US2238023A - Equalizer - Google Patents

Description

AWM 'mmm F. W. Mmmm-11 EQUALLZER 2 sheets-Smm 2 Filed March 23,1939

ATTORNEYS Patented Apr. 8, 1941 UNITED STATES-'PATENT OFFICE EL... i t

Paul W. Klipsch, Houston, Tex., assigner to Esme E. Rosaire, Houston, Tex.

Application March 23, 1939, Serial N0. 263,614 s claims. ii. 17a-44) This invention relates to wave transmission networks, particularly to equalizer networks hav ing adjustable attenuation characteristics.

An object is to provide an adjustable equalizer network having an image impedance which is a constant resistance for all adjustments of equal# ization and one in which the amount of equaliza tion may readily be adjusted with a minimum number of Variables.

Another object is to provide an equalizer with a minimum number of reactive elements and in which the only variable elements are pure resistances.

` `Another object is to provide an equalizer in which both `ends of a frequency spectrum may simultaneously and practically independently be equalized, compensated or predistorted.`

A further object is to form a simple equalizer whose complementary circuit is as readily eonstructed, and such that a given equalizer and its 'A' Fig. 1 shows a form of a lcircuit adapted to transmit the low frequencies lwith less atte'nuaf tionl than the restof the spectrum.

Fig. 2 shows a family of performance curves for the circuit of Fig. 1 for different amounts of equalization. I

Fig. 3 shows ar circuit adapted tov attenuate the high frequencies less than the remainder of the spectrum. a

Fig. 4 shows a circuit for attenuating both the high and low frequencies 'by adjustable predetermined amounts less than the rest of the spectrum.

Fig. 5 is a graphical illustration of the performance of the circuit of Fig. 4. 'f

Fig. 6 is a circuit which generalizes the nven tion by the use of but two impedances.

Fig. 7 -isthe H section equivalent of Fig. 6.

Figs. 8 and 9 are the lattice equivalents of Fig. 6.

Fig. 10 depicts two equalizers used to extend the range of a single one. Fig. 11 graphically shows the performance of equalizers as depicted in Fig. 10 where each of the equalizers is of the form of Fig. 1, but whose midfrequencies are not equal.

Fig. 12 `shows an alternative form of the invention involving a transformer. `.The following list of symbols will j=frequency. u l p ,l f1=mldfrequency for low-pass.

be used:

Fig.`1 shows a form of the invention, an equalizer to boost the low frequencies (hence referred to as a low-pass type) with input terminals I and 2 and output terminals 3 and 4. When operated betweenresistances Ro there are no reflection lossesat vthe terminals. f i

' In'Figs. 1, 3, 4, and 6, the resistor combination .1/2R11, R21 constitutes a simple T attenuator. The

values of R11 and R12 are determined from the line impedance andthe total loss. Thus I 4 "yzRnzRo (l) @FROM 2) where am is themaximum loss in nepers due to the unbridged T and Ro is the characteristic impedance. l c

A convenient table for the determination of R11 and R21 is to be found in a paper by P. K. McElroy in Proceedings Institute of Radiov Engineers, vol.'23, pages 213-233, March 1935. As an example,` suppose 10 decibels loss is desired and the pad is to be used between 500 ohm terminations; p The base lossv or maximum attenuation is lRi|=5oo tsunami '-1260 ohms The values L12 and C22 in Fig. 1 are determined from Ro L12-??1 (3) where f1 is the frequency at which approximately half the equalization is attained, and is herein called the mid-frequency.

An alternative to and exact equivalent of the R11, R21 T pad is the bridged T shown by McElroy (mentioned above) in his Fig. 5, page 222, and table VII, page 233.

