US2165838A - Electric signal transmission system - Google Patents

Description

July 1 l, 1939.

J. COLLARD ELECTRIC SIGNAL TRANSMISSION SYSTEM Filed Feb. 16, 1938 ANGULAR FREQUENCY? INVENTOR Patented July 11, 1939 ELECTRIC SIGNAL TRANSMISSION SYSTEM John Collard, Hammersmith, London, England,

assignor to Electric & Musical Industries Limited, Hayes, Middlesex, England of Great Britain a corporation Application February 16, 1938, Serial No. 190,832

In Great Britain February 18, 1937 20 Claims.

This invention relates in general to wave transmission systems, but more particularly, though not exclusively, to electric signal transmission systems.

The properties of any wave transmission path in which in a specific frequency range the constants are substantially smoothly distributed are known when the complex propagation constant is determined for all frequencies within the specified range, where (x is the attenuation constant and [3 the phase constant and R, L, G and C are respectively the resistance, inductance, leakance and capacity of the transmission line per unit length and w is the angular frequency of the signals being transmitted. If the attenuation constant 0: is independent of frequency then all oscillations caused to travel over the path will do so without the occurrence of variations in relative amplitude. If also the phase constant ,8 is proportional to to so that the time delay d6 HE is constant, then relative phases will also be transmitted undisturbed.

In general, with a cable or transmission line, these conditions are not satisfied and it is therefore necessary to employ equalising or compensating circuits whereby the attenuation constant is made substantially independent of frequency and the phase constant substantially directly proportional to frequency over the frequency range of the signals transmitted along the transmission line or cable. The variation with frequency of the attenuation and phase of the transmission line or cable arises either due to the variation with frequency of the effective resistance and inductance of the cable or the effective capacity and leakance of the cable or due to variation of all of these constants. In telephony, however, variations in phase are relatively unimportant, so that the equalising circuits are provided mainly for the purpose of correcting the attenuation or loss characteristic. Some effect on phase is always introduced by the use of such circuits, but this is purely arbitrary so that if it is desired to correct for phase the addition of phase-correcting circuits is necessary. If such phase-correcting circuits are used it may be found thatthe loss will have to be corrected again, and so on. Such methods of correction therefore are generally those of trial and error and the compensation that is obtained is usually subject to random errors.

In transmitting a wide frequency range of sig- 7 nals along a cable, such as television signals which may extend from zero frequency up to some megacycles per second, the problemis considerably more complex. Not only are variations in amplitude particularly important, but relative phases in addition may be allowed to vary only within very small limits. In an actual high frequency cable, owing to the skin effect in the conductors, the resistance of the cable increases with frequency and the inductance falls. Further, owing tothe fact that the capacity of the cable acts not like an ideal condenser but like a somewhat complicated network of condensers and resistances, the capacity tends to decrease slightly and the leakance to rise as the frequency rises. With such a cable it will be apparent that since all four primary constants will vary with frequency, the attenuation constant will vary with frequency and the phase constant will not be proportional to frequency. Distortion of the signals transmitted along such cable both in amplitude and phase will therefore result. The use of equalising and compensating means is therefore necessary to reduce the distortion. However, the use of the methods of correction previously referred to, which necessarily involve the introduction of random effects, is of little value since the random effects may total to a magnitude of considerable extent, especially over a long length of cable.

The present invention is primarily concerned with the simultaneous equalisation of the attenuation and phase of a cable or transmission line designed to handle a wide frequency band of signals, but as will be apparent hereinafter, the invention is capable of a much wider application.

In this specification and in the appended claims, what is meant by equalisation of attenuation and phase is that the attenuation constant is made substantially independent of frequency and the phase constant is made substantially directly proportional to frequency over the range of frequencies for which equalisation is effected.

It is known that where oscillations, such as mechanical or acoustical oscillations, are required to be transmitted, similar difficulties are encountered due to the attenuation and phase of the transmission path and it is also well known that the analogues of resistance, inductance, capacity and leakance exist in the mechanical and acoustical cases.

applicable to mechanical and acoustical transmission systems.

The object of the present invention is to provide an improved transmission system in which the variation of loss and phase due to variation with frequency of the effective resistance and inductance or capacity and leakance, or both, (or their analogues) is simultaneously equalised and in which the equalisation is effected with considerably reduced random errors.

Various forms of equaliser sections for electrical signal transmission lines have been proposed comprising combinations of inductance and capacity or resistance arranged so as to produce the complement of the variation of attenuation and phase introduced by a cable, but with such equalisers it was necessary to equalise loss and phase separately.

