27.1. Analog Electronic Circuits

So, welcome back after the short break. So, where we are discussing? We are talking about the small signal equivalent circuit and then we are trying to find the corresponding gain of the circuit.

In this section, we reintroduce the topic of common emitter amplifiers after a brief intermission. The focus is on understanding the small signal equivalent circuit, which simplifies the analysis of the amplifier's behavior under small input signal conditions. We aim to derive the gain of the circuit, critical for assessing its performance.

Think of it like tuning a musical instrument: just as musicians make small adjustments to achieve perfect pitch, engineers analyze and adjust amplifier circuits to ensure they respond well to small input signals, thus 'tuning' their performance.

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

The output voltage (v_out) of the common emitter amplifier can be expressed in terms of the transconductance (g_m) and the load resistance (R). The equation v_out = -g_m × R × v indicates that the output voltage is inversely related to the input voltage (v) when multiplied by the transconductance and load resistance.

Imagine a water pipe: the output flow rate depends on the pressure applied at the input (akin to voltage), but factors like the pipe's width (representing resistance) and the force of the pump (analogous to transconductance) can drastically change the output flow.

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

The inclusion of emitter resistance (R_E) serves a dual purpose; while it stabilizes the operating point against variations in beta (current gain of the transistor), it can also degrade the circuit's voltage gain. This trade-off is crucial in amplifier design because while stabilization is necessary, maintaining a high gain is often desired.

Consider the balancing act of a tightrope walker: they may use a pole (R_E) to stabilize themselves. However, the pole can also restrict their movements, much like how R_E can limit gain while ensuring stability.

So, 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.

In addition to the voltage gain, it’s essential to understand two other parameters of the voltage amplifier: input resistance (R_in) and output resistance (R_out). The input resistance affects how much input signal the amplifier can accept without drawing too much current, while output resistance determines how the amplifier behaves with load circuits.

Imagine a sponge absorbing water: a sponge with low resistance (high absorbency) can soak up more water (input signal). Conversely, if it’s hard and unyielding (high output resistance), it won't release water (signal) easily when pressure is applied.

To simplify what you can do, we may say that if I do have i which is i flowing from base to emitter terminal.

To determine the input resistance of the amplifier, we analyze how the base current (i) is influenced by the applied voltage. The input resistance can be calculated as the ratio of the input voltage to the base current, incorporating factors such as the emitter current and base-emitter voltage drops.

Think of this like checking the resistance of a road for traffic: the smoother the road (lower resistance), the easier the flow of traffic (current) and the better the capacity to handle vehicles (input voltage).

While we will be doing this similar kind of exercise, we need to find as I said that we need to find what will be the output resistance R of this voltage amplifier.

To find the output resistance of the common emitter amplifier, we stimulate the output with a voltage and measure the resulting current. This calculation determines how much voltage drop occurs across the output for a given current and is essential for understanding how the amplifier behaves when connected to a load.

This is akin to testing the strength of a bridge: by applying a load (voltage) and observing how much it bends (current) under that load helps engineers know the capacity and resistance of the bridge to additional traffic.

So, 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_s.

Coupling capacitors play a crucial role in ensuring that the AC signals can pass through without altering the DC operating conditions. By strategically using capacitors to ground the emitter for AC signals, the gain can return to expected levels without compromising stability for DC signals.

Consider a swimming pool with a filter system: the filter allows water (AC signals) to flow while keeping the pool's water level (DC stability) unaffected. Thus, how water flows is enhanced without changing the amount already in the pool.

So, we need to be careful that now while you are picking this R_BB, we need to satisfy this condition to make sure that circuit is remaining insensitive to beta variation.

While designing these amplifiers, selecting appropriate resistor values is important for achieving both high gain and stability. The designer must ensure that the resistance values do not clash, leading to performance degradation. Managing these parameters effectively is key to building reliable amplifiers.

It’s like cooking: just as a chef must balance ingredients for flavor without making dishes too salty or bland, engineers need to balance resistor values to achieve desired amplifier performance that is stable and effective.

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