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load line UL v.s. triode

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I will admit that my search skills may be substandard but I couldn't find any mention of this.

I have seen many designs incorporate and UL/Triode mode switch. However it would seem intuitively that the optimal load line might be different for the two modes of operation. Is that in fact the case? If so how would you determine an optimal load line for UL mode? If one could do that and also determine the desired load line for Triode mode than an intelligent choice of compromise would be easier to determine.

the first thing you have to define is "optimal". More linear, more power, better harmonic distribution, lower output impedance. ?? thats why these things aren't so easy to sum up and just say "the best load line". I think you're right.. with some of those amps with UL/triode switches there is one mode that was designed for and the other is sub-optimal. Or some designs will compromise. Triodes can be forgiving because you can load them with a higher load than normal and they will work well, even more linearly, but just give less and less power. So thats a compromise thats often used because we already know that triode mode will yield less power anyway so its ok if its a little less than can be made maximally.

Still, how do you calculate an UL load line? In the OPT's I build, that have UL taps, most amp designers want a 43% voltage tap, per half of the PP primary windings. Some have asked for a 10% tap for cathode UL. Other numbers vary between 20% to 48 %, but no one has ever asked for more than 50%. Where do these numbers come from and how are they decided upon.

Been a lot of questions in mind about UL, for a while now.

Another set is, just what is the relationship between the grid the UL tap is attached to, and negative feedback, or is it positive feed back? Or is this grid only used to suppress electron bounce from the plate, as I have heard talked over? If so, why the % chosen and what controls those choices? We need SY and EC8010 and some other smart guys to help out here.

BudP said:

Still, how do you calculate an UL load line?....

Where do these numbers come from and how are they decided upon.

Been a lot of questions in mind about UL, for a while now.


Hi Bud:

Best to go directly to the source in a search for answers to your questions. Check out the patents by both Hafler and Keroes. They go into considerable detail on the logic and optimization of UL operation and how to select a specific UL loading for a specific tube type.

Another good reference is the article Hafler and Keroes wrote on building a UL amp in the early fifties which was published in Audio Engeering (hope I got the name right) magazine.

Also--- Norman Crowhurst wrote an excellent article on UL operation and optimizing an output transformer for UL. This was republished in Audio Amateur (glass audio I believe) around 1991 or so.

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
dshortt9 said:
There is an excellent discussion of UL mode with a chart showing the effects of UL taps from 0 to 100% here:


Characteristics for Triode, Pentode, 43% UL and 70% UL shown here:


The biggest issue with the existing U-L literature is that it is centered around max-power designs. There are no Class A operating points with U-L curves. The curves depend on where you start, not just the tap location. There is also no mention of fitting tube characteristics or amplifier performance to screen grid tap location. I also don't buy the radical curve shape they claim for distortion v. tap location. It lists triode( or 100% tap ) as the worst....I do doubt it. Smells like marketing indulgences to me.

A tertiary winding OPT is another way to deliver U-L performance. That topology offers additional benefits, and only a few OPT are made with both taps and tertiary coils. There are fortunately several designs available with cathode FB/tertiary windings to modify...:) Thordarson, Acrosound and Chicago all have excellent designs...and to a step down, the Dynaco 440/441.
I didn't know that UL curves were available however I did find them for some of the tubes that I was thinking of (6550, KT88, EL34, 6L6). So my thought for a practical approach is start with the selection of possible OTs under consideration (in my case edcor open frame SE) and run a few load lines on the UL and Triode curves and see what is possible.

For example I suspect the 5K transformer and EL34 might be a reasonable choice. If it appears that a lower impedance would be preferred then the 16ohm version could be ordered and loaded with 8 ohms.

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