The present invention can be employed with any suitable type of equaliser section providing that the equaliser sections employed produce similar characteristic curves such as can be expressed as a function of where p is an angular frequency defined in the same way for all sections employed and w is the angular frequency at which the property whose behaviour characterised by the curves is evaluated. This implies that the zero frequency loss for all sections is the same. The frequency p will hereinafter and in the appended claims be referred to as the reference frequency. In sections of the simple type comprising series arms composed of resistances shunted by condensers and shunt arms composed of inductances in series with resistances a convenient reference frequency to take is that frequency at which the reactance of each arm becomes equal to its associated resistance. In more complicated types in which several reactances and resistances may be employed the reference frequency may be taken as that at which some particular reactance becomes equal to some particular resistance. It will be found that the reference frequency will always correspond to a value at which the loss of the section has fallen to a certain fraction of its maximum value. The reference frequency may therefore be regarded as that angular frequency at which the loss of the section has fallen to some arbitrarily chosen fraction of its maximum value, which fraction is substantially constant for all sections. The present invention is based upon the principle of arranging the equaliser sections in such a manner that their reference frequencies are spaced at values corresponding to substantially equal increments of variation of the transmission path. By employing such a principle it is possible to equalise a cable without the introduction of serious random errors, provided, for example, that the loss curve of the path can be resolved into one or more component curves of the form Ana)", or that the phase curve of the path can be resolved into one or more component curves of the form Bnw"; moreover, if the cable is such that the type n B =A tan are satisfied, then simultaneous equalisation of loss and phase delay is achieved.

In general the principle of equal spacing may be applied to equalise distortion arising from any frequency characteristic which may be expressed as a finite power series in frequency.

Accordingly, the present invention broadly comprises a wave transmission system including a transmission path with substantially smoothly distributed constants along which oscillations extending over a range of frequencies are caused to travel, and in which the path is such as to cause distortion of the oscillations which varies with the frequencies of the respective oscillations owing to the variation with frequency of the effective resistance and inductance or the capacity and leakance, or both (or their analogues), and in which the characteristic curve of the cable can be analysed into the form mentioned above and wherein a compensating or equalising path is associated with said transmission path comprising a plurality of equaliser sections the reference frequencies of which are spaced at values corresponding substantially to equal increments of variation on the component curve or curves of the transmission path, said sections being designed in such a manner, in conjunction with their spacing, as to produce substantially the complement of the increment of variation so that the loss and phase distortion due to variation with frequency either of effective resistance and inductance or of capacity and leakance. or both,. are simultaneously equalised.

More specifically, the invention is concerned with the case in which the path is such as to cause attenuation and phase distortion of the oscillations and in which the reference frequencies of the equaliser sections are located at frequencies corresponding substantially to equal increments of loss of the component curve or curves of the transmission path and designed in such a manner that the loss of the transmission path is made substantially independent of frequency and the phase constant substantially directly proportional to frequency.

The present invention is especially applicable to an electric signal transmission system which is designed for the transmission of signals extending over a very wide frequency range extending at least up to 100 kilocycles per second. The invention is also applicable to the case in which the transmission line is designed for the transmission of frequencies from substantially zero frequency up to about two or three megacycles per second, such latter frequencies being ordinarily encountered in the transmission of television signals. When dealing with signals extending over such a wide range of frequencies the variation of attenuation and phase is due to variation with frequency of all four primary constants of the cable and the present invention can accordingly be applied to such a system for equalising simultaneously the greater part of the variation of the loss and phase. The invention may also be applied to transmission lines or cables transmitting signals extending over much smaller frequency ranges. It may also be employed in a transmission line or cable for equalising the effect only of variation with frequency of the resistance and inductance or capacity and leakance. It is also possible to apply it to a cable in which the equalisation is effected by loading the cable at intervals along its length, which intervals are short compared with the wavelength of the highest frequency to be transmitted or to the case in which an arbitrary length of cable or transmission line is equalised as a whole by the use of a. plurality of equaliser sections.

In all cases the reference frequencies of the equaliser sections will be located at frequencies corresponding to equal increments in the variation of the transmission path and, subject to certain conditions hereinafter to be referred to, any type of equaliser section may be employed in the invention. The invention preferably employs equaliser sections of the so;-cal.led constant resistance type but is not limited in scope to the use of such sections.

In order that the said invention may be clearly understood and readily carried into effect the same will now be more fully described with reference to the accompanying drawing in which:

Figure 1 illustrates the manner in which the loss of a cable, such as might be employed for television purposes, varies in the range from zero frequency to frequencies of several mega cycles per second,

Figures 2, 3 and 4 illustrate networks which may be employed in the invention, and

Figure 5 illustrates an improved type of equaliser section according to a feature of the invention.

The invention will now be described more fully and as applied to a transmission line or cable in which variation of the four primary constants of the cable occurs With variation in frequency and in which it is desired to equalise simultaneously the greater part of the loss and phase due to the variation of these four primary constants.

Figure 1 illustrates a typical loss curve of a cable. In order to avoid a relative variation in the amplitude of signals at various frequencies transmitted along a cable having such a-characteristic, it is necessary, as stated above, to employ an equaliser which may take the form of loading at intervals along the length of the cable but moreconvem'ently the equaliser is in the form of an artificial line inserted in series with the cable at a convenient point before or after suitable amplifiers. The equaliser is designed to produce the complement of the loss produced by the cable so that when the equaliser is connected to the cable the overall loss is substantially constant over the frequency range for which the equaliser is designed. It has been found that an equaliser of the form described here which is designed to make the overall loss of a cable substantially independent of frequency simultaneously makes the phase constant directly proportional to frequency.

