Inverting Feedback Ratios

Changing Feedback Ratio Changes Gain

exact fractional current

This changing-feedback-ratio-changes-gain lesson keeps the input current fixed and changes the feedback resistor to change the inverting gain. The 1 V over 2 ohm input gives 1/2 A, and 8 ohm feedback gives -4 V exactly only for the stated ideal op-amp row. Real implementations add resistor tolerances, finite gain, offset, bias current, bandwidth and slew limits, rail limits, finite precision, and measurement uncertainty.

Changing the feedback resistor changes the exact inverting gain. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A fraction current stays exact

The 1 volt input across 2 ohms gives one half ampere.

I=12 AI = \tfrac{1}{2}\ \text{A}
Fraction currentThe exact one-half ampere current is pinned.+-op amprails -12 V to 12 VVout -4 VV+ 0 VV- 0 VI+ 0 AI- 0 ARin 2 ohmIin 1/2 ARf 8 ohmIf 1/2 AV+ = V-inverting

Changing only the feedback ratio changes gain

With 8 ohms in feedback, the output is -4 volts.

Vout=−(12 A)⋅8 ohm=−4 VV_{\text{out}} = -\left(\tfrac{1}{2}\ \text{A}\right)\cdot 8\ \text{ohm} = -4\ \text{V}
Changed feedback ratioOnly the resistor ratio changed.+-op amprails -12 V to 12 VVout -4 VV+ 0 VV- 0 VI+ 0 AI- 0 ARin 2 ohmIin 1/2 ARf 8 ohmIf 1/2 AV+ = V-inverting