47.3.6. Output Impedance Calculation

So, output impedance it is looking at the output terminal, what we have it is at this point. So, we do have conductance here, conductance of the r , then r and then also the g part.

Output impedance in electronic circuits is a measure of how much the voltage at the output of an amplifier changes in response to changes in output current. Here, we consider several components that contribute to the total output impedance, which are the conductances associated with the resistances in the circuit. The key factors are the collector-emitter resistance, the output resistance of the transistor, and any source resistance. To find the overall output impedance, we effectively calculate the reciprocal of the sum of these conductances.

Think of output impedance like water flowing through a pipe. If you have a regular-sized pipe (low resistance), water can flow easily. If you insert a narrower pipe (higher resistance), the flow of water (output voltage) will be affected more significantly by any changes in the pressure (output current).

So, looking into the emitter here and if we stimulate the circuit with the output voltage v x, we will be having 3 current components: one is from g m v x, and then the resistance R , which gives us a hint that the output resistance it will be 1 divided by all the 3 conductances.

In this part, we consider the small signal model of the output circuit and what happens when we apply a small voltage. The total output current comes from three components: the transconductance current and the current from the resistances in series with the output. We recognize that the total output resistance can be determined by adding up the conductances of these elements and then taking the reciprocal to find the output resistance. This is essential to analyze how the amplifier will respond to varying output loads.

Imagine you're pouring water into three connected buckets. They will fill up at different rates depending on the size of the pipes feeding them. If one pipe has a larger diameter (less resistance), it will fill up faster. To find out how fast your main bucket fills, you'd need to figure out the total input rate from all buckets, just as we do with conductances in our output impedance calculations.

Even though we are connecting this R S; since we do have the ideal current source and the small signal parameters remain the same, so, the performances of all the circuits remain the same.

This chunk highlights the assumption that when modeling electronic circuits, we often consider ideal conditions—like perfect current sources. Despite introducing practical resistances, as long as some parameters remain unchanged (like small signal models), the overall performance characteristics do not vary significantly. The analysis focuses on understanding that even real-world influences can sometimes be neglected for simplified analysis.

Think about a car's performance being tested in an ideal environment, like a controlled racetrack. The car's specs are calculated without wind resistance or bumps. If you then take it on a normal road (with minor obstacles), the car still performs close to what was originally expected because the major factors haven't changed significantly.

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