Capacitors And Inductors
know that thing with metal balls hanging from strings? The one where you pull
back a ball on one end, let go, and it hits the others, knocking the one on the
opposite end loose? (It is called a Newton's Cradle if you want to Google up a
picture.) Okay, now imagine slipping a piece of paper between the middle balls.
That's actually a pretty good visualization of a capacitor at work. The paper
represents the insulator between the plates and the balls are electrons. When an
electron enters one side of the capacitor, one leaves the other side. If two
enter on one side, two will leave on the other. After a period of time, the
balls that left return, and an equal number of balls from first side leave.
In the real world, the balls in a Newton's Cradle are obeying
Newton's Laws of Motion. An object at rest will remain at rest unless acted upon
by an outside force and all that. In a real world capacitor the motivating force
is electrostatic repulsion. Opposite charges attract, and like charges repel.
When an electron enters one side of the capacitor, it carries with it a negative
charge. That charge drives a like negative charge (in other words, an electron)
off the other side and balance is restored. A signal only moves through a
capacitor as long as electrons are in motion, otherwise the charges reach
equilibrium and electrons cease moving out of the other end of the capacitor. If
you apply DC to a capacitor, you'll get a surge out of the other end,
representing the change from 0V to whatever your DC voltage might be —
technically a short-term AC signal — then things stop. But if you apply an AC
signal, you'll see motion for as long as you care to keep the AC going.
Capacitors are easy to make. In fact, you can easily make one
at home. Take two sheets of aluminum foil, place a piece of paper between them,
and attach one lead to each sheet of foil and...Voila! Your first capacitor!
Practical capacitors are rolled up with an additional sheet of
insulation — technically called dielectric — to keep the two sheets of foil
from shorting together. This also makes them less fragile and more compact. That's
really all there is to the physical design of a basic capacitor. You can change
the dielectric from paper to plastic film (think Saran Wrap for your kitchen
capacitor), or you can use vacuum, or air, or most anything else that won't
The parameters that matter most in a capacitor are the surface
area of the two sheets of metal (called plates — bigger gives you more
capacitance) and the thickness of the dielectric (thinner gives you more
capacitance). The composition of the plates and dielectric matters, too, and
this is where we begin to run into problems. For instance, copper conducts
electricity better than aluminum, so if you make the plates out of copper,
electrons will be able to get in and out of the capacitor more easily. This is a
good thing…but copper is more expensive than aluminum and heavier too, so
companies tend to use aluminum foil when making capacitors. The increase in
resistance means that two otherwise identical caps — one made with copper, the
other with aluminum — will not perform the same. The resistance is,
electrically speaking, in series with the capacitance, and this means that the
capacitor no longer functions as a pure capacitance. It has now become a filter.
If you look on the spec sheets for capacitors, you'll see an entry for
Equivalent Series Resistance (ESR), which takes into account the resistance of
the plates and leads.
Something spooky happens when you charge a cap with a DC
voltage, then discharge it…if you've got a meter hooked to it, after its
discharged you'll see voltage come out of nowhere, slowly recharging the cap,
even if it's not hooked to a circuit. (The effect is particularly pronounced
with electrolytic caps.) Those electrons were hiding in the dielectric. When
they think nobody's looking, they sneak back out into the plates. Some
dielectrics are better than others; plastics and mica tend to be very good, so
when possible use plastic or mica dielectric caps.
Capacitors are prone to another ill, which is that the
rolled-up plates are a pretty good imitation of an inductor, which, like
resistance, introduces another imperfection into what would otherwise be a
theoretically perfect capacitor.
Capacitors, unlike resistors, change behavior with frequency. High frequencies pass with ease, whereas low frequencies face increasing difficulty. Direct current cannot pass at all, which leads to one of the most important uses for a capacitor — a gatekeeper that is able to discriminate between DC and AC. Circuits, particularly tubed circuits, often make use of this function. In addition, the size of the capacitor determines how close to 0 Hz (i.e. DC) the frequency response will go. This property is useful in filters.
Capacitors do not perform their magic in isolation; they need
a dance partner, that being the impedance of the circuit they find themselves
in. Impedance is similar to resistance, but takes into account the AC-related "resistance"
of the other parts nearby. Technically this is called reactance because it
varies with frequency. Impedance is the sum of the resistance and reactance.
The formula for the reactance of a capacitor is:
X = 1/(2πfC)
In practical use, a Farad is an awful lot of capacitance. Most
capacitors used in audio circuits are in the picofarad (10-12) to
microfarad (10-6) range. That's quite sufficient for day to day use.
Inductors are, functionally, the mirror image of capacitors.
