Characteristic Impedance

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♦ PDF Cover Page ♦ ♦ Verso Filler Page ♦ SEPTEMBER 28tll, 1939. Wireless 299 World Characteristic Impedance

By "CATHODE RAY" -AND ALL THAT

EADERS of The Wireless World (where present) reactance, which in turn of other values of R, such as IS, 20, 25, include all grades from beginners · is of two opposite kinds, capacitive and 30, etc., you can plot them as a graph . R. to highly qualified radio en­ inductive. This matter was dealt with in (see Fig. 2). From this it can be seen gineers, and it would obviously the issues dated June 23rd and 30th, that the greatest power-45 watts-is be very tedious for the latter if all the 1938. delivered to R when R is equal to the technical terms in every article were ex­ Before considering what .. character­ internal resistance of the batterY-20 plained on the spot so fully as to be in­ istic impedance" is, it will be helpful to ohms. An equal amount of power is telligible to the former. In the more ad­ , prepare the ground by disposing of a com­ wasted in the battery, so the efficiency is vanced articles it is necessalY to assume paratively simple idea-that of im­ only 50 per cent. This is not necessarily a corresponding amount of technical pedance matching. According Lo the the most suitable condition for all pur­ knowledge. My own quotalion, there is poses. One may care to have less power chief aim is to fill in SOME DIFFICULT an aerial of 250 at a higher efficiency, in which case R is the explanations that ohms and a feedt:r made more than 20 ohms. In fact, it can m u s t perforc$'! be TERMS EXPLAINED (connecting line or be said that one always does care to do "taken as read" ill cable linking the so, because any ordinary battery would such articles. Criti­ aerial to the receiver be destroyed in a very short time by the cisms and suggestions, by the way, are or transmitter) of 70 ohms, and it is im­ above treatment. always welcome. plied that if these were directly connected ,. The characteristic impedance of the to one another there would be loss€s. In Loudspeaker Matchin� aerial is of the order of 250 ohms, and, order to pass the maximum power from to avoid the losses which would result if one part of a system to another, it is Turning to a more interesting example, this were connected direct to a 70-ohm lIecessary for them to have equal impe­ in which AC power is involved, consider feeder, a transforming device is required dance at the points of connecilOII. But the output valve in a receiver_ It has in­ at the junction."-(The Wireless World, because impedance is a complex thing let ternal resistance-the AC anode resist­ August 31st, 1939, page 207.) us talk about resistance instead. For­ ancc-and it supplies power to a loud . The above quotation appears to have tunately, in many practical sYstems the speaker. The resistance of the valve is been a stumbling-block to some, with impedance is nearly all resistance, so we usually thousands of ohms; the loud­ whom I have a good deal of sympathy, won't go very far wrong. It is quite easy speaker coil may be only about 2 ohms 'because one can know quite a lot about to prove the truth of the above equal­ 60 resistance and impedance without being resistance principle by the use of algebra, able to see how a cable of unspecified but some people are more easily con­ - 40 V ...... length can be said to be 70 ohms, or how vinced by examples. To take one that I ...... an aerial consisting of a few yards of sub­ is particularly simple because it is not ...... - '" stantial copper wire cut into well-insulated even complicated by AC, suppose we l- sections can possibly have an impedance have a 60-voIt battery, with an internal i / of 250 ohms. resistance of 20 ohms. It is used to supply -L The whole answer to this is rather a long power to a circuit of which the resistance 10 I story, which, to be properly told, in­ can be varied. The problem is to adjust . evitably demands the use of smhs and Lhe resistance so that the greatest power coshes and other strange oaths used by is obtained from the battery. Such a o 10 20 30 40 50 60 70 80 highbrow mathematicians. I hope to shed simple circuit hardly needs a !;liagram, R OHMS but here it is in Fig. I. The battery is Fig. 2.-Working out values and plotting a - graph, the value of R taking most power is ,'------\ represented by what is inside the dotted equal to the internal resistance of the bat­ 20 OHMS I line-a resistanceless battery in series with I tery. This a perfectly general law, applying a 20-ohm resistance, this figure represent­ to all power systems, DC or AC. ing a �-ohm internal resistance per cell. AC resistance. Actually, it varies quite T Ohms Law A�ain I ( a lot, according to the frequency, bllt let's were : eo VOLTS neglect that. If the speech coil con­ V VOLTS R OHM8 To go to one extreme let us make R , nected directly to the valve, or through a I equal to 0 (nil). By Ohm's Law the 1 : .L � I ratio transformer, the efficiency current is �, or 3 amps. The voltage would be very low indeed, and nearly all the power would be wasted in the valve.

