Capacitors
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Written by Bryce Ringwood   
Friday, 02 November 2012 11:39

Capacitors are used in electric circuits to store electric charge. In old radio books they are called condensers. They are different words for the same thing.

Early use of capacitors

The first experimenters were interested in storing electrostatic charges. Nearly everyone in the South African highveld knows all about static electricity through the numerous elecric shocks experienced in the dry season due to electic charge building up on our bodies. This happens because when we move, excess electrons are removed from our skin and clothing by the dry air. Then when we put our metal key in a grounded car door - the electrons flow from the metal door to our hands via the key.

 

The ancient Greeks were aware of this phenomenon of charges building up in insulated materials. They used amber, which is a good insulator and the ancient greek name for amber was - electron. 

Static electricity, as implied by its name, does not flow - it remains as a charge on an insulator. If there is an excess of electrons, the insulator has a negative charge. If it is depleted of electrons, it has a net positive charge.

Experimenters wanted to store charge for later use, and they devised the "Leyden Jar". This is a glass jar coated on the inside and outside about three quarters of the way up with metal foil. A conducting rod terminating in a chain was placed through a stopper in the mouth of the jar. Charge could be stored by connecting the conducting rod to a source of static electricity. In Mary Shelley's novel about Dr Frankenstein, the source of the static to be stored was atmospheric electricity from thunderstorms. Ms shelley's father was an experimenter who used to do exactly that - but, as they say, don't do this at home.

Several Leyden Jars could be connected together to form a battery - the word was taken from the idea of a gun battery. Leyden Jars are a form of capacitor consisting of two metal plates (the foil) and a dielectric (the glass of the jar).

Capacitor Construction

A capacitor simply consists of two metal plates separated by an insulating material called a dielectric. In early radios,you will encounter "paper capacitors". In this case the two metal plates are formed from tinfoil strips separated by wax impregnated paper as the dielectric. The assembly is rolled into the shape of a cylinder, and connecting wires are soldered to the tinfoil and brought out at each end of the cylindrical tube. The whole thing is dipped in wax. The value of the capacitor is governed by the area of the tinfoil or other metal plates, the spacing between them and the properties of the dielectric material - the so-called dielectric constant.

Another form of capacitor consists of a mica dielectric with silver deposited on the mica forming the metal plates. This is the"Silver-Mica" type, and are still available. Other dielectric materials are ceramics, plastics, such as mylar and polystyrene and so on.

Electrolytic capacitors consist of metal plates in a solution that deposits aluminium hydroxide as the dielectric. The dielectric is "formed" using a process akin to electroplating during the manufacturing process. Electrolytic capacitors normally have a polarity - they have to be connected the correct way round.

Finally, we come to variable capacitors used for tuning radio receivers. In old radios these are composed of fixed and moveable metal plates separated usually by air (or sometimes ceramic or plastic) as the dielectric. Semiconductor junctions also form a capacitor, and the value can be made to change by applying a bias voltage - see the beacon transmitter project.

Capacitor Values

Capacitance is measured in Farads. Most radios use capacitors ranging from a few milliFarads (mF) to less than a picoFarad (pF). Power supplies use capacitors in the microFarad (µF) range. (See section on SI Units).

Capacitors also have a "Working Voltage". Exceed this in your circuit at your peril. Especially perilous is exceeding the voltage on an elecrolytic - the electrolyte boils and the cap explodes giving you a fright and putting messy bits of stuff all over the insides of your project.

Capacitors have very wide tolerances, with electrolytics sometimes having a 50% tolerance on the marked value. Mica capacitors, on the other hand are pretty accurate. You need to be mindful of this in your projects and check the capacitor specifications. Capacitors can be "trimmed" to the exact value you need by means of a small capacitor in parallel called a trimmer.

What capacitors are used for

Fairly obviously, a perfect capacitor will not let a DC current flow through it because the dielectric is an insulator. Somewhat less obvious is the fact that a capacitor will allow the passage of an alternating current. This property means they can be used to transfer a signal from one part of a radio circuit to another. In an audio amplifier, for example, you can't connect the anode of the preceding amplifier stage to the grid of the next stage - because if you did that, the grid would have lots of positive voltage on it and the output valve would conduct like a crazy thing and glow bright red (before it popped). If you place a capacitor between the stages, the DC is blocked, but the audio signal (composed of AC signals) gets through and the amplifier works.

