We have avoided mentioning capacitors in any detail as it has not been necessary for understanding the circuitry covered so far.   Capacitors come in many sizes, types and makes.   Their size is stated in ‘Farads’ but as the Farad is a very large unit, you are unlikely to encounter a capacitor marked in anything larger than a microfarad, which is a millionth of a Farad.   The symbol for a microfarad is mu-F where ‘mu’ is the letter of the Greek alphabet.   This is a pain for normal text production as Greek letters do not occur in your average font.   Some circuit diagrams give up on ‘mu’ and just write it as uF which looks like mu-F slightly mis-printed where the descender of the mu has not printed.

Anyway, very large capacitors which you may encounter range from 5,000 microfarads to maybe as much as 20,000 microfarads.   Large capacitors range from 10 microfarads to 5000 microfarads.   Medium sized capacitors run from 0.1 microfarad to about 5 microfarads and small capacitors are those below 0.1 microfarad.

1000 nanofarads (‘nF’) = 1 microfarad.
1000 picofarads (‘pF’) = 1 nanofarad


0.01 microfarad can be written as 10nF
0.1 microfarad can be written as 100nF
0.1nF can be written as 100pF

Capacitors larger than 1 microfarad tend to be ‘polarised’. In other words, the capacitor has a ‘+’ connector and a ‘-’ connector, and it does matter which way round you connect it.   The larger capacitors have a voltage rating and this should not be exceeded as the capacitor can be damaged and possibly even totally destroyed.   Capacitors can be added together, but surprisingly, they add in the reverse way to resistors:

If two capacitors are wired in series, as shown in Example 1 above, the overall capacity is reduced while the voltage rating increases.   The reduction in capacitance is given by:

1/Ct = 1/C1 + 1/C2 + 1/C3 + …..

In Example 1, then,   1 / total capacitance = 1 / 100 + 1 / 100   or   1 / Ct = 2 / 100   or   1 / Ct = 1 / 50 so the overall capacitance reduces from 100 microfarads to 50 microfarads.   The advantage in wiring the capacitors like this is that the voltage rating has now increased to 32V (16V across each of the capacitors).

In Example 2, the overall capacitance has reduced to a third of 100 microfarads but the voltage rating has tripled.

In Example 3, the capacitors are wired in parallel.   The voltage rating is unchanged but the overall capacitance is now the sum of the three capacitors, namely 300 microfarads.

There is no need for the capacitors to have similar values, there are merely shown that way in the examples to make the arithmetic easier and not distract you from the ways in which the capacitors interact together.

Occasionally, a circuit needs a large capacitor which is not polarised.   This can be provided by placing two polarised capacitors back-to back like this:

When the capacitors are connected this way, it does not matter which end of the pair is connected to the positive side of the circuit and which to the negative side.

The time has come for a serious warning:   High voltages are very, very dangerous.   Do not become so familiar with them that you treat them casually.   High voltages can kill you.   Capacitors are capable of building up high voltages and some good makes can hold the charge for several days.

In particular, do not try to make adjustments to, or take parts from, the inside of a TV set.   A black and white TV set uses 18,000 Volts on the magnetic coils used to create the moving picture on the tube.   A capacitor inside the set may well have that voltage on it three days after the set was last used.   Don’t fool around inside a TV set, it could kill you quick, or if you are really unlucky, it could injure you for life.   A colour TV set uses 27,000 Volts to operate the coils inside it and that will fry you in jig time if you touch it.

Also, please don’t think that you are safe if you don’t quite touch it; 27,000 volts can jump across a gap to your hand.   If you try to discharge a TV capacitor using a metal screwdriver with a wooden handle, please ensure that you medical insurance is up to date before you do it.   You can receive a hefty shock through the screwdriver handle.

Voltages up to 24 Volts should be quite safe.   However, some circuits will generate very high voltages even though the battery driving the circuit is low voltage.   A standard off-the-shelf inverter circuit produces 240 Volts AC from a 12 Volt battery.   Just because the battery is only 12 Volts does not mean that the circuit is not dangerous.   Circuits which have inductors in them can produce high voltages, especially if they contain large capacitors.   The voltage which produces the spark in your car engine is very high and it comes from the 12-volt car battery.   You know enough about this by now, so pay attention!

