Cathode Follower Impedance Calculator

A cathode follower is a common configuration in vacuum tube amplifiers that provides voltage amplification while maintaining a stable output. This calculator helps determine the input and output impedance of a cathode follower circuit, which is crucial for proper amplifier design and troubleshooting.

What is a Cathode Follower?

A cathode follower is a single-stage amplifier circuit that uses a vacuum tube (or transistor) to amplify a signal while maintaining a stable output voltage. The term "follower" comes from the fact that the output voltage follows the input voltage, but with amplification.

The basic cathode follower circuit consists of:

A vacuum tube with a heated cathode
A grid connected to the input signal
A plate connected to a positive voltage supply
A load resistor connected to the plate
A bypass capacitor connected between the cathode and ground

Cathode followers are commonly used in audio amplifiers, oscillators, and signal processing circuits due to their high input impedance and low output impedance characteristics.

Impedance Calculation

Impedance in a cathode follower circuit refers to the opposition to alternating current flow. There are two key types of impedance to consider:

Input impedance - The impedance seen by the signal source
Output impedance - The impedance seen by the load

The calculation of these impedances depends on several factors including the tube characteristics, load resistor value, and bypass capacitor value.

Input Impedance

The input impedance of a cathode follower is primarily determined by the grid-to-cathode capacitance (Cgk) and the transconductance (gm) of the tube. The formula for input impedance (Zin) is:

Zin = 1 / (2πfCgk + gm)

Where:

f = frequency of the input signal
Cgk = grid-to-cathode capacitance
gm = transconductance of the tube

For most audio applications, the input impedance is very high, typically in the range of several thousand ohms to megohms.

Output Impedance

The output impedance of a cathode follower is determined by the parallel combination of the plate resistance (Rp) and the load resistor (RL). The formula for output impedance (Zout) is:

Zout = Rp || RL = (Rp * RL) / (Rp + RL)

Where:

Rp = plate resistance of the tube
RL = load resistor value

The output impedance is typically much lower than the input impedance, providing good load-driving capability.

Practical Considerations

When designing or analyzing a cathode follower circuit, several practical considerations must be taken into account:

Frequency response - The impedance calculations become more complex at higher frequencies due to parasitic capacitances
Tube characteristics - Different tube types have different Cgk and gm values
Bypass capacitor - The value of the bypass capacitor affects the low-frequency response
Load requirements - Different loads may require different impedance characteristics

Understanding these factors is essential for achieving the desired performance from a cathode follower circuit.

Frequently Asked Questions

What is the difference between input and output impedance in a cathode follower?: The input impedance is the impedance seen by the signal source, while the output impedance is the impedance seen by the load. The input impedance is typically much higher than the output impedance.
How does the bypass capacitor affect the impedance of a cathode follower?: The bypass capacitor provides a low-impedance path for AC signals between the cathode and ground, which helps maintain a stable DC bias while allowing signal amplification.
What factors affect the transconductance (gm) of a vacuum tube?: The transconductance is primarily determined by the tube's construction and operating conditions, including the grid voltage, cathode current, and tube type.
How can I measure the impedance of a cathode follower circuit?: You can measure the impedance using an impedance meter or by applying a known AC signal and measuring the resulting voltage and current.
What are some common applications of cathode follower circuits?: Cathode followers are commonly used in audio amplifiers, oscillators, signal processing circuits, and as buffer stages in more complex amplifier designs.