If you place a resistor in series with a capacitor and then attach a battery to the circuit, the capacitor will gradually charge to the same level as the battery voltage. The greater the value of the resistor (and the capacitor), the greater the length of time taken for the capacitor to charge. This capacitor-resistor combination is used in timing circuits and oscillators. Note that if you place a resistor across a fully charged capacitor - the time to discharge will depend on the resistor and capacitor value also.

A capacitor placed across an inductor (coil) forms a parallel tuned circuit. This is used in radio receivers to tune in to stations, usually using a varable capacitor, because the combination will resonate at a certain frequency (see reactance chart). In the article on superhet receivers, the function of the various tuned circuits is explained, and the tuned circuit is the basis of being able to set your radio to receive a particular station. A series tuned circuit is formed from an inductor in series with a (variable) capacitor. Some radio receivers use a fixed capacitor and vary the value of the inductor to tune the station. The Collins R390 is the prime example, but much humbler radios like the Pye Piper also do this.

A supercapacitor is a capacitor with an enormous value, usually several Farads. As might be expected, they behave like batteries and are similarly used.

This idea leads us to power supplies, where capacitors are used as a reservoir of charge. If you remove the final capacitor in an audio power supply with a choke input filter, one of the effects you will notice is that the amplifier doesn't amplify as much. There is no reserve of power for the audio valve to draw on.

Capacitor Problems

Capacitors have a bad reputation for being the most unreliable component in an item of electronic equipment. Many radio restorers and repairers believe that the first job should be to "recap the set".  If you are new to repairing radios - please ignore this advice,because the chances of your incorrectly replacing a capacitor are extremely good. This will lead to hours of frustration and possible abandonment of the project. Sometimes you do have to pre-emptively replace capacitors, where disaster would ensue. In very old radios, I do replace the power supply capacitors. Another example is the coupling capacitor to mechanical filters in radios like the R390a - if that goes short-circuit one or more filters will die with it.

The commonest problem is the power supply capacitors. These will be either short-circuit (easily checked) or dried-out, leaving them open circuit with no capacitance value - again easly checked. Don't be daunted by the fact that the modern replacment is a fraction of the size of the original and DO NOT be tempted to replace the capacitor with one having much more capacity because the "size looks right". You will end up with a blown rectifier valve.

Capacitors are supposed to block the path of DC - but in time may behave like resistors. They become "leaky" and cause a variety of problems, from motorboating in audio amplifiers to inability to tune a circuit to resonance. Tuned circuits should use mica capacitors, which don't often give trouble. If you are making your own superhet - beware, the voltages across tuned circuits can reach very high values. The moral is to use quite high working voltage (600 V) silver mica capacitors. Silver mica can also be annoying if the silver starts to flake off the mica, making it have random values of capacitance. This rarely happens, I'm happy to say.

My experience is that the most unreliable capacitors are electrolytics, followed by the old paper caps dipped in wax. The paper contained acid,causing the deterioration. Some makes of plastic capacitor are also unreliable. I have a box of unused (and unusable) polyester capacitors. Tantalum capacitors are a modern form of electroyltic, said to be very unreliable. You don't often see them - which could account for the fact they have never caused me any trouble.

You can check for capacitor leakage using a megger on small value capacitors. It doesn't work on electrolytics, which tend to be leaky anyway. All you will do is charge up the capacitor and get a nasty shock. 

In the sets I have had to repair, the capacitors have not been the most unreliable component. My advice would be to trace the problem, correct it and only replace the capacitors if disaster could ensue. Finally - don't replace a 1934 elecrolytic with another "brand new and unused" capacitor also made in 1934.

The late Mr Valve reckoned that old electrolytics could be re-formed by very slowly (over a period of a day or so) bringing them up to working voltage. The advantage is not so much the saving in money, but the preservation of the original equipment. This is something to research.

The Mathematics of Capacitors

As always, if mathematics is not your forte - skip this section until you are ready, or simply skim it to get an idea of the principles involved. In the workshop, you only are interested in replacing a faulty component with one of the same value, so you may need the formulae for capacitors in series and parallel. If you are dreaming up your own projects, you might need to delve a little more deeply. On the other hand if you love mathematics - skip my article altogether and read the one in Wikipedia.

The basic equation relating charge (Q) to voltage (V) and Capacitance (C) is:

\textstyle Q  = {\displaystyle {C \times V}}   ..... (1)
  

Q is measured in Coulombs. 1 Coulomb is 1 Amp - Second. Think of it like your car or inverter battery which also holds a charge. A 100 Amp-Hour battery has an equivalent charge of 360 000 Coulombs. Contrast this with a 1 Farad (Very Large!) Capacitor charged to 1 volt - that's a single solitary Coulomb. As a further piece of useless information, a lighning bolt may have between 36 and 350 Coulombs, so all our highveld thunderstorms probably won't solve our power crisis. (What crisis?). The thing is, the voltage and current are very high - so there's quite a bit of power there, after all.