The more advanced stuff:
You do not need to bother with this section if you are just starting out with some basic switching circuits of the type already described in this tutorial, so please feel free to skip this section and move on to the “Prototype Construction” section which you will find immediately useful.

This section is a lightweight introduction to Alternating Current circuits and pulsed DC circuits. Let me stress again that I am mainly self-taught and so this is just a general introduction based on my present understanding.

Alternating Current, generally called “AC” is called that because the voltage of this type of power supply is not a constant value. A car battery, for instance, is DC and has a fairly constant voltage usually about 12.8 volts when in it’s fully charged state. If you connect a voltmeter across a car battery and watch it, the voltage reading will not change. Minute after minute it says exactly the same because it is a DC source.

If you connect an AC voltmeter across an AC power supply, it too will give a steady reading, but it is telling a lie. The voltage is changing all the time in spite of that steady meter reading. What the meter is doing is assuming that the AC waveform is a sine wave like this:

and based on that assumption, it displays a voltage reading which is called the “Root Mean Square” or “RMS” value. The main difficulty with a sine wave is that the voltage is below zero volts for exactly the same length of time as it is above zero volts, so if you average it, the result is zero volts, which is not a satisfactory result because you can get a shock from it and so it can’t be zero volts, no matter what the arithmetical average is.

To get over this problem, the voltage is measured thousands of times per second and the results squared (that is, the value is multiplied by itself) and then those values are averaged. This has the advantage that when the voltage is say, minus 10 volts and you square it, the answer is plus 100 volts. In fact, all of the answers will be positive, which means that you can add them together, average them and get a sensible result. However, you end up with a value which is far too high because you squared every measurement, and so you need to take the square root of that average (or “mean”) value, and that is where the fancy sounding “Root Mean Square” name comes from – you are taking the (square) root of the (average or) mean value of the squared measurements.

With a sine wave like this, the voltage peaks are 41.4% higher than the RMS value which everyone talks about. This means that if you feed 100 volts AC through a rectifier bridge of four diodes and feed it into a capacitor the capacitor voltage will not be 100 volts DC but instead it will be 141.4 volts DC and you need to remember that when choosing the voltage rating of the capacitor. In that instance I would suggest a capacitor which is made to operate with voltages up to 200 volts.

You probably already knew all of that, but it may not have occurred to you that if you use a standard AC voltmeter on a waveform which is not a sine wave, that the reading on the meter is most unlikely to be correct or anywhere near correct. So, please don’t merrily connect an AC voltmeter across a circuit which is producing sharp voltage spikes like, for instance, one of John Bedini’s battery pulsing circuits, and think that the meter reading means anything (other than meaning that you don’t understand what you are doing).

You will, hopefully, have learned that power in watts is determined by multiplying the current in amps by the voltage in volts. For example, 10 amps of current flowing out of a 12 volt power supply, represents 120 watts of power. Unfortunately, that only holds true for circuits which are operating on DC, or AC circuits which have only resistors in them. The situation changes for AC circuits which have non-resistive components in them.

The circuits of this type which you are likely to come across are circuits which have coils in them, and you need to think about what you are doing when you deal with these types of circuit. For example, consider this circuit:

This is the output section of a prototype which you have just built. The input to the prototype is DC and measures at 12 volts, 2 amps (which is 24 watts). Your AC voltmeter on the output reads 15 volts and your AC ammeter reads 2.5 amps and you are delighted because 15 x 2.5 = 37.5 which looks much bigger than the 24 watts of input power. But, just before you go rushing off to announce on YouTube that you have made a prototype with COP = 1.56 or 156% efficient, you need to consider the real facts.

This is an AC circuit and unless your prototype is producing a perfect sine wave, then the AC voltmeter reading will be meaningless. It is just possible that your AC ammeter is one of the few types that can accurately measure the current no matter what sort of waveform is fed to it, but it is distinctly possible that it will be a digital meter which assesses current by measuring the AC voltage across a resistor in series with the output, and if that is the case, it will probably be assuming a sine wave. The odds are that both readings are wrong, but let’s take the case where we have great meters which are reading the values perfectly correctly. Then the output will be 37.5 watts, won’t it? Well, actually, no it won’t. The reason for this is that the circuit is feeding the transformer winding which is a coil and coils don’t work like that.

