Vacuum Tube Transconductance gm vs Amplification Factor µ

The transconductance or mutual conductance of a valve or vacuum tube and the amplification factor are often confused: find out what they are and the differences.

Vacuum Tube / Thermionic Valves Includes:
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In vacuum tube or valve theory, the transconductance, gm and the amplification factor, µ are two of the three fundamental "constants" that describe how a valve or tube behaves.

While they both describe how the grid controls the tube, they measure different things: current vs. voltage.

ECC83 & ECC88 double triode valves / vacuum tubes
ECC83 & ECC88 double triode valves / vacuum tubes

Transconductance gm

The transconductance which is also called the Mutual Conductance defines how effectively the grid voltage controls the plate current.

Transconductance or mutual conductance definition:

The transconductance is the change in plate current (Δ Ip ) divided by the change in grid voltage (Δ Vg ), for a constant anode or voltage.






g m = Δ I p Δ V g

The units for the transconductance are measured in millimhos (mA/V) or micromhos (μmhos).

Today, using more modern notation, the transconductance would be measured in Siemens, S, so the notation of the transconductance is Sm.

To gain a clearer idea of this, think of it as the "responsiveness" of the valve or tube. A high gm means a tiny change in grid voltage causes a large change in current.

To put this in context, this is probably the most important specification parameter for power devices like an EL34 or KT88. Here the aim is to drive a lot of current in the anode circuit, possibly into a transformer, RF circuit, etc.

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Triode vacuum tube / valve circuit symbol
Circuit symbol for the triode vacuum tube / valve

Amplification Factor, µ

The amplification factor Mu or µ measures how effectively the grid voltage controls the anode or plate voltage.

It represents the theoretical maximum voltage gain the tube can achieve. Often it is the voltage gain that is important in a circuit.

Amplification factor, µ definition:

The amplification factor of a valve or vacuum tube is the ratio of a change in anode or plate voltage (ΔVp ) to a change in grid voltage (ΔVg ), while keeping the plate current constant.




μ = Δ V p Δ V g

There are no units for the amplification factor as it is a pure ratio of anode voltage divided by the grid voltage.

The amplification factor is the key spec for preamp valves or tubes (like a 12AX7 or 12AU7), where the goal is to increase the voltage of a small input signal.

A key relationship

The transconductance or mutual conductance and the amplification factor are linked mathematically by a third value which is the anode resistance or plate resistance rp.

This is a key equation or relationship for valves or vacuum tube and it is often called the Barkhausen Equation

μ = g m × r p

Summary table

Here is a summary comparison comparing the parameters transconductance or mutual conductance and the amplification factor.

Feature Transconductance (gm) Amplification Factor (μ)
Measured In Current change (mA/V or μmhos) Voltage ratio (Pure number)
Core Focus How much current flows? How much voltage is gained?
Primary Use Assessing tube health and power stages Determining gain in preamp stages
Example (12AX7) ~1600 μmhos ~100

Ian Poole   Written by Ian Poole .
  Experienced electronics engineer and author.



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