Transconductance, Mutual Conductance and Other Tube Numbers. 21 May 2013 (revised 2 Mar 2019) Mike at MDBVentures.com http://www.MDBVentures.com When Gm and rp are shown in datasheets, they are for specific operating conditions. As an example for the 12AX7 in the GE Essential Characteristics handbook, you will see different values given for both Gm (1,250 and 1,600 umho) and rp (80,000 and 62,500) with two different plate currents (0.5 and 1.2 mA.) However the mu is 100 for both. Gm is derived from the gain of the tube (mu) divided by the plate resistance (which is derived from the delta plate voltage divided by the delta plate current). Most attempts at describing the operation of a tube focus on numbers like Gm, mu, rp and the like. The problem is that if you don't understand the basic physics that the numbers are measuring, it gets very confusing and hard to understand. The basic physics of a tube (for a triode anyway) is very simple. The easiest way to look at it is that it is a voltage variable resistor. More grids add a bit of complexity, but the basic physics doesn't change. For a given instantanious voltage on the control grid, the resistance between the cathode and plate will be a specific value. As long as the tube is being operated within its "linear" range, the resistance will be the same every time. It is a property of the distance between the cathode and plate and the construction and position of the grid located between them. When you make the control grid more negative relative to the cathode, it prevents fewer electrons from getting to the plate. That results in the tube having more resistance. The other thing that affects the resistance is the number of electrons emitted from the cathode. As the cathode material wears out, there are fewer electrons emitted, so the plate resistance increases. This is why the Gm goes down as the tube wears out. Now the problem is that the resistance change is not of direct use in itself, and cannot be directly measured. Although it is in reality not that hard to determine (it is simple ohms law). Measure the voltage across the tube (plate to cathode) and the current flow through the tube (plate current) and the simple calculation of R=V/A gives you plate resistance. If you read some of the documents, they talk about using a constant voltage source and others talk about using a constant current source. For a simple DC grid voltage you don't need that if you can measure the current and voltage directly across the tube. The tricky part is that only gives you a plate resistance at a particular DC grid voltage. Tubes are normally used as AC amplifiers not DC, and the plate resistance specification is a dynamic resistance (delta) not a static resistance. So to measure how the tube will work in an AC circuit, you need a better measurement method that doesn't interfer with measuring the plate current over the range of input voltages (the sinewave input). That means either using a constant voltage source, or a constant current source. With a constant voltage source you measure the AC plate current, and since the voltage source is constant, you know what it is all the time so rp=V/I. With a constant current source you measure the AC voltage across the tube (plate to cathode) and the equation becomes again rp=V/I. The only thing that has changed is which part of the equation is the variable that tells you what the plate resistance is. So it doesn't really matter which way you do the measurement. Which method (current or voltage) you use is really an issue of what sort of circuit is being used to take that information and convert it to the other desired information (mu and Gm). Note: One thing that can be confusing is understanding the plate resistance value. The plate resistance stated in the GE essential characteristics manual is not a static plate resistance value. It is derived from a dynamic measurement of the tube current at the design center. That is why if you divide the stated plate voltage by the stated plate current, you do not get the stated plate resistance. eg for the 12AX7 : 100V/0.0005A=200000 yet the manual says 80000. So why the difference? The plate resistance is a dynamic plate resistance. That means it is determined by measuring the plate current at a given plate voltage, then changing the plate voltage and measuring the plate current again (DeltaV/DeltaA=PlateResistance). The one constant for the tube is mu. Within the linear portion of the tube operating range mu remains relatively constant (that is what makes the linear portion of the tube linear). Very simply, mu is the change in the output resistance of the tube relative to the change in the control grid voltage. This is normally defined as mu being computed as a change in the plate voltage relative to a change in the control grid voltage using a constant current source for the plate. mu then is simply mu = DeltaOut / DeltaIn. Although I've also seen definitions that use a constant voltage source. It doesn't really matter, Ohm's law makes it all the same. It just depends on how you want to measure it. mu will always be the same. It is set by the physical construction of the tube at the time of manufacture. The only thing that will change it is damage to the tube (causing the physical elements inside the tube to change position), or operating the tube outside it's linear range. Which can happen as the tube wears out and the linear operating range shrinks. Although it should be noted that tubes are not perfect linear devices, so mu will change