50.2.3. Voltage Gain

By considering this small signal equivalent circuit, let us see what are the now what are the conditions we are getting. First of all we do have v , base node it is grounded and emitter it is having some signal and that signal is incidentally v . So, we can say v is essentially 0 ‒ v . So, and v it is same as v . So, in fact, v is v . So we can say that v it is ‒ v . So, this is the first thing we obtain.

Here we are examining the voltage gain of the common base amplifier. The voltage at the base is grounded, which means it has a value of zero. The voltage at the emitter is introduced as 'v', which can be considered as the input signal. The relationship expresses how these voltages interact: since v (the voltage at the emitter) is just the opposite of v (the base voltage), we can write that v is equal to -v, showing they are out of phase.

Think of it like a see-saw balanced at the center. If one side rises (emitter voltage), the other side (base voltage) must lower, maintaining balance. So if the emitter goes up, the base comes down, depicting their inverse relationship.

On the other hand, at the collector node, we do have three current elements. One is one current is flowing through this r another current is flowing through on this device and then also we do have a current flowing through this R. The current flowing through this R it is . So, , it is summation of these two currents. So, if I consider this is the polarity of the positive direction of the current, then this current it is and v it is nothing, but v .

At the collector node, we have three currents at play. The first current is flowing through the collector resistor (r), the second current is through the transistor (g m * v_in), and the third current flows through another resistor (R). By applying Kirchhoff's Current Law (KCL), which states that the sum of currents entering a junction must equal the sum of currents leaving, we can derive an equation that correlates these currents. This allows us to formulate the relationship between the input voltage and the output voltage.

Imagine a busy intersection where three roads converge. The amount of traffic (current) flowing in must equal out under each road. If more cars enter from one direction, they affect what can exit down the other roads, illustrating how KCL dictates the flow of currents in the circuit.

So, we can write the expression of v in terms of v . So, with the rearrangement property rearrangement what we are getting here it is v = v ( ). So, this relationship it is helping us to get the voltage gain expression.

From the relationships and using rearrangement, we can express the output voltage (v_out) in terms of the input voltage (v_in). This leads us to understand how the circuit amplifies the signal. We denote this relationship as v_out = v_in * (some gain factor), which helps us identify the amplifier's voltage gain.

Consider a speaker connected to a small audio player. The speaker amplifies the small signals from the player to produce sound at a larger volume. The initial, small input signal (v_in) relates to the large sound output (v_out) through a specific gain factor of the speaker.

We have assumed that there is no source resistance. As a result, we are saying that entire v it is coming here and then R is not having any role and then we are really not bothered about the input resistance and so on.

In this circuit analysis, an important consideration is the source resistance. If we assume there is no source resistance, our analysis simplifies, and we can cleanly identify our signal voltages and components without distraction. However, in real-world applications, this assumption may not hold, and the source resistance could significantly impact the input voltage seen by the amplifier.

Think of a garden hose providing water to a sprinkler. If the hose has no kinks (source resistance), the water pressure remains high, allowing the sprinkler to work effectively. But if there are kinks (resistance caused by sources), the water flow drops, affecting how the sprinkler operates.

To get the input impedance what we can say? If I stimulate the circuit by say v and then if we observe the corresponding current here say i then if I take the ratio of that will be giving us the input resistance.

To understand the input impedance of this amplifier, we need to apply an input voltage (v_in) and measure the resulting input current (i). By calculating the ratio of voltage to current (v_in / i), we can derive the input impedance, which tells us how much the input signal is affected by the circuit's resistance.

Imagine trying to push a shopping cart. The easier it is to push (lower impedance), the better the cart rolls forward. If you have obstacles (high input impedance), they resist your push, slowing progress. This illustrates how input impedance impacts the effectiveness of the amplifier.

... we may say that the input impedance it is quite low, it may be in 10s of Ω ... we will see that what may be the consequence if I consider source resistance of this circuit.

When we find that the input impedance is quite low, it indicates that the circuit can potentially absorb signals without significant loss. However, when we consider the source resistance in practice, we discover that this low impedance could lead to signal attenuation or weakening. This means that what we expect as a voltage gain might not be achieved due to the interaction between the circuit and its source.

This is similar to trying to hear someone speaking in a loud concert. If the speaker (input source) is not strong enough (due to high resistance), you won't be able to pick up their words clearly, similar to how low voltage gains can render a circuit ineffective.

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