Hi there,

How do I linearise the following function:

Vo = Vs - K(Vi - Vt)^2

around the point Vi

Thanks

 

The first derivative at the point Vi will be a linear approximation to the original quadratic function.

 

Don't forget to actually build a line that will have the inclination of the tangent, but will also cross the point around which the linearization will take place.

 

Right. I should have said that you:

Write the equation of the linearization using the point-slope method using the point Vi, and evaluating the first derivative at Vi for the slope to fix the intercept.

Some algebra and you have the equation of the line in slope-intercept form.

Of course this approximation is only valid in a delta-neighborhood of the point Vi.