US2392476A - Wide band phase shifter - Google Patents

Description

Jan. 8, 1946. v KLG. HODGSON 2,392,476

WIDE BAND PHASE SHIFTER Filed Feb. 27, 1942 4 SheetsSheet 1 Fig. 1

L06. FREQUENCY Jan. 8,1946.

K. G. HODGSON 7 WIDE BAND PHASE SHIFTER Filed Feb.- 27, 1942 4 Sheets-Sheet 2 2 1 a||. HI! I ||||||1| L06. FREQUENCY.

Fig. 6. Fig. 7. C12 C12 -4F -ll 1. L0 L0 8 Fig. 9.

lg. rz' C12 r2 Loam L0(I+K') Lo H Jan. 8, 1946.

may/4mm 0v pa K. G. HODGSON WIDE BAND PHASE SHIFTER Filed Feb. 27, 1942 4 Sheets-Sheet 3 Fig. 12.

Jan. 8, 1946.

K. G. HODGSON 2,392,476 WIDE BAND PHASE SHIFTER Filed Feb. 27, 1942 4 Sheets-Sheet 4 Fig. 1 4.

m w by "f Patented Jan. a 1946 UNITED STATES PATENT OFFICE xennetn gfgmrjoffinaon w; c. 2, England, assignor to International Standard Electric Corporation, New York, N. Y.

Application 13 flalms.

It. is frequently necessary in the communication art that currents or voltages in two or more branches 01' a circuit shall, over a certain frequency range, difler in phase by a constant angle -most usually 90 degrees-and have the same amplitude or a constant amplitude ratio. It is the V purpose of this invention to provide improved means for obtaining a close approximation to this condition over a wide frequency range.

In order to achieve this object a network having substantially constant attentuation over the required frequency range is placed in' each branch of the circuit. the networks being so designed that their insertion phase angles in the required frequency range follow approximately the following ance, all-pass networks can be designed to an- February 27, 1942, Serial No. 432,680 Great Britain January 31, 1M1

InFigure 3.11

KeR "c -ea nmmn and KsR :f 1(p' then e=2 tenwhere in and Ir: are the resonant and antiproximate very closely to the desired characteristics. a

Figures 1, 2 and 3 show three types of all-pass lattice networks. In each case the impedance arms are inverse i. e.

and

than

eff Em and I fr being the resonant irequency oi one impedance arm and the anti-resonant frequency oi the other arm,

then 1: 0==2 tan 1 resonant frequencies of the impedance arms and jri==pfrz Figure 4 shows the phase angle 0 of the network of Figure 2 plotted against log I for various values of K1. For all values of K1 the phase angle at Jr is 180 and for values of K1 greater than about 2, this curve is approximately linear over a considerable frequency range. Two such networks therefore with their resonance frequencies (fr) relatively displaced will give an approximately constant difference in phase. In general, the values of K1 for the two networks should be the same or nearly the same. The optimum value of Kr and the ratio of resonance frequencies for any given case depends upon the phase angle difierence and frequency range required, and on the amount by which the phase angle diiierence may be permitted to depart from the desired value; however, K1 will generally be iound to be between 3 and 8 and the greater the permissible tolerance the greater is the frequency range which can be covered. By way of example Figure 5, shows a family of curves in which the phase difierence between a pair of Figure 2 networks each having the same value of K1 and designed by adlusting the ratio 114 f oi the resonance frequencies of the two networks to give a mean phase difierence or 90, isplotted against a logarithmic frequency scale. Thus for.

Kr=3.4 a frequency range oi about 5% to 1 is chtained for 0=90:i:0 .5, while K1=5 gives arange of about to 1 ior'0=90:7. It i of interest that for a curve which varies equally above and below the ratio is approximately given by asoasvo oi elements or of a plurality of networks in tandem enables smaller deviations or larger frequency ranges tobe obtained, and networks containing fewer elements may be used where it is only necessary to cover a small frequency range.

The network of Figure 3 for instance has a phase angle of 180 at its lower resonanc frequency and 360 at its upper resonance frequency; these two points may be located at any desired .points in the frequency range by the choice of values for the constants In and p, while choice of the third parameter K2 enable the value of 6 to be fixed at one other point in the frequency range.

