What I was trying to achieve here was to measure inherent tube distortion. In order to better understand what I mean by saying “inherent distortion” we need to take a quick look at what is the main distortion production mechanisms in tubes. To keep it more accessible for inexperienced reader let’s first  get back to the core basics.

There are two types of distortion: linear and nonlinear. When we speak about linear distortion, we assume that it doesn’t change with amplitude and there is no additional frequencies at the output of device we are measuring. Typical example would be amplifiers frequency response.

At some point in frequency amplifier will not be able to produce same amplitude signal as before and it’s amplitude will begin to change. And tubes are particularly good at minimizing this type of distortion. That’s because the main reason which causes amplitude changes at different frequencies is the internal device capacitances. In case of tubes they are usually order of magnitude lower then with silicon devices. These capacitances are well understood and defined in datasheets and it’s up to circuit designer to ensure they will not cause trouble in audio band. So there is really no good reason to measure linear distortions in tubes, without taking whole circuit into account. Instead let’s concentrate on nonlinear distortions. It’s easier to visual them by drawing device transfer function. 

If device output voltage changes linearly with input voltage, then we call this device linear. Typical example of linear device with GAIN=1 would be ideal resistor. Otherwise we say that device has nonlinearities which are represented by it’s transfer function. This un-linear amplification of input signal has an effect of producing frequencies that were not a part of input signal.

These frequencies are not random, but are integer-multiples of input frequency and we call these new signals “Harmonics”. First harmonic H(1) is fundamental and is our input signal. Second harmonic H(2) is a new signal with its frequency being twice higher, H(3) – three times higher and etc. When these voltages are combined in our output we get a distorted signal.

So summing up what was said, we can measure any device nonlinearity by tracing it’s transfer function and looking at curvature or by measuring it’s distorted output signal. Both approaches are useful, but when dealing with really linear tubes – curvature are very hard to spot visually and distorted signals are very small in amplitude. So it’s far more feasible to measure distortion signal in frequency domain by producing it’s spectrum and drawing it on decibel scale.  

Sources of nonlinearities in tubes

As shown above a valve distorts because of the curvature in it’s anode current (Ia) vs. grid voltage (Vg) transfer characteristic. This distortion in triodes is predominantly 2nd harmonic. To show why this is the case without using any math we must introduce a term “internal (or anode) resistance – Ra”. In triodes, Ra is changing with anode current and can be found from tubes plate characteristics.

When tube is loaded with resistor Rload, this resistor together with anode resistance Ra forms a voltage divider.  Now when we supply a signal to this voltage divider – Rload stays constant, but Ra changes together with signal current. This produces more attenuation in one half of the signal then in other, as can be seen in voltage waveform above. Whenever we have asymmetrical distortion – this distortion will always be 2nd (or even order) predominant. In order to reduce this distortion we have to increase Rload >>Ra so that attenuation would be negligible or keep current Ia=constant so that Ra would not vary at all.

Another source of distortion is tube amplification factor μ variance with anode voltage Va. μ can be easily found from plate characteristics and is equal to ratio of plate and grid voltage changes. To minimize this type of distortion we must avoid operation in nonlinear region at small currents (choose right AC operating point) and keep load line as horizontal as possible. This means keeping Ia=constant and high enough. 

And finally we have distortion due to grid current. Whenever grid voltage Vg approaches 0V, tube input resistance Ri increases dramatically and grid current starts to flow. Although distorted signal waveform is similar to Ra distortion, but it has more symmetrical clipping. This symmetrical clipping is not 2nd (or even order) predominant, but instead has a lot of high order uneven harmonic content and is much more wrecking. To avoid this distortion we must minimize voltage source resistance Rs and choose such a DC operating point, that with maximum AC input voltage grid current stayed negligible. 

Summing up what was said above, we can conclude that in order to minimize tube distortion we must:

• Increase Rload >>Ra and keep Ia=constant
• Choose right AC and DC operating points to keep out of nonlinear and grid current regions

Whatever distortion is still left after that, we can call inherent tube distortion as it can no longer be mitigated without some sort of distortion cancellation or negative feedback mechanism.

Practical realisation

To satisfy first part of the requirements (Rload >>Ra, Ia=constant) we can substitute resistor load with active load such as constant current source (CCS). Theoretically CCS internal resistance is →∞, but since we will be building it from real components it’s resistance will be finite.    

In practise, CCS made of BSP129 and DN2540 depletion mosfet cascode will have a resistance of a couple MΩ at lower currents, that are usual for some small triodes. This resistance will fall down to couple hundred kΩ  at higher currents when used to bias output power tubes. This is still a lot when you consider that if a real resistor of 200kΩ would be used to bias tube at 100mA it would require supply voltage of 20kV! This is all true for single 1kHz frequency that we will use in all our measurements. With increased frequency this performance will degrade further.

As can be seen from measurement setup schematics, real life performance will be further limited by an input resistance of a measurement device used. This means that tube will see a total load resistance between of ~200kΩ (best case) and ~100kΩ (worst case) depending on CCS current. 

220kΩ resistor forming voltage divider could be further increased to boost effective load resistance but only in expense of measurement noise floor. Practise had shown that driving sound card input with high impedance source produces spray of high order harmonic content that is masking low level details and 220kΩ was found to be a good compromise. This could be rectified by introducing additional low distortion buffer with very high impedance (jfet) input and is something to implement in the future. For now I feel that a load of 200kΩ is very close to what you would expect in tube amp when coupling from one stage to another, so these measurements should better match real life results.

Couple more notes

In order to fulfil second part of requirements (choosing right AC and DC operating points) plate characteristics for each individual tube was traced manually. Limiting factor here was my HV power supply that only goes to 300V DC. Traced curves already gave a good idea on what operating points should be avoided. Also a quick look at RAW measurement data quickly revealed onset of grid current.

Then 5 to 10 different CCS current points was chosen and grid bias voltage was swept on-the-fly for each current to find lowest THD point. Spectrum of this op. point was captured and saved. Further, for some more promising tubes, absolute lowest THD current point was chosen and THD changes by sweeping grid voltage was recorder. This enabled production of crude THD statistics that are available for some of the tubes in data library.

Finally I should elaborate on the choice of 10Vrms (+22dBu) output voltage for all measurements. Here the limiting factor was audio card output voltage which is 2Vrms. This means that only tubes with μ>5 could produce required output voltage of 10Vrms. In practise this proved to be sufficient as only one tube (EL509) in my stash had lower μ of 4.