The adjustable resistors R12 and R22 are related itl-312:1@

Table I 95 a R12 R22 Correction decibels nepr R12/R0 ohms ohms m 3. 72 1, 86o 135 1. 21 i 557 412 D. 394 197 1, 270

Since the circuit of Fig. 6 is the generalized circuit of Fig. 1 and since the circuits lof Figs. 6 and 8 are equivalent, the total insertion loss is giveny by the constant R lattice equation where ZA in Fig. 8 is the impedance of 1/zlitn in parallel with 1/2Z12 and l/2R12 in series in Fig. 6 and I* is the transfer constant defining the loss and phase angle. Note that (7) defines both the transfer constant and total insertion loss when there are no reiiection losses, that is when the network is operated between terminal impedances equal to Ro.

Using Equation 7, the performance of the circuit of Fig. 1 is computed and shown in Fig. 2, in which curves of loss against reactance are plotted for different values of R12.

Fig. 3 is the high-pass counterpart of the klowpass circuit of Fig. l. It may be made complementary thereto whereby the sum of the losses of the circuits of Figs. 1 and 3 are substantially constant by proper choice of the value of f2, thereby making, in combination with the circuit of Fig. 1, a convenient predistorting-restoring network. Its performance may be found from Fig. 2 simply by using the reciprocal of the abscissa. Equations 1, 2 and 5 to '7 are applicable. Equations 3 and 4 are applicable to Fig. 2 if L22 is written for L12 and C12 for C22.

Obviously more complicated impedances than, for example, L12, C22 in Fig. 1 may be used. Resonant and anti-resonant circuits and multiple branch impedances may be employed, and the simplicity oi the variable feature will be retained. Fig. 6 illustrates the invention in this broader form. The design of such impedances may be accomplished by the use of such references as Everitts Communication Engineering McGraw Hill, 1932, 1937, a book, Chapter IX, and the references given therein, Equations 1, 2, and 5 to 7 still apply, and suitable impedance design may be substituted for (3) and (4) see also A reactance theorem, R. N. Foster, Bell System Technical Journal, vol. III, No. 2, April 1924.

As an example of such an elaboration, suppose Z12 is a reactance in the form of an induotance L12 in series with a capacitance C12. The resulting performance will be a certain maximum loss with a dropy to a smaller loss at a frequency f1 determined by the product L12-C12. The correction at f1 will be cam-an and the width of the resulting pass band or the stepness of the loss-frequency curve for a given set of values am, an will be determined by the ration L12/C12. Still another type of impedance Z12 would result from the two terminal impedance of a reactive ladder with resistance or reactance termination. The impedance in such a case would not be a nearly pure reactance, but would contain a larger dissipative component than when nearly pure reactive elements are used.

Fig. 4 is a combination high-pass and low-pass equalizer by means of which both ends of a spectrum may be boosted relative to the middle somewhat in the same way that the circuits of Figs. 1 and 3 would perform in tandem, but the .total base insertion loss is that of a single circuit only. In the case of Fig. 4 however the equalization is accomplished with resonant and anti-resonant circuits whereby the performance curve slopes are made more steep and the losses increase beyond the limits of 50 and 8000 cycles. The high and low ends may be equalized substantially independently if the mid-frequencies f1 and f2 are separated a suiiicient amount.

Fig. 5 is the performance of the circuit of Fig. 4 where the low-pass mid-frequency (f1) is 50 cycles, the high-pass mid-frequency (f2) is 8000 cycles, the pad loss, am, is 10 decibels, and the values of R12, R22 and R13, R23 are chosen from Table I.

The numerical values 0f L12, C12, L22, C22 etc. for Fig. 4 may be computed from (3) and (4) and for the example given where f1=50, f2=8000, v

and Rar-500 ohms they are:

' Table II L12=0.795 henry C12=12.5'7 2f. L22=3.18 henry C22: 3.19 2f. L13=0.005 henry C13: 0.08 2f. L2a=0.020`henry C23: 0.02 pf.

.And the values of R12, R22 and R13, R23 are given in Table I.

It should be understood that the numerical values given are not intended to limit the scope of the patent, but to serve as illustrations of computation by means of the various equations given.

