462 ABSTRACTS OF PAPERS

PULSE RESPONSE: A NEW APPROACH TO A.C ELECTRIC-NETWORK THEORY AND MEASUREMENT

By E. C. CHERRY, M.Sc.(Eng.), Associate Member.

[ABSTRACT of a Radio Section paper {communication from the Staff of the Research Laboratories of The General Electric Co., Ltd., Wembhv, England}which was published in September, 1945, in Part III of the Journal.]

Tn this paper the idea is developed of the interchange of timeand frequency in the conventional steady-state a.c. theory.Practical application of the theory is suggested by the use of asignal generator, intended for transient-response measurement,which generates a pulse wave of extremely short duration (ideallyzero), and a means of recording oscillographically the responseof a network to this pulse.

It is considered that the ordinary sine-wave standard signalgenerator, such as is used in communication measurements, isnow unsatisfactory for use in certain systems (for example,television) in which the transient response of networks is ofmuch greater importance than are their steady-state frequencycharacteristics. It is appreciated that the response of a networkto a transient may be calculated from the frequency charac-teristic by means of Fourier's theorem, but it is not usual, andindeed it is extremely difficult, to measure the phase-shift com-ponent, although the standard signal generator may be employedto measure the amplitude component.

E.M.F?

Time t

\ Amplitude offrequency components

1 0 T•-Frequency f

Fig. 1A.—A.C. wave in time plane.

E.M.Fe cos Znft

Vectordiagram

•*- Frequency f

\ Amplitude of pulses

—•• Time t

Fig. 1B.—A.C. wave in frequency'plane.

Many publications have appeared, to which references aregiven, which recognize the importance of transient response intelevision and similar channels, but most of these advocate theuse of square waves or step waves, i.e. a Heaviside unit function,and if pulses are mentioned it is always in connection with theirdifferential-coefficient relation to a step wave. Another way ofregarding the response of a network to an extremely short pulse,say of duration T, is that such a test signal puts energy into thenetwork in the short time T, and the response which follows is

-0-57"

0-*• Time

(a)

(Negative)

\ Voltageamplitude

6Frequency(b)

(Positive)

Fig. 2.—Ideal pulse wave and its spectrum.

90%-

1

my

-A

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/ /

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Il

II,I /

i;1 /,711//

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11

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w

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-03 / -01T 0Time t-

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Fig. 3.—Pulse spectra and waveforms (A).A—Rectangular.B—Cosine-squared.C—Half-cosine.

D—Triangular.E—Gaussian.F—Trapezium.

ABSTRACTS OF PAPERS 463

the force-free response of the network. The test-pulse durationmust be very short compared with the build-up time of thenetwork under test.

In the paper, the advantages, for practical measurementpurposes, of such a pulse-testing set are outlined, and the effectsare discussed of relying on practical forms of pulse having finitetimes of duration.

tion of the degree of their departure from the ideal. The effectsof such departure may be estimated by the observer, the accuracyof the estimate depending entirely on his experience. Thus hemay assess the rate of cut-off of a filter, or the effective band-width, etc., note its variation from the ideal, and decide whetherthe filter is suitable for transmission of a particular type ofsignal.

relative component amplitude

•anK or an.f. I-

Frequency corresponding to time takenfor wave to rise between 10% and 90%

Fig. 4.—Pulse spectra and waveforms (B).A—Rectangular.B—Cosine-squared. ,C—Half-cosine.

An interpretation is given of the method of transient-responseanalysis sometimes known as the "method of paired echoes," interms of the pulse response, together with a proof that thismethod follows directly from the principle of superposition.

Networks designed for use in communication circuits are fre-quently based on some form of standardized network—basicfilter structures, etc.—for which idealized steady-state charac-teristics are readily available. When such networks are con-structed, some practical measurement is made to give an estima-

D—Triangular.E—Gaussian.F—Trapezium.

The same judgment may be applied to pulse response charac-teristics, assessing the quality of a network by the shape of theresponse curve—the rate of build-up and decay, the degree ofoverswing, etc.

Mathematical explanation is given in the paper in support ofthe use of pulse-type signals as the natural counterpart of sine-wave signals for determining standard transient-response charac-teristics. This is based on the fact that a sine wave and anindefinitely short pulse are Fourier transforms. Thus Fig. 1A

464 ABSTRACTS OF PAPERS

1g

|f

E

rw - Frequency

T.m-

Fig. 5.—Frequency and time (pulse response) characteristics of anon-symmetrical network.

