A current controlled current source (CCCS) has an input impedance of 10 Ω and output impedance of 100 kΩ. When this CCCS is used in a negative feedback closed loop with a loop gain of 9, the closed loop output impedance is

CCCS Output Impedance with Negative Feedback

This problem requires calculating the output impedance of a Current Controlled Current Source (CCCS) when it is part of a negative feedback configuration.

Negative Feedback Effects on CCCS Impedance

A Current Controlled Current Source (CCCS) is defined by its input and output characteristics. Key parameters provided for the open-loop CCCS are:

- Input Impedance ($Z_{in}$) = $10\Omega$
- Output Impedance ($Z_{out}$) = $100\text{ k}\Omega$

When a CCCS is used in a negative feedback loop with a given loop gain ($A\beta$), the circuit's impedance parameters are modified. For a CCCS, which inherently deals with current control and sampling, negative feedback typically increases the output impedance. This is because the feedback mechanism actively opposes changes in the output current, effectively acting as a higher impedance source.

Calculate Closed Loop Output Impedance

The standard formula for the closed-loop output impedance ($Z_{out,CL}$) when negative feedback increases impedance is:

$$Z_{out,CL}=Z_{out}\times (1+A\beta )$$

In this formula:

- $Z_{out}$ represents the original output impedance of the amplifier without feedback.
- $A\beta$ signifies the loop gain, which is given as $9$.

Step-by-Step Calculation of Output Impedance

We are given:

- $Z_{out}=100\text{ k}\Omega$
- $A\beta =9$

Substitute these values into the formula:

$$Z_{out,CL}=(100\text{ k}\Omega )\times (1+9)$$

Calculate the factor $(1+A\beta )$:

$$1+9=10$$

Now, multiply the open-loop output impedance by this factor:

$$Z_{out,CL}=100\text{ k}\Omega \times 10$$

$$Z_{out,CL}=1000\text{ k}\Omega$$

Thus, the closed-loop output impedance is $1000\text{ k}\Omega$.