7

I'm reverse-engineering a CRT anti-pincushion circuit and it uses a complex diode-resistor circuit to approximate the function X-k×X×Y², 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 = 6XY² + 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?

Schematic of the circuit

Ken Shirriff
  • 2,694
  • 15
  • 23
  • 1
    Might [start here](https://patentimages.storage.googleapis.com/0f/c5/d7/4f34774355fad4/US2758248.pdf)? Good question though, so +1. – jonk Aug 10 '21 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. – Ken Shirriff Aug 11 '21 at 01:31
  • 1
    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 Aug 11 '21 at 01:36
  • @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. – Ken Shirriff Aug 11 '21 at 01:41
  • 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 Aug 11 '21 at 01:53
  • Log then addition then anti log? – user69795 Aug 11 '21 at 01:54
  • @Antonio51 Thanks. I appreciate the confirmation! But it was only mathematical intuition where I didn't see another solution set. You did the work. Thanks, again! – jonk Aug 13 '21 at 08:26
  • @Antonio51 The simulation that you call strange is the expected behavior. The curves show how the X deflection gets pulled in at the edges to counteract the pin cushioning. (The curve makes more sense if rotated 90 degrees.) – Ken Shirriff Aug 13 '21 at 17:01
  • @Antonio51: Thanks for looking at this. I tried to reproduce your tanh, but there's a problem: you're computing tanh of v (i.e. the output) not i. tanh(v/10)*10 is an identity function for small v, so of course it's a perfect fit with v. The curve is similar to tanh but not as good a match as the image implies. – Ken Shirriff Aug 13 '21 at 17:38

0 Answers0