The sections of an equaliser constructed in accordance with the invention are arranged so that their reference frequencies, as hereinbefore defined, are spaced at values corresponding substantially to equal increments of loss of the cable. As shown in Figure 1, the angular frequency p1, 1122, etc., correspond to substantially equal increments in loss of the cable characteristic. The equaliser designed in accordance with the invention has the reference frequencies of the sections arranged so that they are equal to 121, 2122, etc.

In the following explanation of the invention it will be shown how the proper spacing of the angular frequencies 111, 102, etc., may be determined. The equaliser sections employed produce similar characteristic curves as stated above, such as can be eXpressedby a function of B Let) (q) where p being the reference frequency, be the variable part of the loss at frequency w due to any one of a number of like sections so that the variation of loss due to all the sections maybe expressed as where a dash signifies a first differentiation, and due to this number of sections there will be contributed an amount of loss at a frequency w equal to The total loss at this frequency is, therefore,

i ;'"(p)f( d X 0 0) p The sections will accordingly possess the same total loss characteristic as the curve along which they have been distributed if This can be shown' to lead to a finite value of :c if F(w) is of the form Aw It is in fact then found directly that Turning now to a consideration of the phase characteristic that will be obtained with this distribution let (q) represent the phase characteristic of any one section. Performing an integration'in the same way as before the total phase at an angular frequency w willbe Subject, therefore, to, a consideration of the finiteness of these integrals it appears that if in the loss characteristic of a network constructed as herein supposed there occurs a term ca in the loss characteristic, then there will also occur a term w in the phase characteristic. This is a completely fundamental relation for all equalisers having sections possessing similar character curves and spaced as stated above, since it is independent of the forms of f (q) and (q).

In order to determine the conditions of finiteness for the integrals iii) and

it is necessary to consider special cases, since such conditions will clearly depend on the special forms of f (q) and (q). The special case of a constant resistance section will be selected for purposes of illustration but it will be understood that the in-- vention is not limited in its use to the constant resistance type of section.

It is necessary for this problem to determine the propagation constant as a function of q since the propagation constant has already been supposed to possess a variable real part f(q) and an imaginary part (q). Now in a constant resistance section, by which is meant a section possessing a series arm of impedance Z1 and a shunt arm of impedance Z2, such that Z1Z2=Zo and having an additional resistance Z0 connected either across the series arm or in series with the shunt arm, the current ratio 70, as is well known, is given by In terms of k, the propagation constant is simply given according to It is therefore necessary to express Z2 as a function of q, and it has been found possible to do this in a very general manner by a process of building up any impedance from elementary impedances comprising either resistance in series with inductance, resistance in parallel with inductance, resistance in series with capacity or resistance in parallel with capacity. By this method it may to zero the value of the attenuation constant tends to Zlog and that as w tends to infinity the attenuation tends to i. e., to

2 log g s Q( t cool so that if Q(t) Q(a) then the attenuation at infinite frequency is greater than that at zero frequency. It Q(t) Q(a) then the attenuation at finite frequency is less than that at zero frequency. Thus by adjusting the relative values of Q) and Q(a) it is possible to give the attenuation curve of the section a general rise or a general fall over the whole frequency range from zero to infinity. The curve over any particular part of the frequency range, however, may rise or fall according to values of the individual terms (q +t and (q -l-a In proceeding to consider the previously mentioned integrals it is permissible to deal with each term in f(q) and (q) separately. Thus corresponding to the general term in f(q) there is the integral 1. e., to

p being a constant frequency as defined in any arbitrary way and as stated in the so-called reference frequency.

By virtue of this fact it is possible to write for k the very general expression 1(q+j 1) 2(q+j 2) i(q+j 1) 2(q+j 2) where s1, s2, etc'., and t1, t2, etc., are further real constants of the kind as referred to above. For convenience this form will be contracted to:

Q( )Q(q+j Q( )Q(q+j by using the notation Q(z)=z1, 22, 23, It

follows directly from this form that q t2 1 +a (q)=2 tan" %-2 tan" In passing, and before proceeding to employ these derivations it may be pointed out that as w tends Now it can be shown that is finite provided b-I exceeds a. Applying this result to the first integral in the expansion, since this term constitutes the greatest restriction on n, it follows that n-I must be less than unity, and, therefore, that 11 must be less than two.

By a similar procedure it may be shown that is finite for all values of 12 less than unity.

Also if n is less than unity it can be shown that 117i q"" (q) q 0 For n= this becomes I17! COS T The following conclusions are therefore to be drawn:

(a) If the power of w is two or over the spacing factor a: is infinite, so that in practice an equaliser of this type cannot be produced so as to possess a loss varying as a power of no equal or greater than two:

(b) If the power of w is equal or greater than unity the phase becomes infinite at all frequenc1es:

(c) For powers of to less than unity a term Aw in the attenuation is accompanied by a corresponding term in the phase.

