27.7. Lower Cutoff Frequency Consideration

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).

In this chunk, we are deriving the expression for the voltage gain (A) of the circuit, which is calculated using the formula A = − g × R / (1 + g × R). Here, g represents the transconductance of the transistor and R is the load resistance. This expression allows us to understand how the gain is influenced by the values of g and R. We note that as the value of the emitter resistance (RE) increases, the gain decreases due to the additional term in the denominator, which represents the voltage drop across RE.

Think of an amplifier like a water faucet. The water flow (output voltage) is affected by how much pressure (gain) you have, which is similar to how the voltage gain depends on the resistance and transconductance. If a resistor (like RE) is added to restrict the flow, less water will come out, just as a higher emitter resistance reduces the voltage gain of the amplifier.

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.

Here, we explain why the emitter resistor (RE) is important in the circuit—it provides stability for the operating point despite variations in the transistor's beta (β), which represents the current gain of a transistor. Without RE, changes in β could lead to significant variations in the amplifier’s performance, which could destabilize the output. Therefore, while RE lowers gain, it provides a beneficial trade-off by stabilizing performance.

Consider RE as the ballast in a hot air balloon. If the temperature changes (analogous to beta variation), the ballast helps keep the balloon at a stable altitude. This stability is necessary to ensure a smooth ride, just like how RE stabilizes the circuit's operating point despite changes in beta.

So, we need to be careful that now while you are picking this R, we need to satisfy this condition to make sure that circuit is remaining insensitive to β variation. But at the same time, the lower cutoff frequency to keep it low the value of this R should not be very small.

In this chunk, the focus is on the relationship between the emitter resistor (RE) value and the lower cutoff frequency of the amplifier. When designing an amplifier, it’s important to ensure that RE is not too small, as this would affect the lower cutoff frequency negatively. The cutoff frequency is essential because it defines the lowest frequency at which the amplifier operates effectively. If RE is too low, it could lead to a high cutoff frequency, which may limit the amplifier's ability to amplify lower frequencies. Therefore, an optimal balance must be found when choosing RE.

Imagine tuning a musical instrument, like a guitar. The strings need to have the right tension (analogous to RE) to produce the correct notes (frequencies). If the strings are too loose (lower resistance), they might not play the lower notes well - just like a poorly chosen RE can affect the amplifier's ability to handle low frequencies.

So, the practical design guidelines we follow for this circuit are that the smaller this resistance is better. So, can I make this resistance really small or is there any trade off.

This chunk discusses the practical design guidelines concerning the emitter resistor. While a smaller resistance is generally preferable for improved performance, it can lead to challenges such as increased power dissipation, which can be detrimental to the circuit. Designers must consider these trade-offs; while aiming for low values to achieve low cutoff frequencies, they must also account for the power draw and the risk of overheating the circuit.

It’s like trying to save on fuel (making resistance small) when driving a car. While aiming for better fuel efficiency, you might overload the engine or risk overheating, which requires you to find a careful balance between performance and reliability in the design.

--