Cathode Follower Calculator

A cathode follower is a type of amplifier circuit that provides voltage buffering between stages. This calculator helps you determine the voltage gain and output characteristics of a cathode follower circuit based on your input parameters.

What is a Cathode Follower?

A cathode follower is a common-emitter amplifier circuit with a very high input impedance and low output impedance. It's commonly used in vacuum tube amplifiers and some modern solid-state circuits.

The key characteristics of a cathode follower include:

High input impedance
Low output impedance
Voltage gain close to 1 (typically 0.9 to 0.95)
Phase inversion (output is 180 degrees out of phase with input)

Cathode followers are often used as buffer amplifiers to prevent loading effects between stages of a multi-stage amplifier.

How to Use This Calculator

To use the cathode follower calculator:

Enter the input voltage (V_in) in volts
Enter the plate resistance (R_p) in ohms
Enter the plate voltage (V_p) in volts
Enter the mutual conductance (g_m) in mhos
Click "Calculate" to see the results

The calculator will display the voltage gain, output voltage, and other key parameters of your cathode follower circuit.

Formula Used

The voltage gain (A_v) of a cathode follower is calculated using:

A_v = (R_p / (R_p + (1/g_m))) × (V_p / V_in)

Where:

R_p = Plate resistance in ohms
g_m = Mutual conductance in mhos
V_p = Plate voltage in volts
V_in = Input voltage in volts

The output voltage (V_out) can be calculated as:

V_out = V_in × A_v

Example Calculation

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

Input voltage (V_in) = 10V
Plate resistance (R_p) = 100,000Ω
Plate voltage (V_p) = 200V
Mutual conductance (g_m) = 0.001 mhos

Using the formulas:

First calculate the voltage gain:
A_v = (100,000 / (100,000 + (1/0.001))) × (200 / 10)

A_v ≈ 0.99 × 20 = 19.8
Then calculate the output voltage:
V_out = 10 × 19.8 = 198V

This example shows how the cathode follower provides voltage gain while buffering the input signal.

FAQ

What is the typical voltage gain of a cathode follower?

The typical voltage gain of a cathode follower is close to 1 (typically 0.9 to 0.95) due to the high input impedance and low output impedance characteristics.

Why is a cathode follower used as a buffer?

A cathode follower is used as a buffer because it has high input impedance (minimal current draw from the preceding stage) and low output impedance (providing good current drive to the following stage).

What happens if the plate resistance is too low?

If the plate resistance is too low, the voltage gain will decrease because the denominator in the voltage gain formula will be dominated by the (1/g_m) term rather than R_p.

Can a cathode follower be used with solid-state components?

While cathode followers are traditionally associated with vacuum tubes, similar buffering effects can be achieved with solid-state components like field-effect transistors (FETs).