US2811697A

US2811697A - Magnetoelectric induction devices

Info

Publication number: US2811697A
Application number: US380580A
Authority: US
Inventors: Clarence L Hogan
Original assignee: Bell Telephone Laboratories Inc
Current assignee: AT&T Corp
Priority date: 1953-09-16
Filing date: 1953-09-16
Publication date: 1957-10-29
Anticipated expiration: 1974-10-29

Description

Oct. 29, 1957 c. L. HOGAN 2,811,697 MAGNETOELECTRIC INDUCTION DEVICES Filed Sept. 16,-1953 F IG. 2 FIG. .3

FIG. 6

LOW HIGH mpsmmc: 1 5 0 IMPEDANCE AC. sou/ms VOL mus/e I INVENTOR y C. L. HOG/4N A T TOR/V5 V 2,811,697 Patented Oct. 29,1957

ice

a corporation of New York Application September f6, 1953; Serial No. 380,586 2' claims. Cl. 333-32) This "'veiitioii relates r01 electrical reactive devices and to coup fig structures'utili'zing t e principles of magnetoelectric induction; a v I a I t I,

It iswnwamat an electric field is generated by a magnetic d a cemem current. This phenomenon has been designated e ctromagn'etic induction and is eniployd in litan p'ra" 'cal devices such as transformers and generators: The analogous generation of p a magnetic field by aiiel'ectrcaldisplacement field, which may be termed'mag'netoelectr'i'c induction, is not widely recogniie'd andh'as' only recently been verified experimentally. In this prior art experimental work in which conducting magnetic cores were used, the observed effects were exceedinglyweak and very little coupling was obtained.

Accordingly oh e object of the present invention is to make an improved electrical coupling structure utiliz ing the principles of magnetoelectric induction.

A more specific object is toincrease the electrical coupling of magnetoelectric' impedance transforming structures.

In accordance with the invention, it hasbeen discovered that the use of ma'gn'e'tik': cores having 10w condnctiyity greatly increases the effective coupling between the'm'agnetic and the electrical displacement circuits in magnetoelect'ric devices; More specifically, and injaccordanc with one embodiment of the invention illustrated in'th je drawings, a' polycrystalline ferrite cylinder having a coaxial hole therethrough is employed to obtain impedance transformation between a pair of electrodes securedito its ends anda coil threaded through the hole. Other specific embodiments of the invention involvethe coupling of electric displacement currents in a circuit of high dielectric material, with a magnetic circuit having high permeability and low conductivity. I,

In the measurement of the dielectric constant of various samples bythe conventional method in which electrodes are secured to the sample, considerable difiiculty has been encountered at high frequencies with materials having high dielectric constants; Specifically, if the electrodes do not make intimate conta'ctwith the sample throughout thecomm'on surface" areas, errors of large magnitude may appear, particularly when'thedielectric constants involved are of the order of magnitude of 50,000 or 100,000 or higher. p I,

An additional object of'the present invention is, there fore, to improve and simplify the appar'a tusfor measuringdielectriccon'stants of materials having-relatively high dielectric constants. v e I v e Other objects and certain features and advantages be'de e-idpea iii the course of the detailed description of the drawings.

In the drawings: V

Fig: 1" shows a'core of high permeability material encircledfby a wire of hi'gh'dielectri' constantmaterial'in' accdrdance .with the invention;

. Fig .--2-illlistrates a condenser having dielectricmaterial between its plates;

Fig. 3 is an equivalent circuit diagram for the structure of Fig. 2 at high frequencies;

Fig. 4 depicts an inductance made up of an annular core of high dielectric material encircled by a wire of high permeability material; m

Fig. 5 illustrates a transformer patterned after the iiiductance of Fig. 4; t

Fig. 6 represents an arrangement for testing the dielectric constant of high dielectric constant materials at high frequencies; v

Fig, 7 is a diagram employed in an analysis which is presented in the specification; and I Fig. 8 is an electromagnetic transducer constructed of a material having a high" dielectric constant and a high permeability.