I "cross R is, of course, nil, because it is It can be shown, either in the pruper alge­ ------'J a dead short-circuit. The power in watts braical way or by drawing a graph in the - . is, therefore, 3 x 0, or nil. Going to the same manner as for thc battery, that the Fig. I.-A battery (represented diagram­ other extreme, make R infinity, or, ill greatest power is put into the loud speaker matically by the components within the other words, an open circuit. There is no dotted line) supplies power to a resistance R. when its lesistance is the same as that of What value of R draws the greatest power current, and although the full 60 volts is the valve. As it is generally impracticable from the battery? See Fig. 2. maintained across the terminals, the watt­ to make it so, a sort of liaison officer is age is again zero. Now try a shot in the employed for bringing the two together in some light on the subject without recourse dark-Io ohms. Total resistance, 20 + 10, the right relationship. It is the output to such desperate measures, but to do . 60 transformer, or, as it might appropriately 30 ohms. Current, -, 2 amps. Voltage even that much in a reasonable space it 30 be termed here, the impedance-matching is necessalY to assume a clear knowledge across terminals, 2 (amps) x 10 (ohms), transformer. of what impedance means ill the ordinary 20 volts. Watts, 20 X.2, 40. If you work I'm not going to be sidetracked into an sense-a: combination of resistance ang out the result in the same way for a number exhaustive treatise on the theory of· the SEPTEMBER 28th, 1939. Wireless 300 World

Characteristic Impedance- That, however, is by the way. Th'.: problem. A period will, however, be transformer, however. Even if one's ideas idea to grasp is that the 60: I transformer allowed for the fevered brow to cool in on this subject are extremely elementary, makes the 2-ohm loud speaker look like readiness for a renewal of the struggle. they probably run to something like this: 7,200 ohms to the valve, while it makes .. A transformer is a thing for stepping the valve look -like 2 ohms to the speaker voltage up ancl cur­ rent down, or vice versa." Taking a definite e x amp I c .pRIMARY 20 7.2000 again, a l : 2 trans­ fomler 'W i t h 100 volts applied to the SECONDARY primary gives 200 v 0 Its from the secondary, and if (a) (b) 10 amps �liow in the primary the secon­ dary supplies ,'). The power is the same both sides, &0:1 so it must be assumed that the transformer itself Ie- consumes no power. Actually, 7':,)000' large power trans­ (e) formers are made that are better than 99 per cent. per­ fect; valve output transformers never reach t his stan­ dard. But we are neglecting subsidi­ ary effects of this (0) sort. The impor­ Fig. 3.-This familiar bit of circuit, {a), the output stage in a receiver, tant thing to notice is electrically equivalent to (b), in the example chosen. The effect of is that a doubling the transformer is to make (c), looking in the direction of the arrow, of voltage is (by equivalent to (d) ; and (e) to (f). Ohm's Law) a doubling of resistance, and so IS a coil. Fig. 3 puts this -in diagram form. halving of current. So when both The transformer itself has a very much things occur at once, the resistance is higher impedance if nothing is connected multiplied fourfold, or by the sqtlare of to the other winding; in fact, if it were a the step-up ratio. Therefore, if one wants perfect transformer it would have infinite to match an impedance of 1,000 ohms to impedance. But the load cf 2 ohms con­ one of 4.000 ohms, the correct trans­ I)ected to the secondary is the same as former ratio is not I: 4, but the square 7,200 ohms looking at it from the primary. root of this, I: 2. To match a 7,2oo-ohm So far we have (I hope) assimilated valve to a 2-ohm load, the correct trans- (I) the necessity for matching the im­ former ratio is .j7 ,200: 2, which is 60: J. pedances of any two items which stand in Actually, this ratio is correct for get­ the relation to one another of gt:nera�or ting the maximum power, but is rarely and load, and (2) the way in which im-

Characteristic impe.danc� becomes a matter of importance .when dealing with high-frequency cable, some of the various types of which are shown here.

adopted, because it takes no account of pedances can be matched. If maximum distortion. The ratio giving the greatest· power transference is the object, thc im­ output power for a limited amount of di;;­ 'pedances ought to be equal; but often tortion is obtained by USillg' the •• opti- . there are overriding considerations, as mum load resistance" stated by the we have seen. makers, instead of the valve resistance. Now'we are ready to look at the original. NOVEM/JER; I939 Wireless 10 World Characteristic Impedance By .. CATHODE RAY" -AND ·ALL THAT

