93.1.2. Output Resistance and Feedback Connection

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 section, we revisit the topic of output resistance after previously discussing input resistance. We're focusing on voltage amplifiers and how their output resistance changes when feedback connections are applied. The goal is to understand these changes using an ideal voltage amplifier as a starting point.

Think of an amplifier as a water tap. Just as turning the tap adjusts the water flow, feedback adjusts the amplifier's output, affecting the water pressure (output resistance) at the spout.

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 us 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.

In feedback circuits, two traits are examined: the input and output resistances. An ideal feedback network has infinite input resistance, meaning it does not draw any current from the input source, and zero output resistance, indicating it can provide maximum voltage to the load. This idealization simplifies the analysis of how feedback affects performance.

Imagine a perfect feedback loop in a restaurant where feedback (customer opinions) comes in infinitely without affecting the chef's performance (input resistance). The chef serves food perfectly every time (output resistance).

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 the forward amplifier. Now, to know the output resistance what we can do?

In realistic scenarios, both input and output resistances are finite and play a critical role in determining the output performance of the amplifier. The next step is to establish a method for determining the output resistance when a voltage source is applied at the amplifier's output.

This situation is like a car that uses gasoline (input resistance) and outputs exhaust (output resistance). To find out how efficiently the car can run, you need to consider both the quality of gasoline and the exhaust system.

So, if you see if I consider this is short, then if I consider KCL in this mixer what we are getting it is v, input voltage of the amplifier it is ‒ v. But then v it is same as βv; v is the voltage appearing at the input port of the feedback circuit and v in this case the moment we connect v here it is v, it is same as v.

Using Kirchhoff's Current Law (KCL), we analyze the feedback circuit to relate the input voltage to the output voltage. The equations reveal that the input voltage is inversely proportional to the feedback, indicating how techniques such as negative feedback stabilize and control output resistance.

Imagine a seesaw where one side is affected significantly by weight ( voltage). The input affects output in the same proportion, just as feedback in an amplifier helps balance the circuit.

So, to get the output resistance; 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.

When a source resistance is introduced, we need to readjust our calculations for output resistance in the circuit. By shorting the signal to simulate zero condition, we redefine the relationship between the input and output voltages, leading to new equations for resistance.

This is like having a water pipe with a narrow section (source resistance). As water flows, you need to account for the constriction when measuring water pressure (output resistance).

Now, if we also have to consider say finite value of this resistance, so if I include say this resistance as well. So, if I consider R of the β network, R_out_β then this relationship it will be getting changed and the change it will be R_out_β is also influenced by how components in the feedback network resist or support the circuit.

The equations for output resistance become more complex as we add additional resistive elements in the feedback paths. Each resistance modifies overall resistance differently, affecting how feedback changes the amplifier’s performance.

Think about a road with speed bumps (feedback components). Each speed bump slows down the car (increases resistance) differently, influencing how fast you can reach your destination (output resistance).

So, we might have observed that the output resistance is increasing due to components in parallel or series, but they also create a cumulative effect on overall performance.

In practical circuits, various non-ideal elements can be present. These affect the output resistance significantly. The total output resistance can increase or decrease, depending on whether components are in series or parallel.

Consider layers of clothing on a winter day. Each layer adds warmth (increased output resistance) but could also restrict movement (decreasing circuit efficiency).

So, in the next slide we will be talking about change of output resistance of a trans-impedance amplifier due to the feedback connection.

The discussion transitions to how output resistance behaves in a different type of amplifier called a trans-impedance amplifier. This sets up the next phase in understanding feedback mechanisms in varied amplifiers.

Just as a versatile mobile phone can serve different functions (like a camera or gaming console) depending on its setup, different amplifiers adjust their output resistance based on their design and connections.

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