slightly as the voltage and currents change through the tube, but generally it will be less than 5% change within the operating range of the tube. The exception is non-linear tubes like pentagrid converters which actually need to be non-linear to perform their job. That is why you don't normally see Gm readings for pentagrid converters. It is a meaningless measurement. (It is also why tube testers that try to test the Gm of a pentagrid converter have problems and will often claim a perfectly good tube as being bad.) That brings us to Gm, which is a combination of the mu (gain) and rp (dynamic plate resistance) values (Gm=mu/rp). Since dynamic plate resistance is not normally measured directly, you will sometimes see the equation written relative to the dynamic plate voltage, or to the dynamic plate current. As an exercise, look at the GE essential characteristics handbook for the 12AX7. It shows the rp as 80000, the Gm as 1250 and the mu as 100. 100/80000=0.00125 (ie 1250umhos). You will also notice that a second set of rp and Gm values are listed. rp=62500 and Gm=1600. Again the math is 100/62500=0.0016mohs or 1600umohs. Notice that the Gm has changed because the plate resistance is different, and plate resistance is dependant upon the input bias to the tube. That is why when you adjust the bias control on the tube tester the Gm reading changes. Some descriptions will note that the Gm is dependant upon the current flow through the tube. That is not exactly correct. It is dependant upon the plate resistance, which is what controls the current flow through the tube. So the primary view should be to the plate resistance, not the current flow so that an understanding of the basic function of the tube is maintained during the thought exercise. It is not about current flow, it is about cathode to plate resistance, which is what determines the current flow. One thing that is important to keep in mind is that tube testers do not normally have circuits that properly measure Gm (which requires a constant voltage or constant current source). This is why you see a varience of Gm readings amoung different testers. Even amplifier circuits do not use constant current or voltage sources because of the expense. Instead what most use are either long tail current sources or short tail voltage sources. A long tail current source is simply a resistor in series with the plate. The resistor is significantly larger than the plate resistance during use. That makes the source current varience minimal enough to not be a significant effect. Most small signal amplifiers use a long tail current source for the plate supply (because it is just a simple resistor). Power tubes normally use a short tail voltage source (the output transformer winding). It has a resistance that is small relative to the tube plate resistance which makes it an effective constant voltage source. Unfortunately it is not perfect and is a primary source of non-linearities in the output. That is what the ultralinear amplifier circuits compensate for. They sample the output of the transformer and feed it back to the circuit input to compensate for the amplification errors. For tube circuit designers, Gm is not really used. What is important is mu and rp plus all the other stuff like max operating voltage and current. But what is really important is the curve trace charts for the tube so they can see how the tube operates under various conditions. The Gm value is an attempt to munge all that into a single value that can be used as a test reference to decide if the tube is functioning without having to go to the time expense of doing a curve trace and an engineer to interpret the results as to whether the tube is still functional. The Gm just provides a single number that can be used as a go/no-go decision reference. So the Gm provided in the Essential Characteristics is based on the design center voltages that are typically used for the tube. The 12AX7 shows two different Gm values because those are the two most common design centers used for the tube. That doesn't mean that a tube tester will use either of those values for its reference, nor that a tube tester showing a Gm reading different than the GE Essential Characteristics Gm values is wrong. What is important to remember is that the Gm value is a relative measurement to a particular operating condition of the tube. A tube tester is not likely to operate the tube in the same condition as it is used in a circuit. Luckily for small signal tubes, the tube tester can usually come close, but you should use the Gm value listed on the tube tester as your reference not the GE Essential Characteristics value, because the two are not likely to match the operating conditions for the tube. Tube testers are general purpose beasts and have to compromise the test circuits to cover all of the tubes that they can test. The only way to truely measure the tube is while it is being operated in the circuit for which it was designed to be used. Also see the companion files: http://www.fourwater.com/files/restr666.txt http://www.fourwater.com/files/666-667-mod.png http://www.fourwater.com/files/eicotesting.txt http://www.fourwater.com/files/eico666-667-repair.txt http://www.fourwater.com/files/mutualconductance.txt http://www.fourwater.com/files/eico666meter-power-notes.txt http://www.fourwater.com/files/eico666tester-meter-check.txt http://www.fourwater.com/files/testertypes.txt http://www.fourwater.com/tubeinfo.htm Visit us at http://www.MDBVentures.com - Great prices on great tubes!