45.2.3. Output Resistance

The output resistance coming from the rest of the circuit coming in parallel with R.

The output resistance in a circuit is a measure of how much opposition the circuit presents to the current from the output terminal. In this context, the output resistance of the common collector amplifier is influenced by any resistive elements connected in parallel with the output. Essentially, it helps determine how effectively the amplifier can drive a load without significant voltage drop.

Imagine you have a garden hose (the amplifier) connected to a sprinkler (the load) and that sprinkler has a small valve at the end. If the hose is very thick and no other water source is connected, the water flows freely to the sprinkler. But if you connect an additional hose (representing the parallel resistive elements), it will affect how much water flows to the sprinkler. The combined resistance from both hoses determines the overall water pressure at the sprinkler.

To get the output resistance, we stimulate this circuit by applying a voltage and observe the corresponding current. The output resistance is the ratio of voltage to current at the output terminal.

To determine the output resistance, we analyze the circuit by applying a small AC voltage while keeping other signals at ground potential (AC ground). The resulting current flowing through the circuit is noted, allowing us to calculate output resistance as the ratio of the applied voltage to the resulting current. This is an essential method in circuit analysis as it gives us insight into how the circuit will respond to load changes.

Think of a water tank connected to several pipes (the output). To see how well the tank can supply water, you would turn on the faucet and measure how quickly the water flows out when a certain pressure is applied. The ratio of the pressure you applied to the resulting flow rate will give you the 'resistance' of the system – the lower the pressure drop (output resistance), the more effectively the system can supply water.

Total output resistance is approximately the reciprocal of the total conductance, dominated by the transconductance of the active device.

In this part of the analysis, we note that the overall output resistance can be viewed as the reciprocal of the total conductance from multiple elements in the circuit. The different components contributing to the conductance, such as transconductance of the active device, affect the total output resistance significantly. Often, the transconductance term will dominate, simplifying calculations.

Consider a group of friends at a party, where each friend represents a component contributing to the overall fun (output resistance). If one friend is very engaging (the active device with high transconductance), their presence enhances the overall experience significantly more than the others combined, just like a dominant conductance influencing the output resistance.

Even if we consider practical values of resistances, such as source and collector resistances, the output resistance remains close to its ideal value when certain conditions apply.

When analyzing the effect of the source and collector resistances, we find that even with non-ideal components, if those resistances are high enough relative to the transconductance, the output resistance does not deviate significantly from its ideal value. The careful selection and calculation of these parameters ensure that the common collector amplifier continues to perform its intended function effectively.

Think of temperatures in a room controlled by an air conditioner (the transconductance). If you turn off the AC temporarily (introducing a high resistance), but the room is filled with well-insulated walls (high source resistance), the temperature remains steady—showing that the overall performance remains consistent despite minor changes.

--