SPICE Modeling of Magnetic Components in Software

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SPICE Modeling of Magnetic Components
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.SUBCKT CORE 1 2 3 F1 1 2 VM1 1 G2 2 3 1 2 1 E1 4 2 3 2 1 VM1 4 5 RX 3 2 1E12 CB 3 2 {VSEC/500} IC={IVSEC/VSEC*500} RB 5 2 {LMAG*500/VSEC} RS 5 6 {LSAT*500/VSEC} VP 7 2 250 D1 6 7 DCLAMP VN 2 8 250 D2 8 6 DCLAMP .MODEL DCLAMP D(CJO={3*VSEC/(6.28*FEDDY*500*LMAG)} + VJ=25) .ENDS
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A netlist for a nonlinear magnetic core using SPICE 2 primitive elements.
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The parameters that must be passed to the subcircuit include the following: Flux capacity in volt-seconds (VSEC) Initial ux capacity in volt-seconds (IVSEC) Magnetizing inductance in henries (LMAG) Saturation inductance in henries (LSAT) Eddy current critical frequency in hertz (FEDDY) The saturable core may be added to a model of an ideal transformer to create a complete transformer model. To use the model, just place the core across the transformer s input terminals and specify the parameters. A special subcircuit test point has been provided to allow the monitoring of the core ux (node 3). Because there are two connections in the subcircuit, no connection is required at the top subcircuit level other than the dummy node number. A sample PSpice call to the saturable core subcircuit looks similar to the following:
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X1 2 0 3 CORE Params: VSEC = 50U IVSEC = 25U LMAG = 10MHY + LSAT = 20UHY FEDDY = 20KHZ
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The generic saturable core model is listed in Fig. 2.21. How the Core Model Works Modeling the physical process performed by a saturable core is most easily accomplished by developing an analog of the magnetic ux. This is done by integrating the voltage across the core and then shaping
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A simple B-H loop model detailing some core parameters that will be used for later calculations.
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mag, Lmag
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A simple B-H loop model detailing some core parameters that will be used for later calculations.
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the ux analog with nonlinear elements to cause a current ow that is proportional to the desired function. This gives good results when there is no hysteresis, as illustrated in Fig. 2.22. The input voltage is integrated using the voltage-controlled current source G and the capacitor CB (Fig. 2.23). An initial condition across the capacitor allows the core to have an initial ux. The output current from F is shaped as a function of ux using voltage sources VN and VP and diodes D1 and D2. The inductance in the high-permeability region is proportional to RB, while the inductance in the saturated region is proportional to RS. Voltages VP and VN represent the saturation ux. Core losses can be simulated by adding resistance across the input terminals; however, another equivalent method is to add capacitance across resistor RB in the simulation. Current in this capacitive element is differentiated in the model to produce the effect of resistance at the terminals. The capacitance can be made a nonlinear function of voltage,
G1 CB E4 VM RS
RB VP D1
X1 CORE V(3) FLU
Figure 2.23 The saturable reactor model. The symbol below the schematic reveals the core s connectivity and subcircuit ux-density test point.
SPICE Modeling of Magnetic Components
which results in a loss term that is a function of ux. A simple but effective way of adding the nonlinear capacitance is to specify a value for the diode parameter CJO. The other option is to use a nonlinear capacitor across nodes 2 and 6; however, the capacitor s polynomial coef cients are a function of saturation ux, thereby causing their recomputation if VP and VN are changed. Core losses will increase linearly with frequency. A noticeable increase in MMF occurs when the core exits saturation, an effect that is more pronounced for square-wave excitation than for sinusoidal excitation, as shown in Fig. 2.25. These model properties agree closely with observed behavior [5]. The model is set up for orthonol and steel core materials that have a sharp transition from the saturated to the unsaturated region. The transition out of saturation is less pronounced for permalloy cores. To account for the different response, the capacitance value in the diode model (CJO in DCLAMP), which affects core losses, should be reduced. Also, reducing the levels of voltage sources VN and VP will soften the transition. The DC B-H loop hysteresis, which is usually unnecessary for most applications, is not modeled because of the additional model complexity. This causes a prediction of lower loss at low frequencies. The hysteresis, however, does appear as a frequency-dependent function, as seen previously, and provides reasonable results for most applications, including magnetic ampli ers. The model in Fig. 2.23 simulates the core characteristics and takes into account the high-frequency losses associated with eddy currents and transient widening of the B-H loop, which is caused by magnetic domain angular momentum. The saturable core model is capable of being used with both sine(Fig. 2.24) and square- (Fig. 2.25) wave excitation. The circuit in Fig. 2.27 was used to generate the graphs. Calculating Core Parameters The saturable core model is de ned in electrical terms, thus allowing the engineer to design the circuitry without knowledge of the core s physical composition. After the design is completed, the nal electrical parameters can be used to calculate the necessary core magnetic/size values. The core model may be altered so that it accepts magnetic and size parameters. The core could then be described in terms of N, Ac , Ml, , and Bm , and would be more useful for studying previously designed circuits. But the electrical model is better suited to the natural design process. The saturable core model s behavior is de ned by the set of electrical parameters below. The core s magnetic/size values can be easily calculated from the following equations that use CGS units.
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