Charging - Keith-Snook.info

1 Wireless World, August 1971 391. Charging means that a current (call it 1) is flowing through R, and 'Ohm's law' tells us it is equal to E/R. That same current is flowing into C, Charging it. After one second, t=1, so equation (2) tells us that Q=I. And we already know that I=E/R, so Q=E/R, A further look at the eR coupling so V=E/CR. The capacitor voltage is rising at the rate of E/CR volts per second. But not quite. By the end of the first second the voltage across R is no longer by cathode Ray E; it is E - V. So the Charging current is less than it was, so the rate of Charging is less. The nearer the capacitor voltage gets to E, the less voltage is left to drive current through R and the slower the Charging continues. This is shown by the familiar rate-of- Charging curve, Fig. 2. Theoretically the capacitor never quite gets In reviewing basic theory since 1911 in which C is any capacitance (in farads), charged to the full voltage applied, E, but for the 60th birthday issue of Wireless Q the electric charge stored in it (in the deficiency soon becomes negligible.)

2 World I mentioned that during the second coulombs) and V the between its To continue this lesson in elementary World War I was shocked to find radar plates (in volts). We usually think in terms theory we draw the dotted line sloping instructors teaching that when (say) a of current (amps) rather than coulombs, upwards in Fig. 2 to show how the capacitor positive-going input signal was applied so we also have to remember that would charge if the starting rate could to a CR coupling the output also went Q=It (2) somehow be maintained. The instant at positive because of the Charging of c. In which means that the charge Q in equation which C would be charged to the applied actual fact (as I went on to say) any charg (1) is equal to the amount of current I voltage E is indicated by the point at which ing or discharging of C appears only as (in amps) that has been flowing into C, and the sloping line reaches the E level.

3 Distortion of the signal at the output. I t is the time in seconds during which it has Dropping a vertical dotted line from there included also the words 'of course', by been flowing. (To make things simple we to the time scale shows (or would do if the way of apology to readers for wasting are assuming I is constant.) Putting (1) scale were graduated in seconds) how long their time by explaining where the quoted and (2) together, therefore, we see that the this would take. As our scale is not teaching was wrong. Wasn't it too obvious voltage across a capacitor cannot change graduated we will call the answer T. in these enlightened days? unless the capacitor receives a propor From what we already know we can find Apparently not, for I soon got a letter tionate charge, and that takes time. If time a general formula for T. Combining to say that it was I, not the instructors, were not allowed, t would be zero, so for equations (1) and (2) by substituting who was wrong.

4 Touched though I was any charge at all I would have to be It for Q in (1) we get by this loyalty to a fine body of men, I infinitely large, which is impossible. felt that this evidence that my own ex Fig. 1 shows the classic capacitor V=!J. C. perience of them was not unique called Charging experiment. Before the switch At the end of our imaginary uniform-rate for some more detailed exposition of the is closed the capacitor C is uncharged, charge, V=E, f=T, and I=E/R. So point in question, in case the fallacy so in the basic equation (1) Q=O, so lingered on in a bigger way than I had V=O. The moment the switch is closed E_ET. suspected. I admit that some trainees the voltage E is applied across C and R -CR. might have misunderstood what their in series. No time has elapsed since it was and for that to be true instructors taught about this. I will go closed, so t=O, so Q=O, so v=o still.

5 T=CR. farther and declare that many trainees So the whole of E appears across R. That I'm quite sure that all the radar did misunderstand what their instructors instructors included this result in their taught about this and about many other repertoire, whether or not they proved it things. So not all that they taught in 1941 in the above or any other way. T, the time should be judged by what their trainees a capacitance C would take to charge to thought they said. And even if some of the applied voltage through a resistance them were wrong on this point of circuit R if the starting rate could be maintained, theory, we won the war so what the hell? is called the time constant of the series No one is likely to argue that uncertainty jZ combination of C and R. If they are in on the part of some radar mechs about farads and ohms (or more conveniently the precise mode of functioning of inter in microfarads and megohms) T will be stage couplings in pulse amplifiers was in seconds.