Envision an inductor as an electromagnet. If you ever wound a wire around a nail
and hooked it to a battery, you found that it picked up other nails. Having a
magnet that you can turn on and off is very useful, but there are other things
going on that are of more interest to us at the moment.
If you examine the current flow as the magnet is first switched on, you will find that it doesn't simply leap from zero current to full current in an instant. There's a time delay. That delay results from the magnetic field. As the magnetic field builds, it pushes back — an electronic application of the law that every action has an equal and opposite reaction. If you leave the current going, the growing magnetic field will prevail over the pushback and the current will reach its full value. When the electromagnet is turned off, the collapsing magnetic field creates an electronic current even though there is no longer current being supplied by the external circuit.
The important thing to note is that inductors resist change.
Low frequencies (DC being the ultimate low frequency, since its frequency is
zero) pass through the inductor easily. The faster the change (i.e. higher
frequency AC), the more the inductor fights back. This is opposite from the
behavior of a capacitor, which is quite content to allow high frequencies to
pass, yet blocks DC.
Like simple capacitors, inductors are easily built. The nail
in the electromagnet above is optional, but increases the efficiency. The
essential element is the coil of wire. The more turns of wire, the more
You won't be surprised to learn that inductors are imperfect.
The DC resistance of the wire used to build the coil is a problem, although it
can be offset to some degree by using larger gauge wire. There is also
capacitance between the adjacent turns in the coil. Not much, but it adds up as
the number of turns increases. Assuming that you use an empty coil — this is
called an air-core inductor — you'll have no problems with the magnetic
properties of air, but if you use some sort of magnetic core in an effort to
increase the efficiency of the inductor, you'll run into all sorts of odd things
that you'll need to account for. And finally, inductors are heavy and expensive
when compared to resistors and capacitors. More than anything else, weight and
expense have contributed to the comparative scarcity of inductors in today's
The formula for an inductor looks like this:
X = 2πfL
Real world resistors approach the theoretical model very
closely, indeed. For our purposes, you can ignore their imperfections.
Capacitors and inductors... well... let's just say that the problems are
manageable, but it won't do to ignore them. Generally, the higher the frequency,
the worse they will behave.
With the description of resistors, capacitors, and inductors
behind us, we can add them together, the simplest way being to put like parts
together in series or in parallel. Series means that one part follows another
and that a single electron will travel through both parts. Parallel means that
two or more parts are side-by-side and that any given electron will travel
through one, and only one, of the parts. Think of the rungs on a ladder. If you
place an electron on one side, it has the option of traveling through any rung
to get to the other side but once there, it's time to move on.
Resistors in series add their value together, increasing the total resistance:
Resistors in parallel decrease total resistance:
Like resistors, inductors increase inductance if wired in series:
And decrease inductance if wired in parallel:
Capacitors, being opposite of inductors, decrease capacitance if wired in series:
And increase if wired in parallel:
Note that a curious thing happens if you wire capacitors in
series: The voltage across the capacitors varies with the value of the
capacitor. If the capacitors are all the same voltage rating and capacitance
rating, and if they are of reasonably tight tolerance, then this can be done
safely, assuming that the voltage rating has been chose carefully. However, if
you're using two unlike values, the voltage across the capacitors will vary,
possibly exceeding the rating of one of the parts. This is easy enough to cure,
though, in that a string of high value resistors in parallel with the capacitors
will force the voltage to divide in a predictable manner. The downside is that
there will be a small loss of current through the resistor stack. If in doubt,
don't do it, as capacitor failure can be a dangerous business; they tend to
explode... yes, as in BANG!
Electrolytic capacitors have a vent system that — in theory — allows them to
release pressure safely. Do not trust this system to function properly. No
matter how small the capacitor, never exceed the rated voltage. "But it was just
a teeny little capacitor!" is not
going to convince the doctors in the emergency room as they try to save your
eye. Although you sometimes see capacitors in circuits run at, or even above
their rated voltage, don't do it. Should you run into a capacitor with too much
voltage on it, either troubleshoot the circuit to determine why the voltage is
high or replace the part with one rated for more voltage. Your best case
scenario is that the part will simply fail at some point in the future. The
worst case is that it will explode, potentially hurting you or your system.
So how much leeway should you give, voltage-wise? I like at
least 5%, minimum. If you're running, say, 16V, use a 25V part, not 16V, even
though 16V on a 16V part seems reasonable. Anything more than 25V is overkill.
The extra cost is minimal. Go ahead and pay the pennies.
Inductors are rated for how much current they will take. Here, you have more leeway, but don't get stupid. In small signal applications the current is so minor that it won't be a problem. In larger current applications, such as a filter in a power supply, make sure the inductor is well ventilated and you can run pretty close to the rated current. That said, I still suggest some elbow room. Just because inductors can take some punishment doesn't mean that you should abuse them.