How to Calculate Output Impedance of A Cathode Follower

What is a Cathode Follower?

A cathode follower is a type of amplifier circuit that uses a vacuum tube or semiconductor device to provide voltage amplification while maintaining a low output impedance. It's called a "follower" because the output voltage follows the input voltage, though with some amplification.

The basic cathode follower circuit consists of a single triode vacuum tube or a bipolar junction transistor (BJT) with the grid or base connected to the output. This configuration provides several advantages:

• High input impedance
• Low output impedance
• Good voltage regulation
• Ability to drive low-impedance loads

These characteristics make cathode followers useful in many applications, including audio amplifiers, signal buffers, and impedance matching circuits.

Output Impedance Basics

Output impedance is a measure of how much the output voltage of a circuit changes when a load is connected. It's defined as the ratio of the change in output voltage to the change in output current:

In practical terms, output impedance represents the opposition to current flow at the output of a circuit. A low output impedance means the circuit can deliver current to a load with minimal voltage drop, while a high output impedance means the circuit struggles to deliver current to a load.

For a cathode follower, the output impedance is typically much lower than the input impedance, which is one of its key advantages. This makes it ideal for driving low-impedance loads like speakers or other amplifiers.

Calculating Output Impedance

The output impedance of a cathode follower can be calculated using the following formula:

Where:

• Z_out = Output impedance
• r_p = Plate resistance (or collector resistance for transistor circuits)
• μ = Amplification factor (or current gain for transistor circuits)
• R_L = Load resistance

This formula accounts for the interaction between the plate resistance, amplification factor, and load resistance. The term (1 + μ * (R_L / (R_L + r_p))) represents the voltage gain of the cathode follower, which affects the output impedance.

Example Calculation

Let's calculate the output impedance for a cathode follower with the following parameters:

• Plate resistance (r_p) = 10 kΩ
• Amplification factor (μ) = 50
• Load resistance (R_L) = 1 kΩ

Using the formula:

The output impedance in this example is approximately 1.8 kΩ. This means the cathode follower can deliver current to a 1 kΩ load with minimal voltage drop, demonstrating its low output impedance characteristic.

Practical Considerations

When calculating or designing with cathode followers, consider these practical factors:

1. Temperature effects: The amplification factor (μ) and plate resistance (r_p) can vary with temperature, affecting the output impedance.
2. Load regulation: The output impedance affects how well the circuit maintains its output voltage when the load changes.
3. Stability: High amplification factors can make the circuit more susceptible to oscillation, requiring proper compensation.
4. Biasing: Proper biasing is essential to ensure the tube or transistor operates in its linear region for accurate impedance calculations.

Understanding these considerations helps in designing more reliable and efficient cathode follower circuits.