Considering now the expression for f(q) it will be clear that for every constant resistance network obtained in the manner that has been described above and having an attenuation component given by Anna there is always a complementary network having a component equal to the negative of this term, to be obtained by an interchange of the respective constants t1, t2, etc, and a1, a2, etc. Moreover, if the first network possesses a phase characteristic with a component Bnw this interchange produces a network with a component -Bnw Thus, by putting these two networks together in series the resultant loss will be constant and there will be no phase distortion. If, therefore, the cable has such characteristics that any variation of loss can be represented by a series of terms: A1w Azw and such that the variation of phase can be represented by a corresponding series of terms:

it follows that it can be equalised by a structure of the type described here.

From the above it will be appreciated that by constructing an equaliser having the reference frequencies of its sections spaced at values corresponding to substantially equal increments of loss, the loss and phase distortion of a cable can be simultaneously equalised.

It is necessary now to consider the limitations that must be imposed on the sections employed in the equaliser. It has already been stated that the loss of a single equaliser section must be small compared with the loss required to be equalised. Since the loss characteristic of a cable is one which rises with frequency it is clear that the characteristic of a single section must fall with increasing frequency. Hence Q (a) must exceed Q (t) and it follows that the impedance of the shunt arm must tend to a limit at infinite frequency which is larger than its value at zero frequency.

It follows that the impedance of the shunt arm must never be zero at finite frequencies since otherwise infinite attenuation would result. In particular, it must not be zero at zero frequency.

The corresponding conditions for the series arm follows of course from the relation Z1 Z2=Z0 Having now indicated in some detail the nature of the methods by which variations in a transmission line may be compensated for, by showing how they may be employed to counteract variations in total loss and phase it will now be shown how they may be applied to equalis e directly variations in inductance and resistance or capacity and leakance in a short length of line,

i. e., short compared with the shortest wavelength transmitted.

' It may be shown by experiment or by calculation that the variations of resistance and inductance, which are the components introducing" distortion into the transmission, are represented with sufficient accuracy for frequencies greater than 50,000 cycles per second by a term wt and mi respectively. Now a resistance varying like wt is provided by a chain of parallel connected resistance and inductance elements such as is shown in Figure 2. Thus, suppose the resistance elements are all the same and of magnitude equal to R, then the impedance of any one element in the chain is RjwL R+jwL from which it follows that the total effective resistance of the whole chain is the sum of all such terms as 1 q where sip . p being that angular frequency at which the reactance becomes equal to the resistance. Performing this summation it is found that any resistance variation like Aw may be obtained if the distribution of elements is made by equal increments as in resistance where This spacing gives rise to a reactance term CXI , and. therefore to an inductance term connected in series with a capacity C if E=R1R2=ZD2 Thus it is possible to simulate the variations of resistance and inductance by a number of suit-- ably distributed shunt elements formed by capacities in series with resistances. As a further possibility the same efiect may be obtained by a combination of the two types of simulating elements to give a network which possesses sections having a characteristic impedance Z0. Such a network illustrated in Figure 4.

Since this network reproduces exactly the effect of the variations in resistance and inductance it follows that it reproduces exactly the variations in loss and phase that occur in the cable due to these variations of resistance and inductance. Now the loss of a single section of this network is R; 1 ((1): VE +q so that the total loss at an angular frequency w of the network is Ace" w lR But the analysis given earlier showed that such a loss characteristic could be provided by a suit? able distribution of any type of section subject only to certain limitations. The cable may therefore be regarded merely an as infinitely finely distributed example of one of the types of structures discussed earlier. By the provision of a complementary structure it is therefore possible to cancel the distortion that arises from variations in inductance and resistance. The effect of variations in capacity and leakage inductance may, using a similar argument, be shown capable of elimination by the same general method.

In compensating for variations by any of the above methods it is not necessary for the construction of an equalising network to be based on the use of a single spacing factor x. It is possible to split up such a network into a plurality of subsidiary structures, each with its own spacing factor provided a certain condition is satisfied by the spacing factors x1, x2, of these subsidiary structures.

Thus, suppose sections possessing a characteristic f(q) are utilised, then by means of a spacing factor act; it is possible to'provide a'characteristic A plurality of structures each with their own particular value of am; when connected in series are therefore capable of producing a characteristic expressed by nA at k w fq"" (q) q This may be set equal to I The evaluation of spacing factors may be effected from the formula 93L x Z w 2 COS 7 where the (11, a2 etc., and t1, t2, etc., are the constants that appear in the expression In deriving the above expression for m it was found convenient to utilize an alternative inte- This may be obtained by calculating the total slope of the equalizer characteristic at an angular frequency w and setting it equal to the negative of the slope of cable at 0:.

When n It will be appreciated that so long as the loss and phase curve for the cable or transmission line can be analyzed into the form stated above, and providing the equalizer sections meet the requirements hereinbefore referred to, any suitable type of section may be employed.