Concluded from page 300 of our September 28th issue

T AST month we saw why, when and how the im­ capacity between them is large-again a disadvantage. L pedances of a generator and its load ought Jo apparently-but at least there is no intederence, because be matched. An aerial, because it has a radio- the voltages picked up by two wires very close together frequency voltage set up in it, is a sort of gen­ practically cancel out (one being a "go" wire and the erator; and the receiver to which it is connected is the other a II return " ). If one wire is entirely surrounded load. The object is to connect the two so as to deliver. by the other, as much power as possible to the receiver terminals. which is in the Without bothering just yet about exactly what it form of a tube, means, suppose that the resistance of the aerial is 250 it is completely --��---��;;��-��;--- ohms. The dynamic resistance of the first tuned circuit screened. Obvi­ TERMS EXPLAINED in the receiver-that is to say the comparatively large ously, owing to resistance to which a tuned circuit is equivalent at the the large capa­ resonant frequency-may be perhaps 4,000 ohms at very city of the feeder, which acts as a shunt across the input to the receiver, it is of low impedance, and a consider­ high frequencies. The ratio is 250. or I: 16; and so , able step-up is needed at that end. The closer they arc 4,000 a 1:4 "transformer is needed�. as we saw last month. together the lower the impedance. This is easy to Another thing is that at the wavelengths we are con­ 1 arrange, either sidering the feeder is probably at .least several times as long as the wave. When, therefore, a signal voltage AE� . 1\ as a double- � [[ w 0 u n d tran - is picked up by the aerial, it cannot be supposed that it s . EO former made by reaches the receiver instantly. By the time it gets there several more waves have been picked up and are (Il) (b) coupling a few en .(Fig. (a) ). Suppose that the feeder is discon­ Fig. 4.-Two sorts of impedance- t urn s to the route 5 matching transformer for matching tuned circuit, or nected at that end. What are the arriving waves to do? a low-impedance aerial or feeder to a as an auto-trans- They represent a certain amount of power, which cannot high-impedance tuned circuit. former made by pile up ad lib. at the end of the feeder. They do exactly what a sound wave does when it strikes an impenetrable "tapping down" (Fig. 4). At least, it would be easy were it not that for picking up the greatest voltage the wall-they are reflected or echoed back. If on arriving aerial should be as high up in the air as possible, especially if it is for teleyision or other short-wave pur­ t F[(O£" poses. On the other l'.and. this is an exceptionally in­ ----_ convenient spot to install the receiver. Therefore it is ...... _-_.. A£RIAL desirable to have them in separate places and connect DIR[CTIO� OF WAVES---+ them by a feeder. (Il)

Earthed and Unearthed Aerials

If the aerial is of the self-sufficient type (such as the dipole), needing no earth to complete it, there are two connections to be made between it and the two tt.r­ minals of the receiver tuned circuit. The 'ordinary (DJ elevated wire aerial is just the same, except that the Fig. 5.-A feeder is generally several wave­ lower half of it is the earth. The latter arrangement, lengths long, and the voltage consequently therefore, has its mid-point at ground level, which is varies all the way. If the receiver end is generally convenient for a reasonably direct connection open-circuited, the waves have nowhere to go Ro and are reflected. 1£ a resistance is there, to the set, and so the feeder question seldom arises. generally part of the power is absorbed by it and Assuming, however, that our aerial is entirely up in part. reflected; but one particular value of the air,' and· therefore needs a twin connection, how far resistance, Ro, absorbs all the power. Except, apart should these leads be? If they are widely spaced, (0) for a small loss, (b) is then electrically equivalent. to (c). they are, in effect, a single-turn coil of large dimensions and therefore of high inductance. This seems unsuitable at the aerial again they do not exactly cancel out the for ultra-short wave purposes; and, moreover, is capable latest arrivals, there they are reflected again, and con· of picking up voltages on its own, mostly of an inter­ tinue surging backwards and forwards until frittered feri�g nature. If the wires are very closely spaced, the away in the resistance of the wires. 11 NOVEM/JER; I939 Wireless World

