If the emitter resistance in a common-emitter voltage amplifier is not bypassed, it will

Understanding the role of emitter resistance in a common-emitter (CE) voltage amplifier is crucial for analyzing its performance. The question asks about the consequences if the emitter resistance is not bypassed by a capacitor.

Common-Emitter Amplifier Fundamentals

A common-emitter amplifier is a popular type of BJT (Bipolar Junction Transistor) amplifier known for its voltage gain and current gain. It's widely used in many electronic circuits. In this configuration, the emitter terminal is common to both the input and output signal paths (or connected to ground via a resistor).

Emitter Resistance and Bypassing Explained

Emitter resistance (${\text{R}}_{\text{E}}$) is typically included in the emitter path of a common-emitter amplifier for several reasons, primarily to improve bias stability and linearity. However, this resistance also affects the AC performance of the amplifier.

- **Purpose of ${\text{R}}_{\text{E}}$:** It provides negative feedback for DC stability, helping to stabilize the operating point (Q-point) against variations in transistor parameters (like $\beta$) and temperature.
- **Bypassing ${\text{R}}_{\text{E}}$:** To prevent ${\text{R}}_{\text{E}}$ from reducing the AC voltage gain, a large capacitor, known as the bypass capacitor (${\text{C}}_{\text{E}}$), is usually connected in parallel with ${\text{R}}_{\text{E}}$. For AC signals, this capacitor acts as a short circuit, effectively "bypassing" ${\text{R}}_{\text{E}}$ and preventing the AC signal from developing across it. This ensures that the AC voltage gain remains high.

Impact of Unbypassed Emitter Resistance

When the emitter resistance (${\text{R}}_{\text{E}}$) is not bypassed by a capacitor, it remains in the AC signal path. This introduces a specific type of negative feedback, often called "emitter degeneration," which significantly alters the amplifier's characteristics.

Voltage Gain Reduction

The primary effect of an unbypassed emitter resistance is a significant reduction in voltage gain. Here's why:

- When an input AC signal is applied to the base, it causes a change in collector current. This change in collector current also flows through the emitter resistance ${\text{R}}_{\text{E}}$.
- As current flows through ${\text{R}}_{\text{E}}$, an AC voltage develops across it. This voltage across ${\text{R}}_{\text{E}}$ is in phase with the input voltage at the base.
- This voltage effectively reduces the AC voltage between the base and emitter (${\text{V}}_{\text{BE}}$), which is the actual input to the transistor's intrinsic amplifier action. This is a form of negative feedback.

Mathematically, the approximate AC voltage gain (${\text{A}}_{\text{v}}$) for a common-emitter amplifier with an unbypassed emitter resistance is given by:

$${\text{A}}_{\text{v}}\approx -\frac{{\text{R}}_{\text{C}}\parallel {\text{R}}_{\text{L}}}{{\text{r}}_{\text{e}}^{\prime }+{\text{R}}_{\text{E}}}$$

Where ${\text{R}}_{\text{C}}$ is the collector resistance, ${\text{R}}_{\text{L}}$ is the load resistance, ${\text{r}}_{\text{e}}^{\prime }$ is the intrinsic AC emitter resistance of the transistor, and ${\text{R}}_{\text{E}}$ is the unbypassed emitter resistance.

In contrast, if ${\text{R}}_{\text{E}}$ were bypassed, the gain would be approximately:

$${\text{A}}_{\text{v}}\approx -\frac{{\text{R}}_{\text{C}}\parallel {\text{R}}_{\text{L}}}{{\text{r}}_{\text{e}}^{\prime }}$$

Since ${\text{r}}_{\text{e}}^{\prime }+{\text{R}}_{\text{E}}$ is greater than ${\text{r}}_{\text{e}}^{\prime }$, the magnitude of the voltage gain is clearly reduced when ${\text{R}}_{\text{E}}$ is not bypassed. This reduction in gain also leads to improved linearity and increased bandwidth.

Input Impedance Increase

Another significant effect of an unbypassed emitter resistance is an increase in the input impedance of the amplifier when viewed from the base terminal. Here's the explanation:

- The negative feedback introduced by ${\text{R}}_{\text{E}}$ effectively makes the transistor "appear" to have a higher input resistance.

The input impedance looking into the base (${\text{Z}}_{\text{in(base)}}$) for a common-emitter amplifier with an unbypassed emitter resistance is approximately:

$${\text{Z}}_{\text{in(base)}}\approx \beta ({\text{r}}_{\text{e}}^{\prime }+{\text{R}}_{\text{E}})$$

Where $\beta$ is the current gain of the transistor.

If ${\text{R}}_{\text{E}}$ were bypassed, the input impedance would be approximately:

$${\text{Z}}_{\text{in(base)}}\approx \beta {\text{r}}_{\text{e}}^{\prime }$$

Because ${\text{R}}_{\text{E}}$ is positive, $\beta ({\text{r}}_{\text{e}}^{\prime }+{\text{R}}_{\text{E}})$ will be greater than $\beta {\text{r}}_{\text{e}}^{\prime }$, indicating an increase in input impedance. A higher input impedance is often desirable as it reduces loading effects on the previous stage.

Unbypassed Emitter Resistance Effects Summary

The table below summarizes the changes in a common-emitter amplifier's characteristics when the emitter resistance is not bypassed:Therefore, when the emitter resistance in a common-emitter voltage amplifier is not bypassed, it will reduce the voltage gain and increase the input impedance.