Emitter degeneration

Emitter degeneration is adding an un-bypassed resistor $R_E$ in the emitter of a Common-emitter amplifier. It introduces Negative feedback, deliberately trading away gain in exchange for predictability, linearity, higher input resistance, and better bandwidth. It is the exact BJT analogue of Source degeneration in a MOSFET.

The feedback mechanism

Without $R_E$ the emitter is at AC ground and the full input appears as $v_{be}$. Add $R_E$: now a rise in collector current $i_c$ also raises the emitter voltage by $i_e{R}_E\approx i_c{R}_E$. That rise subtracts from the input, so the effective base–emitter signal is reduced — the output opposes the change that caused it. That is series–series negative feedback. The collector current is now set largely by $R_E$, not by the touchy device parameters.

$R_E$ provides negative feedback: gain is reduced by the factor $(1+g_m{R}_E)$, but the amplifier becomes much more predictable and linear.

Gain

Working through the BJT T-model from the emitter loop, the collector current is set by $v_{in}$ across $(r_e+R_E)$, and $v_{out}=-\alpha i_e(R_C\parallel R_L)$:

$A_v=-\frac{\alpha (R_C\parallel R_L)}{r_e+R_E}\approx -\frac{R_C}{r_e+R_E}\approx -\frac{R_C}{R_E}\text{for }{R}_E\gg r_e$

Equivalently, in terms of the un-degenerated gain $-g_m{R}_C$, degeneration divides it by $(1+g_m{R}_E)$:

$A_v=-\frac{g_m{R}_C}{1+g_m{R}_E}$

(These agree: $g_m{R}_C/(1+g_m{R}_E)=R_C/(1/g_m+R_E)=R_C/(r_e+R_E)$ since $r_e\approx 1/g_m$.) When $g_m{R}_E\gg 1$ the gain collapses to $-R_C/R_E$ — set purely by a resistor ratio, independent of the process- and temperature-dependent $g_m$, $\beta$, $I_C$. That robustness is the entire point.

Detailed analysis of CE with an emitter resistor: the feedback action and the input-impedance increase from $R_E$.

Input resistance and the rest of the trade-off

The un-bypassed $R_E$ raises the input resistance via the Resistance reflection rule — a resistor in the emitter is seen from the base as $(\beta +1)$ times larger:

$R_{in}=r_{\pi }+(\beta +1)R_E=(\beta +1)(r_e+R_E)$

The output resistance looking into the collector stays $\approx R_C$. The four effects of adding $R_E$:

1. $R_{in}$ increases by the factor $(1+g_m{R}_E)$ (to $r_{\pi }+(\beta +1)R_E$) — less loading of the source.
2. $|A_v|$ decreases by the same factor — the price paid.
3. Gain depends much less on $\beta$ — it’s now $\approx R_C/R_E$, two resistors you control, not a sloppy device parameter.
4. Frequency response improves — negative feedback widens the bandwidth (lower Miller effect sensitivity, flatter response).

Effects of $R_E$: $R_{in}$ up, $|A_v|$ down by the same factor, less β-dependence, better frequency response.

T-model analysis: $A_v=-\alpha (R_C\parallel R_L)/(r_e+R_E)$, $R_{in}=(\beta +1)(r_e+R_E)$, $R_o=R_C$.

Negative feedback trades gain for performance — the recurring design philosophy.

To keep $R_E$ for DC bias stability while restoring the AC gain, a Bypass capacitor is placed across $R_E$ so it is a short at signal frequencies but still present for DC — see Discrete-circuit BJT amplifier.