[sdiy] An Improved Sine Shaper Circuit

[René Schmitz]

On 17.04.2020 23:15, Donald Tillman wrote:
> I did find that if you don't get close to the 0.710 optimum beta value, 
> then there's little improvement over the standard long tail pair.  With 
> beta value of 0.710 the harmonics are down 76dB.  With a beta of 0.600, 
> the harmonics are only down 44dB.

Keeping this stable could be interesting. There are kT/q terms all over 
the place. (one place...) In the first order you could scale the Vbe in 
a very familiar way.

> So the order of magnitude improvement happens at a golden point.

Intuitively, for each amount of drive you give to the tanh function 
(i.e. the interval of the tanh that actually is used), there is a 
corresponding beta for the linear term, such that at the ends (+-pi/2) 
the curve is horizontal (d/dt=0). And we have a fixed point at f(0) = 0. 
But there is only one such combination (drive, beta), where the 
pointwise difference to an ideal sine is minimal over the entire interval.

Best,
  René

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