For example, a network similar to Figure 2 may be used in one branch of the circuit with a network similar to Figure 3 in the other branch. By choice of in and p the resonance frequencies of the latter will be located at or near the frequencies at which the Figure 2 network gives angles of 90 and 270 respectively. The value of K: may then be chosen so that the Figure 3 network gives a phase angle of 270 at the resonance frequency (fr) of the-Figure 2 network. Under these conditions:

K2=p approximately The dotted curve of Figure!) shows the phase difierence between a Figure 2 network in which K1=3.4. and a Figure 3 network in which Ks:- 50.5p= 13.9: the ratio oi the two networks is 3.73. With this arrangement =90; l.7 over a'frequency range of as to one.

With reference to the special case where a frequency diflerence of 90 is required it should be noted that the various networks give multiples of 180 at the frequencies in the following table:

Network Figural Q Flam-e2 fr. FigureB Jrz..." In... a

e network of Figure 1 gives 90 phase angle at the frequency jr/Ko and is symmetrical with respect to ice j about this point. In the network of Figure 2, the curve of 0 against log is symmetrical about the point where j=fr. In the network of Figure 3 if Ka=p the curve oi? a agt log f is symmetrical about the point where f= vjrifrs where s=270. Thus a favourable ary ranget consists of a pair or networks one of which has nelements per impedance arm and the other has n+1 elements per impedance arm.

Each network will be desmned so that its phase The lattice network or :r; e 2 can be replaced ticsshown in Figure 6. Where K1 is greater than 1 the shunt inductance g t p es-i 1:

becomes negative and must be introduced by means of coupling between the inductances in the '1 arms; the network then takes the form shown in Figure 7, the coupling factor between the inductances Lo being K. As is well. mown the coupled inductances of Figure 7 may be represented by the 1' network of Figure 8, and it Figure 7 is equivalent to Figure 6, then:

The networks considered up to this point have all been of the constant resistance type and present their characteristic propagation constants, i. e., zero loss and an approximately logarithmic relation between phase angle and-frequency, when terminated in their characteristic impedance; two i such networks having their inputs connected in parallel, and each terminated in their characteristic impedance will give output voltages or currents of exactly equal amplitude and diflering in phase by an approximately constant angle over the frequency range for which they are designed, the maximum angular deviation from the design value depending on the range to be covered. It has been found, however, that the performance can be improved by theinclusion oi resistances in the networks and/or by modii the terminating impedance.

The efiect of such modifications is to reduce the angular deviation at the expense of a deviation from equality of amplitude.

A further advantage of the use of such resistance elements is that the unavoidable resistance of inductance coils may be absorbed in the said resistances thereby enabling coils of comparativelv low Q value to be empioyed.

For many applications and in particular or the single sideband modulator described later,

deviations in angle and amplitude are both undesirable, but it has been found that the use of resistance elements in the networks makes it possible to reduce the efiective maximum deviation (due to both phase and-amplitude) over a given frequency range to a lower value than is obtainable with non-dissipative networks.

The aggregate eflect of given deyiations in angle and amplitude varies with diiferent applications of the circuit, but in most cases a devia= tion in angle is approximately equivalent to an amplitude difierence of 0.15 db. per degree, so

' long as the deviation is small. For example, in

the single sideband modulator described later, the power ratio ofthe transmitted and suppressed sidewnds is given by:

ere a is the amplitude ratio of the two input voltagm and 60 is the angular deviation from of the ph difierence between the input voltthe amplitude ratio a which, with no andby a bridged i network of identical charactas lar deviation. gives the same suppression as an angular deviation 60 with no amplitude deviation, is given by:

1-si.n so

. 1+sin 60 From this formula, it can be shown that as to varies from 1-10, a varies between .1512 and .1534 db. per degree.

