33.5.4. Output Resistance

The second parameter it is the output resistance. So, if you look into this circuit and then if you observe this circuit from outside and if you see what is a corresponding output resistance. So, while we will be doing this as we said that we can connect a signal source here and then we have to make this part equals to 0. So, once you make this is equal to 0, this part it is 0. So, that makes this current it is also 0 and then if you stimulate this output port by say v and then if you observe the corresponding current here as i .

The output resistance of an amplifier is an essential parameter as it defines how much the output voltage can change in response to a change in load current. Here, we imagine connecting a signal source to the circuit being studied. We effectively isolate the output characteristics by setting certain parameters to zero, specifically ensuring that the current flowing through the circuit is minimal, thereby simplifying our analysis.

Think of this like a water faucet. When you turn it off (make the part equals to zero), there’s no water flowing (current). If you ask how much pressure (voltage) you would get when the faucet is open with a certain knob position (output resistance), it is much simpler to predict if you know what happens when the faucet is off.

In fact, the current it is only going through this resistance. So, then v and the i relationship you will get is basically v = R × i . So, that gives us the expression of v which is defined as v = R ; so, that is the second parameter we obtained.

To determine the output voltage (v), we utilize Ohm's law, which states that voltage (v) is the product of current (i) times resistance (R). By analyzing the flow of current through the resistance present in the circuit, we can calculate the output voltage. This relationship allows us to define output resistance as a crucial supporting factor in the overall functioning of the amplifier.

Let’s consider a garden hose that constricts flow due to kinks in the hose. If you push water through, the pressure and flow draw a direct connection between the water pressure (voltage) and how hard you push (current). The resistance provided by the kink in the hose simulates output resistance, affecting how effectively water can reach your garden.

Now, the third parameter it is; so, at the input port if we see and if you see what is the corresponding resistance here. And, since the circuit here it is open namely the gate current is 0 whether it is large signal or small signal as long as we are not considering the effect of the capacitance from gate to source we can assume that this is equal to 0.

When we look at the input port of the amplifier circuit, we evaluate the resistance observed from this point of view. Since we assume there is no current (open circuit condition), we can simplify our calculations by considering the input resistance to be negligible. Under normal small-signal analysis, we do not consider the influence of capacitance, emphasizing the linearity of the circuit response.

Imagine a door that is kept permanently open (no current). Your ability to interpolate air (current) through this door is clearly minimal, so the resistance against airflow at this door (input resistance) can be considered as effectively zero. In practical terms, this means that when you blow into one side, you won't be met with much opposition.

So, what do you obtain here it is A expression of A = – g × R ; R = (R ⫽ R ); it is coming from the bias circuit and then output resistance equal to R . So, that is how the entire circuit you can map into this voltage model.

We combine our previously discussed parameters into a comprehensive model for the amplifier circuit. Here we derive the overall voltage gain (A) of the amplifier, which is associated with the output resistance (represented as R) and the transconductance (g). This mathematical representation is essential for understanding how the amplifier behaves under varying conditions and provides a simplified version of our analysis.

If we consider a classroom with multiple students contributing to a group project (amplifier), the effectiveness of the project can be summarized (the gain) by how well the students (input signals) collaborate and the teaching method applied (parameters R and g). Their combined effect leads to a robust choice in presenting the project findings.

And of course, from outside if we are giving a stimulus say v and then if you are connecting some load here then you can find the corresponding primary input to primary output voltage.

When we connect a load to our amplifier circuit and apply an external signal (v), it affects the output voltage that can be observed. This stress-test scenario helps us evaluate how well the amplifier handles different loads, providing a clearer understanding of practical applications and requirements in real-world settings.

Relate this to how plants react to fertilizers (stimulus) in a garden. If a gardener adds fertilizer (the load) to the soil, it enhances the ability of plants (amplifier) to grow (output voltage). Depending on how much fertilizer is added, the plants will show various levels of growth, exhibiting the amplifier's adaptability and strength in performance.

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