Characteristic Impedance

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Public access to copy of this document is provided on the website of Cornell Law School at http://www4.law.cornell.edu/uscode/17/107.html and is here reproduced below: Sec. 107. - Limitations on exclusive rights: Fair Use Notwithstanding the provisions of sections 106 and 106A, the fair use of a copyrighted work, including such use by reproduction in copies or phono records or by any other means specified by that section, for purposes such as criticism, comment, news reporting, teaching (including multiple copies for class- room use), scholarship, or research, is not an infringement of copyright. In determining whether the use made of a work in any particular case is a fair use the factors to be considered shall include: 1 - the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes; 2 - the nature of the copyrighted work; 3 - the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and 4 - the effect of the use upon the potential market for or value of the copyrighted work. The fact that a work is unpublished shall not itself bar a finding of fair use if such finding is made upon consideration of all the above factors ♦ PDF Cover Page ♦ ♦ Verso Filler Page ♦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.

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