Referring more specifically to the drawings, Fig. 1 shows by way of example and for purposes of illustration, a closed loop of high permeability material. 21 hav ing a toroidal coil 22 of high dielectric constant wire wound thereon. Because of the historical emphasis on iron and copper inductances, it is contrary to expectations to that the structure ofFigl l, which is made up entirely of 10W conductivity material, exhibits substantialimpedanc. However, the symmetry of Maxwells equations indicates thatit makes no difference whether the current density in the coil 22 arises from conduction or displacement cur re'nt. Therefore, assuming that theelectric fluiris entirely confi'nedto the dielectric wire and does notleak' between turns, the self-inductance of the coil can be" defined as? dielectric wire 22 of Fig; 1 is'given by the expression'z' where:

[W th'elen'g th of the dielectric Wire, i Aiv'is the cross-sectional area of the dielectricgwirie, and w is the angular frequency of the source of electromagnetic waves.

is of course not the' proper expression for the dielectric constant as the term is normally used, the fallacy being that the inductance of the structure is ignored" In other words the apparent dielectric constant as determined by the foregoing Expression (2), is not the true dielectric. constant because it is measured in terms of the applied rather than the total field. N e A Having now established that dielectric samples can exhibit inductance in the same way that'metallic samples can, it is important to investigate how im r this" mightbe in experiments designed ame; dielectric constant. In order to do this it is advantageoustotreat the dielectric medium as an equivalent circuit. For the present purpose only lossless enamnwiu be considered. This implies that'the dielectric constant is real and hence the equivalent circuit will contain no resistance. The loss in the dielectric material can easily be included by adding a resistance to the equivalent circuitfif de siredl I Fig. 2 illustrates the apparatus 'whic'hlh' usua cylindrical sample 25. Since this dielectric sample has both inductance and capacitance, it can be represented by the equivalent circuit of Fig. 3, in which the capacitance 26 is equal to The inductance 27 of the sample can for the present be considered as the inductance of a single straight conductor, and is thus equal to However, for reasons which will become apparent later it is assumed that the magnetic flux which is created by the displacementcurrent is confined entirely within the dielectric material. This is a valid approximation if the dielectric is ferromagnetic- With these assumptions, the expression for the apparent dielectric constant is where e is the true dielectric constant of the material, and A is the cross-sectional area of the sample 25 taken perpendicular to the direction of the electric field. At low frequencies, the effective dielectric constant is the same as the true dielectric constant. However, athigher frequencies, approaching the resonance frequency at which the denominator terms are equal, the apparent dielectric constant is much different from the true dielectric constant. This indicates the danger of ignoring the inductance of a ferromagnetic dielectric in the megacycle range.

Proceeding now to a consideration of magnetic displacement currents rather than electric displacement currents, Fig. 4 shows a ferromagnetic wire 31 wound around a toroid 32 having a high dielectric constant. The source 33 and coil of conducting wire 34 establish the magnetic displacement current in the magnetic wire 31. It will be assumed for simplicity that there is no magnetic flux leakage between turns of. the coil of magnetic wire 31 but instead the magnetic flux is confined entirely to the Wire. Due to the symmetry in Maxwells equations it may be inferred that magnetic displacement currents encounter inductance and capacity in the same way that electric displacement currents do. Hence it should be expected that at the center of the magnetic coil in Fig. 4 an electric field will exist if a magnetic flux is changing in the ferromagnetic wire. In fact, treating the changing magnetic flux (magnetic displacement current) as a magnetic current an inductance for this coil may be readily derived. The expression for this inductance is N A E 1' where:

N is the number of turns of the wire 31,

AT and IT are the area and length of the dielectric toroid 32, and

e is the dielectric constant of the toroid.

where:

lw is the length of the wire 31,

Aw is the cross-sectional area of the wire, and

Cm and Lm are the effective capacitance and inductance of the structure.

At low frequencies the inductive reactance can be neg lected and, under these conditions the ratio between the flux density B and the magnetic field H will give the true permeability of the ferromagnetic wire even though it is wound over a barium titanate toroid. The apparent permeability, however, shows a resonance phenomenon which will create large disparities between the apparent and the true permeabilities at higher frequencies.

In Fig. 5, a transformer structure is shown which is similar in construction to the inductance of Fig. 4. The impedance transformation between the source 41 and the load 42 is determined by the turns ratio of the magnet coils 43 and 44 on the dielectric core 45, with the conducting coils 46 and 47 being identical.

