50.2.7. Output Resistance Analysis

To find the output resistance, we stimulate the circuit by a voltage called v and then observe the corresponding current i. The output resistance is defined as the ratio of v to i.

To determine the output resistance of a circuit, we apply a small voltage (which we call 'v') to the circuit and measure the current that flows as a result (which we call 'i'). The output resistance (A) is then calculated by taking the voltage 'v' and dividing it by the current 'i'. This gives us a measure of how much the circuit resists the flow of current when a voltage is applied.

Imagine trying to push water through a pipe. If the pipe is narrow (high resistance), it becomes harder to push the water through, much like how output resistance affects how much current flows with a given voltage.

The output resistance can be simplified by observing the circuit structure. The resistances in the circuit can be analyzed in parallel and series configurations.

In our circuit, we can simplify our analysis by focusing on how the resistances are arranged. If certain parts of the circuit connect directly to ground, we can think of these resistances as being in parallel. This means that we can analyze smaller parts of the circuit independently to understand how they contribute to the total output resistance. We find the equivalent resistance of components in parallel and add them to the resistance of other components in series to find the overall output resistance.

Think of it like a series of roads leading to a single narrow street. The roads (resistances) can divide, with some paths meaning cars (current) can choose different routes toward the destination, which affects the overall traffic (current) flow. The total output resistance is like asking how congested the more narrow road is just before we get to it.

To find the expression for output resistance, we drop certain parts of the circuit for simplification and find an equivalent resistance at the output.

We can derive the output resistance expression by simplifying our circuit. By ignoring some parts of the circuit that have minimal effect on the output resistance, we can focus on the significant components. These components are often arranged such that we can calculate the total output resistance by combining them, usually through calculations involving either series or parallel combinations of resistances. This resultant equivalent resistance gives us a clearer insight into how the amplifier behaves under varying load conditions.

This can be illustrated with a series of water tanks where we ignore the smaller tanks that don't significantly add to the flow pressure. Focusing on the biggest tank (representing the larger resistances) gives us a way to estimate how effective the whole setup is in terms of pressure (or current) output.

We summarize that for the common base configuration, the output resistance is quite high if proper arrangements are made with the DC biasing.

The final result of analyzing the common base configuration indicates that under certain conditions, particularly with careful DC biasing, the output resistance can be very high. A high output resistance is often desirable in amplifier circuits because it leads to better signal handling and less unwanted interaction with the load connected at the output. This means that the circuit can effectively amplify without being significantly loaded down by external components.

Think of a high-output pressure system like a fire hose that can deliver water without losing pressure when people hold it at various angles. A good amplifier needs to maintain 'pressure' or voltage levels while delivering current, much like how the system needs to maintain pressure even as external influences (the load) change.

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