BYPASS CAPACITORS - WHY TWO DIFFERENT VALUES

Roger KD6CC and Mike K1MG

Question:

I has always bothered me why capacitors are apparently ganged-up/in parallel with high and low values for bypassing. I always figured that surely the larger one had the smaller ones value included, and the extra small value was unnecessary.
I gather that it has something to do with the construction of the cap.

Ve3gyy
Whitby

It has to do with heating. In an oscillator, the demon is heat. Heat whether from an external source such as the weather and or high power resistors/transistors, or from internal sources such as RF currents flowing in the circuit. The latter is the primary purpose in using many smaller capacitors as opposed to a large single value component. When we design an oscillator, one parameter always adhered is to keep the RF currents low to the point of only allowing a reliable start of the oscillator. A designer could use capacitor values that would allow large RF currents to flow and hard immediate start of the oscillator as soon as power is supplied however, that would mean extremely large (proportionately) RF currents and thus high levels of internally generated heat. Result is drift. If we design the oscillator to just barely but reliably start upon power up, we can reduce the amount of internally generated heat and lower the drift characteristics. Analogous to shoving a pendulum of a clock with full force as opposed to gently nudging the same cantilever.

Heat is the enemy because as RF currents flow, the elements that comprise the plates of a capacitor will bend or flex, expand and/or contract ever so slightly, thereby increasing or decreasing the spacing between the elements and changing the net capacitance. Then we have a change of frequency that follows the heating/cooling cycle. A large plate or film will expand and/or contract in proportionately larger excursions as compared to smaller plates/film. By using more but smaller values of capacitance in parallel, the net effect of flex under heat is reduced thus less drift or frequency excursion. In addition, because there is a larger number of plates/film, the amount of excursion of each is far less. Or perhaps a better way to say it is that each will bend/flex independently of each other, in varying degrees with a net change totaling less than larger plates all bending to the same degree at the same time.

If you have been able to conjure up a mental image picture of this phenomenon, then now you can see what is happening in Negative, Positive and npo Caps.

A positive Temperature compensated capacitor is one which has been designed with a built in Concave curve to the plates/film, so that when it does flex under heat, the flex follows the natural concave curvature of the plates, therefore decreasing the net capacitance of the unit and raising the frequency. Of course the opposite is true of Negatively compensated caps. They are built with a convex curvature, bending further outwards under heat and therefore increasing the net capacitance and lowering the frequency of the parallel resonant circuit. NPO's are built with alternating convex and concave plates/film with the net result hopefully being zero. Regular caps are thrown together any ol' way and the net result is unpredictable.

It also explains why Metal Film caps are to be avoided at all costs in VFO's. The metal film bends wildly and uncontrollably and can vibrate if struck.

Smaller caps drift in proportionately smaller steps and are somewhat self compensating. I.e.., A 10% 10pf cap will drift up/down by 1 pf. A 10% 100 pf cap will drift up/down by 10 pf. The ultimate result of 10x10 pf caps to equal 100 pf may seem the same however, 5 of the 10 pf caps may drift up and 5 of the 10 pf caps may drift down resulting in a net change of zero whereas a single 100 pf cap will always drift in one direction by the tolerance spec. Of course, it is improbable that you will get symmetrical results like 5 up and 5 down however, the odds are that you will NOT get 10, 10pf caps that all drift in the same direction. ( You thought this was a science? :-) )

I did not mention Silver Micas that are commonly used in VFO's. The Silver Mica film tends to be more rigid than ceramic film and are less likely to flex with the same intensity under the same proportionate degree of heat however, when they do flex, they flex at a higher ratio than ceramics. Plus, the drift direction is unpredictable. In tightly controlled temperature environments, they *can be* more stable than an NPO ceramic. In the real word this generally does not hold true.

## K1MG

In theory, all capacitors are pure and stable, strictly obeying the impedance formula, x = 1/2piFC. In practice, they change value with temperature, they have lossy dielectrics, they have resistive contacts, and they also have a bit of inductance in the leads and plates.

If you remember the impedance formulas from your ham exam, you will recall that the impedance of a fixed value of capacitance decreases as you increase the frequency of the signal you are passing through it. The impedance of a fixed value of inductance increases with frequency. What happens, as you increase the frequency of the signal, to the impedance of a typical ceramic capacitor which has a little bit of stray inductance? At low frequencies, the inductive part contributes very little impedance, so the capacitive impedance predominates -- that is, it behaves like a capacitor! As you increase the frequency, the capacitive impedance decreases and the inductive impedance increases. Would there be a particular frequency at which the capacitive impedance equals the inductive impedance? Absolutely! And if you increase the frequency still further, the inductive impedance becomes higher than the capacitive impedance, and your poor capacitor behaves just like an inductor! The frequency at which both impedances are equal is known as the self-resonant frequency. This frequency is set by the materials used and the construction of the capacitor. It can also be affected by how the capacitor is installed, which is why all the kit instructions tell you to mount the cap very close to the board, with the minimum lead length necessary. In general, for capacitors of the same type and general construction, the larger value cap will have a lower self-resonant frequency.

The ideal bypass component would have infinite resistance at DC, and zero impedance everywhere else. Unfortunately, this component is not yet available, but a capacitor comes close. It has very high impedance at DC and decreasing impedance at higher and higher AC frequencies -- this is, until you hit its self-resonant frequency. At that point and beyond, it becomes less and less effective as a bypass component because its impedance is becoming larger. The capacitor is a very effective bypass at some frequencies but useless at frequencies somewhat above its self-resonant frequency.

How do we handle this problem? If we use a large value cap which is a good bypass at low frequencies but useless at high frequencies, and put a small value cap in parallel with it, the small cap will not be very effective at the low frequencies, but since its self-resonant frequency is much higher, it will be effective at the high frequencies where the big cap is useless. Simple!

If you pull out some data sheets for capacitors, you will often find graphs of this and other characteristics of the component (impedance vs. frequency showing the self-resonant point, equivalent series resistance, etc). Keeping all these practical limitations of real components in mind and adapting the design to accommodate them is part of the engineering process.

Incidentally, this is also the reason why you won't find a cell phone built with anything other than surface mount components. The self-resonant frequency of chip caps is much higher than leaded caps.

BTW - inductors have similar flaws. The latest QRPp has an interesting article about the RF choke used in the Back-to-the-Future project. It's an interesting education in the real impedance of an inductor at HF frequencies.

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