Coupling capacitor

A coupling capacitor sits in series between two parts of a circuit so the AC signal passes through while the DC voltage on each side is blocked. Also called a DC-blocking capacitor; connecting two stages this way is AC coupling.

Why it is needed

Every transistor amplifier has to be biased: the transistor is held at a specific DC operating point (a particular DC voltage on its input terminal) so it sits in its active region and can amplify. Different stages, plus the input source and the load, all sit at different DC levels. Wire them together directly and the DC bias of one gets dragged off by the next, destroying the operating point you chose.

A coupling capacitor fixes this. From Capacitive reactance, a capacitor’s impedance is $Z_C=1/(j\omega C)$ with magnitude $X_C=1/(2\pi fC)$:

• To DC ($f=0$): $X_C\to \infty$. The capacitor is an open circuit. Each stage keeps its own DC bias; the DC levels never see each other.
• To the signal (frequencies of interest): if $C$ is large enough, $X_C$ is small compared with the surrounding resistance, so the AC signal passes through with negligible attenuation.

So the capacitor “couples” the signal from one stage to the next while DC-isolating their bias networks.

It is just an RC highpass filter

A coupling capacitor never sits alone. It works against the input resistance of the stage it feeds (and the output resistance of the stage driving it). That series-$C$, shunt-$R$ combination is exactly an RC highpass filter. Its Transfer function is

$H(j\omega )=\frac{j\omega RC}{1+j\omega RC}$

with the same Cutoff frequency

$f_c=\frac{1}{2\pi RC}$

where $R$ is the total resistance the capacitor works into. Below $f_c$ the signal is attenuated; above it the signal passes nearly unchanged. Being a highpass, the coupling capacitor sets the low-frequency end of an amplifier’s Amplifier frequency response. Size $C$ so $f_c$ falls comfortably below the lowest signal frequency you care about. For audio you want $f_c$ down around $20\text{Hz}$ or lower, so a larger $C$ is needed for a given $R$.

Contrast with a bypass capacitor

A coupling capacitor is in series with the signal path; its job is to pass AC and block DC between stages. A Bypass capacitor is in parallel (shunt), placed across a bias resistor to short it out for AC while leaving it in place for DC. Same frequency-dependent reactance, opposite topological roles: coupling caps connect signal through, bypass caps shunt signal around a resistor. A Common-source amplifier or Common-emitter amplifier usually has both, coupling caps at the input and output and a bypass cap across the source/emitter degeneration resistor.