27.5. Solutions to Gain Issues

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 ). So, this is one important parameter of the voltage amplifier out of this circuit.

The voltage gain (A) of the circuit is derived from its output voltage and is represented by the formula A = − g × R / (1 + g × R ). Here, 'g' is the transconductance and 'R' is the resistance at the emitter. This gain tells us how much the input signal is amplified when it goes through the circuit. A key point to remember is that the negative sign indicates a phase inversion, typical in common emitter amplifiers.

Think of voltage gain like a megaphone amplifying your voice. If you speak softly (the input signal), the megaphone (the amplifier) increases your volume (the output). The ratio of your voice's amplification can be likened to the gain expressed by the formula, where adjustments in the megaphone's settings (the components in the circuit) determine how loud you can speak.

In fact, a main motivation of putting this R E is to stabilize the operating point of the circuit in case if beta is changing. However, 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.

The emitter resistance (R E) is critical for stabilizing the operating point of the circuit. As the current gain (beta) fluctuates, having R E helps to keep the circuit functioning effectively. However, it can also reduce the overall gain of the amplifier because it lowers the effective voltage that can be used for amplification. This means while the circuit is more stable, it may not amplify signals as well as it could without R E.

Imagine a bicycle with training wheels. The training wheels provide stability (like R E stabilizing the operating point), making it easier to ride without falling. Yet, the training wheels also limit how fast you can go and how agile you can be (similar to how R E reduces the gain). So, you have to weigh the need for stability against the desire for speed or agility.

So, what we say that how do you get back gain of the circuit. So, as you can discuss before in that whenever we are feeding the signal here say, v significant part of that voltage it is getting dropped across this one. If we make this voltage whatever the emitter voltage; if we make 0, then we can then force this v to be equal to v.

To recover the loss in gain that comes from the presence of the emitter resistor (R E), we can apply a capacitor in parallel with the emitter. This capacitor allows AC signals to ground while maintaining the DC voltage at the emitter, effectively nullifying the impact of R E for AC signals. This enables the circuit to function well for audio signals (small AC inputs) while retaining stability for DC.

Consider a water pipeline with a valve (R E). If the valve is partially closed, water pressure (gain) drops. However, if we put a bypass (capacitor) around the valve that only allows water to flow during peak demands (AC signals), we can maintain pressure for high flow while still controlling the overall flow when needed. This way, we retain both stability and performance.

Typically to satisfy this condition what we said is that R BB should be ≤ (1+β) / 10 × R E to get this approximation valid. So, this is what the practical design guidelines we follow for this circuit.

In real-world designs, to ensure that R BB (the base resistor) does not interfere with the gain recovery, it should generally be set to less than or equal to one-tenth of (1 + β) times R E. This guideline helps maintain a balance between stable operation and sufficient gain, ensuring the amplifier circuit performs as expected under varying conditions.

Think of this design rule like a recipe for baking a cake. If you use the wrong proportions of flour (R BB) to sugar (R E), your cake may not rise properly and could collapse (loss of gain). Following the recipe's guidelines ensures a consistent and successful bake every time, just as adhering to these electrical design principles ensures a well-functioning amplifier.

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