27.2.2. Parameters of Voltage Amplifier

So, the output voltage as I said that output voltage, it is this one. So, v = – g × R × v.

Now, this v of course, it is function of v, but we need to find what is the exact expression of that.

So, we may say that v equals to divided by 1 + g × R.

The voltage gain (A) of a circuit is a key parameter. In this case, the relationship is given as v (output voltage) is equal to negative gain times the resistance (R) of the circuit times the input voltage (v). The main focus is on expressing this gain accurately and understanding how input voltage affects output voltage. The formula v = -g × R × v/ (1 + g × R) shows how gain relates to the resistance and how it can be affected by other circuit parameters.

Think of a microphone connected to a speaker. The microphone picks up sound (input voltage) and converts it into an electrical signal, which is then amplified by the circuit (the ‘gain’). The louder you speak (increase input voltage), the louder the sound from the speaker (output voltage). However, if the speaker has a lot of resistance (R), it can reduce the overall volume, similar to how a gain expression shows diminishing returns based on resistance.

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

The emitter resistor (R_E) serves an essential role in stabilizing the circuit against variations in beta (which defines current gain). While this stabilization is beneficial for consistent performance, it has a downside: it reduces the overall gain of the amplifier. The trade-off presents a challenge where the necessary stability degrades the circuit's ability to amplify signals significantly.

Imagine you're trying to stabilize a plank on a shaky table. If you place something heavy on the plank to hold it down, it stabilizes it (just like R_E) but also makes it harder to move (reducing gain). In contrast, if you don't apply any weight, the plank wobbles a lot (unstable beta) but might move more freely when you try to use it. Balancing stability and responsiveness is key in both scenarios.

Apart from the voltage gain, open loop voltage gain, we do have two more important parameters namely input resistance and output resistance of the model. ... . So, while we will be talking about input resistance, we may consider this R_BB, but while here we are deriving this voltage gain A, we have ignored it.

In addition to voltage gain, two more essential parameters are input resistance and output resistance. Input resistance indicates how much the input signal voltage will drop when fed into the amplifier due to loading effects. Output resistance defines how much the circuit can provide the needed current for the load connected. When deriving voltage gain, some components may be ignored for simplification, particularly when they do not significantly contribute to the main behavior of the circuit during the analysis.

Consider a garden hose. The thickness of the hose (input resistance) influences how much pressure is lost when water flows through (input signal). The faucet at the end (output resistance) determines how strong and consistent the water flow is when you turn it on. Just as different hoses and faucets interact differently, various circuit components shape the behavior of voltage amplifiers.

What we have said that we are placing this emitter resistor to make the circuits operating point desensitized against beta variation, but it is making the gain also dropping to a smaller value namley what we say it is that g × R_m C / (1+g × R_E).

Finding the output resistance involves a method of connecting a signal source and measuring the current flow. When determining the output resistance, the circuit's configuration, including the emitter resistor's effects, needs to be factored in since it influences both stability and overall gain. The resulting output resistance formula indicates how it can be uniquely determined based on the existing components in the circuit.

Think of adjusting a fire hose's nozzle. Changing the nozzle affects how the water (current) flows out (output resistance), just as different configurations in circuits affect amplifier outputs. If you place a stronger nozzle (emitter resistor) at the end, it can stabilize the flow but also limit how fast the water exits, similar to how output resistance shapes circuit performance.

So, as a result we can put a capacitor here and so the what you are looking for is basically this capacitor, it will not be interfering the dc operating point, but then for ac signal this will be making this ground.

In practical circuits, manipulating AC and DC operations requires a strategy to avoid conflicts between stabilization needs and performance. A capacitor can be employed to ground the AC signal, which allows the amplifier to operate seamlessly without interference by keeping the circuit stable under DC conditions. This clever design allows both steady operation for DC while maintaining responsiveness to AC signals.

Imagine using an elevator that has a heavy counterweight (DC stability) to ensure it can carry passengers efficiently (AC performance). This clever mechanism ensures that the elevator is stable while still able to respond quickly when people enter or leave. Capacitors in a circuit achieve a similar balance between voltage gain and stability.

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