Using the tanh function for modelling non linearity in a Programmable Gain Amp ?

[Ranand]

Hi,
I am trying to write a Real number Model for a Programmable Gain amplifier and came across the following expression for limiting the output voltage , can some one please help me understand how this is derived?

Vodif = Vomax*tanh(Av*(INP-INN)/Vomax)

where,
Vodif is the closed loop differential output voltage.
Av is the closed loop voltage gain.
Vomax is the maximum outo put voltage swing.
INP , INN are the differential inputs to the amplifier.

Thanks,
Ranand

 

[FvM]

I0*tanh(ΔVin/Vt) is the transfer characteristic of an ideal differential BJT pair (without emitter degeneration).

 

[Ranand]

Hi ,
Thanks FvM,
So in general the output voltage limiting function can be modeled by a tanh curve.
Since the max output swing is Vomax , the max input swing will be Vimax (i.e .Vomax/Av) ,So by substituting the terms in the BJT transfer characteristic expression ,we get ,

Vomax*tanh((Vi_diff)/Vimax) ,which is same as my expression.

here Vi_diff is the input differential voltage.

Please confirm if this is correct?

Thanks,
Ranand