Characteristic Impedance- But when capacity and inductance are distributed a long Suppose that, instead of being· disconnected at one parallel wires, so that different sections of it are at quite end, the feeder is connected to a -resistance. If it is . different phases (see Fjg. s(a», the capacity and induct­ high, the current passed by it when the wave arrives is ance of the whole feeder is of less significance than those small, and the power delivered to it is therefore small­ of a section equal, say, to one wave- less than the waves are bringing. The surplus is there­ length. It is as if one had a tuned fore reflected. There is one particular r esistance that circuit in which both inductance and uses up power just as fast as it is delivered, and then capacity are proportional to the there is no reflection, no surplus power surging to and wavelength. Now \\ie know that the fro, and maximum efficiency is reached. T he only loss wavelength at which a circuit is in is that due to a s ingle journey through the resistance of tune in proportional to v'LC. So the feeder wires, which is comparatively small. This the interesting result emerges that the particular re:>istance is called the characteristic resist­ inductance and capacity of a feeder ance " or often the characteristic impedance, b ut n or­ cancel out at all wavelengths. That mally it can be regarded as a resistance. Its value is why everything can be ignored ex­ depends chiefly on the diameter and spacing of the feeder cept the resistance (it is assumed all 200 the time that the feeder is infinitely long, so that wav .. // es starting at one " I z � end never return; or that it is ter­ .. 2bl: I--,a / to Q'" minated somewhere by the character­ iii t- .- � -I-r- istic resistance, which amounts ' to �hOWlDg th e � � Io� " % fi.i.O�� the same thing). construction of t= 0 100 II Telcon twin HF on Although the foregoing statements - 0 ,.o:�h c ,d �o... c i.p able. �o: �.r a ought, f or the reasons given, to lJe � �Ltl.l not beyond ..'" .,.. the belief of anybody familiar with the .. � % V behaviour of ordinary tuned circuits, their exact truth (,) / / cannot be proved without s ome of the riper grades of 0 mathematics, as •{/ 2 3 • • • 7 8 . SUC�1 I have promised to spare you. It IS. a matter of mterest, howe,:er, that if unimportant RATIO 1- detall e neglected the characteristic resistance is equal � . Fig. 6.-Characteristic resistance of twin-wire and con­ . . centric feeders. to Lo W h ere h t ese quantItIes are the inductance and JCo wires; the smaller the spacing, the lower the impedance. capacity per unit length. As formula! for them are When the feeder is correctly terminated-that is to given in any radio or telephony reference book, the say, with a resistance equal to the characteristic re­ characteristic resistance is easily calculated. connected, as in Fig. 5 (b }-then excep sistance t for t he What is �'Aerial Resistance"? slight loss in the feeder it is the same as if the feeder • point has still to be cleared up You were asked were abolished and the resistance joined to the aerial. One . to take it on trust that the resistance of a c ertain aerial The two things to know about any grade of feeder arc, was 250 ohms. What does this mean? T ort of then, the characteristic resistance and the loss per unit he s aerials we are considering-dipoles, .. tilted, wires," of length (generally gi ven in d ecibels per 100 feet). You etc. -differ from the ordinary garden aerial in that they may be wondering where the c apacity of the feeder has made of such dimensions as to comprise gone. In a cable of the type used for television it may are a complete � ne ned i ' r=J a amount to 1,500 p.p.F in a Ioo-foot feeder. Knowing � �" g that at these high frequencies every p.p.F counts, it seems r :�:F that it would never do just coolly to ignore such a large I ! �inductance and "',000 0 : . . amou'nt. But do not let us forget the inductance, even �;:£ c paclty are dls- if it is small. The principle of the ordinary tuned circuit . � r tnbuted, the y is that a t any given frequency there is a value of induct­ r '0.0000 neverthele ance that just neutralise s a given capacity. The greater i are ss \.J n true tuned cir- the capacity the smaller the inductance, and vice versa. cuits. Now it is We have already noticed that when a pair of feeder wires U well known that are closely spaced their capacity is large and inductance a tuned circuit, small, and vice versa; so it may not come as a gr eat sur­ at the resonant prise to know that when the spacing is varied these two J r e qu e n c y, is effects exactly balance one another. f "cO" I} equivalent to a '--Y Distributed Capacity and Inductance °U resistance. The When an inductance and a capacity are concentrated Fig. 7.-Showing how the resistance amount of that oi a resonant tuned circuit depends on resistance de­ or localised, as in the ordinary form of tuneq circuit, the ,points between which it is pends on th e such a balance holds good a t only one frequency. That measured. The same applies to is the principle on which tuning and selectivity depend. reson.ant aerials, lines, etc. points between NOVEMBER, 1939 Wireless 12 World

Characteristic Impedance- which it is measured. If across the whole coil (and co n­ denser), the resistance is large. If tapped across part of the coil, or across part of a split condenser: it is less, until it becomes nil when the two points coincide (Fig. 7). The same is true of the resistance of an aerial or other distributed tuned circuit. If points can be found be­ tween which the resistance is equal to the characteristic resistance of a suitable feeder, one is in luck, because they can be directly connected. This is so with the ordi­ nary dipole. But when it is not (as in the case that started the whole argument) a matching transformer must be used if losses due to mismatching are to be a voided. 'Please note now, by comparison with the beginning of the first jnstalment, that •• this is where w e came in." I hope that by now th.e plot is clearer. One more point. The article quoted goes on to de­ scribe the matching transformer used. It is neither the ordinary double-wound nor auto-transformer. It is a carefully measured length of special feeder. By now that ought to cause no surprise, because we have become quite used to the resemblance between localised tuned circuits and distributed ones. If points A, B, X, and Y are selected on a distributed system, such that it has a resistance between points AB of 250 ohms (when a resistance of 70 ohms is coimected between points XV) and a resistance of 70 ohms between points XY (when a resistance of 250 ohms is connected between points AB) it can be used as a transformer for matching systems having these diverse resistances; and it may well be more convenient and durable in the open air than the conventional coil-wound transformer.