93.1.5. Output Resistance Change in Voltage Amplifiers

So, yeah dear students, so welcome back after the short break and before the break we are talking about the change of input resistance of the different configuration. And whereas, we are going to talk about change in output resistance to start with let we consider it is a voltage amplifier and we want to see the change due to feedback connection.

In this chunk, we are being reintroduced to the topic of output resistance specifically in the context of feedback connections in voltage amplifiers. The section emphasizes that we are interested in how the output resistance changes when feedback is applied to a voltage amplifier. Essentially, we want to explore the effects of feedback on the performance of the amplifier, which is a crucial concept in analog electronics.

Think of a water faucet being regulated by a feedback valve. When you turn the faucet on, you want to maintain a steady stream of water. The feedback valve monitors the flow and adjusts if the pressure changes, similar to how feedback in amplifiers stabilizes output despite changes in input.

And since it is voltage amplifier as we have discussed, the circuit is given here. The configuration here it is referred as shunt series feedback or voltage series Feedback circuit. And to start with let we consider the feedback network it is ideal namely its input resistance, it is infinite and the output resistance as it is producing voltage, output resistance it is 0.

This chunk discusses the characteristics of an ideal feedback network within a voltage amplifier setup. In ideal scenarios, the input resistance should be infinite, meaning the circuit does not draw any current from the input source. Meanwhile, the output resistance being zero means that the amplifier can deliver maximum voltage output without any loss due to resistance. This sets the foundation for understanding how practical systems deviate from these ideal conditions.

Imagine a perfect spigot (like a sink faucet) that never leaks and can deliver a perfect stream of water when turned on. Its ‘infinite input resistance’ means no loss of water from the hose it connects to, and a ‘zero output resistance’ means all the water gets delivered to where you point it, allowing maximum flow without waste.

However, for the forward amplifier we are considering finite input resistance and finite output resistance. We do have the voltage dependent voltage source A v, v it is appearing at the input of v in in the forward amplifier. Now, to know the output resistance what we can do? We can stimulate this output port by say voltage source v and then we observe the corresponding current say i and the then port impedance or port resistance it is defined by R out_f.

This chunk shifts focus from ideal to practical situations by introducing the concept of finite resistances in the amplifier. We define a real-world scenario where the forward amplifier has both finite input and output resistances. To determine the output resistance, we apply a voltage source to the output port and measure the resulting current. This setup allows us to calculate the port's impedance, which is crucial for understanding the actual performance of the amplifier under feedback conditions.

Imagine that the faucet we previously discussed now has some restrictions in the pipe, which represents the finite resistances. When you try to turn it on, some water flows out, but you need to measure how much comes out compared to how much you’ve put in to understand how resistant the system is to flow under these conditions.

So, while we are doing this exercise we have to keep the input port appropriate. So, that it will support the feedback connection, namely we in this case the signal here it is voltage and so, we do have the ideal signal voltage source connected. However, we have to keep its magnitude, signal magnitude should be 0. Which means that we are essentially shorting this input port while we are doing this exercise to find the output resistance. Now, that is the condition and let we derive the expression of this R out_f in terms of R and probably A and β.

In order to derive the expression for the output resistance again, it's crucial to maintain certain conditions. Specifically, we must ensure that the input signal is zero, essentially creating a short circuit at the input. This allows us to accurately measure the output resistance without interference from input signals. The derivation involves expressing the output resistance R_out_f in terms of the forward amplifier's parameters, including its resistances and feedback factors (denoted as β).

This is similar to taking measurements in a controlled environment where you've blocked all other variables. If you're trying to measure water pressure at a point in a pipe, you ensure other valves are closed (akin to shorting inputs) to get the clearest reading of pressure solely from the source you want to measure.

So, let us consider that we do have a source resistance called R_s. So, to get the output resistance R_out_f in presence of a series resistance called source series resistance called R_s and of course, we have to keep the signal here it is 0, so; that means, it is getting shorted like this. Now, in this condition; v_in, the input voltage at this port can be written in terms of βv.

As we introduce non-ideal conditions by adding a source resistance (R_s), the calculations become more complex. The input voltage can still be related to the output by the feedback factor β. This chunk illustrates how real-world components interact within the amplifier circuit, impacting the output resistance calculation. Specifically, we observe how the output resistance changes due to the series resistance, which influences the voltage distribution across components.

Consider a hose with a small leak (the source resistance) affecting water flow. If you measure how much water comes out when the faucet is running, you must account for the leak, as it reduces the effective flow (voltage) reaching the end. You'll need to adjust how much you expected to flow based on the leakage.

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