Editing Common emitter (section)

== Characteristics ==
At low frequencies and using a simplified [[hybrid-pi model]], the following [[small-signal model|small-signal]] characteristics can be derived.

<div align="center">
{| class="wikitable" style="text-align:center;"
! rowspan=2 |
! rowspan=2 | Definition
! colspan=2 | Expression
|-
! With emitter <br />degeneration
! Without emitter <br />degeneration; i.e., ''R''<sub>E</sub> = 0
|-
! '''[[gain (electronics)#Current gain|Current gain]]'''
| <math>A_\text{i} \triangleq \frac{i_\text{out}}{i_\text{in}} \,</math>
| <math>\beta \,</math>
| <math>\beta </math>
|-
! '''[[gain (electronics)#Voltage gain|Voltage gain]]'''
| <math>A_\text{v} \triangleq \frac{v_\text{out}}{v_\text{in}} \,</math>
| <math>-\frac{ \beta R_\text{C} }{ r_\pi + (\beta + 1) R_\text{E} }\,</math>
| <math>-g_m R_\text{C}</math>
|-
! '''[[Input impedance]]'''
| <math>r_\text{in} \triangleq \frac{v_\text{in}}{i_\text{in}}\,</math>
| <math>r_\pi + (\beta + 1) R_\text{E}\,</math>
| <math>r_\pi</math>
|-
! '''[[Output impedance]]'''
| <math>r_\text{out} \triangleq \frac{v_\text{out}}{i_\text{out}}\,</math>
| <math>R_\text{C}\,</math>
| <math>R_\text{C}</math>
|}
</div>

If the emitter degeneration resistor is not present, then <math>R_\text{E} = 0\,\Omega</math>, and the expressions effectively simplify to the ones given by the rightmost column (note that the voltage gain is an ideal value; the actual gain is somewhat unpredictable). As expected, when ''<math>R_\text{E}\,</math>'' is increased, the input impedance is increased and the voltage gain <math>A_\text{v}\,</math> is reduced.

===Bandwidth===
The bandwidth of the common-emitter amplifier tends to be low due to high capacitance resulting from the [[Miller effect]]. The [[parasitic capacitance|parasitic]] base-collector capacitance <math>C_{\text{CB}}\,</math> appears like a larger parasitic capacitor <math>C_\text{CB} (1 - A_\text{v})\,</math> (where <math>A_\text{v}\,</math> is negative) from the base to [[ground (electricity)|ground]].<ref name="TAoE">{{cite book
 |author=[[Paul Horowitz]] and [[Winfield Hill]]
 |title=[[The Art of Electronics]]
 |edition=2nd
 |year=1989
 |pages=[https://archive.org/details/artofelectronics00horo/page/102 102–104]
 |publisher=Cambridge University Press
 |isbn=978-0-521-37095-0
}}</ref> This large capacitor greatly decreases the bandwidth of the amplifier as it makes the [[time constant]] of the parasitic input [[RC circuit|RC filter]] <math>r_\text{s} (1 - A_\text{V}) C_\text{CB}\,</math> where <math>r_\text{s}\,</math> is the [[output impedance]] of the signal source connected to the ideal base.

The problem can be mitigated in several ways, including:
* Reduction of the voltage gain [[Magnitude (mathematics)|magnitude]] <math>\left|A_\text{v}\right|\,</math> (e.g., by using emitter degeneration).
* Reduction of the [[output impedance]] <math>r_\text{s}\,</math> of the signal source connected to the base (e.g., by using an [[emitter follower]] or some other [[voltage follower]]).
* Using a [[cascode]] configuration, which inserts a low input impedance current buffer (e.g. a [[common base]] amplifier) between the transistor's collector and the load. This configuration holds the transistor's collector voltage roughly constant, thus making the base to collector gain zero and hence (ideally) removing the Miller effect.
* Using a [[differential amplifier]] [[topology (electronics)|topology]] like an [[emitter follower]] driving a grounded-base amplifier; as long as the emitter follower is truly a [[common collector|common-collector amplifier]], the Miller effect is removed.

The [[Miller effect]] negatively affects the performance of the common source amplifier in the same way (and has similar solutions). When an AC signal is applied to the transistor amplifier it causes the base voltage VB to fluctuate in value at the AC signal. The positive half of the applied signal will cause an increase in the value of VB this turn will increase the base current IB and cause a corresponding increase in emitter current IE and collector current IC. As a result, the collector emitter voltage will be reduced because of the increase voltage drop across RL. The negative alternation of an AC signal will cause a decrease in IB this action then causes a corresponding decrease in IE through RL.

It is also named common-emitter amplifier because the emitter of the transistor is common to both the input circuit and output circuit. The input signal is applied across the ground and the base circuit of the transistor. The output signal appears across ground and the collector of the transistor. Since the emitter is connected to the ground, it is common to signals, input and output.

The common-emitter circuit is the most widely used of junction transistor amplifiers. As compared with the common-base connection, it has higher input impedance and lower output impedance. A single power supply is easily used for biasing. In addition, higher voltage and power gains are usually obtained for common-emitter (CE) operation.

Current gain in the common emitter circuit is obtained from the base and the collector circuit currents. Because a very small change in base current produces a large change in collector current, the current gain (β) is always greater than unity for the common-emitter circuit, a typical value is about 50.