27.4. Impact of Emitter Resistor on Gain

So, as a result if I say that what is the gain of this circuit starting from primary source to the primary output, we can say the voltage gain A = − g × R / (1 + g × R ).

This statement introduces the concept of voltage gain (A) in an amplifier circuit. The formula shows that the gain is determined by the transconductance (g) of the amplifier and the load resistance (R) in the circuit. The gain will vary based on the combination of these parameters, and the negative sign indicates phase inversion, which is common in common emitter configurations.

Think of the voltage gain as a water hose. The water pressure is equivalent to the input voltage, and the hose's resistance represents the load. If you increase the hose's diameter (analogous to increasing R), more water can flow, meaning a higher gain. However, there’s a point where the hose also starts to create more turbulence, which represents the (1 + g × R) in the denominator, making it less efficient.

In fact, the main motivation of putting this R_E, it is to stabilize the operating point of the circuit in case if beta is changing.

The emitter resistor (R_E) plays a crucial role in stabilizing the operating point of an amplifier, which refers to the steady state of the amplifier’s output when there is no input signal. This is important because the current gain (beta) of transistors can vary due to different factors, including temperature. By introducing R_E, the effect of varying beta on the circuit's performance is diminished, resulting in a more reliable operation.

Imagine driving a car on a road that has bumps (which represent beta variations). If you have good suspension (like R_E in the circuit), your ride remains smooth regardless of the road conditions. Without good suspension, your car could bounce around a lot, making it hard to control, just like how the circuit's performance could degrade without the emitter resistor.

However unfortunately, this is also desensitizing this circuit against input signal and as a result it is making the gain much smaller than whatever the original gain of the CE amplifier potentially can provide.

While the emitter resistor provides stability against variations in beta, it has the downside of reducing the overall gain of the amplifier. This means that while the amplifier is working more reliably, it may not amplify signals as effectively as it could without the resistor. This trade-off must be considered in circuit design, as stability and gain need to be balanced.

Think of a sponge soaking up water. If the sponge is too big, it can absorb more water (higher gain), but it might weigh too much to lift easily (stability). By adding a smaller resistor (like a smaller sponge), you may make it easier to lift (stable operation) but at the cost of soaking up less water (lower gain).

So; obviously, this is not acceptable particularly if R_E is significant and this multiplying factor will be quite large.

As the resistance value (R_E) increases, the negative impact on voltage gain becomes more pronounced. Designers must take care to select appropriate values for R_E to maintain a balance between stability and amplification. If R_E is too high, the gain can drop significantly, possibly below usable levels, thus limiting effectiveness for real-world applications.

Consider balancing a seesaw. On one side, you may have weights representing gain (heavy side), and on the other side, stability (lighter side). If you add too much weight for stability, the seesaw tilts too much towards stability (lower gain), making it ineffective for play. The right combination allows for a functional seesaw where both sides can be used properly.

So, we can put a capacitor here and this capacitor will not be interfering the DC operating point, but then for ac signal this will be making this ground.

To address the gain reduction due to the emitter resistor, designers can use a bypass capacitor. This component allows AC signals to effectively bypass R_E, restoring the gain for alternating currents while keeping the DC operating point stable. In essence, the capacitor acts as a short for AC signals, maintaining the benefits of the resistor while avoiding its drawbacks for signal amplification.

Think of a water valve that can be turned down to allow for a steady flow of water (DC operating point) but has an emergency bypass (capacitor) that helps during a surge (AC signals). When there's too much pressure (AC signals), the bypass opens, preventing overflow while ensuring normal flow continues steadily without an interruption.

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