The problem is that, unlike a resistor, when you apply a voltage across a coil the coil starts absorbing energy and feeding it into the magnetic field around the coil, so there is a delay before the current reaches it’s maximum value. With DC, this generally doesn’t matter very much, but with AC where the voltage is changing continuously, it matters a great deal. The situation can be as shown in this graph of both voltage and current:

At first, this does not look like any great problem, but it has a very significant effect on the actual power in watts. To get the 37.5 watts output which we were talking about earlier, we multiplied the average voltage level by the average current level. But these two values do not occur at the same time and that has a major effect.

As this can be a little difficult to see, let’s take the peak values rather than the averages as they are easier to see. Let’s say that in our example graph that the voltage peak is 10 volts and the current peak is 3 amps. If this were DC we would multiply them together and say that the power was 30 watts. But with AC, this does not work due to the timing difference:

When the voltage is peaking, the current is nowhere near it’s peak value of 3 amps:

As a result of this, instead of getting our expected peak power at the top of the voltage peak, the actual power in watts is very much lower – less than half of what we were expecting. Not so good, but it gets worse when you look at the situation more closely. Take a look at what the voltage is when the current crosses the zero line, that is, when the current is zero. The output power is zero when the current is zero but this occurs when the voltage is at a very high value:

The same goes for when the voltage is zero. When the voltage is zero, then the power is also zero, and you will notice that this occurs when the current is at a high value:

The power is not the average current multiplied by the average voltage if there is a coil involved in the circuit – it will be less than that by an amount known as the “power factor” and I’ll leave you to work out why it is called that.

So, how do you determine what the power is? It is done by sampling the voltage and current many times per second and averaging those combined results:

Both the voltage and the current are sampled at the times indicated by the vertical red lines and those figures are used to calculate the actual power level. In this example, only a few samplings are shown, but in practice, a very large number of samples will be taken. The piece of equipment which does this is known as a wattmeter as it measures watts of power. The sampling can be done by windings inside the instrument, resulting in an instrument which can be damaged by overloading without the needle being anywhere near full deflection, or it can be done by digital sampling and mathematical integration. Most digital sampling versions of these meters only operate at high frequencies, typically over 400,000 cycles per second. Both varieties of wattmeter can handle any waveform and not just sine waves.

The power company supplying your home measures the current and assumes that the full voltage is present all of the time that the current is being drawn. If you are powering a powerful electric motor from the mains, then this current lag will cost you money as the power company does not take it into account. It is possible to correct the situation by connecting one or more suitable capacitors across the motor to minimise the power loss.

With a coil (fancy name “inductor” symbol “L”), AC operation is very different to DC operation. The coil has a DC resistance which can be measured with the ohms range of a multimeter, but that resistance does not apply when AC is being used as the AC current flow is not determined by the DC resistance of the coil alone. Because of this, a second term has to be used for the current-controlling factor of the coil, and the term chosen is “impedance” . The wire in any coil has a resistance and that opposes current flow through the coil irrespective of whether the voltage applied to the coil is DC or AC. The capacitance between the neighbouring turns of wire in a coil, introduces a feature of the coil which “impedes” AC current flow through the coil and the amount of that impedance depends on the frequency of the AC voltage being applied to the coil.

The impedance of a coil depends on it’s size, shape, method of winding, number of turns and core material. If the core is made up of iron or steel, (usually thin layers of iron which are insulated from each other), then it can only handle low frequencies. You can forget about trying to pass 10,000 cycles per second (“Hz”) through the coil as the core just can’t change it’s magnetisation fast enough to cope with that frequency. A core of that type is ok for the very low 50 Hz or 60 Hz frequencies used for mains power, which are kept that low so that electric motors can use it directly.

For higher frequencies, ferrite can be used for a core and that is why some portable radios use ferrite-rod aerials, which are a bar of ferrite with a coil wound on it. For higher frequencies (or higher efficiencies) iron dust encapsulated in epoxy resin is used. An alternative is to not use any core material and that is referred to as an air-core coil. These are not limited in frequency by the core but they have a very much lower inductance for any given number of turns. The efficiency of the coil is called it’s “Q” (for “Quality”) and the higher the Q factor, the better. The resistance of the wire lowers the Q factor.

