= Loaded voltage gain
{title2=$A_v(Z_L)$}
\b[Loaded <voltage gain>] is the ratio of an amplifier's output to input signal <electric potential differences> with a specified load connected. In a small-signal model, let the open-circuit output be $v_{\rm oc}=A_0v_{\rm in}$ and let the complete amplifier have <output impedance> $Z_o$. A load $Z_L$ then gives
$$
A_v(Z_L)=\frac{v_{\rm out}}{v_{\rm in}}=A_0\frac{Z_L}{Z_o+Z_L}.
$$
This is the <voltage divider> result from <Thévenin's theorem> at the output terminals. The university source explains why a linear circuit can be replaced at specified terminals by a source and series impedance.<Thevenin and Norton Equivalents, University of Houston teaching notes>[pp. 1–2, The Idea and Important Notes]{ref} The <output impedance> used here must describe the complete amplifier at the stated <operating point> and frequency, including its feedback.
The input terminal matters too. For a generator $v_s$ with source impedance $Z_s$ driving amplifier <input impedance> $Z_i$, the corresponding source-to-load ratio in a unilateral model is
$$
\frac{v_{\rm out}}{v_s}=A_0\frac{Z_i}{Z_s+Z_i}\frac{Z_L}{Z_o+Z_L}.
$$
This includes both input and output loading; it differs from the terminal-to-terminal <voltage gain> defined above.
For an original resistive example, choose $A_0=12$, $Z_o=100\,\Omega$, $Z_L=900\,\Omega$, $Z_i=1\,\mathrm{k\Omega}$ and $Z_s=50\,\Omega$. The loaded terminal gain is $10.8$, while the source-to-load gain is $72/7\approx10.286$. Reducing the load to $100\,\Omega$ makes the terminal gain six, even though the stipulated open-circuit gain remains twelve. These are model parameters, not device specifications.
A direct test holds the actual amplifier input signal fixed, changes a known load and measures the output with an <oscilloscope> whose probe impedance is included in the effective load. Use small enough signals to retain linear operation and respect the <amplifier output range>. If the output-to-input ratio changes with loading, an unloaded gain alone is insufficient to predict the circuit's behavior.
At nonzero frequency the impedances and gain can be complex. A <reactive-load phase shift in a finite-output-impedance amplifier> can change both magnitude and phase, while input-output coupling or nonlinear current limiting can invalidate this simple unilateral divider model. The ideal feedback resistance-ratio examples in the manufacturer's introduction apply within their corresponding operating assumptions.<Op-Amps, Comparator Circuit by Renesas>[Op-Amp Basics (1) and (2), Figures 2–3 and resistance-ratio gains]{ref}
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