Transfer function of a gain stage

[Dave H]

Thanks Steve. I can’t even remember the correct terminology

[bob p]

The resulting transfer function captures the frequency-domain behaviour (and therefore the time-domain behaviour too) but it's a linear approximation that ignores the non-linear behaviour. You can write another kind of transfer function that captures the non-linear behaviour but not the frequency-domain behavour. This is a more complicated affair, basically done by curve fitting. Korg have a patent that describes how they did it.

If you want to capture both aspects in a single function, the math gets horrible. One way of doing it uses a "Volterra kernel". Volterra series - Wikipedia, the free encyclopedia I've seen this used in DSP modelling plugins.

Nice information. I have always wondered how those guys accounted for the non-linear behavior. I guess I'm going to have to look for that Korg patent.

[eschertron]

Nice information. I have always wondered how those guys accounted for the non-linear behavior. I guess I'm going to have to look for that Korg patent.

Google "Phase Distortion"

[überfuzz]

If I may stray off topic, slightly. At what range should I have my treble pot? Eh, I mean the treble pot, what frequency range should it affect? Eh, what range for all pots if I have a bass, mid and treble pot?

[Enzo]

The freq ranges of each control are affected by the others, they are all interactive, so there is no specific freq for the treble control.

Go over to Duncan Amps web page and find the Tone Stack Calculator. it is a free little download that lets you look at the freq response curves of popular tone stacks as you move the controls. It does this in real time. Really cool.

[überfuzz]

Enzo - I'm pretty familiar with the technical aspect. I was hoping for some input on where you folks like to put each pots effective range. You know based on experience rather than teory.

[jazbo8]

As Enzo mentioned there are so many variables involved and they do interact, but based on the popular FMV tonestack, the low seems to be 80-200, the mid 200-1k, and the hi 1k and above. But more experienced builders may have their own preferences.

I also made an attempt at the transfer function for the typical common cathode stage used in guitar amps, you can download it here. Please take a look to see if that's what you wanted. As mentioned by Steve earlier, the transfer function is only valid for small-signals, it can not be used when the stage is over-driven and becomes non-linear. I did not string together all the transfer functions as that would make it very difficult to read, but if you want to see it, I can send you a copy.

Jaz

[Steve Conner]

Phase distortion synthesis was developed by Casio for their keyboards. It's just a form of FM synthesis similar to many other synths of the era, and has nothing to do with either Korg or amp modelling. I don't have a link for that patent, I've lost track of it.

[trobbins]

[QUOTE=loudthud;299002]The attached photo is an X-Y plot of a 12AX7 ...QUOTE]

Loudthud, that's a nice practical plot - thanks for showing it. The difference in transfer slope when in cutoff versus when in grid-current limiting, and the transition into those limiting regions, is easy to appreciate in this type of presentation.

With about 1.8V bias on cathode, this looks like about 100k anode load. The further fall off in anode voltage from about 100V to 90V with a further increase in grid voltage of about +4V indicates a grid current of about 0.17mA at +8V grid, where the grid-cathode voltage looks like being about +0.2V (assuming somewhat linear extrapolation of generic 12AX7 grid curves along a loadline) although I note that Merlin's plot (Fig 1.22) indicates a grid-cathode voltage of +0.4V would come from a 0.17mA grid current, but calculating slopes is little hazy in that region.