A coil has inductance, and resistance caused by the wire, and capacitance caused by the turns being near each other. However, having said that, the inductance is normally so much bigger than the other two components that we tend to ignore the other two. Something which may not be immediately obvious is that the impedance to AC current flow through the coil depends on how fast the voltage is changing. If the AC voltage applied to a coil completes on cycle every ten seconds, then the impedance will be much lower than if the voltage cycles a million times per second.

If you had to guess, you would think that the impedance would increase steadily as the AC frequency increased. In other words, a straight-line graph type of change. That is not the case. Due to a feature called resonance, there is one particular frequency at which the impedance of the coil increases massively. This is used in the tuning method for AM radio receivers. In the very early days when electronic components were hard to come by, variable coils were sometimes used for tuning. We still have variable coils today, generally for handling large currents rather than radio signals, and we call them “rheostats” and some look like this:

These have a coil of wire wound around a hollow former and a slider can be pushed along a bar, connecting the slider to different winds in the coil depending on it’s position along the supporting bar. The coil connections are then to the slider and to one end of the coil. The position of the slider effectively changes the number of turns of wire in the part of the coil which is in the circuit. Changing the number of turns in the coil, changes the resonant frequency of that coil. AC current finds it very, very hard to get through a coil which has the same resonant frequency as the AC current frequency. Because of this, it can be used as a radio signal tuner:

If the coil’s resonant frequency is changed to match that of a local radio station by sliding the contact along the coil, then that particular AC signal frequency from the radio transmitter finds it almost impossible to get through the coil and so it (and only it) diverts through the diode and headphones as it flows from the aerial wire to the earth wire and the radio station is heard in the headphones. If there are other radio signals coming down the aerial wire, then, because they are not at the resonant frequency of the coil, they flow freely through the coil and don’t go through the headphones.

This system was soon changed when variable capacitors became available as they are cheaper and more compact. So, instead of using a variable coil for tuning the radio signal, a variable capacitor connected across the tuning coil did the same job:

While the circuit diagram above is marked “Tuning capacitor” that is actually quite misleading. Yes, you tune the radio receiver by adjusting the setting of the variable capacitor, but, what the capacitor is doing is altering the resonant frequency of the coil/capacitor combination and it is the resonant frequency of that combination which is doing exactly the same job as the variable coil did on it’s own.

This draws attention to two very important facts concerning coil/capacitor combinations. When a capacitor is placed across a coil “in parallel” as shown in this radio receiver circuit, then the combination has a very high impedance (resistance to AC current flow) at the resonant frequency. But if the capacitor is placed “in series” with the coil, then there is nearly zero impedance at the resonant frequency of the combination: While the circuit diagram above is marked “Tuning capacitor” that is actually quite misleading. Yes, you tune the radio receiver by adjusting the setting of the variable capacitor, but, what the capacitor is doing is altering the resonant frequency of the coil/capacitor combination and it is the resonant frequency of that combination which is doing exactly the same job as the variable coil did on it’s own.

This draws attention to two very important facts concerning coil/capacitor combinations. When a capacitor is placed across a coil “in parallel” as shown in this radio receiver circuit, then the combination has a very high impedance (resistance to AC current flow) at the resonant frequency. But if the capacitor is placed “in series” with the coil, then there is nearly zero impedance at the resonant frequency of the combination:

This may seem like something which practical people would not bother with, after all, who really cares? However, it is a very practical point indeed. In Chapter 3, some of the very high-power devices produced by Don Smith are described. Typically, he uses an off-the-shelf neon-tube driver module as an easy way to provide a high-voltage, high-frequency AC current source, typically, 6,000 volts at 30,000 Hz. He then feeds that power into a Tesla Coil which is itself, a power amplifier. The arrangement is like this:

People who try to replicate Don’s designs tend to say “I get great sparks at the spark gap until I connect the L1 coil and then the sparks stop. This circuit can never work because the resistance of the coil is too low”.

If the resonant frequency of the L1 coil does not match the frequency being produced by the neon-tube driver circuit, then the low impedance of the L1 coil will definitely pull the voltage of the neon-tube driver down to a very low value. But if the L1 coil has the same resonant frequency as the driver circuit, then the L1 coil (or the L1 coil/capacitor combination shown on the right, will have a very high resistance to current flow through it and it will work well with the driver circuit. So, no sparks, means that the coil tuning is off. It is the same as tuning a radio receiver, get the tuning wrong and you don’t hear the radio station.

Electronics Tutorial

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