Well, a pentode or tetrode is a compound device of sorts, the screen grid provides something similar to cascode operation with transistors.

Then we can classify:

- Triode mode: No cascoding takes place

- Pentode/Tetrode mode: Full cascoding with a constant cascode voltage

- UltraLinear mode(s): partial cascoding, or better termed modulated cascode voltage

To find a good loadline, we basicly need an understanding of the triode output characteristics plate current vs. plate voltage, with control grid voltage as a parameter. This gives us the typical graph, but it is better to image it as a three-dimensional surface, x is plate voltage, y is plate current and z is grid voltage. A good loadline (with regard to distortion) is placed at that section of the surface which has the least curvature in any direction (remember speaker loads are reactive, which gives us "load-areas", not only load-lines with the simple I-V relationship). Some constraints have to be met also, mainly power dissipation and voltage/current limits, which cuts away much of the surface, efficiency/headroom considerations etc. Also one must keep in mind that an xformer output places two different types of load on the tube, a DC load (a stable, but very steep load line) and AC load, with a continuous transition between them as frequency rises from sub-Hz terrain to audible regions. And if we have a push-pull design, two of those surfaces need to be combined in a mirrored fashion. Further, sensivity to paramter shifts (systematic and due to aging) in actual parts has to be looked at.

With a screen grid, things complicate, we add another dimension to the surface, screen voltage. This could be best imagined as a scalar potential (of plate current), for any given point in the 3D-space formed by plate voltage, grid voltage and screen voltage we can read the plate current. When we have a fixed realationship between plate voltage and screen voltage (in the form of Vs=a*Vp+b, which covers all the basic variations), this accomplishes a "projection" back from the scalar 3D-potential to the 3D-surface.

The same considerations about where to best locate the load-areas on this surface again apply. And we also get two further constraining variables, screen current and dissipation, screen current can be handled with a change in representation from a scalar field to a vector field (vector components being plate current and grid current). Screen current also adds its part to total transformer flux, a detailed analysis must take that into account. Not to forget dynamic aspects, that is dependency of the variables of previous (in time) states.

This type of geometrical understanding of the output characteristics might seem a bit overdone and too academical at first but will prove to give the best result in the quest for the lowest possible distortion or other kind of optimization. Of course one needs to measure the complete characteristics which is comletely impossible without automated test equipment and computer software processing the data, given the millions of data points which are needed for a closely spaced scan. Even more we should worship the efforts (and their outcome) of the tube pioneers, when all they had were function tables, slide rulers and a deep knowledge ot math. I really take my hat off to these people.

I can recommend

Pete Millet's website with tons of scanned books on tubes, a most impressive source of information.

- Klaus