Straight Line Frequency Capacitor

[pwdrive]

Given time I could probably work this out, however I have posted the question on here for discussion.
I need a 150 pf straight line frequency variable capacitor, not to many around, however it is quite feasable for me to obtain one of a value of 225 pf.
With the one I have in mind the whole rotor plates assembly can be removed from the shaft and it would be feasable to remove some of the rotor plates in order to get the value to the desired 150 pf, alternatively if I pad the 225 pf out with a suitable series capacitor to give a combined series value of 150 pf will the straight line frequency characteristic still be the same ie: almost linear on the tuning scale.

Lawrence.

[Skywave]

I did a bit of maths. on this and concluded that the S.L.F. will be preserved, but, in effect, the minimum capacitance increases - which, of course, is what we would expect. But as always, the proof of the pudding is in the eating. So, if you have some suitable test gear for measuring capacitance, then that seems to be the next logical step.

Al.

[pwdrive]

Thanks Al, yes I have an reasonably accurate bridge for meaurments (TF2700) if and when I can aquire a suitable capacitor.
Did you mean the minimum capacitance increases? or decreases?

Lawrence.

[Skywave]

Elementary considerations of capacitors indicates that minimum capacitance is decreased.
Two capacitors in series have a total capacitance that is less than either individual capacitor, e.g. 200 pF in series with 100 pF = 67 pF. Having said that of course, the larger the difference between the two capacitors is, the closer the final, net value of capacitance approaches the value of the one with the smaller capacity.
You meet this situation when calculating the value of padding capacitors in the oscillator circuit of superhet receivers. For the padding capacitor, you usually get a large value on L.W. and much smaller ones on S.W.; variations in the value of the large-valued padder on L.W. have a small effect; comparable variations in the S.W. padder have a large effect.

Al. / April 5th. /

[pwdrive]

Hi Al, yes I understand that but your original reply seemed to suggest that the minimum capacitance would be increased with the scenario I described unless I am reading it incorrectly.

Lawrence.

[Skywave]

You're a bit too fast off the mark for me, Lawrence!

Having made that last post, I walked away and put the kettle on and had a cup of coffee - and reviewed my calculations that I made last night - and then realised that I had made a silly error In my analysis, I had effectively 'added' the padder capacitor in parallel to the variable cap.; whoops! So I've just come back here to correct that - and found your post!
Sorry for the confusion. That'll teach me to 'do maths.' when I'm half asleep!

Al.

[pwdrive]

No Worries, cheers.

Lawrence.

[Skywave]

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 //

[pwdrive]

Thanks for your efforts on that Al, so the conclusion is that the SLF will not be preserved by the addition of a fixed series capacitor, next question is by how much will it not be preserved assuming the the variable capacitors value is 225 pf and that it needs to be effectively reduced to 150 pf by the addition of a series capacitor, ie: marginal, way out or somewhere in between?
If I had my bench rigged up I could check it out for myself by practical means but that is likely to be some time off at the moment.

Lawrence.

[pwdrive]

Now just seen the link you posted, the maths is a bit above my head but nevertheless a good definitive reference document.

Lawrence.