Figure 9 shows by way of example a network similar to that of Figure 7 in which resistances r; are included in the T arms and resistances r: in the bridge arm. It is found that the attentuation frequency characteristic of this network is symmetrical about the resonant frequency of the network when r1=r:, and this condition is most generally useful. In particular cases it may be desirable to make 11 and r2 unequal in order to make the attentuation more constant over a part of the frequency range at the expense of less constancy over the remainder of the range. Figum 10 shows a pair of networks similar to Figure 9 having their inputs connected in parallel to a generator G and their outputs terminated in load impedances RL, R1} respectively. Currents or voltages in loads Rn, RL will be approximately equal in amplitude and will differ in phase by an approximately constant amount over a range of frequencies. The analytical determination of the optimum values of the various parameters to meet any given requirements is a matter of great complexity owing to the number of variables involved, and it has been found more convenient to use trial and error methods. By way of example the curves of Figure 11 show results which can be obtained with circuits designed for a phase difference of 90; the useful frequency range expressed as the ratio of the highest and lowest frequencies is plotted against the maximum deviation which occurs in that range, deviation being expressed in clb. The dotted curve i is for a pair of non-dissipative circuits of the type shown in Figure 2 or Figure 6. The full line curve I for a circuit of the type shown in Figure 10 in which:

Ti=T2=T1 =T2 =Tc RL=RL =Ro and K1 is the samefor both networks.

In this case it appears that for a given deviation the increase in frequency range obtained by the addition of resistance varies from 10 to 20%.

The values which must be assigned to 10, Re and K1 in order to give the optimum results for this type of circuit depend upon the frequency range to be covered. For frequency ranges from /1 to 50/1 it is found that re varies from 027R to 0.5R, Ro varies from 0.753 to OAR and K1 varies from 3.5 to 5, where R is the characteristic impedance of the non-dissipative network.

An important application of the principle of theinvention occurs in the design of frequency translating devices or modulators for single sideband working, especially where the carrier frequency is high compared with the input frequency, in which case the selection of one sideband by filters may be diificult or impracticable.

Figure 12 shows a known type of frequency translating device which is adapted to suppress one side-band; this circuit has not hitherto found much application for lack of convenient means to obtain over a suilicient frequency range a 90 phase shift with constant amplitude ratio between two circuits.

Modulators i, i are supplied with the same carrier frequency from generator 2 but with a phase difference of 90". If this carrier frequency is constant, the required conditions can readily be attained by the use of an inductance and capacitance 3, 3 in the carrier supply circuit. If the carrier frequency is variable the inductance and capacitance should be replaced by a pair of networks in accordance with the invention. The modulating frequency from generator 4, which is frequently variable over a wide range. is applied to the translating device through phase networks 5, 5 whose output terminals are connected to the input terminals of modulators I, I respectively, and whose input terminals are connected in parallel or over a hybrid coil or differential transformer. Networks 5, 8 which may be of the type shown in Figure 2 or Figure 3 are designed in accordance with the invention, so that currents or voltages in their output circuits differ in phase b 90 and have a constant amplitude ratio; The output circuits of modulators I, l are connected in parallel or over a hybrid coil to line 6. Each modulator generates an upper and a lower sldeband in its output circuit, but the phase relations are such thatfor one sideband the I components from the two modulators are in phase and for the other sideband the component are 180 out of phase. Either sideband may be suppressed by suitable poling of the input, output 1 advantages. In the circuit of Figure 13 the modulating frequency from generator 4 passes through phase networks 5, 5 designed for 90 phase difference, to the input circuits of modulator l, 6 The carrier frequency from generator 2 is connected in the same phase to modulators I, i and a second pair of phase networks I, 1 similar to 5, 5 but designed to have a phase difference of 90 over the frequency range covered by the upper and lower sidebands are connected in the output circuits of modulators i, I

The translating device of Figure id is similar to that of Figure 13 except that the input network 5, l are omitted and the carriers supplied to modulators I, i have a phase difference of 90. Whereas the circuit of Figure 12 with one poling will suppress in its output the upper sideband of any input frequency, and with the other poling will suppress the lower sideband of any input frequency, the circuits of Figures 13 and 14 possess the property of discriminating between input frequencies, which lie respectively above and below the carrier frequency. The circuit of Figure 13 with one poling will suppress the upper sideband of input frequencies, which lie below the carrier frequency, and both sidebands of input frequencies which lie above the carrier frequency; with the other poling it will suppress the lower sideband of input frequencies which lie below the carrier frequency and. neither sideband of input frequencies which lie above the carrier frequency.