This equation leads on to another

\textstyle I \times t  = {\displaystyle {C \times V} } ..... (2)

but this is usually rearranged and expressed in calculus form:

\textstyle I \times dt  = {\displaystyle {C \times dV} } ..... (3)
or
\textstyle I   = {\displaystyle {C \times {dV \over dt}}} .... (4)  

The "d" is calculus notation and means simply "a small amount of".  Let's see where this leads us.

Charging a capacitor through a resistor

Intuitively, I think we can see that at the end of the charging process, the voltmeter will read the same as the battery voltage. On the other hand, the voltage on the capacitor must start at zero. Also, we can see that the current through R will gradually reduce as the voltage across it diminishes.

Fairly obviously, the larger C and R, the longer it will take to charge the capacitor.

Mathematically, we combine Ohm's Law for the resistor R with equation (4)

\textstyle V{_i} - V  = {\displaystyle {C R} {dV \over dt}} ..... (5)

(Corrected)

This is a differential equation which means that the change in voltage V across the capacitor with time is proportional to the difference between the battery voltage and the voltage across the capacitor (i.e. voltage across the resistor). The solution is:

\textstyle V  = {\displaystyle {V_i{ (1 - e^{-t /{RC}})  } }} ..... (6)
 

"e" is Euler's constant = 2.71828.....(The numbers go on forever).

Vi is the applied battery voltage. The equation complies with ourCapacitor charging exponential curve intuition - when t is very large indeed, then V = Vi and when t = 0, V = 0.

A plot of the equation looks like the small graph on the right, which I just sketched by hand:

The product of C and R is called the time constant of the circuit, and is often given the symbol τ (tau). It takes a period of 5 x τ to arrive at almost the full charging voltage, and about 0.7 x τ to arrive at half the voltage. 

Note: In experimenter's corner there is an analog computer circuit that can be modified to solve the differential equations here. Sadly - you have to do the modification!

Discharging a capacitor through a resistor

As may be expected, the process begins quite raidly, and then the capacitor takes forever to fully discharge. The formula is:

\textstyle V  = {\displaystyle {V_i{ e^{-t /{\tau}}  } }} ..... (7)
  

When t=0, then V = the initial voltage on thecapacitor. When t /CR is very large, the V is almost 0. Also see Maths review on differential equations.Exponential decay

Practical applications

Most often, these will involve the use of a 555 timer chip, where you will see much evidence of the CR combination in the formulae.

I can't say that I have seen much use of capacitors in timing circuits in radio sets except in radio control transmitters and receivers, but that's a whole new story.

Be that as it may, if you have managed to read this far - the idea of a capacitor as a charge storage device will now be second nature.

Capacitors in Series and Parallel

Fairly obviously, if you connect two capacitors in parallel, the resulting capacitance is the sum of the two individual capacitances. You can work it out  from formula (1), or simply visualise the total plate area as the sum of the two individual plate areas.

\textstyle C_{total}  = {\displaystyle{ C_1 + C_2} } .....  (8)
  

The formula for capacitors in series is not that obvious. The total voltage across the combination must equal the sum of the voltages across each capacitor :

\displaystyle V_{total}  = {\displaystyle{ V_1 + V_2} } .....  (9)

So:

\displaystyle {Q \over C_{total}}  = {\displaystyle{ {Q \over C_1} + {Q \over C_2}} } .....  (10)
and
\displaystyle {1 \over C_{total}}  = {\displaystyle{ {1 \over C_1} + {1 \over C_2} } } .....  (11)

The capacitors all have the same charge on them. Why ? - because they all get the same current flowing through them per unit of time.

Practical Capacitors in series and Parallel

Most of the time, you would use these formulae to get a value you want from two caps that you have. Where you need accurate capacitance values, a trimmer can be placed in parallel with another fixed capacitor. Most of the time this is done when designing tuned circuits.

Summary

  • Capacitors store electric charge,
  • Capacitors block DC but let AC pass,
  • A capacitor and a resistor form a timing circuit,
  • Electrolytic capacitors have large tolerances on their value,
  • Capacitors have a safe working voltage which must not be exceeded, and
  • treat capacitors like you would any other component.

References:

Horowitz P, Hill W "The Art of Electronics"  - Cambridge University Press, 1988

 

        

Last Updated on Sunday, 07 December 2014 13:59
 
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