Input and output resistance (amplifier)

The input resistance $R_{in}$ of an amplifier is the resistance seen looking into its 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 when real sources and real loads are connected — they are 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 is lost 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 $R_{out}$

Putting both together, the actual end-to-end gain is the intrinsic $A_v$ multiplied by 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). This is exactly why the Source follower and the op-amp-style Buffer amplifier are so useful despite a gain of only ~1: they have near-infinite $R_{in}$ and very low $R_{out}$, so they can 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 illustrate 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. Choosing a configuration is largely choosing the input/output resistance profile you need for the source and load you actually have.