Difference Amplifier Subtracts First - Electronic Circuits V & VI: Front-End Conditioning and Op-Amp Feedback Step by Step

A balanced difference amplifier subtracts one input from the other and scales the result by a matched resistor ratio, rejecting any signal common to both inputs. The matched ratios of 2 give 2 times (6 V minus 3 V) equals 6 V exactly for the ideal op-amp model; real stages add resistor mismatch, common-mode error, input offset, finite open-loop gain and bandwidth, rail limits, source impedance, loading, and measurement uncertainty.

A balanced difference amplifier subtracts two inputs and applies an exact resistor ratio. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The resistor ratios are matched

Both resistor ratios are 2, so the difference network is balanced.

\frac{R_f}{R_{\text{in}}} = \frac{R_{\text{bottom}}}{R_{\text{top}}} = 2

Subtract first, then multiply

The inputs differ by 3 volts, and ratio 2 gives 6 volts.

V_{\text{out}} = 2\cdot(6\ \text{V}-\left(3\ \text{V}\right)) = 6\ \text{V}