Internal Magnetic Field Analysis and Synthesis for Prescribed Magnetoelastic Delay Characteristics

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Abstract
A systematic procedure is given for synthesizing the internal magnetic field required to realize prescribed magnetoelastic delay characteristics. The method is based on the expression Tr = (2/c) {y+ω[γHi′(y, He)]−1} for the transit time of magnetoelastic waves in ferromagnetic insulators. Here Hi′(y, He) is the gradient of the internal magnetic field at the turning point, and He is the external magnetic field. Some necessary conditions for physical realizability are discussed and a delay‐bandwidth invariant is demonstrated. Field distributions are obtained having the characteristics: (a) ∂Tr/∂ω = 0, independent of ω at specified Hi(0, He), and (b) ∂Tr/∂ω = 0, independent of Hi(0, He) at specified ω. The last case is used as a basis for evaluating the bandwidth capabilities of magnetoelastic variable delay lines. Limitations on the bandwidth, delay variation, and delay distortion are discussed. Realization of a desired internal magnetic field is greatly simplified by a method for determining the field from measurements of the transit time Tr(ω, He) of magnetoelastic pulses and the separation Sm(ω, He) in magnetic field between adjacent standing‐wave modes. The relation Hi′ = ωSm/πc gives y = Φ(ω/γ, He) = (c/2)[Tr−2π/γSm] in terms of measurable quantities; inversion of the function Φ at constant He recovers the internal field in the form ω/γ = Hi(y, He). This method has been applied to data from an yttrium iron garnet rod immersed in a steady, uniform, axial field He; a comparison of the measured results with existing theory is presented.