The present invention relates to broadband magnetically tunable resonators and to tunable devices using such resonators such as filters, particularly bandpass and band reject filters, oscillators and other devices. The resonators disclosed herein and the devices in which they are used are tunable generally over a broad frequency range extending from VHF to microwave.
Magnetically tunable resonators operated at radio frequencies, particularly microwave frequencies, employ resonator bodies made of a ferrimagnetic material. Such resonator bodies are usually spherically-shaped, made of single-crystal YIG (yttrium-iron-garnet), nickel ferrite, lithium ferrite, etc., materials and operated in the uniform precessional mode ((100)-mode. Known resonators, using such resonator bodies and suitable coupling arrangements, with proper design techniques, can be tuned to resonate over a frequency range in excess of 10:1. However, the minimum resonance frequency at which known magnetically tunable resonators can be tuned at a reasonably high Q and for a reasonably large signal level has been limited to about 1000 MHz or more, depending on the magnetic material. So far as the applicants are aware, efforts to lower the minimum resonance frequency of such tunable magnetic resonators have been unsuccessful.
The existence of a lower limit for the resonance frequency of ferrimagnetic resonators, is however, well known, and it was commonly accepted that this lower limit is related to what are known as demagnetizing effects. A convenient starting point for an analysis of the basis for the lower frequency limit of ferrimagnetic resonators is the equation for the internal field (Hi) in a saturated ferrimagnetic body, EQU H.sub.i =H.sub.dc -N.sub.z (4.pi.M.sub.s), (Expression 1)
where: H.sub.dc is the applied static magnetic field, oriented along the z-axis of a rectangular coordinate system, measured in Oersteds; N.sub.z is the demagnetizing factor in the z direction (direction of the H.sub.dc field); and 90M.sub.s is the saturation magnetization measured in Gauss.
The relationship of Expression 1 assumes that the saturation magnetization is parallel to the applied external field; that is, the external field is strong enough not only to move the "Bloch" walls away so that the body is uniformly magnetized, but also to turn the magnetization into the direction of the external field.
The demagnetizing factors in the x, y and z directions, i.e. N.sub.x, N.sub.y and N.sub.z, respectively, are related by: EQU N.sub.x +N.sub.y +N.sub.z =1. (Expression 2)
For a body with circular symmetry about the z axis, the two demagnetizing factors N.sub.x and N.sub.y, which are transverse to N.sub.z, are equal, and each is referred to as N.sub.t, which leads to: EQU N.sub.z +2N.sub.t =1. (Expression 3)
The resonance frequency "fo" in MHz of a ferrimagnetic body with circular symmetry in terms of the magnetic field in Oersteds is given by: EQU fo=2.8[H.sub.dc -(N.sub.z -N.sub.t)4.pi.M.sub.s ]MHz. (Expression 4)
As indicated above, Expression 3 applies to a resonator body with circular symmetry, where N.sub.t is the demagnetizing factor in the direction transverse to H.sub.dc (i.e., transverse to the internal field H.sub.i =H.sub.z, and transverse to the saturation magnetization). The factor "2.8" is the gyromagnetic ratio for a ferrimagnetic body having circular symmetry and equals ge/2mc.sub.o, where e is the charge of an electron, m is the mass of an electron, g is the gyromagnetic factor for a ferrimagnetic body and c.sub.o is the speed of light in a vacuum.
In order to obtain good resonance (reasonably high Q, and no limiting with reasonably high signal levels), the ferrimagnetic body must be saturated. This can only happen if the internal field H.sub.i is larger than zero.
From the above relationships, the minimum resonance frequency "fo min" of a body with circular symmetry can be determined to be: EQU fo min=1.4(1-N.sub.z)4.pi.M.sub.s MHz. (Expression 5)
For a sphere, since N.sub.z =1/3, the equation for the minimum frequency reduces to: EQU fo min=0.93 4.pi.M.sub.s MHz. (Expression 6)
If the ferrimagnetic body is made of pure YIG material, 4.pi.M.sub.s is about 1750 Gauss, resulting in a minimum resonance frequency of about 1630 MHz. By reducing 4.pi.M.sub.s (by, for example, doping YIG material with gallium, and/or by heating the ferrimagnetic material to a temperature close to the Curie point), the minimum resonance frequency can be reduced to 1000 MHz, or even lower, at the expense of lower Q, lower signal limiting level and higher resonance frequency/temperature sensitivity.
So far as the demagnetizing effects are concerned, it was thought that the minimum resonance frequency of a ferrimagnetic resonator body could be lowered if a disk-like shape were used instead of a sphere. Taking a disk-like shape (e.g. a flat ellipsoid) for the resonator body, with the static magnetic field H.sub.dc applied normal to the large surfaces of the disk-like body, the demagnetizing factors N.sub.x, N.sub.y, and N.sub.z change, with N.sub.z getting larger, and N.sub.x and N.sub.y getting smaller (N.sub.x is equal to N.sub.y since circular symmetry exists for a disk-like shape as well as for a sphere). For a disk-like shape having a diameter-to-thickness ratio of 30:1, N.sub.z is about 0.95, and N.sub.x and N.sub.y each are 0.025. For such a disk-like shape, theoretically, the minimum resonance frequency given by Expression 5 decreases to 0.07 4.pi.M.sub.s, which for a pure YIG material is about 123 MHz and for a gallium-doped YIG material, can be less than 50 MHz.
Experimentally, however, even using disk-like shapes, it was, so far as applicants are aware, not possible to reach the low resonance frequencies which appeared theoretically possible from Expression 5. In fact, Matthaei et al. (Matthaei, G. L., Young, L., Jones, E.M.T., "Microwave Filters, Impedance Matching Networks and Coupling Structures", McGraw Hill, N.Y., 1964, p. 1036) state: "In theory, by using flat, disk-like ellipsoidal shapes, the minimum resonance frequency could be reduced greatly. However, in practice, disk-shaped resonators do not appear to work very well, possibly because of the difficulty in obtaining disk-like resonators that are sufficiently perfect ellipsoids."
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