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Chapter 13: ELECTRON TUBES

# Tube Parameters

For bipolar junction transistors, the fundamental measure of
amplification is the Beta ratio (β), defined as the ratio of collector
current to base current (I_{C}/I_{B}). Other transistor
characteristics such as junction resistance, which in some amplifier
circuits may impact performance as much as β, are quantified for the
benefit of circuit analysis. Electron tubes are no different, their
performance characteristics having been explored and quantified long ago
by electrical engineers.

Before we can speak meaningfully on these characteristics, we must define several mathematical variables used for expressing common voltage, current, and resistance measurements as well as some of the more complex quantities:

The two most basic measures of an amplifying tube's characteristics are
its amplification factor (µ) and its mutual conductance (g_{m}), also known as *transconductance*.
Transconductance is defined here just the same as it is for
field-effect transistors, another category of voltage-controlled
devices. Here are the two equations defining each of these performance
characteristics:

Another important, though more abstract, measure of tube performance is its *plate resistance*.
This is the measurement of plate voltage change over plate current
change for a constant value of grid voltage. In other words, this is an
expression of how much the tube acts like a resistor for any given
amount of grid voltage, analogous to the operation of a JFET in its
ohmic mode:

The astute reader will notice that plate resistance may be determined by dividing the amplification factor by the transconductance:

These three performance measures of tubes are subject to change from
tube to tube (just as β ratios between two "identical" bipolar
transistors are never precisely the same) and between different
operating conditions. This variability is due partly to the unavoidable
nonlinearities of electron tubes and partly due to how they are
defined. Even supposing the existence of a perfectly linear tube, it
will be impossible for all three of these measures to be constant over
the allowable ranges of operation. Consider a tube that *perfectly*
regulates current at any given amount of grid voltage (like a bipolar
transistor with an absolutely constant β): that tube's plate resistance *must* vary with plate voltage, because plate current will not change even though plate voltage does.

Nevertheless, tubes were (and are) rated by these values at given operating conditions, and may have their characteristic curves published just like transistors.