Title:

United States Patent 2238023

Abstract:

This invention relates to wave transmission networks, particularly to equalizer networks having adjustable attenuation characteristics. An object is to provide an adjustable equalizer network having an image impedance which is a i constant resistance for all adjustments of equalization and...

Inventors:

Klipsch, Paul W.

Publication Date:

04/08/1941

Export Citation:

Assignee:

Esme, Rosaire E.

Primary Class:

Other Classes:

333/81R

International Classes:

View Patent Images:

Description:

This invention relates to wave transmission networks, particularly to equalizer networks having adjustable attenuation characteristics.

An object is to provide an adjustable equalizer network having an image impedance which is a i constant resistance for all adjustments of equalization and one in which the amount of equalization may readily be adjusted with a minimum number of variables.

Another object is to provide an equalizer with i6 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 i5 simultaneously and practically independently be equalized, compensated or predistorted.

A further object is to form a simple equalizer whose complementary circuit is as readily constructed, and such that a given equalizer and its complement may be used for predistortion and restoration with negligible net distortion.

These and other objects will be evident from the specification and illustrations.

Fig. 1 shows a form of a circuit adapted to transmit the low frequencies with less attenuation than the rest of the spectrum.

Fig. 2 shows a family of performance curves for the circuit of Fig. 1 for different amounts of equalization. Fig. 3 shows a circuit adapted to attenuate the high frequencies less than the remainder of the spectrum.

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.

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

Fig. 7 is the 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 mid-frequencies are not equal. Fig. 12 shows an alternative form of the invention involving a transformer.

The following list of symbols will be used: f=frequency.

ft/ mid-frequency for "low-pass." f2=mid-frequency for "high-pass." a=attenuation constant at frequency f.

al=attenuation at frequency fi.

am=maximum attenuation, or base loss due to pad Rn, R12.

a.=minimum attenuation due to pad Ru, Ria bridged by R21, R22.

p=phase angle of output voltage with respect to input voltage.

r=a+jp, the transfer constant.

Ro=characteristic (image) impedance.

1. r.=linear range, or range of frequencies over which the attenuation varies linearly with the log of the frequency.

Xmn=reactance of arm mn.

Zmn=impedance of arm mn.

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 between resistances Ro there are no reflection losses at the terminals.

In Figs. 1, 3, 4, and 6, the resistor combination /2Rn, R21 constitutes a simple T attenuator. The values of Ru and R12 are determined from the line impedance and the total loss. Thus where am is the maximum loss in nepers due to the unbridged T and Ro is the characteristic impedance.

A convenient table for the determination of Rn and R21 is to be found in a paper by P. K.

McElroy in Proceedings Institute of Radio 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. The base loss or maximum attenuation is 10 a=g 8= 1. 15 nepers %Rin=500 tanh 0.575 =260 ohms R21=500On and 5sinh 1.15 = 351 ohms The values L1 and C22 in Fig. 1 are determined from L1= 2f (3) 5 1 C22 Ro (4) where fi 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 Rn, 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 R12 R22= Ro (5) tanh % am-tanh ý a, (6) '2J12=R ? tanh 2 am-tanh ½ a20 20 where an is the minimum loss in nepers due to the T with Ri2 and R22 connected.

The dotted lines in Figs. 1, 3, 4, 6, and 9 indicate that R12 and R22 are simultaneously variable whereby the relation in Equation 5 is satisfied. Continuing the example in which Ro=500 and am=10, suppose it is desired to make R12 and R22 adjustable in a series of steps in which the correction or equalization values are 0, 2.5, 5, 7.5 and 10 decibels. Using Equations 5 and 6 the following values may be found.

Table I Correction decibels a,. Ru1fRo 1s R R2 neper ohms hmis 35 0o__ _ ____ 0.575 a a 0 2.5-----------.----- 0.431 3.72 1,860 135 5.0-------- -------- 0.288 1.21 557 412 7.5 ---.------.----------------- 0.144 0.394 197 1,270 10.0 ...........--------------- 0.0 0.0 0 Since the circuit of Fig. 6 is the generalized circuit of Fig. 1 and since the circuits of Figs. 6 and 8 are equivalent, the total insertion loss is given by the constant R lattice equation 45 tanh VTr=ZA/RO (7) where ZA in Fig. 8 is the impedance of /2Rn1 in parallel with /zZ12 and 1/2R12 in series in Fig. 6 and r is the transfer constant defining the loss 50 and phase angle. Note that (7) defines both the transfer constant and total insertion loss when there are no reflection 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 Ri2.

Fig. 3 is the high-pass counterpart of the lowpass circuit of Fig. 1. 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 of 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 Everitt's "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 inductance Li2 in series with a capacitance Ci2. The resulting performance will be a certain maximum loss with a drop to a smaller loss at a frequency hi determined by the product L.2-C12. The correction at fl will be am-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/Ci2. 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 fi and f2 are separated a sufficient amount.

Fig. 5 is the performance of the circuit of Fig. 4 where the low-pass mid-frequency (fi) 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 of L12, C12, L22, C22 etc. for Fig. 4 may be computed from (3) and (4) and for the example given where fi=50, f2=8000, Y=2Ro and Ro=500 ohms they are: Table II L12=0.795 henry L22=3.18 henry Lu3=0.005 henry L23=0.020 henry C12=12.57 pf.

C22= 3.19 Af.

C13= 0.08 if.

C23= 0.02 Af.

And the values of R12, R22 and Ru3, 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 Zi2 and Z22 be inverse, that is that they be related by Zi2-Z22=RO2 It may be noted that in Fig. 1 this requirement is met since jwL12z = Ro Thus the determination of Z12 by whatever design procedure is employed is sufficient also to determine Z22. Inverse networks are discussed and the method of their derivation shown by T. E.

Shea "Transmission Networks and Wave Filters," 10 van Nostrand, 1929, chapter 5.

Obviously, the circuits of Figs. 1, 3 and 4 may be made 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. 9 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 2ZA 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 1/2Rn 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 "5 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 flia, fib, . . . 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 11 shows the linear range 1. r.1, curve 12 shows the performance of a unit with a mid-frequency fib greater than fla by the amount of the linear range, and curve 13 shows the sum of curves 1 and 12 produced by the cascaded units. The linear range 1. r.2 of the combination is roughly twice the value of 1. r.a.

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 Ri3 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 Rl2-R =R 13 -R23=X12 X22=X13 X23=Ro02 2. 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 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 first impedances, said first 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 configuration and having a predetermined finite base loss and image impedance the combination therewith of circuit elements for producing adjustable amounts of attenuation comprising variable resistances bridging the T, other variable 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 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 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 first 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 first 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 base 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 finite 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 first 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 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 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 comprising a T, the first mentioned impedances 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 finite 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 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 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 S5 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 first arms with respect to the image impedance of the network so that the product of each second arm with its corresponding first 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 first arms with respect to the image impedance of the network so that the product of each second arm with a corresponding first arm is equal to the square of the image impedance of the network.

PAUL W. KLIPSCH.