US2450930A - Electrical bridge network - Google Patents

Description

T. BACLAWSKI ELECTRICAL BRIDGE NETWORK '4 Sheets-Sheet 1 mod Oct. 3, 1945 INVENTOR. mfaouzz BACLAW5/C/ "W A M Oct. 12, 1948. T. Bmmwsm 2,45

ELECTRICAL BRIDGE NETWORK Filed 06%. 3, 1945 4 Sheets-Sheet 2 Oct. 12, 1", BALAWSK| 2,450,930

ELECTRICAL BRIDGE NETWORK 4 Shoots-Shoot 3 Filed Oct. 3, 1945 IN VEN 70R.

WEQYDME mums/U Oct. 12 1948. g c wg 2,450,930

' ELECTRICAL BRIDGE NETWORK I Filed ca. s, 1945 4 Sheets-Sheet 4 INVENTOR.

7750mm 34cm wsx/ m M #1 Patented Oct. 12 1948 ELECTRICAL BRIDGE NETWORK Theodore Baclawski, Philadelphia, to Philco Corporation,

sylvania Pa., assignor a corporation of Penn- Application October s, 1945, Serial No. 620,154

This invention relates to electrical phase-shifting networks. More particularly, it provides a network which over a frequency band, shifts the phase of an output voltage with respect to the input voltage linearly with respect to the logarithm of the frequency. This network is a derivative of a bridge type of network which is common in elternating current circuits, particularly in circuits used in phase shifting, and of a network whose input impedance is a resistance at all frequencies and is constant.

Networks may be constructed with a wide variety of phase characteristics. Among these characteristics is one which is linear with the logarithm of frequency. It is this latter which I will describe in detail.

By mathematical transformation of the electrical part of the network, I have discovered an easy way of cascading any number of networks of the type from which this invention-is evolved without incurring any serious discrepancies between the theory and the actual practice.

This is at variance with other similar networks proposed for this same purpose. Those bridge circuits are usually considered as unloaded, and yet in actuality the bridge circuit is loaded.

Thus, in those other networks, either one of two things must happen. First, the second bridge circuit which is cascaded after the first must be of a high input impedance to prevent the performance of the whole network from departing substantially from that of the theory, or the theory must be used as a guide only, not as a detailed indication of th output phase.

Usually, the first of these proposals has been adopted with the result that many of these bridge networks have a great loss in power, 1. e., the output power is very much less than the input power.

In my network, since I have discovered how to cascade these networks without violatin the theory involved, I find that I can predict the output of my network, and that this output is not excessively below the input. More specifically, for each bridge network which I introduce in the system I lose half of the input voltage to that bridge network. This corresponds to a loss of 6 db, for

cache! the networks introduced, which is a much smaller loss per bridge circuit than is common to the other types of phase-shifting networks which have previously been described.

Thus it becomes a purpose of my invention to provide a means for obtaining a specified phase curve from a network with a minimum of loss of voltage in the network.

A further object of my invention is to provide 7'Claims. (01. 323-75) such a phase curve as may be desired with little or no variation in the output amplitudes, as the frequency is changed,

A still further purpose 01' my invention is to I provide a phase curve which is linear with the logarithm of frequency, so that two such phase shifting networks can be used for the obtaining of a. 90 phase shift between two signals over a band of frequencies.

My invention can better be. described by reference to the drawings, in which:

Figure 1 shows the basic bridge network;

Figure 2 shows the same network with an addedresistor;

Figure 3 shows a transformation of the network of Figure 2; v

Figure 4 shows the network of Figure 3 cascaded with another bridge network;

Figure 5 shows the phase curves of Figures 3 and4;

Figure 6 shows three bridge networks cascaded;

gure '7 shows the phase curves of the network of Figure 6; v

Figure 8 shows the basic bridge circuit with the resistances which are present in practice, to which added resistance has been provided to compensate for the presence of inherent resistances;

Figure 9 shows a vector diagram illustrating Figure 8;

Figure 10 shows a modification of my inv vention;

Figure 11 pertains to the theoretical treatment of the properties of Figure 10;

Figure 12 is an extension of Figure 11; and

Figure 13 likewise is used for the theoretical treatment of Figure 10.

