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## Matching Triodes and Pentodes

Discussion of tube based amplifier projects

### Matching Triodes and Pentodes

A vacuum tube has three important electrical parameters to measure - Mu (voltage gain), Gm (transconductance) and Rp (plate resistance). These three parameters define the overall electrical characteristics of a vacuum tube. Importance of these three parameters differs for triodes and pentodes. Triodes and pentodes both have the characteristics Gm (transconductance) and Mu (voltage gain). However for the triodes the most important parameter is Mu and for the pentodes the most important parameter is Gm.

1.Triodes

In a triode the relationship between Mu (voltage gain), Gm (transconductance) and Rp (plate resistance) is determined by the Ohm's law:

Mu = Gm x Rp

Gm is measured in the units of mhos or amps per volt. Rp is measured in the units of Ohms or Volts per Amperes. When these two parameters are multiplied, their units cancel, making Mu (voltage gain) unit-less parameter. A Mu of 25 means that voltage of 1 Volt applied to grid of a vacuum tube is amplifier 25 times and increases to 25 Volt on anode of the tube.

For triodes, Mu (voltage gain) is the most important parameter to measure and is the parameter that makes the biggest impact on sound quality of amplifier. Since Mu is what defines voltage gain of a tube, and the voltage gain is what we hear, matching Mu for tubes in the right and left channel is the most important task in a triode based amplifier. For example, let's say we have an amplifier where a triode in the right channel and a triode in the left channel are matched by their Gm (transconductance) values. However, there is no guarantee that these two triodes will have equal voltage gain, because Mu (voltage gain) is the product of multiplication of Gm and Rp. Since Mu is a product of multiplication of Gm and Rp, the triodes in the right and left channel may have unequal values of Mu. And if we have a triode with a Mu of 25 in the right channel of an amplifier and a triode with a MU of 31 in left channel, we will have a 2 dB imbalance in this amplifier. Accordingly, Rp (plate resistance) must also be measured and matched.Thus, for a triode Rp (plate resistance) is the second most important parameter to measure and match as it is directly affects Mu, and also directly affects the output impedance of an amplifier. For these reasons amplifier designers are primarily concerned with Mu, followed by Rp, and hardly ever at all consider Gm. Presently, there is only one tube tester - Amplitrex - that gives us ability to measure and match Rp.

The two examples below illustrate importance of Rp in matching triodes. The first example represents measurements of two well matched triode sections of the same 6922 tube as well as a plot of plate voltage against related plate current for each section of the 6922. The measurements are made on Amplitrex tube tester.

The second example represents measurements of two poorly matched triode sections of the same 6922 tube as well as a plot of plate voltage against related plate current for each section of the 6922.

In the first example sections of the 6922 have Mu of 29.7 and 28.1 respectively. This is a significant mismatch of Mu for 6922 tubes and without consideration of plate resistance would probably render this 6922 as poorly matched. However, the plate resistance of both sections is the same - 2.2 KOhm. The plate resistance offsets the Mu disbalance and produces perfectly matched sections of the 6922.

In the second example sections of the 6922 have Mu of 26.2 and 28.3 respectively. This is also a significant mismatch of Mu for 6922 tubes which is further compounded by difference in the plate resistance of 300 Ohm. As the result, the Mu disbalance and the difference in plate resistances produce profoundly mismatched sections of the 6922. Take a note that the plot represents the correlation of the plate voltages and the related plate currents between 45V and 90V. Once the plate voltage increases to more usual for the 6922 150V - 200V operating range, the mismatch between the two sections will become even more profound.

2.Pentodes

Pentodes are primarily installed in the output (power) stages of amplifiers. Voltage gain of a pentode is defined by pentode's Gm multiplied by the impedance of an output transformer connected to the pentode. For this reason, Gm (transconductance) must be matched for optimum performance of pentode within the same channel and pares of pentodes in the right and left channels. Further, Gm of a pentode (or pares of pentodes) has to stay matched over the range of bias currents of an installation of that particular pentode or pentode pare. Typically, pentodes that are matched for both their bias current and for their Gm (transconductance) tend to stay matched over a wide range of bias currents applicable to power stages of amplifiers.
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