Last word on caps

[Magnus Danielson]

From: "Hugo Haesaert" <hugo.haesaert at skynet.be>
Subject: Re: Last word on caps
Date: Tue, 7 Dec 1999 07:49:33 +0100

> Hi All !
> 
> But what determines the value/size of the cap used ?
> 
> NPO gets good marks from Bob, but is not readily available in 0.1 µF, 
> the value mostly seen for multiplexed dac outputs .  And styrene caps 
> only go to 56nF at my supplier .
> 
> The longer the hold time required, the larger the cap, the kbd/SH cap 
> of the Roland System 100 is huge .  Otoh, my MKS80 (it's fine Paul :) 
> uses tiny ceramic discs for s/h caps (followed by TL064's, now why's 
> that ?) .
> 
> Hmm...

Caps seems to be a confusing chapter to many...

The capacitance between two flat electrical conductors with some dielectric
between them is

        A
C = c * -
        l

where

C is the capacitance (in Farad)
c (usually a small epsilon) is the permittivity of the dielectrum
A is the cross section area (in m^2)
l is the plate distance (in m)

This is the standard formula that everyone learns, in reality you don't build
caps just like a pair of flat plates, but rather build a sandwich of

plate1/dielectrum/plate2/dielectrum/plate1/....

or roll the capacitor together to acheive the same layering. Anyway, this
calls for correction, also the edges needs to be corrected for.

Except for these corrections the formula applies well. Now, we can obvious
change the area, so that seems feasable enougth to change the capacitance.

By changing the dielectrum thickness we also change the plate distance l.
Why would we like to change that?

Well, diffrent dielectrums will break down and start to conduct at some
material specific breaktrough electrical fieldstrength. Since the fieldstrength
follows

    U
E = -
    l

will for a acceptable fieldstrength Ebreak the thickness of the dielectrum be

    Ubreak
l = ------
    Ebreak

So, the thickness of the dielectrum will increase linearly with the voltage
range that you would like to apply. So, that will also be a major consideration
of a capacitor scaleing.

Further, the permittivity of the dielectrum may vary alot. The permittivity is
usually discussed in its relative form, that is relative to the permittivity of
vacuum. So, dividing it up into

c = c  * c
     0    r

Where c0 is about 8.854187817.. * 10^-12 F/m and cr is 1 for vacuum.

Many materials have the property of having cr values above 1, here are some
examples:

Type		Dielectric	Comment
		Constant	
PTFE(Teflon)	2.1		Polymere
Polystyrene	2.55		Polymere
PVC		4.55		Polymere
Barium titanate	3600,2300,150,80	Ceramic, field orientation sensitive
Diamond		5.87,5.66		Crystal, diffrent types exists
Potassium tantalate niobate (KTN)
                34000		Ceramic, highly temperature sensitive
Quartz		3.75		Glass
Pyrex 1710	6.00		Glass

Notice that the ceramics here acheive very high ratios, so now you can have
very thin layers while acheiving the same voltage rating as a much thicker
layer of polystyrene or teflon. You can make high voltage rating caps with
large capacitances in very small packages, great! Where's the catch?

First, the dielectric constant (permittivity) is not temperature stable, and
as your constant goes up you can bet that you do have temperature changes on
the capacitance values. For this reason will ceramic caps have diffrent
ratings due to their temperature stability (like NP0 and X7R) which translates
into various dielectrics. Another thing, the dielectric constant is not very
constant from a frequency perspective, it actually becomes lower as you move
upwards in the frequency spectra. Even further, they are not very linear at
all, they behave much like inductor cores as you pushes the limits. Also,
you have diffrent amount of conductivity (leakage) due to the material.
For instance will Teflon, Polystyrene and Polypropylene show excelently low
leakage as compared to ceramics.

So, the dielectrum will certainly set up a bunch of troubles, but it doesn't
end there....

What many people haven't understood is the way the physical construction of a
capacitor will effect in parasitic resistance and parasitic inductance in a
capacitor. These things will be important as you go up in frequency or down in
rise times. Capacitors with inherently low dielectric constants needs to be
much hugher than caps with higher dielectric constants, this will naturally
effect in the physical size which translate into longer electrical conduction
paths which then becomes larger parasitic resistance and inductance. These
shortcommings can be reduced by diffrent physical designtechniques but still
will these changes in dielectric constants be a burden. So, for highspeed
designs (like the motherboards in the computer you sit at) ceramics is being
dominating the field since you can make the parasitic inductance much lower
and thus the frequency where the cap still works as a cap can be kept high
enogth.

So, this is the basic story on why the caps comes in all diffrent sizes and
shapes.

Now, how do YOU select your caps?

I strongly recommend people to look at Robert A. Peice's papers on caps and
related things, it is good reading and he has some good experience to share.
At times the solution to real problem is both simpler and cheaper than you
would expect.

Cheers,
Magnus