Making reference to Figure 1, an output voltage is fed into the network over conductors l and 2. This network is composed of two branches: one branch being composed of resistor 3 and capacitor l, and the other branch being composed of resistor 5 and inductor I. The output voltage from this network is obtained between terminals I and 8, and for the present purpose I measure the positive direction to be from 1 to I.

Now, it is well known in this type of network has two special properties. In the first place, if the two resistors ,are equal and each equals then the impedance looking in the input at terminals I and 2 is a constant resistance at all irequencies, and the value of this input resistance is electrical theory that The second well-known property of this network is that the output voltage at zero frequency high frequencies. Such a phase curve is shown in Figure 5 by either one of the solid lines 5! or 52.

This phase performance is obtained with the network unloaded, i. e., with no impedance connected to the output terminals I and 8. However, since it is desired to cascade several of these networks, it is desirable to connect a resistor between terminals 1 and 8, and still predict the voltage across the output terminals. In order to develop this theoretically, a resistor 9 (Fig. 2) of value R is placed in series with the bridge. Moreover, this resistor is taken to be of the same value R as the two resistors in the bridge. 1 This resistor 9 has the following eflect upon the circuit. It reduces the output voltage to half of the previous value, since now the voltage applied to the bridge proper is half of what it was before. However, the circuit of Figure 2 can be transformed to the circuit of Figure'3 by the well-known Y-delta transformation. Since all of the three arms-3, 5 and 9 (Fig. 2) form a Y circuit inwhich each arm has the sam value R, it is very easy to transform these to a delta circuit shown in Figure 3, and composed of resistors in, H and I2, each having a value of SR.

Electrically now, the combination of three resistors Ni, ii and I2 is identical with the combination of resistors 3, 5 and 9, as far as the voltage between terminals 1 and 8 is concerned. Thus, the voltage between terminals I and 8 in Figure 3, which is the output voltage, is half of the input voltage and changes in phase with frequency in the same manner in which the voltage of the output signal in Figure 1 changes with frequency. In Figure 3, however, it is apparent that resistor I2 is in the proper postion to be a load on the bridge circuit made up of arms 4, 6, i and i l'. Thus, by this transformation I have shown how one can design a special bridge circuit in which the output voltage can be predicted in its phase when the output is properly loaded.

If now, just a single network were required, it could be provided by the circuit of Figure 3. Resistor [2, however, may be merely a symbolic representation for the input impedance of another bridge circuit.

Accordingly, the circuit of Figure 4 may be constructed. In this circuit, resistors I0, H, and condenser I and coil 6 are still in the circuit. However, resistor l2 has been replaced by the bridge circuit composed of resistors l3 and il, condenser l4 and coil 6. Thus, Figure 4 shows two bridges cascaded one after the other with the output voltage taken from the output of the second bridge.

In this circuit, the output voltage will be onehalf of the input voltage of the first bridge, and will vary in phase as the sum of the phases of the two individual bridges. the circuit of Figure 4 is shown in Figure 5 as .the sum of the individual phases of the two bridges, i. 3.51? curve 53, which is the sum of curves 5| an 3 the value of each of the individual resistances, 1 which values I designate as R.

Thus, the phase of I In this particular bridge of Figure 4, several I special conditions have been met. First of all, the ratio of L to C is equal to R, and resistors III and Ii are three times this value R. Furth rmore, the bridge which is cascaded onto the first bridge uses two resistors which are of value IR, in order that the input resistance of this second bridge shall at all frequencies also be IR.

However, in this bridge the ratio of the value of coil 16 to condenser l5 must now be equal to the square of 3R, 1. e., equal to 9R This, of course, could be accomplished in any of a great many ways, but I have chosen in this figure to increase the inductance by nine times and to leave the value of the capacitance at the same value asthat of the capacitor in the first bridge. Therefore, the inductance of coil i6 is nine times the inductance of coil 6, and the capacitance of r capacitor I5 is at the same value as the capacitance of capacitor 4.

The effect of this cascading is apparent in Figure 5, in which the curve 5| shows the phase characteristics of the outer bridge, and curve 52 shows the phase characteristics of the inner bridge. It will be observed that the steepest rise of the phase characteristic for this inner bridge is at a considerably lower frequency than that for the outer bridge. In fact, it can be shown that this point of inflection is at one-third of the frequency of the point of inflection of the outer bridge.

