Op-Amp Circuits

Applying the Golden Rules to Real Circuits

Now that you know the two golden rules (no input current, virtual short with negative feedback), you can analyse every standard op-amp configuration by writing KCL equations at the inverting input node. Each circuit below follows the same method.

Inverting Amplifier

The input signal goes to the inverting input through R_in. A feedback resistor R_f connects the output back to the inverting input. The non-inverting input is tied to ground. The gain is G = −R_f / R_in. The negative sign means the output is inverted (180° phase shift).

The input impedance equals R_in (relatively low compared to the non-inverting config). The inverting input is at virtual ground (0 V) because V⁺ = 0 V (Golden Rule), so current into R_in is V_in / R_in, and all of that current flows through R_f to the output.

Non-Inverting Amplifier

The input signal goes directly to the non-inverting input (V⁺). R_in goes from the inverting input to ground, and R_f goes from the inverting input to the output. The gain is G = 1 + R_f / R_in. Since there's no negative sign, the output is in phase with the input.

The input impedance is extremely high (the op-amp input itself), making this ideal when the source can't provide much current (e.g., sensors).

Voltage Follower (Buffer)

A special case of the non-inverting amplifier where R_f = 0 and R_in = ∞ (output connected directly to inverting input, no R_in to ground). Gain = 1 — the output exactly follows the input. Purpose: impedance buffering. The op-amp provides current drive that the source cannot.

• •Use case: placing between a high-impedance sensor (e.g., pH probe) and a low-impedance load (e.g., ADC input with capacitive filtering).
• •The buffer prevents the load from 'loading down' the source and distorting the signal.
• •It's one of the most practically useful op-amp circuits despite having no voltage gain.

Summing Amplifier

An extension of the inverting amplifier with multiple inputs, each through its own resistor (R_1, R_2, ...) feeding the same inverting node. The output is the inverted, weighted sum: V_out = −R_f × (V_1/R_1 + V_2/R_2 + ...). If all input resistors are equal, it simply adds the voltages.

• •Audio mixing — combine multiple audio signals with independent volume controls (change each input resistor).
• •Digital-to-analog conversion — sum weighted binary inputs (R, 2R, 4R, 8R) to produce an analog voltage.

Difference Amplifier

Amplifies the difference between two signals: V_out = (R_f / R_in) × (V_2 − V_1) when the four resistors are properly matched. This is essential for measuring signals in noisy environments — the common noise appears on both inputs and is cancelled out (common-mode rejection).

Practical Resistor Value Tips

• •Keep resistors in the 1 kΩ to 1 MΩ range. Too low = excessive current, too high = noise pickup.
• •Standard pairs: 10 kΩ / 100 kΩ (gain = 10), 10 kΩ / 10 kΩ (gain = 1 or 2).
• •Use 1% tolerance resistors for accurate gain.
• •The ratio R_f/R_in determines the gain — not the absolute values. 10 kΩ/1 kΩ and 100 kΩ/10 kΩ both give gain = 10.