Ui) Real or symmetrical component.(/>) Imaginary or skew-symmetrical component.

shows a continuous sine wave, its conjugate vector diagram, andits conjugate frequency spectrum. In Fig. 1B the variables/ and / have been interchanged (using the reciprocity propertyof Fourier transforms) so that a sine wave plotted on a frequencyscale /, is represented by two pulses in time t\ also a vectordiagram may be drawn in which the vectors rotate with fre-quency. The conventional concepts concerning sine waves (intime) may thus be completely inverted and applied to pulsewaves; this inversion is more direct and obvious with pulses thanwith square or step waves, and the theory is probably moreacceptable to engineers trained in sine-wave measuring techniquewith no special knowledge of transient analysis. The idea isextended to complex transients, and to the measurement of net-work response. A single pulse has a uniform spectrum fromzero to infinite frequency (Fig. 2), so that the response of anetwork to such a signal is determined by the Fourier integralof the frequency characteristics of the network. Simple explana-tion is given for interpreting the pulse response and frequencycharacteristics in terms of one another in a way which avoidsreference to the complex plane, so that pulse response charac-teristics, when used for practical measurement may readily beinterpreted without elaborate analysis.

Figs. 3 and 4 illustrate some elementary "idealized" pulsewaveforms with their frequency spectra, and Fig. 5 shows thecomponent parts of a pulse response characteristic, with theirrelation to the parts of the corresponding steady-state charac-teristics of a band-pass network.

THE PLACE OF RADIANT, DIELECTRIC AND EDDY-CURRENT HEATINGIN THE PROCESS HEATING FIELD

By L. J. C. CONNELL, B.Sc, O. W. HUMPHREYS, B.SC, F.Inst.P., Associate Member, and J. L. RYCROFT, B.SC.

[ABSTRACT of an Installations Section paper {communication from the Staff of the Research Laboratories of The General Electric Co., Ltd.,Wembley, England) which was published in October, 1945, in Part II of the Journal.]

CHARACTERISTICS OF THE METHODS OF HEATINGIn the great majority of industrial heating processes, heat

transfer systems have in the past been accepted as the onlymeans for raising the temperature of the charge. Articles have"either been placed in contact with the source of heat, transfertaking place by conduction, or have been placed in an enclosureand heated mainly by convection, with radiation sometimesmaking a lesser additional contribution.

These methods have now been supplemented. Heat transfersystems depending almost entirely on radiation have been de-veloped, and systems whereby heat is generated electricallywithin the charge by dielectric or eddy-current losses have beenintroduced. There is nothing new in principle in these methods,but it is only recently that equipment permitting their use on acommercial scale has become available.

In assessing the place which the newer methods are likely tooccupy in the process heating field, it becomes necessary toexamine their characteristics in relation to those of the estab-lished methods. Thus, contact heating permits high rates oftransfer, but can be used only for articles so shaped as to becapable of making good contact with the surface of the heater.Convective heating imposes no such limitations on shape, butcan give only low rates of transfer. Radiant heating helps tobridge the gap between the two, and can give high rates oftransfer without the necessity for contact.

Sources of radiation for industrial use are of three main types:the lamp filament, operating at a temperature so high as tonecessitate enclosure in a protective atmosphere to preventoxidation; open-coil and sheathed-wire elements operating at redheat; and non-luminous sources in the form of metal panelsheated electrically or by gas. Each has its special characteristics,but, except when materials semi-transparent to radiation arebeing heated, all share with the two other heat transfer systemsthe feature that heat absorption is a surface effect, and that theextent to which the centre of an article heats is determined bythe rate at which heat is conducted through it.

With dielectric heating this limitation does not apply, for heatcan be generated throughout the thickness of an article. Inconsequence, the method finds its principal uses with materialswhich are poor thermal conductors.

In eddy-current heating, the well-known skin effect of thecurrent results in the greater part of the heat being generatednear the surface. As with the transfer methods, heating of thecentre of an article is dependent on conduction.

COMPARISONS

The characteristics of the various methods of heating are sum-marized in Table 1, and certain general conclusions may bedrawn from the form taken by this Table. Thus, articles maybe separated into classes according to whether, electrically and