This difference between the curve of phase of the outer bridge and the curve of the phase of the inner bridge is precisely the thing which makes it possible to add the two curves for the two bridges and obtain as a summation a much more linear curve than'either one of the bridges would give in itself. This is apparent in the curves oi Figure 5 in which the linear range of curve 53 is quite apparently larger than the linear range of curve 5! or 52.

The process of cascading could be continued as is shown in Figure 6. Here the value of the resistors of the inner bridge may be the same as those ofthe intermediate bridge if the output of the final bridge is not loaded.

The outer bridge is composed of resistors II and II condenser 4 and coil 6. The second bridge is composed of capacitor [5 and inductor i8, and

'two resistors i1 and i8 which are three times as large as resistors l2 and H in Figure 4. This is done, of course, to enable th second bridge to be loaded with the third bridge composed of resistors l9 and' 20, capacitor 2! and coil 22. In this bridge, resistors l9 anad 2|! are both of the same value as resistors l1 and IS in order that the load on the second bridge shall be the same as the value of resistors l1 and I8, namely 9R.

Again, with this third bridge, I have chosen each capacitor to be the same in value as the other capacitors, and I have chosen the inductonce 22 to be eighty-one times th inductance of coil 6. This causes the point of inflection of the phase curve of the third bridge to be at oneninth 0f the frequency at which the point of inflection of the phase curve of the outer bridge occurs.

This is apparent in Figure '7, which shows the three phase curves for the three cascaded bridges, curve SI for the outer bridge, curve 52 for the second bridge, and curve 53 for the innermost bridge. The sum of these three curves is curve 55 showing a substantially greater linear range of variation than is shown in curve 53 of Figure 5.

Theoretically, this process of cascading of bridges could go on almost indefinitely. The phase characteristic of each bridge when plotted to a logarithmic scale of frequency is exactly the same as the phase characteristicof each other accopao bridge except that the frequency of the point of in which, of course, L is. the inductance value in the bridge and C is the capacitance value in the bridge.

Thus, it becomes apparent that with this method of cascading of bridge networks, the designing engineer can obtain a wide variety of variations of phase with frequency merely by the process of cascading a series of these bridge networks together, and by the proper choice of the frequency of the point of inflection of the individual bridges in its complete-network.

By making the individual phase curves overlap properly, the engineer can compensate for the curvature in one curve by the curvature in another curve, and thus obtain a substantially linear phase characteristic over a certain range of frequencies, as I have done in Figures and 7.

Alternatively, other methods of variation in phase can be obtained by specifying the frequencies of the points of inflection of the various curves in another manner. So far, the developed theory has indicated the performance of the bridge network under the conditions that there was no series resistance in the coil, i. e., that the coil has no loss.

Usually, the resistance of the coil must be considered during this analysis. This can be done in accordance with the diagram of Figure 9. Fig ure 8 shows the bridge of Figure 1 with the actual resistance of the coil represented as resistor 23 in series with the coil. A compensating resistor 24 having the same value as resistor 23 is placed in series with condenser 4. The resistors 3 and 5 must be reduced in value by the amount of resistance which resistors 23 and 24 supply. This is .done so that the input impedance appears as a resistance at all frequencies. In the design of the second bridge of cascade systems, consideration must be given to the fact that resistors 3.

and 5 are reduced by the amounts added by resistors 23 and 24.

The vector diagram is shown in Figure 9. The input voltage vector Em is shown as a horizontal vector. The current through resistor 5, resistor 23 and inductance 6 is shown as the current vector I in Figure 9. The vector 25 is the voltage drop across inductor 6. The vector 26 is the voltage drop across resistor 24, and the vector 21 is the voltage drop across resistor 5. 'I'hevector sum of these voltages is equal to the input voltage Em.

