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Author Topic: Flat Sliding Air Variable Capacitors  (Read 8379 times)
AA5WG
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« on: February 05, 2013, 06:00:59 AM »

Hi to all,

The shape of the variable plates for Straight-Line Capacitance, Straight-Line Wavelength and Straight-Line Frequency air variable capacitors are shown pictorial in the Radio Engineering book by Terman, 1937, 2nd ed., page 30.

(1)  Instead of the above traditional design, what would the shape of the straight-line frequency air variable plates look like   if they were flat plates in the horizontal plane sliding over each other?   i.e. A brass plate sliding over another brass plate separated by glass, cardboard or air on top of my work bench.

For practice the stator plate could be taped horizontally flat to the work bench and the rotor plate could be taped to a piece of cardboard and also laid flat on top of the work bench.  This flat rotor could be pushed over the fixed stator to change capacitance.

What shape should these two flat plates look like to act as an straight-line frequency air variable capacitor?

Chuck
« Last Edit: February 05, 2013, 06:09:56 AM by AA5WG » Logged
G3RZP
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« Reply #1 on: February 05, 2013, 07:38:16 AM »

For straight line frequency, you want the overlap area to change by a square law function as you move the plate. So the shape will be similar to that for a rotating capacitor.
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AA5WG
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« Reply #2 on: February 05, 2013, 07:47:18 AM »

Hi Peter, G3RZP:

The shape of a rotating straight line frequency plate is similar to a cam shape.  Do you think a cam shape is going to work for this example, a flat sliding plate variable capacitor?

Would a triangle shape be better?

Chuck
« Last Edit: February 05, 2013, 07:53:32 AM by AA5WG » Logged
WB6BYU
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« Reply #3 on: February 05, 2013, 08:52:35 AM »

The shape is going to be a smooth curve, something like a parabola,
rather than a straight line.

To get an exact Straight Line Frequency (SLF) you have to know the tuning
range and the fixed (minimum) circuit capacitance.  The commercial SLF
capacitors are typically designed for tuning the broadcast band, and
will only give SLF behavior over about a 3 : 1 frequency range.

The bottom plate can be the same shape as the upper one, or can be a
rectangle or any other shape, as long as it extends at least as far as
the upper plate.  (Assuming the upper plate is the one that is shaped
to provide the specified tuning rate.)

Let's take an example:  assume we want to tune 3.5 - 4 MHz and the
fixed minimum capacitance in the circuit is 50pf.

At 4 MHz we have only the 50pf fixed capacitor in the circuit, so the
inductance must be 31.66uH.  Based on that we can calculate the
additional capacitance required for each 100kHz increment:

3.9 MHz needs 52.6 pf, for a delta of 2.6pf
3.8 MHz needs 55.4 pf, for a delta of 2.8pf
3.7 MHz needs 58.4 pf, for a delta of 3pf
3.6 MHz needs 61.7 pf, for a delta of 3.3pf
3.5 MHz needs 65.3pf, for a delta of 3.6pf

Since the delta isn't constant, you can't use a plate with straight edges.
However, if you break the tuning range into small enough steps you can
calculate the plate size for each based on straight lines between steps
and get pretty close.

Or you can derive the shape mathematically by calculating a curve with
the proper integral to give the tuning function, but that would take more
thought than I can give it at the moment.

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W5LZ
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« Reply #4 on: February 05, 2013, 10:55:53 PM »

Slice a non-curving trumpet in half.  That general 'shape' slid onto a plate, pointy end first, will yield a 'linear' increase in capacitance.  There's a geometrical description for that sort of 'curve', damned if I can remember what the name of it is, way too long since I was out of school.
 - 'Doc
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G3RZP
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« Reply #5 on: February 06, 2013, 12:30:08 AM »

To get SLF characteristic, you need a capacitance, which for given mechanical delta, has a square law characteristic of area, since f is proportional to C squared. It won't be a hyperbola, but it will be cam shaped and there should be somewhere a way to figure this shape out. More math than I care to do.....

But it won't be straight line, because a straight line is y=mx+c, where m is the slope and c is a constant. Differentiating gives the delta as always equal to m.
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G8HQP
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« Reply #6 on: February 06, 2013, 03:51:53 AM »

With zero stray capacitance (the simple 'ideal' case) you get SLC by sliding two rectangular plates.

SLW (wavelength) comes from a triangular plate, as overlap area varies as the square of the displacement.

SLF requires some stray capacitance; without this you get 'infinite frequency' with no overlap. Given the strays, some algebra then gives the required overlap area variation with displacement. Calculus (differentiation) then gives the required shape.
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AC2EU
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« Reply #7 on: February 06, 2013, 06:57:04 AM »

You can find the capacitance formula for two flat plates in any physics book. the dielectric is a multiplier.
I think glass is around a "2".
I don't know how linear it would be , but it is simple enough to make one and try it.
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AA5WG
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« Reply #8 on: February 06, 2013, 02:08:15 PM »

Can we use these numbers as a starting point/example?

28.000 MHz = 113.6821 pico farads (pf)

28.250 MHz = 112.67607 pf

28.500 MHz = 111.68768 pf

28.750 MHz = 110.71648 pf

29.000 MHz = 109.76203 pf

29.250 MHz = 108.82389 pf

29.500 MHz = 107.90166 pf

29.750 MHz = 106.99492 pf (out of band)

As a starting point how can we arrive at a straight line frequency flat plate shape (flat in the horizontal plane or plate laid flat on top of the work bench) from these numbers?

When the above numbers are plotted they show a direct curve.  The plotted curve looks like a near perfect 45/90/45 degree triangle.

Chuck
« Last Edit: February 06, 2013, 02:23:44 PM by AA5WG » Logged
G3RZP
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« Reply #9 on: February 07, 2013, 12:38:13 AM »

The basic equation is

C= 1/(4pi squared f squared L)

so for a SLF characteristic, C is proportional to f squared.

Chuck,

Your numbers don't align with that formula. So it's not a simple tuned circuit. which I certainly assumed we were talking about.

73

Peter G3RZP
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G8HQP
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« Reply #10 on: February 07, 2013, 04:32:36 AM »

For a sufficiently narrow band SLF~=SLC~=SLW, so just use two rectangular plates.
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W9GB
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« Reply #11 on: February 07, 2013, 12:23:17 PM »

Quote from: W5LZ
Slice a non-curving trumpet in half.  That general 'shape' slid onto a plate, pointy end first, will yield a 'linear' increase in capacitance.  There's a geometrical description for that sort of 'curve', damned if I can remember what the name of it is, way too long since I was out of school.
Doc -

For the geometric shape, are you thinking of Torricelli's trumpet ? (also called Gabriel's Horn) y = 1 / x, x => 1.
http://en.wikipedia.org/wiki/Gabriel's_Horn
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W5LZ
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« Reply #12 on: February 18, 2013, 09:24:04 PM »

W9GB,
Certainly could be!  It was quite a while ago when I saw an example of the shape and it wasn't talking about exactly the same thing.  This was well before computer simulation came along so there are bound to be 'differences' or exceptions to what's accepted now.  Oh well, some of that 'old' stuff is still worth remembering at times.
 - Paul
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AA5WG
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« Reply #13 on: February 20, 2013, 06:25:26 AM »

Thank you for all the help.

Chuck
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