Op-Amp Fundamentals: Inverting and Non-Inverting Amplifiers

The two ideal-op-amp rules

An op-amp has two inputs, $V_+$ and $V_-$, and (with negative feedback) two assumptions make circuit analysis almost algebra-free:

• No current flows into either input terminal (infinite input impedance).
• The op-amp drives its output to force $V_+ = V_-$, the virtual short, even though the two inputs aren't actually connected.

Inverting amplifier

The input signal drives $R_{in}$ into the $V_-$ terminal, with a feedback resistor $R_f$ from output back to that same terminal, while $V_+$ is grounded. Since $V_-$ is forced to $0$V (a "virtual ground") and no current enters the input, the current through $R_{in}$ must equal the current through $R_f$, giving:

Worked example: $R_{in}=1\text{k}\Omega$, $R_f=10\text{k}\Omega$, $V_{in}=0.5\text{V}$:

Non-inverting amplifier

The input signal now drives $V_+$ directly, and $R_1$ plus $R_f$ form a voltage divider from output back to $V_-$, forcing $V_- = V_{in}$ by the virtual-short rule:

always positive (no inversion) and always at least 1, even if $R_f=0$.

Worked example: $R_1=1\text{k}\Omega$, $R_f=9\text{k}\Omega$, $V_{in}=0.5\text{V}$:

Same resistor ratio magnitude as the inverting example above, but the output here is positive and one unit of gain higher, a direct consequence of the $+1$ in the formula.