6 Responsible for a major loss of effective Because it refers to a mode of Charging ness in Britain's wartime radar defences, Fig. 1 The familiar circuit used to study that doesn't exist in normal practice you but I will and do hold that anybody who the Charging of a capacitor. might consider all this a waste of time. But wants to be clever with electronic circuits as we noted earlier one cannot say how ought not to have a fundamental miscon long a capacitor takes to charge in the real ception about how capacitors function in practical Fig. 1 way, because theoretically such circuits. So let's make sure. it always takes an infinitely long time, and The vital fact to be remembered is that V that is not a very helpful piece of informa . the potential difference between the plates E tion. The only thing left, then, is to decide of a capacitor cannot change instantane - -;7,- , I --" -=.

7 =---- . 7L - '. on how charged is 'charged'; 99%, say? ously, but only as a gradual process due to O"632E --- I. I I. I. The mere suggestion may bring before current flowing in or out. , I you a vision of endless committee meetings I. This follows from the basic equation for I. I all over the world trying to agree on a capacitance, as important for it as 'Ohm's T t percentage to use as an international law' for resistance: standard. Happily, there is no need for this. Q Fig. 2 The familiar (exponential) It turns out that the actual Charging curve V= (I) Charging curve; a graph of voltage in Fig. 2 has a fixed shape, so that the time C against time. taken to charge to any given percentage of 392 Wireless World, August 1971. 'full' is an easily calculated factor of T, v so by removing R altogether, leaving which is so simply equal to CR. The b c a gap. But then the grid potential would simplest possible factor is of course I, and Er_- == '- be at the mercy of stray circuit leakages.

8 To CO to r---- it happens that CR is the time taken to ensure that it starts definitely from zero (or charge to of 'full', as shown in Fig. any other designed voltage) R must be used, 2. That looks like rather short measure. but its resistance should be made not lower 99% requires an odd factor, so I suggest that is needed to anchor the grid to zero a choice of either 4CR (for ) or volts. Provided that C also is made large 5CR (for ). enough, the drop in output signal voltage, The radar instructors probably men represented in Fig. 4 by cc', can be kept tioned the name of the curve of this d e small, as shown. Incidentally, because the O L. O. ____ _____ __. particular shape (the exponential curve) a dO e -' t voltage across R is nearly constant, the rate but they may well have decided it was of charge is nearly constant and bc' is nearly unnecessary (for the purpose of fitting Fig. 4 The solid-line square wave is the a straight line.)

9 People to keep radar equipment working) input to CR (shown in Fig. 3), less any At c the input returns abruptly to zero to go into the mathematics of the thing. I continuous voltage bias, and the volts (d), and as the across e cannot too am saying it is unnecessary for our dotted line is the output at the junction change so quickly the grid side of e drops present purpose, and anyone who really of C and R. by the same voltage (E). As it started wants to know can find it in almost any of from c', less than + E volts, it now goes the textbooks on electricity (with or slightly negative, d'. This negative voltage, without magnetism). The only vital dd', to which e became charged during the point to carry away just now is that some input to the next , the junction period bc', is now applied to R, through idea of how long in seconds C,uF takes to of e and R. Of course if direct coupling which the charge leaks away during the charge through R M Q is given by is used e and R are not needed and period d'e'.

10 Because the voltage is so small multiplying C by R, and that Charging is distortion does not arise, but with valve the rate of discharge is very small and practically complete in 4 or 5 times CR. circuits especially it is usually necessary d'e' is practically horizontal. So when the Now we have got the basic principles to maintain a fixed between the two input goes positive again, from e to J, the straight we can apply them to a circuit of the stages by means of e, to keep the output at f is practically the same as at type which might have given rise to the electrode working voltages right. When c'. It therefore starts its decline during the lecture on eR time constants. It is a considering signal voltages this fixed next positive half-cycle from a lower voltage circuit in which a square wave developed can be ignored. So in the signal-voltage,! than it did in the first. in the output of one stage has to be passed time graph (Fig.)