Whatever the nature of Z12, it is necessary that Z22 be inverse thereto. Thus in order that the network of Fig. 6 have an iterative or image impedance which is a constant resistance it is necessary that Z12and Z22 be inverse, that is that they be related by g It may be noted that in Fig. 1 this requirement .iS met since l y JLLLLh-g50) Cj22.1%02

Thus the determination of Ziz by whatever design procedure is employed is suiiicient also to determine Z22. Inverse networks are discussed. and the method of their :derivation shown by T. E. Shea Transmission Networks and Wave Filters, vanNostrand, 1929, chapter 5,

Obviously, the circuits of Figs. 1, 3 and 4 may bemade into networks which are balanced and symmetrical with respect to ground simply by transforming them into their equivalent lattices or H sections. This procedure is well known ,(Bartlett, A. C., Phil Mag. 4, pages 902-907, Nov. 1927) for lattices and is obvious for H sections. Fig'. 9 shows a lattice which is equivalent to the `bridged T of Fig. 6, and Fig. 8 shows the generalization of Fig. 9. Fig. 7 shows the balanced bridged H which is equivalent to the bridged T of Fig. 6. A still further possible equivalent configuration consists in the reduction of the lattice of Fig. 49 or Fig. 8 to a bridged T containing a transformer t as shown in Fig. 12.

Fig. 12 illustrates an equivalent of Fig. 4 when ZZA is equal to the impedance of terminals I and 3 of Fig. `4 ( terminals 2 and 4 not being connected) and ZB is equal to the shunt arm plus 1/2l7t11 of Fig. 4. By similar reasoning Fig. 8 is the equivalent of Fig. 4 when ZA and ZB have the same meanings as defined above for Fig. 12. Development of Fig. 4 into a balanced H consists simply of creating a mirror image of Fig. 4 below the line between terminals 2, 4 whereby the line between terminals 2, 4 becomes a neutral which may be retained or eliminated as desired.

The circuits shown, when designed according to the equations herewith, are characterized by an image impedance which is a constant resistance at all frequencies so that the real part of the transfer constant is equal to the total insertion loss when a given circuit is operated between terminations having the same image impedance.

Depending upon the degree of linearity demanded, the attenuation of the circuit of Fig. 1 is linear over a range of two or three octaves. By using a plurality of such equalizers with their mid-frequencies fia, fit, etc. spaced at two to four octave intervals, the linear range may be extended over any desired frequency range. Fig. 10 shows two units cascaded, and Fig. 11 shows the results of cascading where curve II shows the linear range l. r.1, curve I2 shows the performance of a unit with a mid-frequency fit greater than fia by the amount of the linear range, and curve I3 shows the sum of curves II and I2 produced by the cascaded units. The linear range l. r.2 of the combination is roughly twice the value of l. r.1.

The invention claimed is:

1. A constant resistance variable attenuation equalizer comprising a dissipative T network, two arms comprising reactances X12 and X13 bridging said T, variable resistances R12 and R13 in series with said reactances, and two arms comprising reactances X22 and X23 each in shunt with a variable resistance R22 and R23 and connected in series with the shunt arm of said T, said reactances and resistances being related substantially a second pluralityT of impedances in series with each other and with another arm of said base loss network, said second impedances each comprising reactance in parallel with a resistor which is variable in inverse relation to the resistors contained in the first mentioned impedances, said second impedances being inverse to said first impedances, said rst and second impedances and said base loss network being arranged to form a lattice and to exhibit a constant image impedance in both directions of transmission for all values of adjustments of the variable resistors.

3. In an equalizer having fixed resistances in a T conguration and having a predetermined iinite base loss and image impedance the combination therewith of circuit elements for producing adjustable amounts of attenuation comprising variable resistances bridging the T, other varia-ble resistances in series with the pillar arm of said T, impedances in series with said first variable resistances, other impedances in shunt with said other variable resistances; said impedances being mutually inverse and said variable resistances being mutually inverse for all values.