The vector 3| represents the voltage across the inductance 8, and the condenser 4, in series with each other. The locus of the ends of this vector ll is a circle 38 passing through the ends of the vector representing the input voltage Em. However, this voltage of vector 3| is not available for use because the resistance 23 is the internal resistance of the inductance 6. The voltage between terminals 1 and 8 is available-and it is represented in Figure 9 as the vector Eout between point 30 and point 28. By reason of therelation in values of resistors 23 and 24 to resistors 5 and 2, the vector Em is parallel to the vector 3|. It may be shown that points 28 and 30, the ends of the vector Em, will fall on a circle, passing through point 34 and having its center at point 2!, the intersection of the vectors Em and Em.

The characteristics of this circuit as shown in the vector diagram include the following:-

The output voltage is always proportional to the input voltage, the proportion being the ratio of the value of resistor I or 5 to the value of resistors 2 and 24 or 5 and 23 in series. low frequenciesthe vector Em is almostparallel to the vector Em. As the frequency increases, the vector Emit revolves, about its center 35, clockwise with respect to the vector Em, and it is perpendicular thereto, representing a phase difference between the input and output voltages when 21r times the frequency is equal to the reciprocal of the square root of the product of the values of inductance 6 and capacitance 4. As the frequency increases further, the vector Em will continue to revolve until, at the highest frequencies, it will be substantially-parallel to the vector Em but in the opposite direction, representing a difference in phase between the output and the input voltages.

Strictly speaking, the representation of Figure 9 is precise only under the assumption that the internal losses of inductance 6 and capacitance 4 do not change with frequency. For ordinary engineering purposes such changes are ignored, but the method of analysis set forth herein may be modified to account for them or in the alternative, further modifications in the circuit may be made to compensate for these difllculties.

It will be evident from further consideration of Figure 9 that if resistor 24 be omitted from the circuit of Figure 8, the output voltage will hear an approximately proportional relation to the input voltage over the frequency range. The output will increase to a minor extent with frequency because one end of its output vector will fall at point 33, and the other end at point 28 on the diagram, but for many purposes this approximation will be sufficient without the use of a compensating resistor 24. This fact justifies the statements made respecting the devices of Figures 1 and 6, in which such compensating resistors as resistor 24 are absent.

The device of Figure 8 may be modified according to the method outlined in relation to Figures 1 to 3 to permit a load circuit to'be applied to it.

A modification of my invention is shown in Figure 10. In this circuit, the circuit of Figure 8 has been modified by replacement of resistors 3 and 5, each by a branch like the diagonally opposite branch in Figure 8. Thus coil 46 has the same inductance as coil 6, and the equivalent series resistance of this coil represented by resistor 43 has a value equal to the equivalent series resistance 23 of coil 6. Similarly, capacitor 42 is equal to capacitor 4, and resistor 44 is equal to resistor 24.

This circuit is similar to a phase-equalization circuit which is old in the art, but differs in that the losses in the coils, represented by resistors 23 and 24, are compensated for by resistors 24 and 44. With this compensation, the circuit of Figure 10 has an input impedance which is a resistance constant over the useful frequency range of the circuit, and a transfer ratio, (Emit/Elli), which varies in phase only over the aforementioned frequency range.

To mathematically prove that the bridge has a constant input impedance looking like a resistance R-l-r, the load resistor 45 of Figure 1 is first made to represent two resistors 41 and 48, each valued at 2(R-r), as shown in Figure 11. This makes two deltas of the one bridge. Figure '11 is now redrawn into two Ys representing the At very.

assopao the two deltas in Figure 12. The Y-delta transwhich shows that the input impedance is a pure resistance.

It is now desired to show that the output voltage swings in phase relative to the input voltage and that the ratio of the magnitude of the input voltage to output voltage is constant at all frequencies. To do this I assign currents I1, I: and I: to the meshes in accordance with well-known means for solving electric circuits, as shown in Figure 13.

Solving this circuit is carried out as follows, using the algebra of matrices.

' 1 1 l -I =%(2r+jwL-i-m)(wL-m 11 12-13; ar-moo I. 'j +2R+1/i (12) In equation (12) if If la then r' a J t -L 13 I1 gi /LH The ratio of the input voltage to the output voltage will be:

8 The fraction (fuVfi-D/(juH/fi-i-l) has an absolute value of 1, but varies in phase angle with 0. Therefore, the voltage ratio is fixed by the ,value (Rr)/(R+r), which states that if the (R-r) value of the resistor.

input voltage is constant, the output voltag is constant. If r is small the ratio of the input and output voltage is nearly unity.

