I did a bit of wandering around the 'Net and found this:
http://theradioboard.com/pix/01669553.pdf
The maths. gets a bit heavy - as is often the case with explanations like this, and the author's mathematical reasonings & explanations are not that easy to follow - again, as is so often the case. However, I did manage to re-write what he has written so that is was understandable (well, 'understandable' to me) and, yes, it is valid. √
The final equation (equation 6) is the one that is of interest to us: the relationship between the effective capacity of the variable capacitor and the angle x of overlap of the capacitor vanes. (I've used 'x' where the author has used 'theta': I can't produce the Greek letter 'theta' here, so I've used 'x' instead). It looks a bit fierce, but when you identify the fixed-value terms and replace them by single constant-value terms, such as a, b, c, etc., equation 6 eventually reduces to the form:
C(x) = ax^3 + bx^2 + cx + d . . . . (equation 7)
where C(x) denotes the capacity at angle x and x^3 means x to the power of 3, etc.
Now equation 7 is a cubic. If we introduce a padding capacitor, say k, then the 'effective C' becomes: C(x).k / [C(x) + k].
If you substitute C(x) from equation 7 into that, you get an equation for Ceffective in the form of [one cubic function] ÷ [another different cubic function]. And that tells me that since the nature of equation 7 is now different, when adding a series padding capacitor to the SLF variable capacitor, the SLF law of the variable capacitor will not be preserved.
Al. / April 6, 2013 //
http://theradioboard.com/pix/01669553.pdf
The maths. gets a bit heavy - as is often the case with explanations like this, and the author's mathematical reasonings & explanations are not that easy to follow - again, as is so often the case. However, I did manage to re-write what he has written so that is was understandable (well, 'understandable' to me) and, yes, it is valid. √
The final equation (equation 6) is the one that is of interest to us: the relationship between the effective capacity of the variable capacitor and the angle x of overlap of the capacitor vanes. (I've used 'x' where the author has used 'theta': I can't produce the Greek letter 'theta' here, so I've used 'x' instead). It looks a bit fierce, but when you identify the fixed-value terms and replace them by single constant-value terms, such as a, b, c, etc., equation 6 eventually reduces to the form:
C(x) = ax^3 + bx^2 + cx + d . . . . (equation 7)
where C(x) denotes the capacity at angle x and x^3 means x to the power of 3, etc.
Now equation 7 is a cubic. If we introduce a padding capacitor, say k, then the 'effective C' becomes: C(x).k / [C(x) + k].
If you substitute C(x) from equation 7 into that, you get an equation for Ceffective in the form of [one cubic function] ÷ [another different cubic function]. And that tells me that since the nature of equation 7 is now different, when adding a series padding capacitor to the SLF variable capacitor, the SLF law of the variable capacitor will not be preserved.
Al. / April 6, 2013 //