4. An adjustable attenuation equalizer for independently adjusting the transmission loss over a plurality of ranges within a frequency spectrum, said equalizer comprising a base lossnetwork having a given nite loss and a given image impedance, a plurality of impedances in shunt with each other and with an arm of the Abase loss network, each of said impedances'comprisl ing reactance in series with a variable resistor, a second plurality of impedances in series with each other and with another arm of said base loss network, said second impedances each comprising reactance in parallel with a resistor which is variable in inverse relation to the resistors contained in the rst mentioned impedances, said second impedances being inverse to said iirst impedances, said first and second impedances and said base loss network being arranged to exhibit a constant image impedance in both directions of transmission for all values of adjustments of the variable resistors, said iirst mentioned plurality of impedances and the arm of the base loss network shunted thereby bridging a unity-ratio series-aiding transformer, and said second plurality of impedances and the arm of the ybase loss network in series .therewith being connected to the mid-point of said transformer to form a pillar arm.

5. An adjustable attenuation equalizer for independently adjusting the transmission loss over a plurality of ranges within a frequency spectrum, said equalizer comprising a base loss network having a given nite loss and a given image impedance, a plurality of impedances in shunt with each other and with an arm of the base loss network, each of said impedances comprising reactance in series with a variable resistor, a second plurality of impedances in series with each other and with another arm of said base loss network, said second impedances each comprising reactance in parallel with a resistor which is variable in inverse relation to the resistors contained in the first mentioned impedances, said second impedances being inverse to said rst impedances, said first and second impedances and said base loss network being arranged to exhibit a constant image impedance in both directions of transmission for all values of adjustments of the variable resistors.

6. An adjustable attenuation equalizer for independently adjusting the transmission loss over a plurality of ranges within a frequency spectrum, said equalizer comprising a base loss network having a given finite loss and a given image impedance, a plurality of impedances in shunt with each other and with an arm of the base network, each of said impedances comprising reactance in series with a variable resistor, a second plurality of impedances in series with each other and with another arm of said base loss network, said second impedances each comprising L reactance in parallel with a resistor which is Variable in inverse relation to the resistors contained in the rst mentioned impedances, said second impedances being inverse to said first impedances, said iirst and second impedances and said base loss network being arranged to exhibit a constant image impedance in both directions of transmission for all Values of adjustments of the Variable resistors, said base loss network comprising a T, the rst mentioned im- ,f

pedances bridging the T, and the second impedances being in series with the shunt arm of the T.

7. An adjustable attenuation equalizer for independently adjusting the transmission loss over a plurality of ranges within a frequency spectrum, said equalizer comprising a base loss network having a given nite loss and a given image impedance, a plurality of impedances in shunt with each and with an arm of the base loss network, each of said impedances comprising reactance in series with a variable resistor, a second plurality ofimpedances in series with each other and with another arm of said base loss network, said second impedances each comprising reactance in parallel with a resistor which is Variable in inverse relation to the resistors contained in the first mentioned impedances, said second impedances being inverse to said rst impedances, said first and second impedances and said base loss network being arranged to exhibit a constant image impedance in both directions of transmission for all values of adjustments of the variable resistors, said base loss network having an attenuation between 10 and 20 decibels.

8. A constant resistance variable attenuation equalizer comprising a dissipative T network, two arms each comprising a reactance and a variable resistance in series and each arm bridging said T, and two arms each comprising a reactance and a Variable resistance in parallel, said last mentioned arms being connected in series with each other and with the shunt arm of said T, said last mentioned arms being inverse to said rst arms with respect to the image impedance of the network so that the product of each second arm with its corresponding rst arm is equal to the` square of the image impedance of the network.

9. A constant resistance variable attenuation equalizer comprising a dissipative T network, a plurality of arms each comprising a reactance and a variable resistance in series and each of said arms bridging said T, and a plurality of arms each comprising a reactance and a variable resistance in parallel, said last mentioned arms being connected in series with each other and with the shunt arm of said T, said last mentioned arms being inverse to said rst arms with respect to the image impedance of the network so that the product of each second arm with a corresponding rst arm is equal to the square of the image impedance of the network.

PAUL W. KLIPSCH.

Images