The variation in phase angle between the input and output voltage shown by Equation 14 is of the same character as is shown in Figure 5 in curves 5| and 52. Thus the bridge Of Figure 10 can be used in constructing phase shift networks having logarithmic phase response curves over a frequency range.

This bridge can now have another bridge cascaded to it, placing the second bridge in the place of the (R-r) resistor, and its input impedance should have an input impedance equal to the Cascading can go on indefinitely.

While a number of uses of the circuit of my invention will be evident to those skilled in the art, typical uses of it which may be referred to, are: In the Sunstein Electrical System, application Serial No. 585,257; and in the time delay system of Tompkins, application Serial No, 613,457.

While I have illustrated and described several devices relating to my invention, it is subject to general application, and it should be defined in accordance with the appended claims.

I claim:

1. An electrical network having a pair of input terminals and a pair of output terminals, said network comprising a set of bridge networks connected in cascade, the one of said bridge networks which contains said input terminals comprising two resistors each of value 3R ohms, a capacitor of value C farads, and an inductor of value L henries, said values being chosen so that the equation R=L/C is substantially satisfied, said input terminals being placed one at the junction of said two resistors and the other at the junction of said capacitor and said inductor, the second of said bridges being of the same configuration as the first with its input terminals connected one to the junction of one resistor and the capacitor in the first bridge, and the other to the junction of the other resistor and the inductor in the first bridge, the values of the components of said second bridg being proportioned so that the resistors are each of value 9R ohms, and the ratio of the values of the inductor and capacitor of said second bridge being substantially equal to the square of SR.

2. An electricalnetwork having a pair of input terminals, and a pair of load terminals, a first circuit comprising a capacitor of value C and a resistor of value 3R in series, a second circuit comprising an inductor of value L and a resistor of value 3R in series, said second circuit being connected in shunt to said first circuit, said first and said second circuits being connected to one of said pairs of terminals R, L and C being related to each other by the expression R =L/C, the other of said pairs of terminals being connected to the ends of the resistors remote from said first mentioned terminals, and an impedance of value 38 connected to said other pair of terminals.

3. A network having two pairs of terminals adapted to present a fixed resistive impedance of value 2R to one of its pairs of terminals when its other pair of terminals is connected to a circuit, the eil'ective value of which is a resistance of value 3R, said network comprising four arms arranged as a Wheatstone bridge having two 1 pairs of terminals, said arms consisting, in order,

of two resistive elements of value 3R each, an inductive element of value L and a capacitive element of value C, the pair of resistive'elements being shunted across the pair of terminals adapted to be connected to the said circuit having a resistance of value 3R, the values of R, L, and C being related by the equation R'-C=L.

4. A constant resistance network having an input resistance of value 2R at all frequencies, comprising a Wheatstone bridge having a pair of input terminals and a pair of output terminals, a pair of resistors each of value 3R connecting one I of said input terminals to each of said output terinput terminals and a pair of output terminals;

a pair of resistors each of value 3R connecting one of said input terminals to each of said output terminals, an inductor of value L connecting the other of said input terminals to one of said output terminals, a capacitor of value C connecting the said other input terminal to the other of said output terminals, and a circuit having the effect of a resistor of value 3R consisting of a con stant resistance network including resistors and reactors connected across said output terminals, where the values of R, L, and C are related by the equation R C=L.

6. The network of claim 5 wherein the constant resistance network of value 3R consists of two resistors each of value 3R, an inductor of value AL and a capacitor of value BC wherein 9RC'=L, and AB=9.

'7. The network of claim 5 wherein the constant resistance network of value 3R consists of a plurality of constant resistance networks connected in cascade, all having effective input values appropriate to act as the correct resistive loads for the networks which supply energy to them, and all having the same electrical configuration, the values of the electrical elements comprising said configuration being those required to make of said networks constant resistance networks.

THEODORE BACLAWSKI.

REFERENCES CITED UNITED STATES PATENTS Number Name Date 2,042,234 Lyle May 26, 1936 2,093,103 Taborsky Sept. 14, 1937 2,395,515 Stoller Feb. 26, 1946 2,411,423 Guptill Nov. 19, 1946

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