It will thus be appreciated that there is a large number of equalizer sections which are capable of equalizing simultaneously the loss and phase of a cable due to variation with frequency of the four primary constants of the cable and likewise there is a large number of equalizer sections for equalizing either the resistance and inductance of a cable or the capacity and leakance of a cable when the cable has a length short compared with the shortest wavelength transmitted. Any impedance which is suitable as a shunt arm for an equaliser for equalising simultaneously the loss and phase can be used as an element in a chain for equalising leakance and capacity and any impedance suitable for use as a series arm for an equaliser for simultaneously equalising loss and phase can be employed as an element in a chain for equalising resistance and inductance.

The equaliser sections for equalising simultaneously the loss and phase due to variation with frequency of the four primary constants of the cable may be spaced at intervals along the length of the cable which are short compared with the shortest wavelength to be transmitted or, alternatively, an arbitrary length of cable may be equalised as a whole by a series of equaliser sections forming an artificial line disposed at any convenient point in the transmission system. The sections employed for equalising the resistance and inductance or the capacity and leakance may be disposed as stated above at intervals along the length of the cable or where artificial line type of equaliser sections are used for equalising the variations of resistance and inductance or capacity and leakance; such sections may be arranged as a whole at a convenient point in an arbitrary length of cable.

The elementary type of equaliser section referred to above with reference to Fig. 4, i. e., one composed of a series arm consisting of a condenser C1 shunted by a resistance R1 and a shunt arm composed of an inductance L1 in series with a resistance R2 is termed an eightoctave type, since it .is found that its loss changes substantially from maximum to zero in about eight frequency octaves. The present invention contemplates the use of a modified form of section as shown in Figure 5, similar to the eight-octave type except that an additional condenser C2 is inserted in shunt across the resistance R2 of the shunt arm and an additional inductance L2 is inserted in series with the resistance R1 of the series arm, the resistance Z0 being equal to the characteristic impedance of the section. With this modified form of section it is found that its loss falls from maximum to zero in only four octaves and, consequently, with the type of section shown in Figure 5 it is necessary to locate the sections up to only about two instead of four octaves above the highest frequency at which equalisation is required. With the four-octave section, therefore, less sections are required with the consequent reduction in dead loss produced by the equaliser and also a reduction in the amount of amplification required.

It will be appreciated that the sections described above may be replaced by their electrical equivalents. For example, in the elementary type of equaliser section composed of series and shunt arms the series arm. may comprise a number of branches each formed by connecting a resistance in series with a capacity, these branches being shunted by two resistances in series whose joint is connected to the shunt arm, which comprises a resistance in series with a chain of parallel connected resistances and inductances.

In the practical application of the invention the characteristic curve of the cable to be equalised is first analysed either as a single component w" or a series of such terms, the number of terms depending on the character of the curve. Over a large part of the range it may be found that 40 /2 fits the cable curve sufficiently well for practical purposes. The spacing factors appropriate to the values of n are calculated from the above expression for a: substituting for a and t the values for the particular type of section being used. An equaliser for each of the (o components is then constructed and these are then assembled in series to form a complete equaliser of the artificial line type or the sections of the equaliser are distributed along the length of the cable as stated above.

Any errors due to cable distortion which might arise at very low frequencies Where wL is no longer large compared with R may be corrected by any suitable means.

Although in the specific embodiment of the invention described an electrical signal transmission system is referred to, it will be appreciated that the invention can also be applied to any Wave transmission system in which similar difficulties are encountered due to the attenuation and phase of the transmission path and in which the path has properties analagous to those of resistance, inductance, capacitance and leakance. For example, in a long speaking tube for sound transmission its loss and phasedistortion can be equalised in accordance with the invention. The acoustical waves transmitted may be transformed into their equivalent electrical oscillations by a suitable form of microphone, the necessary equalisation being then effected by an electrical equaliser.

It has also been suggested, in order to impart a time delay to electricaljoscillations, to convert the cable, or line, into the form of a power series,v

path.

the electrical oscillations into mechanical oscillations, as by applying the electrical oscillations to a piezo-electric crystal and to pass the mechanical waves through a trough containing fluid and to re-convert the mechanical waves trans-.

,mitted through the liquid into electrical oscilla after the mechanical oscillations have been. re"

converted into electrical oscillations by employing an electrical equaliser of the kind hereinbefore described.

In the appended claims the quantities n, An

and B11 referred to therein are magnitudes determined by an analysis of the characteristics of the cable, or line, which is to be equalised. Thus an analysis is made of the loss characteristic of in the frequency w, of which a typical term is" Amt". The index n is different for each term, and if only the loss is to be equalised, 11 may assume any value less than 2; all that is necessary is that the sum of these power terms in w shall represent with some degree of accuracy the loss characteristic of the line or cable. In the same way the phase characteristic may be, analysed into the sum of a number of power terms Bnw".

