Download Differential equations using the HP-48G by Gill Proctor PDF

By Gill Proctor

Use HP-48 G/GX graphing calculator know-how to help within the computation and visualization of key topics within the arithmetic series: Calculus, Differential Equations, Vector Calculus and Linear Algebra.

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Extra info for Differential equations using the HP-48G

Example text

2. This is a three-winding, three-leg mesh transformer. If a simple threewinding ideal transformer (Fig. 2, upper right) is selected to simulate this transformer, the output voltage phases will be correct only for some excitations. If, for example, the center winding is excited, then the voltages on the other two windings will be correct. However, if one of the SPICE Modeling of Magnetic Components 19 + S1 + P + S2 P S1 + S2 + + - S1 + P + S2 S1 P + -+ + Not Inverted S2 + In Inverted Modeling of mesh transformers requires caution.

The core loss has not been modeled in this SPICE 3 version. The model is based upon the premise that a magnetic element is represented by an inductance. The inductance is related to the permeability and geometrical properties of the core. The current through the inductor can then be simply stated as I= 1 L Vdt This function can be modeled as a simple integrator. To properly represent the B-H loop characteristics, the nonlinearities of the inductance need to be defined. Fortunately, graphical data are available that provide the percentage of initial permeability versus DC bias for several core types.

Note: In PSpice, if all the inductor couplings have the same value the coupling element may also be written as Kall L1 L2 L3 Couple value. 6 SPICE coupled inductor model and associated netlist. 7 Structure of the Pi model. Mutual inductance can be expressed in alternative form using coefficients of coupling, ki j . 3) In a transformer, ki j will normally be very close to 1. A typical PSpice listing for a coupled inductor is shown in Fig. 6. This is an abstract model. Most engineers, however, will be thinking in terms of a circuit model that has leakage and magnetizing inductance and a turns ratio.

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