Input and output resistance (amplifier)

The input resistance $R_{in}$ is the resistance seen looking into the amplifier’s input by the driving source. The output resistance $R_{out}$ is the resistance seen looking back into its output by the load. These two numbers decide how much signal actually makes it through once real sources and loads are connected, and they’re why a “high-gain” amplifier can still deliver almost nothing.

Why they matter: loading via voltage division

No real source is ideal. Model it as a voltage $v_{sig}$ behind a source resistance $R_{sig}$. When it drives an amplifier of input resistance $R_{in}$, those two form a Voltage divider, so the voltage that actually reaches the amplifier input is

$v_{in}=v_{sig}\frac{R_{in}}{R_{in}+R_{sig}}$

If $R_{in}\ll R_{sig}$, most of the signal drops across $R_{sig}$ before it ever enters the amplifier (input loading). Only when $R_{in}\gg R_{sig}$ does the amplifier see essentially the full source voltage.

The same thing happens at the output. The amplifier behaves as an internal voltage $A_v{v}_{in}$ behind its output resistance $R_{out}$; driving a load $R_L$ forms another divider:

$v_{out}=A_v{v}_{in}\frac{R_L}{R_L+R_{out}}$

If $R_{out}\gg R_L$, the gain collapses at the load (output loading). Only when $R_{out}\ll R_L$ does the load get the full amplified voltage.

The ideal: high $R_{in}$, low $R_{out}$

The actual end-to-end gain is the intrinsic $A_v$ times two attenuation factors, one at each port. To lose as little as possible you want $R_{in}$ large (don’t load the source) and $R_{out}$ small (don’t lose voltage to the load). That’s why the Source follower and the op-amp-style Buffer amplifier earn their keep despite a gain of only ~1: near-infinite $R_{in}$ and very low $R_{out}$ let them sit between a weak source and a heavy load and pass the signal through without the loading losses.

Values per MOSFET configuration

The three single-MOSFET stages span the whole spread:

• Common-source amplifier: $R_{in}\to \infty$ (insulated gate), $R_{out}=R_D\parallel r_o$ (moderate). High voltage gain.
• Common-gate amplifier: $R_{in}=1/g_m$ (low, a few hundred ohms), $R_{out}$ high. A current buffer.
• Source follower: $R_{in}\to \infty$, $R_{out}=1/g_m$ (low). A voltage buffer.

where $g_m$ is the MOSFET transconductance, $R_D$ the drain resistor, and $r_o$ the MOSFET output resistance. Picking a configuration is mostly picking the input/output resistance profile the source and load demand.