Calculating Capacitance when making a Capacitor

 Calculating Capacitance

There is a very simple formula for determining the capacitance of an air capacitor. 

C (in pf)= 0.2248 times area of plate divided by spacing between the plates.

If the plate area is 4 square inches (2 inch by 2 inch plates) and the spacing is 1/8 inch we get:

C= .2248 X 32 =  7.2 pf for the two plate capacitor.

For each additional plate you gain 7 pf. ( 7.2 pf if you want to be precise but just using 7 is close enough for most things)

So with 3 plates it’s 14 pf

5 plates makes it 28 pf

10 plates makes it about 63 pf

11 plates is 10x7 = 70 pf

The multiplying factor is the number of plates total minus 1 since it takes two plates to get the first 7 or 7.2 pf.

Even after using 11 plates, the difference between using 7pf and 7.2pf is only 72-70 or 2 pf. 

It is very easy to make a capacitor for something like an antenna tuner for your antenna. Many antenna tuners need capacitors in the neighborhood of 50 to 150 pf.

 In the example above with two plates each with an area of 4 square inches, two pieces of aluminum or copper can be spaced about 1/8 inch apart on ceramic or even plastic spacers creating a 7.2 pf capacitor. To make that 14.4 pf, just make the spacers 1/16 inch. Of course there is a limit to how close you can make the plates. That limit is how accurately you can space the plates and maintain the spacing. Also the spacing becomes critical as the voltage across the capacitor becomes larger. For example I would not use less than 1/10 inch spacing for any capacitor that might see 3000 volts across it. 

Another way to increase the capacitance is to increase the area of the plates.

If we start knowing that if the area of the plates are 4 square inches and spaced 1/8 inch apart the capacity is 7.2 pf, we can easily get 14.4 pf by decreasing the spacing to 1/16 inch. Then if we quadruple the plate size by going from 2 inches by 2 inches  to 4 inches by 4 inches, we will go from 14.4 pf to 57.5 pf. 

Double checking our logic with the formula we get

C= .2248 X 16 / 1/16 = 57.54 pf. 

So it’s fairly easy to build a simple 2 plate capacitor with values from less than 10 pf to over 50 pf that are not too large. Depending on the voltage of the circuit where the capacitor will be used even 100 pf or more can be obtained with small plates. 

The values can also become much larger if something other than air is used between the plates! 

The values obtained with air can be multiplied by a factor of 10 if, for example, a piece of glass were sandwiched between the plates. That could make our first capacitor with 2 inch by 2 inch plates spaced 1/8 inch go from 7.2 pf to 72 pf and the one with 4 by 4 inch plates spaced 1/16 inch go from 57.5 pf to 575 pf simply by putting glass between the plates.

There are various insulating materials that can be used between the plates. While glass multiplies the capacitance by 10, plain Kraft paper multiplies it by 2.6. In addition to multiplying the capacitance these materials usually increase the voltage rating thus permitting closer spacings to be used.

So by choosing the right size of plate, the number of plates, and the material between the plates almost any value of capacitor can be constructed. Capacitors with more than two plates just have to have alternate plates connected so all the capacitors are in parallel. 

I was once helping a friend tune his antenna when we found out his variable capacitor in his L network tuner was not large enough. I told him we could probably build one from junk he had around the radio shack. We found a piece of printed circuit board with copper on both sides. By soldering a wire to each side we had a capacitor! I estimated the multiplication factor of the material between the two copper plates to be between 2 and 3 and then we calculated the area the plates should be to give him a large enough capacitor to tune the antenna. Within half hour we had built and added a homemade capacitor to his antenna circuit and he was on the air.