Mu, Gm and Rp and how Tubes are matched

Mu (voltage gain), Gm (transconductance) and Rp (plate resistance) are the three electrical characteristics that make up the overall electrical characteristics for a vacuum tube. . There is much confusion in the audiophile community about these factors as they affect tubes and their performance in components. Written by world-renowned amplifier, Roger Modjeski, this article, will look at what each of these characteristics mean, how they are measured and what each of them means to the sound of a component. We will also look at tube testing, tube matching and which characteristics are most important when matching tubes for a given circuit.

How these measurements are applied and their relevance differs for triodes and pentodes. Triodes and pentodes both possess the characteristics Gm (transconductance) and Mu (voltage gain). However what is important in triodes is Mu and what is important in pentodes is Gm as these parameters are the dominant characteristics affecting performance when each is used in a typical circuit.

Triodes have an interesting relationship where two parameters relate to make a third. These parameters are locked into a relationship so that knowing any two will yield the third. Just like ohm's law. In the case of triodes, Mu = Gm x Rp. Gm has the units of mhos, (amps per volt) and Rp has the units of ohms (volts per amp) and when multiplied their units cancel, making MU (a measure of voltage gain) unit-less as it should be. A Mu of 30 means that what goes in comes out 30 times bigger.

Triodes are most widely used for voltage amplification in our preamps. Here, Mu (voltage gain) is the more important parameter to measure and most directly affects what you hear. If you have a tube with a Mu of 30 in one channel and a MU of 33 in the other, you will have a 1-dB imbalance in your preamp. So letís say you get two triodes matched for Gm. There is no assurance that these tubes will have equal voltage gain. Voltage gain (Mu) is the product of Gm and Rp. So if Gm is matched to, get matched Mu (the important characteristic in this circuit) Rp must be matched also and Rp is almost never measured. So as you can see although 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 vendor measuring Gm would give you the Rp then you could calculate the Mu by simple multiplication. The reason you don't get the Rp data is that it is hard to measure and no commercial tube tester ever measured it.

Modern audiophiles are more concerned about "matching" than ever before. They want everything to be matched, though they rarely know what it should be matched for. This is a dangerous situation as many of you are buying because the vendor says it is matched, though it may or may not be matched for something unimportant while something important is not matched. Gm and MU are a perfect example.

Rp or plate resistance is the second most important parameter as it directly affects the output impedance of the preamp. Circuit designers are looking at Mu primarily, Rp next and we hardly care about Gm at all. Why then do most vendors measure Gm and Gm alone? Because most testers only measure Gm! No commercial tester ever measured Mu either. And even the Hickock, treasured for measuring Gm, doesnít measure it meaningfully (due to current dependency), accurately (due to calibration difficulties) or consistently (due to internal circuit drift).

Since Mu is what controls voltage gain, and voltage gain is what we listen to, then lets measure that directly. That is just what we do at RAM TUBE WORKS. Of course we had to build our own tester to do that. A few years ago I heard that one of my competitors tried to duplicate the RAM 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 are an entirely different matter. For Pentodes, as used in our power amp output stages, Gm does indeed matter and must be matched for good performance. Not only must Gm be matched, but it must stay matched over the range of bias currents typically found in amps.

In pentodes, Rp is very large and is swamped out by the load impedance. Therefore, gain is Gm times the load impedance presented to the tube (through the output transformer). Gm is the thing to measure here but the Hickok does not measure anywhere near the real world operating voltages and currents found in a typical circuit. Given I had an accurate way to measure bias and Gm at real operating conditions in a 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 (where we measure) would match at 30-70 Ma where sometimes used, or match over the range of screen voltages from 300-450 V encountered in the range of Pentode circuits (RM-200, RM-10, ARC) to Ultralinear circuits (RM-9, MANLEY, CJ).

Effects of Tube Aging
Regarding a tubeís performance as it ages, these parameters will remain stable as long as 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. 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. At RAM, our job is to check up on the tube makers and verify that they keep parameters within the published range (we reject tubes outside that range) and match for variations within that range. In the large batches of tubes we measure we see exactly what would be expected: Bell Curves for each parameter. See my article "Why the sound of your preamp changes when you change the tubes" for more on that.

My recommendation for home testing: get a simple Emission tester like a B&K DYNA-JET, Heathkit, Eico or other 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 specs to be proper when new. Those specs 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.

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