三段形差動変圧器の解析

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Linear differential transformer can be classified into two-sectional and .threesectional types depending upon the winding constructions. In the past, the operation of the differential transformer has been analyzed based on the change of the in the magnetic reluctance of air gap caused by the magnetic core displacement. However, this method of analysis does not fully take in account the properties of core materials and the effect of leakage fluxes. Moreover, the quantitative relation between circuit parameters cannot be made clear. Previously, one of the authors has believed that the phenomena can essentially be clarified only by dealing directly with the magnetic flux itself on the core axis, and already applied this idea to analyze a two-sectional type differential transformer. In this paper, we wish the extend this idea to derive an theoretical equation for the output voltage of the three-sectional type differential transformer taking into account the demagnetization of magnetic core and the flux distribution along the core axis. The equation of the magnetic flux distribution (P(X) is given by Φ(X) = Φ₀cos²(√2C 2X/lc)e⁻γ²C 2X/lc, X≥0, (1) where X is the distance measured from the center of the magnetic core along its axis. When the load resistance of secondary winding is infinitely large, the theoretical expression for the output voltage E₂ (effective value) is obtained by E₂=ωN₂(Φ₂b-Φ₂a)=ωN₂Φ₀ μe-λl₁/2μ / λｌl₂ (P cos 2x/μ sinh λx/μ - Q sin 2x-μ cosh λx/μ - R sinh λx/μ)), (2) where P, Q and R are coefficients which do not depend on the linear displacement, x, as follows : P = λ/√4+λ²{e λ(l₁-lm)/2μ sin(lm/μ+φ) + sin(l₁/μ + φ)}, Q = λ/√4+λ²{e λ(l₁-lm)/μ cos(lm/μ+φ) + cos(l₁/μ + φ)}, R = e λ(l₁-lm)/2μ + 1. The theoretical expression (2) for the output voltage is able to explain the influences of winding constructions, core materials and its dimensions.
信州大学工学部の論文
1969-12-25

三段形差動変圧器の解析

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