Op-Amp Circuits — Basics

An op-amp circuit uses an operational amplifier plus feedback components to control how the output responds to the input. The main idea is simple: the bare amplifier has such large gain that the external circuit, especially the feedback network, is what makes the behavior predictable.

Most classroom formulas come from the ideal op-amp model. Those formulas are reliable only when the circuit has negative feedback and the output stays between the supply rails, so the op-amp remains in its linear region.

When The Ideal Op-Amp Rules Apply

For an ideal op-amp in linear operation with negative feedback, two shortcuts are used again and again:

1. The input currents are zero.
2. The input voltages are nearly equal, so $V_+ \approx V_-$.

The second rule is often called a virtual short. It does not mean the inputs are physically connected. It means feedback drives the output until the voltage difference between the inputs becomes very small.

If the op-amp is saturated or the circuit does not use negative feedback, you should not assume $V_+ \approx V_-$.

Inverting Amplifier Formula

In the standard inverting amplifier, the input signal goes through a resistor $R_{in}$ to the inverting terminal, the non-inverting terminal is tied to a reference such as ground, and a feedback resistor $R_f$ runs from the output back to the inverting terminal.

Under the ideal assumptions,

$$V_{out} = -\frac{R_f}{R_{in}} V_{in}$$

The minus sign means the output is inverted relative to the input.

Non-Inverting Amplifier Formula

In the standard non-inverting amplifier, the input signal is applied to the non-inverting terminal, and the inverting terminal sits inside a resistor feedback network.

Under the same ideal assumptions,

$$V_{out} = \left(1 + \frac{R_f}{R_g}\right) V_{in}$$

This version keeps the output in phase with the input and gives an input impedance that is ideally very large.

Why Negative Feedback Changes Everything

An op-amp has extremely large open-loop gain. Even a tiny difference between $V_+$ and $V_-$ tends to drive the output strongly toward one rail or the other.

Negative feedback tames that behavior. It feeds part of the output back into the input network, so the circuit settles at an output where the required input condition is satisfied. In these basic circuits, that is why resistor ratios usually set the closed-loop gain instead of the chip's raw internal gain.

Worked Example: Solve One Inverting Circuit

Suppose an ideal inverting amplifier has $R_{in} = 2 \, \mathrm{k\Omega}$ and $R_f = 10 \, \mathrm{k\Omega}$. The input voltage is $V_{in} = 0.30 \, \mathrm{V}$.

Use the inverting-amplifier formula:

$$V_{out} = -\frac{R_f}{R_{in}} V_{in}$$

Substitute the resistor values:

$$V_{out} = -\frac{10 \, \mathrm{k\Omega}}{2 \, \mathrm{k\Omega}}(0.30 \, \mathrm{V})$$ $$V_{out} = -(5)(0.30 \, \mathrm{V}) = -1.5 \, \mathrm{V}$$

So the predicted output is $-1.5 \, \mathrm{V}$. This is the right answer only if the power supply allows the output to swing to that value.

If the available supply rails cannot support $-1.5 \, \mathrm{V}$, the op-amp saturates and the simple gain formula no longer predicts the real output.

Common Op-Amp Mistakes

• Using $V_+ \approx V_-$ in any op-amp circuit, even when there is no negative feedback.
• Forgetting that the output cannot exceed the supply rails.
• Mixing up the inverting and non-inverting gain formulas.
• Ignoring the sign of the output in the inverting amplifier.
• Treating ideal rules as exact descriptions of every real op-amp at every frequency and output level.

Where Op-Amp Circuits Show Up

Basic op-amp circuits appear in sensor conditioning, audio preamplifiers, active filters, voltage followers, and measurement systems. They are widely used because one amplifier plus a few passive components can provide gain, buffering, or filtering in a predictable way.

The ideal model is usually the first step. More detailed analysis matters when bandwidth, slew rate, input bias current, offset voltage, noise, or output swing limits become important.

Try A Similar Problem

Keep the same inverting amplifier, but change the feedback resistor to $20 \, \mathrm{k\Omega}$. The magnitude of the closed-loop gain doubles, so the predicted output becomes $-3.0 \, \mathrm{V}$ if the op-amp can still stay in its linear region. If you want to solve a similar circuit from scratch, try your own version with a different resistor ratio and check first whether the rail limits still allow the result.