Fig. 6 is a schematic showing of an arrangement for determining the dielectric constant of a sample 51 of a material having a high dielectric constant without the use of electrodes secured to the material. In this test circuit, the annular dielectric sample 51 is coupled to the low impedance high frequency source 52 and to the high impedance voltmeter 53 by means of the

coils

54 and 55 and the

annular cores

56 and 57 of high permeability material. The

annular cores

56 and 57 must also be of relatively high resistivity or low conductivity materials so that eddy currents will not neutralize the magnetic field set up in these cores. By way of example, the new polycrystalline ferrites such as Ni.3Zn.7Fe203 are suitable materials for the

cores

56 and 57. These

cores

56 and 57 are each made up of two separable portions for ease of insertion of the dielectric test samples such as 51.

Now, assuming that the source 52 is a constant current source and thus that it has zero impedance, and that the voltmeter 53 has infinite impedance, the relationship be tween input and output voltages will be as follows:

where l is the mean circumference of

toroids

56 and 57;

w is the angular frequency of the exciting source;

e is the dielectric constant of the sample 51;

A6 is the cross-sectional area of the dielectric toroid 51;

le is the mean circumference of the dielectric toroid 51;

A,. is the cross-sectional area of each of the

toroids

56 and 57;

e is the input voltage;

a is the permeability of each of the

elements

56, 57; and

e is the output voltage at the voltmeter 53.

Further mathematical analysis discloses two well defined resonances, a series and a parallel resonance at very high frequencies. Below both of these resonances, however, the l in the denominator of Equation 6 may be neglected in comparison with the other term, and the equation becomes:

i p 1 And, assuming that the dielectric test samples are cut to a standard shape, the output voltage e at the voltmeter 53 will be directly proportional to the dielectric constant e of the test sample. Therefore, after an initial output voltage reading using a sample of known dielectric constant, the dielectric constant of any other sample may be quickly and easily determined. Thus, through the use of the arrangement of Fig. 6, the use of electrodes in dielectric measurement techniques is avoided and the principal source of error in such measurements (the lack of intimate contact of the electrode with the high dielectric constant material) is thereby eliminated.

Proceeding to a related matter, the problem of an infinitely long, rod of ferromagnetic material that is being magnetized by an alternating magnetic field acting along the axis of'the rod will now be considered. The magnetic current in the rod will set up circular lines of electric flux around the rod. As these electric fluxalines alternately up and collapse they will induce aback magn'eftomotivg force in the rod. In other words this rod will also have inductance for the flow of magnetic current. In order to find the actual current distribution at high neqnencies, it is necessary to know therg'eometry of the return circuit. .For instance, if the geometry is such .that the problem consists in finding the current distribution in two parallel cylindrical fiw'ires then the current distribution can be regarded as beingmade up of cylindrical sheets only if the distance between the axes of the wires is large compared with their radius. If this approximation is valid, then the current distribution is identical to that obtained by assuming that the return circuit is via a cylinder, coaxial with the dielectric sample and larger in radius. Since this geometry lends itself more readily to mathematical analysis, it is this model which will be used.

The problem is illustrated in Fig. 7 in which the central long rod 61 of ferromagnetic material is inclosed by the coaxial return path 62. If a cylindrical tube of radius r and wall thickness a'r is considered as the sample, then the equation giving the current in the tube is:

Ir is the total current in tube;

i r is the number of lines of induction between two planes perpendicular to the axis of the cylinder and one meter apart which are linked by the current in this cylindrical tube;

E is the difference in applied potential between the two planes bounding the tube;

Qr is the total charge on the two planes bounding the tube 6. Qr=fo lrdt); and

L and C are the efiective inductance and capacity per unit length.

Solving the previous .Equation 8 and neglecting the magnetic flux external to the cylinder (a valid approximation for ferromagnetic materials) the current density distribution is given by the following equation.

where: A is an undetermined constant which depends on the amplitude of the applied field.

As a result of this current density distribution it may be determined that the apparent dielectric constant of the cylinder is:

21m A J(T) X is the operating wavelength;

a is the radius of the cylinder as indicated in Fig. 7; and

Jo and J1 are Bessel functions of the zeroth and first orders respectively.