Here, however, equalisation cannot be effected if.,

it is greater than unity. It will be appreciated therefore that if n is less than unity it may be possible to equalise both loss and phase simultaneously; this can be effected if relations such as l'3,,=A tan hold between the coefficients An and BB, conditions found to hold true in practice.

I claim:

1. A wave transmission system including a n-lr A tan o)" said variations causing distortions, and a compensating path associated with said transmission path comprising a number of groups, including one, of equaliser sections, one group to every pair of said terms Aw" and n A tan o)" said sections of each group having attenuations at certain reference frequencies equal to their attenuation at zero frequency multiplied by an arbitrary factor, said reference frequencies being so distributed as to correspond to substantially equal increments in the associated attenuation term, thereby substantially equalising simultaneously said distortion due to variations of attenuation and phase delay of said transmission 2. A wave' transmission system including a transmission path along which oscillations extending over a range of frequencies are caused to travel and in which range owing to the variation with frequency of the effective inductance and resistance of said path the attenuation of said path varies with the frequency w as the sum of a number, including one, of terms given substantially by Anw" and the phase delay of said path varies as'the sum of a correspondingnumber, including one, of terms given substantially by A tan said variations causing distortions, and a compensating path associated with said transmission path comprising a number of groups, including one, of equaliser sections, one group to every pair of said terms Arm" and 11 A tan ee" the sections of each said group having attenuations at certain reference frequencies equal to their attenuation at zero frequency multiplied by an arbitrary factor, said reference frequencies being so distributed as to correspond to substantially equal increments in the associated attenuation term, thereby substantially equalising simultaneously said distortions due to variations of attenuation and phase delay of said transmission path due to said variation with frequency of the effective inductance and resistance of said path.

3. A wave transmission system including a transmission path along which oscillations extending over a range of frequencies are caused to travel and in which range owing to the variation with frequency of the effective capacity and leakance of said path the attenuation of said path varies with the frequency w as the sum of .a number, including one, of terms given substantially by Anw" and the phase delay of said path varies as the sum of a corresponding number, including one, of terms given substantially by I17! A tan o) said variations causing distortions, and a compensating path associated with said transmission path comprising a number of groups, including one, of equalizer sections, one group to every pair of said terms Auto and n A tan ev the sections of each said group having attenuations at certain reference frequencies equal to their attenuation at zero frequency multiplied by an arbitrary factor, said reference frequencies being so distributed as to correspond to substantially equal increments in the associated attenuation term, thereby substantially equalising simultaneously said distortions due to variations of attenuation and phase delay of said transmission pathdue to said variation with frequency of the effective capacity and leakance of said path.

4. A wave transmission system including a transmission path along which oscillations extending over a range of frequencies are caused to travel and in which range owing to the variation with frequency of the eifective inductance, resistance, capacity and leakance of said path the attenuation of said path varies with the frequency w as the sum of a number, including one,

of terms given substantially by Am" and the phase delay of said path varies as the sum of a corresponding number, including one, of terms given substantially by n'll' A tan a)" said variations causing distortions, and a compensating path associated with said transmission path comprising a number of groups, including one, of equaliser sections, one group to every pair of said terms Anw and the sections of each said group having attenuations at certain reference frequencies equal to their attenuation at zero frequency multiplied by an arbitrary factor, said reference frequencies being so distributed as to correspond to substantially equal increments in the associated attenuation term, thereby substantially equalising simultaneously said distortions due to variations of attenuation and phase delay of said transmission path due to said variations with frequency of the effective inductance, resistance, capacity and leakance of said path.

5. A wave transmission system including a transmission path along which oscillations eX- tending over a range of frequencies are caused to travel and in which range the attenuation of said path varies with the frequency w as the sum of a number, including one, of terms given substantially by Am", said variation causing distortion and a compensating path associated with said transmission path comprising a number of groups, including one, of equaliser sections, one group to every said term Anw", the section of each said group having attenuation at certain reference frequencies equal to their attenuation at zero frequency multiplied by an arbitrary factor, these frequencies being so distributed as to correspond to substantially equal increments in the associated attenuation term, thereby substantially equalising said distortion due to variation of attenuation of said transmission path.

6. A wave transmission system including a transmission path along which oscillations eX- tending over a range of frequencies are caused to travel and in which range owing to the variation with frequency of the effective inductance and resistance of said path the attenuation of said path varies with the frequency w as the sum of a number, including one, of terms given substantially by Anw", said variation causing distortion, and a compensating path associated with said transmission path comprising a number of groups, including one, of equaliser sections, one

group to every said term Aw", the sections of each said group having attenuations at certain reference frequencies equal to their attenuation at zero frequency multiplied by an arbitrary factor, said reference frequencies being so distributed as to correspond to substantially equal increments in the associated attenuation term, thereby substantially equalising simultaneously said distortion due to variation of attenuation of said transmission path due to said variation with frequency of the effective inductance and resistance of said path.

