## Launch me!

### What does this calculator do?

A low output impedance gives the cathode follower circuit an extraordinary ability to act as a buffer between a signal and a load. Output impedance quantifies the ability to drive the next stage. An output impedance of zero ohms signifies that the driving circuit is a pure voltage source. It can supply any amount of current to the next stage. A non-zero output impedance represents the amount of voltage sag that occurs depending on how much current is required. This concept is portrayed by the so-called Thevenin Equivalent Circuit, which represents the driving circuit as a pure voltage source in series with its output impedance.

The higher the current, the more voltage drop across the output impedance, and the more the magnitude of the output voltage is reduced. If the source voltage V is positive, the output becomes less positive. If the source is negative the output voltage becomes less negative.

A basic triode amplifier is great for increasing the voltage of a signal. Its major problem is that it can't drive a very heavy load. Place a low-valued resistance across its output and it easily gets bogged down, which reduces the gain and makes it dependent upon the characteristics of the load. If the next stage is a voltage amp or a phase inverter, this isn't much of a problem. A tone stack, however, typically demands a lot of current from the driving stage, the amount of which depends on the signal characteristics and the tone control settings. A cathode follower mitigates this problem. It has no gain (in fact a slight loss), but it can easily drive the most demanding of tone stacks.

An increasing input signal voltage causes the plate current to increase, which increases the voltage across the cathode resistor, thereby making the cathode more positive with respect to ground. If the input increases the grid-to-ground voltage by 1 volt, then the increased plate current raises the cathode-to-ground voltage by almost 1 volt, leaving the grid-to-cathode voltage almost unchanged. The grid voltage increases but the cathode voltage "follows" it. Thus we get this circuit's name.

The calculator computes the unloaded voltage gain (the gain without being connected to the next stage) and the output impedance of a cathode follower.

### Reference

1Richard Kuehnel, Circuit Analysis of a Legendary Tube Amplifier: The Fender Bassman 5F6-A, 3rd Ed., (Seattle: Pentode Press, 2009).