By Sergei Tretyakov
Textual content presents an creation to using analytical types within the layout of antennas and microwave units. Demonstrates how analytical versions supply an realizing of electromagnetic phenomena in new fabrics and buildings. Equips practitioners with the information and layout instruments for constructing new functions.
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Extra info for Analytical modeling in applied electromagnetics
56 presents the magnetic field profile determined for an array of magnets with various spacing between sensor and hard magnetic layers. For a certain value of this distance (80 m in the analysed case) it is possible to obtain a uniform magnetic field above the sensor. 56 (right) show another important advantage of the design proposed by Hill and Birtwistle (1987). It is possible to obtain the pair of magnetoresistors biased at opposite directions by arrangement of the sensor. Thus it is possible to manufacture a differential pair of magnetoresistors.
50) PART 1 9/5/01 9:23 pm 32 Page 32 THIN FILM MAGNETORESISTIVE SENSORS very easy to prepare the Barber-pole or quasi-linear sensors as the differential pair – by applying the angle of ϩ45° and Ϫ45°. It is more difficult to obtain the differential pair of the sensor with the path along the anisotropy axis. 31). 64) and the resultant output signal may be expressed as: ⌬R ⌬Rx2 2⌬ Hxo Uout ϭ K —–—x1 Ϫ —–— ϭ K —— —— Hx . 31 Two differentially biased magnetoresistive sensors (a) and their resultant transfer characteristic (b).
In this way “the magnetic history” of the thin film has been changed. Now the angle increases as the magnetic field Hx increases, but only to the critical value hxc. 3. 6 (thin film initially magnetized by hyϽϪHk). magnetization jumps to the previous state. Thus hysteresis appears even for the magnetic field in the x direction. 22 presents graphically the determined transfer characteristics for the case when the magnetic field is applied by the angle 45° with respect to the x axis. Every time the magnetic field vector reaches its critical value the vector of magnetization jumps to the opposite direction.
Analytical modeling in applied electromagnetics by Sergei Tretyakov