7. A wave transmission system including a transmission path along which oscillations extending over a range of frequencies are caused to travel and in which range owing to the variation with frequency of the effective capacity and leakance of said path the attenuation of ,60 dueto variation' of phasedelay of said transmissaid path varies withthe frequency w' as the sum of a,number,- including one, of terms given substantially by Anni, said variation causing distortion, and a-compensating pathassociated with said transmission path comprising a number of groups, ,including one, of equaliser sections, one group to every, said term Anw", the sections of each said group havingattenuations at certain reference frequencies equal to their attenuation; at zero freq encymultiplied by an arbitrary factor, Said referencefrequencies being so distributed as,,to correspond to substantially equal increments in the associated attenuation term, thereby substantially equalising said distortion ,du ento variation of attenuation of said transmission path due to said variation with frequency of the effective capacity and leakance of said path.

8. A wave transmission system including a transmission pathalongwhichoscillations extending over. a range of frequencies are caused to travel and in which range owing to the variation withifrequency of the effective inductance, resistance, capacityiand leakance of said path the attenuation of said pathtvaries with the frequency w as the sum of a number, including one, of terms given substantially by Anw", said variation causing distortion and a compensating path asSbiiiate'd withsaidtransmission path comprisirig a numb'erfof groupsin'cluding one, of equaliscr 'sectionsfone groupto every said term Ana), the sections ofeach group having attenuations at certain reference frequencies equal to their attenuation at zero "frequency multiplied by an arbitrary -factor,said' reference frequencies being'sddistributed as to correspond to substantially equal increments in the associated attenuation"term thereby substantially equalising simultaneously saiddistortion due to variation of attenuation of said transmission path due to said variationwithfrequency of the effective inductance, resistance, capacity and leakance of said path.-

9. A walvetransmission system including a transmission -path along which oscillations extending over arange -offrequencies are caused to travel and in which range the phase delay of said path varies with the frequency w as the ua-number, includingone, of terms given substantiallylby' its, said variation causing distor ashes compensating path associated with saidtransmission path comprising a number of groupsfincluding one, of equaliser sections, one group to every said term'Bnw, the sections of each said group having phase delays at certain reference frequencies equal to a single arbitrary value, saidreference'frequencies being so distributed'as to correspond to substantially equal increments in the associated phase delay term, thereby substantially equalising said distortion Sid I i path. p

"10. A wave transmission system including a transmission path along'which oscillations extending over a rangeof frequencies are caused to travel and inw'hich range owing to the variation with frequency of the effective inductance and resistance of said path the phase delay of said path varies with the frequency w as the sum of a number, including one, of terms given substantially by Bad)", said variation causing distortion, and a compensating path associated with said transmission path comprising a number of groups, including one, of equaliser sections, one group to every said term Bnw", the sections of each said group having phase delays at certain reference frequencies equal to a single arbitrary value, said reference frequencies being so distributed as to correspond to substantially equal increments in the associated phase delay term, thereby substantially equalising said distortion due to variation of phase delay of said transmission path due to said variation with frequency of the effective inductance and resistance of said path.

11. A wave transmission system including a transmission path along which oscillations extending over a range of frequencies are caused to travel and in which range owing to the variation with frequency of the effective capacity and leakance of said path the phase delay of said path varies with the frequency w as the sum of a number, including one, of terms given substantially by Batu, said variation causing distortion, and a compensating path associated with said transmission path comprising a number of groups, including one, of equaliser sections, one group to every said term Bmu the sections of each said group having phase delays at certain reference frequencies equal to a single arbitrary value, said reference frequencies being so distributed as to correspond to substantially equal increments in the associated phase delay term, thereby substantially equalising said distortion due to variation of phase delay of said transmission path due to said variation with frequency of the effective capacity and leakance of said path. 7

12. A wave transmission system including a transmission path along which oscillations extending over a range of frequencies are caused to travel and in which range owing to the variation with frequency of the effective inductance, resistance, capacity and leakance of said path the phase delay of said path varies with the frequency w as the sum of a number, including one, of terms given substantially by Bnw", said variation causing distortion, and a compensating path associated with said transmission path comprising a number of groups, including one, of equaliser sections, one group to every said term Bath), the sections of each said group having phase delays at certain reference frequencies equal to a single arbitrary value, said reference frequencies being so. distributed as to correspond to substantially equal increments in the associated phase delay term, thereby substantially equalisir g said distortion due to variation of phase delay of said transmission path due to said variation with frequency of the effective inductance, resistance, capacity and leakance of said path.

13. A wave transmission system including a transmission path along which oscillations extending over a range of frequencies are caused to travel and in which range the attenuation of said path varies with the frequency w as the sum of a number of terms given substantially by AM", and a compensating path associated With said transmission path comprising a number, including one, but less than said number of terms, of groups of equaliser sections, each said group corresponding to a single attenuation term given substantially by Aw", the sections of each said. group having attenuations at certain reference frequencies equal to their attenuation at zero frequency multiplied by an arbitrary factor, said reference frequencies being so distributed as to correspond to substantially equal increments in the associated attenuation term.

