Mu, GM, & Rp & How Tubes Are Matched
Voltage gain (Mu), transconductance (Gm) and plate resistance (Rp) are the three electrical characteristics of a vacuum tube. There is confusion among audiophiles about how these characteristics affect tubes and their performance in components. In this discussion we will look at these characteristics, how each is measured, and how each interacts within a circuit. We will also discuss tube testing, tube matching, and which characteristics are most important when matching tubes for a given circuit. Also, how these measurements are applied differs for triodes and pentodes. Both have Gm and Mu, but Mu is the important characteristic in triodes while Gm is most important in pentodes. As such, these parameters are the dominant characteristics affecting performance when each is used in a typical circuit.
Triodes
With triodes, as in Ohm’s Law, two parameters relate to make a third. The parameters are locked into a relationship so that knowing any two will yield the third. In this case Mu = Gm x Rp where Gm is units of amps per volt (mho) and Rp is units of volts per amp (ohms). When multiplied their units cancel, making Mu unitless as it should be. A Mu of 30 means that what goes in comes out 30 times bigger. Triodes are widely used for voltage amplification in preamplifiers which is why Mu is the more important measurement affecting what you hear. If you have a tube where Mu = 30 in one channel and 33 in the other, you will have a 1 dB channel imbalance. So, if two triodes are matched for Gm, there is no assurance these tubes will have equal voltage gain. Since Mu is Gm x Rp, if Gm is matched to Mu, Rp must also be matched.
However, Rp is rarely measured and while the famous Hickock tube testers are sought for their ability to measure Gm, this was more of a marketing ploy and less useful for real-world testing. If the tube vendor measuring Gm would give you the Rp then you could calculate the Mu by simple multiplication. The reason you do not get the Rp data is that it is hard to measure, and no commercial tube tester ever measured it. Audiophiles want everything to be matched, though they rarely know what it should be matched for, and are buying tubes just because the vendor says they are matched. However, they may or may not be matched for something unimportant while something important is not matched. Gm and Mu are a perfect example.
Although we are primarily looking at Mu, Rp is the second most important parameter as it directly affects the output impedance of the preamplifier. Since we hardly care about Gm here, why do most tube vendors focus on Gm? The reason is most tube testers only measure Gm! Very few commercial testers measure Mu either. Although the Hickock does, it does not measure it meaningfully (due to current dependency), accurately (due to calibration difficulties), or consistently (due to internal circuit drift). Since Mu controls voltage gain, and this is what we listen to, then we should measure that directly. This is what I do, but I had to build my own tube tester to do it. A few years ago, I heard one of my competitors tried to duplicate my tube tester and gave up after spending $100,000. It took me about a year to develop the small tube tester and another 6 months to develop the power tube tester. These were no small efforts.
Pentodes
Pentodes, as used in power amplifier output stages are an entirely different matter. Here Gm does indeed matter and must be matched for good performance. In addition, it must stay matched over the range of bias currents typically found in amplifiers. Since Rp is very large and is swamped out by the load impedance, gain is Gm multiplied by the load impedance presented to the tube (through the output transformer). So, while Gm is the parameter to measure, the Hickok does not measure anywhere near the real-world operating voltages and currents found in a typical circuit. As I had an accurate way to measure bias and Gm at real operating conditions in a tube tester of my design, I found that tubes matched for bias and matched for Gm would "track" each other over the wide range of bias currents encountered in power amps. Without this accurate "double match" there would be no guarantee that tubes measured at 50 mA would match at 30-70 mA, or match over the range of screen voltages from 300-450 V encountered in the range of Pentode and Ultralinear circuits.
Effects Of Tube Aging
Regarding a tube’s performance as it ages, these parameters will remain stable if the cathode emission is 70% or more of its original value. If Gm, Rp, and Mu are right and matched when new, they will stay right and matched through the usable life of the tube. Given that, all we need to measure is the emission to know the tube is still good. Only in rare cases will this not be true. I routinely check up on the tube manufacturers and verify that they keep parameters within the published range and I match for variations within that range. I reject any tube outside that range. When measuring large batches of tubes, I see exactly what would be expected: Bell Curves for each parameter.
My recommendation for home testing: Get a simple emission tester like a B&K DYNA-JET, Heathkit, Eico, or another non-Gm tester. They are simple to use, stable, accurate, and relate well to the life remaining in your tubes. Buy your tubes from someone who certifies their specifications to be proper when new. Those specifications are built into the tube and will remain constant as the tube ages. All you need to do is monitor the condition on the cathode coating, which is easily measured via emission. So if a tube was properly made and tested when new, all one needs to assess its current state is a simple emission tester.