The circuit of Figure 14 has properties inverse to those of Figure 13 and with one poling will suppress the upper sideband of frequencies which lie above the carrier frequency and both sidebands 0 frequency translating devices used in receiving is known as second channel interference," and at the same time to eliminate in the output the upper sideband, due to the desired input ire quency. This is illustrated by the circuit of Figure 15, in which 20 represents a frequency trans= lating device of the type. shown in Figure 12 or Figure 13 supplied with a carrier frequency p from generator 2! and an input frequency a (q less than p) from generator 22. The output of translating device 28 is arranged so that one sideband (say p-ql is suppressed and is connected to line 23. At the receiving end of the circuit line '23 is connected to the input of afrequency translating device 26 of the type of Figure 14, which is supplied with a carrier frequency 11 from generator 25, and whose output is connected to a load 26. The single sideband input of fre-' quency p+q will give rise to a lower sideband of frequency qi in the load as, the upper sided 2p+q being suppressed. Furthermore, a irequency Pq in line 28 e. g., from an adjacent channel, will not give rise to any output in load 25, since both sidebands q and 232-1; are suppressed. If it is required that the lower sideband p-q be transmitted on line 23 instead of the upper sideband, then the frequency translating device 2 3 at the receiving end of the circuit should be of the type of Figure 13 instead of Figure 14. Figures'ls and 17 show alternative arrangements of the output circuits or frequency translating devices, in accordance with Figures 13 or 14. .In Figure 16 the output terminals of networks l, l are connected to conjugate pairs of terminals on a hybrid coil 8. Across the other conjugate pairs of terminals are connected loads s, il The upper sideband will then appear in one load and the lower sideband in the other. The circuit of Figure 17 is only suitable for use where the ratio of the highest and lowest frequencies in the sideband range is small. The outputs of the modulators I, i are combinedin a Maxwell bridge circuit comprising resistances ii, d inductance ii and capacitance s At the mean sidehanol frequency the reactances of inductance and capacitance t are made equal to the resistance of the loads i, & which are themselves equal. With this arrangement one ,sideband will appear in load 6 and the other in load 6 A further application of networks in accordance with the invention is to cathode ray oscillo= graphs having a circular time base with a variable sweep frequency. A variable oscillator controlling the sweep frequency is connected to the vertical plates of an oscillograph through a phase network, and to the horizontal plates through a second phase network, said networks being designed in accordance with the principles of the invention, so that the currents or voltages in their outputs diiier in phase by 90 over the frequency range of the variable oscillator.

What is claimed'is:

1. A transmission circuit capable of producin phase shifts of currents or voltages, which are substantially constant over a relatively vwide range I of frequencies, including a circuit having a pin aaaasre plitudes of said currents or voltages in said branches are substantially constant over the said range of frequencies;

3r A circuit according to claim 1 in which the phase difference between two of said branches is substantially 90.

4. A circuit according to claim 1 in which said networks are all-pass constant resistance networks. E

5. A circuit according to claim 1 in which said networks are all-pass constant resistance networks in a lattice form and have two or more impedance elements in each impedance arm.

6. A circuit according to claim 1 in which said networks in lattice form have two impedance elements in each impedance arm and have substantially identical values of K1.

7. A circuit according to claim 1 in which said networks are of lattice form and at least one network has n impedance elements in each arm while at least one other network has n+1 impedance elements in each arm.

8. A circuit'according to claim 1 in which said networks are of lattice form and at least one network has n impedance elements in each arm while at least one other network has n+1 impedance elements in each arm, and in which each resonance frequency of one of said a. element networks is located approximately at the geometric mean of a pair of adjacent resonance frequencies of one of said n+1 element networks.

9. A circuit according to claim 1 in which said networks are all-pass constant resistance networks in which one or more resistance elements are inserted in one or more of the impedance arms.

10. A circuit according to claim 1 in which said networks are all-pass constant resistance and a shunt arm comprisinga negative induot= ance and a capacitance in series.

12. A circuit according to c 1 in which each network comprises a bridged 1' network he," 1: a series arm comprising a capacitance and a re sistance in series, two equal T arms each comprising an inductance and a'resistance in series and a shunt arm comprising a negative inductance and a capacitance inseries, and in which said resistance in said series arm is approataly twice said resistance in each of said T 13. A circuit according to claim 1 in which each network comprises a bridged T network ha a series arm comprising a capacitance and a re= GEOE HOB

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