Output Impedance Calculation in Voltage Series Feedback

This problem asks us to determine the output impedance of a basic amplifier without feedback, given its output impedance with voltage series feedback, the basic amplifier gain, and the feedback fraction. Understanding how feedback affects amplifier parameters, especially impedance, is fundamental in electronics.

Voltage Series Feedback Configuration

Voltage series feedback is a type of negative feedback where the feedback signal is proportional to the output voltage and is applied in series with the input voltage. This configuration is known for several key effects on amplifier characteristics:

• It reduces the overall voltage gain of the amplifier.
• It increases the input impedance of the amplifier.
• It significantly decreases the output impedance of the amplifier.

The reduction in output impedance is a desirable feature for voltage amplifiers, as it makes them behave more like an ideal voltage source (which has zero output impedance).

Given Parameters for the Amplifier

Let's list the known values from the problem statement:

• Output impedance with feedback (\(R_{of}\)) = \(10 \, \Omega\)
• Gain of the basic amplifier (A) = \(100\)
• Feedback fraction (\(\beta\)) = \(0.01\)

We need to find the output impedance of the amplifier without feedback, which we denote as \(R_o\).

Formula for Output Impedance with Feedback

For a voltage series feedback amplifier, the relationship between the output impedance with feedback (\(R_{of}\)) and the output impedance without feedback (\(R_o\)) is given by the formula:

\[R_{of} = \frac{R_o}{1 + A\beta}\]

Where:

• \(R_{of}\) represents the output impedance of the amplifier with the feedback network connected.
• \(R_o\) represents the output impedance of the basic amplifier before any feedback is applied.
• \(A\) is the open-loop gain (or basic amplifier gain).
• \(\beta\) is the feedback factor or feedback fraction, which determines what fraction of the output is fed back to the input.
• The term \((1 + A\beta)\) is often called the desensitizing factor or feedback factor, which indicates the amount by which feedback modifies the amplifier's characteristics.

Step-by-Step Calculation to Find Output Impedance Without Feedback

Our goal is to find \(R_o\). We can rearrange the formula to solve for \(R_o\):

\[R_o = R_{of} \times (1 + A\beta)\]

1. Calculate the Loop Gain (\(A\beta\)):

First, let's calculate the product of the basic amplifier gain and the feedback fraction:

\[A\beta = 100 \times 0.01\]

\[A\beta = 1\]

2. Calculate the Feedback Factor (\(1 + A\beta\)):

Next, we add 1 to the loop gain to find the feedback factor:

\[1 + A\beta = 1 + 1\]

\[1 + A\beta = 2\]

3. Calculate the Output Impedance Without Feedback (\(R_o\)):

Finally, we substitute the values of \(R_{of}\) and the calculated feedback factor into the rearranged formula:

\[R_o = 10 \, \Omega \times 2\]

\[R_o = 20 \, \Omega\]

Conclusion

The output impedance of the basic amplifier without feedback is \(20 \, \Omega\). This calculation confirms that applying voltage series feedback indeed reduces the output impedance from its original value of \(20 \, \Omega\) to \(10 \, \Omega\), highlighting a key advantage of using this feedback configuration in amplifier design.