14. A wave transmission system including a transmission path along which oscillations extending over a range of frequencies are caused to travel and in which range the phase delay of said path varies with the frequency w as the sum of a number of terms given substantially by Bnw", .and a compensating path associated with said transmission path comprising a number, including one, but less than said number of terms, of groups of equaliser sections, each said group corresponding to a single phase delay term.

' given substantially by Bnw, the sections of each said group having phase delays at certain reference frequencies equal to a single arbitrary value, said reference frequencies being so distributed as to correspond to substantially equal increments in the associated phase delay term.

15. An electric Wave transmission system, particularly for television, including a transmission path as exemplified by a cable and a transmission line, along which path oscillations extending over a range of frequencies up to at least 100 kilocycles are caused to travel and in which range the attenuation of the path varies with the fre quency w as the sum of a number, including one, of terms given substantially by Ana!" and the phase delay of said path varies as the sum of a corresponding number, including one, of terms given substantially by said variations causing distortions, and a compensating path associated with said transmission path comprising a number of groups, including one, of equaliser sections, one group to every such pair of said terms AW" and A tan n A tan w" the sections of each said group having attenuations at certain reference frequencies equal to their attenuation at zero frequency multipled by an arbitary factor, said reference frequencies being so distributed as to correspond to substantially equal increments in the associated attenuation term, thereby substantially equalising simultaneously said distortions due to variations of attenuation and phase delay of said transmission path.

16. An electric wave transmission system, particularly for television, including a transmission path as exemplified by a cable and a transmission line, along which path oscillations extending over a range of frequencies up to at least 100 kilocycles are caused to travel and in which range the attenuation of the path varies with the frequency w as the sum of a number, including one,

of terms given substantially by Ana! and the phase delay of said path varies as, the sum of a corresponding number, including one, of terms given substantially by n A tan w fur A tan w" the sections of each said group having attenuations at certain reference frequencies equal to their attenuation at zero frequency multipled by an arbitrary factor, said reference frequencies being so distributed as to correspond to substantially equal increments in the associated attenua tion term, thereby substantially equalising simultaneously said. variations of attenuation and, phase delay of said transmission path.

17. An electric wave transmission system, particularly for television, including a transmission path as examplified by a cable and a transmission line, along which path oscillations extending over a range of frequencies up to at least 100 kilocycles are caused to travel and in which range the attenuation of the path varies with the frequency w as the sum of a. number, including one, of terms given substantially by Anw and the phase delay of said path varies as the sum of a corresponding number, including one, of terms given substantially by A tan %w" and a compensating path associated with said transmission path comprising a number of groups, including one, of equaliser sections, arranged to constitute an artificial line arranged: in series with said transmission path, one group to every such pair of said terms Ana" and the sections of each said group having attenuations at certain reference frequencies equal to their attenuation at zero frequency multiplied by an arbitrary factor, said reference frequencies being so distributed as to correspond to substantially equal increments in the associated attenuation term, thereby substantially equalising simultaneously said variations of attenuation and phase delay of said transmission path.

18. A wave transmission system including a transmission path along which oscillations extending over a range of frequencies are caused to travel and in which range the attenuation of said path varies with the frequency w as the sum of a number, including one, of terms given substantially by Anw" and the phase delay of said path varies as the sum of a number, including one, of terms given substantially by A tan said variations causing distortion, and a compensating path associated with said transmission path comprising a number of groups, including one, of equaliser sections, one group to every pair of said terms Ana! and A, tan 5w" said sections of. each group having attenuations at certain reference frequencies equal to their attenuation at zero frequency multiplied by an arbitrary factor, said reference frequencies being distributed so as to correspond to substantially equal increments in the associatedattenua tion term, said distortions due to variations of attenuation and phase delay of said transmission path being thereby substantially equalised simultaneously, said distribution being effected using an interval of loss equal to where f(q) is the loss characteristic of a single section and q equals 10 being said reference frequency of a section.

19. A wave transmission system including a transmission path along which: oscillations extending over a range of frequencies on are caused to travel, said oscillations being thereby distorted according to a frequency characteristic expressible as a number, including one, of terms of the form Xnw", and a compensating path comprising a number, including one, of groups of equaliser sections, each said group corresponding .to one said term, the sections of each said group having frequency characteristics of like nature to said frequency characteristic and possessing at certain frequencies a given arbitrary value, said latter frequencies being so distributed as to correspond to equal increments in the said corresponding term, the distortion of said oscillations being thereby substantially reduced.

20. An electric wave transmission network for simulating a desired frequency characteristic as exemplified by that of a transmission line, a cable,=

and a complement thereof, said frequency char-* acteristic being expressible as a number, includ-- ing one, of terms of the form Xnw" which comprises a number, including one, of groups of electrical networks, each said group corresponding to one said term, the networks of each said group having frequency characteristics of like nature to said desired frequency characteristic and possessing at certain frequencies a given arbitrary value, said latter frequencies being so distributed as to correspond to equal increments in the said corresponding term, the networks being so designed to provide a frequency characteristic which substantially simulates said desired characteristic.

JOHN COLLARD.

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