), so each input is weighted by its resistor.
- A difference amplifier with matched resistor ratios gives Vout = (R2/R1)(V2 - V1).
- An ideal inverting integrator gives Vout = -(1/RC) integral of Vin dt, and an ideal differentiator gives Vout = -RC(dVin/dt).
- A first-order active low-pass or high-pass filter has cutoff frequency fc = 1/(2 pi RC).
Vocabulary
- Operational amplifier
- An operational amplifier is a high-gain electronic device that amplifies the voltage difference between its non-inverting and inverting inputs.
- Negative feedback
- Negative feedback sends part of the output back to the inverting input so the circuit becomes stable and follows a predictable gain formula.
- Virtual short
- A virtual short is the ideal op-amp condition where V+ and V- are nearly equal even though the input terminals are not physically connected.
- Inverting input
- The inverting input is the op-amp terminal marked minus, where an increasing signal tends to drive the output in the opposite direction.
- Saturation
- Saturation occurs when the op-amp output reaches a supply rail and can no longer follow the ideal gain equation.
- Cutoff frequency
- Cutoff frequency is the frequency where a filter output falls to about 0.707 of its passband voltage, corresponding to a 3 dB change.
Common Mistakes to Avoid
- Assuming V+ = V- without negative feedback is wrong because the virtual short rule only applies when the op-amp is operating linearly with feedback.
- Forgetting the negative sign in an inverting amplifier is wrong because the input is applied to the inverting terminal, so Vout/Vin = -Rf/Rin.
- Treating op-amp inputs as if current flows into them is wrong for ideal analysis because I+ = I- = 0, so resistor currents must go through feedback paths instead.
- Using gain formulas after the output saturates is wrong because ideal equations only apply while the output remains between the positive and negative supply rails.
- Mixing resistor labels in non-inverting gain is wrong because the formula is 1 + Rf/Rg, where Rf is from output to the inverting input and Rg is from the inverting input to ground.
Practice Questions
- 1 An inverting amplifier has Rin = 10 kOhm, Rf = 47 kOhm, and Vin = 0.20 V. Find the voltage gain and Vout.
- 2 A non-inverting amplifier uses Rf = 90 kOhm and Rg = 10 kOhm. What is its voltage gain, and what output is expected for Vin = 0.15 V?
- 3 A first-order active filter uses R = 3.3 kOhm and C = 0.01 microfarad. Estimate the cutoff frequency using fc = 1/(2 pi RC).
- 4 A circuit looks like an inverting amplifier, but the output is stuck near the positive supply rail. Explain why the ideal gain equation may not predict the real output.
Understanding Op-Amp Circuit Configurations Reference
An op-amp is not naturally a calm, accurate amplifier. Without a feedback path, even a tiny voltage difference between its two inputs drives the output hard toward one supply rail. Feedback returns part of the output to an input terminal and creates a correcting effect.
The circuit settles only when the returned voltage has reduced the input difference to a very small value. This is why the equal-input rule is an approximation, not a law of nature. It works well while the op-amp is operating linearly.
A virtual ground is another useful approximation. In an inverting circuit, the input node may stay near zero volts, yet it is not physically connected to ground and cannot safely supply current like a real ground node.
Resistor choices do more than set a gain. They determine how much current a source must provide. If the input resistor is too small, a sensor or signal generator can be loaded down, changing the voltage before it reaches the amplifier.
A voltage follower is useful when a high-resistance source, such as a light sensor or a potentiometer, must drive a lower-resistance circuit. Difference amplifiers are valuable when the desired signal is a small voltage riding on top of unwanted shared noise.
Good subtraction depends strongly on matched resistor ratios. Instrumentation amplifiers use carefully matched internal resistors and multiple amplifier stages to measure weak signals from strain gauges, temperature probes, or medical sensors without amplifying much of the shared interference.
Capacitors make circuit behavior depend on time because their current changes when their voltage changes. An integrator builds an output from the accumulated input signal. It can turn a steady square wave into a ramp-like waveform.
In real circuits, a tiny input offset or DC component can keep accumulating until the output saturates. Designers often place a resistor across the feedback capacitor to limit this drift at very low frequencies. A differentiator responds strongly to rapid changes, so it can highlight edges in a signal.
It can also amplify high-frequency noise, which makes the ideal version unreliable by itself. Practical differentiators include extra components that reduce gain where noise would dominate.
Filters are used whenever some frequency ranges matter more than others. A low-pass filter can smooth sensor readings or remove hiss from audio. A high-pass filter can block slow baseline changes or remove a DC offset before later amplification.
The cutoff frequency marks a gradual transition, not a sharp boundary. Signals near that frequency are reduced and shifted in phase. Real op-amps add further limits.
Their output cannot exceed the supply rails, their inputs may accept only a limited voltage range, and fast signals may exceed their bandwidth or slew-rate capability. When solving a circuit, first identify the feedback path, then check the operating limits, write currents at the important node, and finally test whether the calculated output is physically possible.