Emitter degeneration

Emitter degeneration is adding an un-bypassed resistor $R_E$ in the emitter of a Common-emitter amplifier. It introduces Negative feedback, trading away gain for predictability, linearity, higher input resistance, and better bandwidth. The 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’s 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 insensitivity is the whole 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 $r_{\pi }+(\beta +1)R_E$), so 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.

To keep $R_E$ for DC bias stability while restoring the AC gain, a Bypass capacitor is placed across $R_E$ so it shorts at signal frequencies but is still present for DC.