This expression has a resonance wherever the zeroth order Bessel function in the denominator has a zero. At lower frequencies the Bessel function of zero order can be adequately represented by the first two terms, and the function of first order can be represented by the first term only. Under these conditions Equation 10 may be reduced to an expression which is identical with Equation 3 which was derived by means of the approximation that the current density was uniform throughout the cylinder. Thus the approximate theory previously developed is even quantitatively valid up to the first resonance. Nevertheless, it

is important to realize that the exact theory does :predict a different behavior above the first resonance 'than;theapproximate theory where the current density is assumed 'to be uniform. I p

' For the case where loss occurs (i. e. .p. and e arecorrr plex), the above analysis is still correct except that the propagation constant cannot be written in terms of the wavelength in such a simple fashion. For lossymaterials,

The 's'arrfe analysis can be carried out for the magnetic cylinder that is carrying a magnetic displacement current, (i. e. being magnetized and demagnetized in alternating cycles). The analysis is identical except that ,u and e exchange places. Hence, the apparent permeability without loss and with loss may be determined by interchanging ,u and e in Formulae 10 and 11, respectively.

Proceeding now to a consideration of Fig. 8, a hollow cylinder 71 of material having a high dielectric constant and a high permeability, such as one of the new nickel zinc ferrites, is provided with a pair of

electrodes

72, 73 at its two end surfaces and with a coil 74 threaded through its central aperture. When an alternating voltage is applied across

electrodes

72, 73 this establishes an electrostatic displacement current in the dielectric material 71 between the electrodes. This electric displacement current will be accompanied by a circumferential magnetic field which will be set up in the cylinder 72 by the electrostatic displacement current. This in turn will establish a current flow in the coil 74 which is coupled to the circumferential magnetic field. The structure of Fig. 8 will thus transform a high impedance input at

electrodes

72, 73 to a low impedance output at the

output terminals

75, 76 of the coil 74.

In the present specification and claims, when the terms high dielectric constant or high permeability are employed it is understood that the relative dielectric constant or permeability will be greater than 1000. When the term low conductivity is employed, a conductivity less than 1 mho/centimeter will be understood. The necessity for employing materials having either a high dielectric constant or a high permeability or both of these properties is again stressed, inasmuch as it is these qualities which prevent undue dispersion of the electric or magnetic fields. In addition, the low conductivity of the high permeability material is important to prevent neutralization of the magnetic fields by circulating currents. Typical materials suitable for use as the high dielectric constant elements are barium titanate and potassium niobate. In addition to the nickel-zinc ferrite mentioned hereinbefore, other materials which have been reviewed in the literature may be employed as the high permeability-low conductivity elements discussed above.

It is to be understood that the above-described arrangements are illustrative of the application of the principles of the invention. Numerous other arrangements may be devised by those skilled in the art without departing from the spirit and scope of the invention.

What is claimed is:

1. In an impedance converter, a cylinder of polycrystalline ferrite material having a permeability greater than 1000, said cylinder having a substantially axial opening therethrough, .a pair of apertured electrodes mounted on the opposite ends of said cylinder, a toroidal coil threaded through the axial opening in said cylinder and the apertures in said electrodes, said toroidal coil having its windings insulated from said electrodes, and separate electric circuits connected to :said electrodes and said coil, respectively.

2. In an impedance converter, a cylinder of polycrystalline ferrite material having a chemical composition substantially that given by the formula NisZnrzFezOs, said cylinder having a substantially axial opening therethrough, a pair of apertured electrodes mounted on. the opposite ends of said cylinder, a toroidal coil threaded through the axial opening in said cylinder and the apertures in said electrodes, said toroidal coil having its windings insulated from said electrodes, and Iseparate electric circuits connected to said electrodes and said coil, respectively.

2,358,462 Mahren Sept. 19, 1944 Donley et a1. Oct. 9,1951 Rex Sept. 16,- 1952 Jaspers ,Oct. -7, 1952 Peek Apr. 21,1953 Harvey May 19, 1953 Tellegen July 28, 1953 Roberts Feb. 28, 1956 OTHER REFERENCES Schlicke: Journal of Applied Physics, Vol. 24, No. 2, February 1953, pages 187-191.