# How to understand a complex diode-resistor function generator circuit?

I'm reverse-engineering a CRT anti-pincushion circuit and it uses a complex diode-resistor circuit to approximate the function $$\X-k×X×Y^2\$$, where $$\X\$$ and $$\Y\$$ are the deflection voltages. My question is if there's any way to understand this circuit conceptually. I put it into LTSpice and I get results but is there any way to understand this at a higher level? How did they come up with this circuit in the first place?

I'm familiar with simple resistor-diode function generators that make a piecewise-linear function by treating the diodes as switches that turn on at various points (like this). But this circuit has four resistor-diode "blocks" that are cross-coupled by R14-R17 which mystifies me. Each block has diodes in opposite directions, which sort of makes sense so everything happens in reverse when X and Y are negative.

The blocks on the right (D9-D14 and D15-D20) implement roughly cubic functions, so I tried to understand this as $$\(X-Y)^3 - (X+Y)^3 = 6XY^2 +\$$ smaller terms, which (scaled) is the desired correction factor, but I couldn't make this explanation work.

Maybe there's a theory of diode function generators that explains this circuit?

• Might start here? Good question though, so +1.
– jonk
Commented Aug 10, 2021 at 23:45
• @jonk: That patent describes the same problem but a totally different solution, interestingly enough. With a raster-scan CRT, the correction can be a function of time as in the patent. But my circuit is for a vector CRT, where the correction needs to be computed from the X-Y values. Commented Aug 11, 2021 at 1:31
• I was hoping to provide a starting point in time -- a reference point -- at least. It includes a diagram that I also felt might stimulate useful ideas. But I've not thought about the problem, yet, except to note that the needed correction looks hyperbolic in shape.
– jonk
Commented Aug 11, 2021 at 1:36
• @jonk: thanks for providing it as a starting point. Looking at the patent, maybe you meant parabolic instead of hyperbolic? This would match the Y² contribution I see from the circuit. Commented Aug 11, 2021 at 1:41
• No, I was actually thinking hyperbolic. Parabolic has a unique shape out of an infinity of nearby shapes and is unlikely to actually occur. Hyperbolic is 'everything else' so to speak. And, given some mild experience talking with experts on this decades back, I'm quite sure they used 'hyperbolic' as a general description. I believe, had I bothered to pin them down, that they would have included 'parabolic' in the limit, though.
– jonk
Commented Aug 11, 2021 at 1:53