## B

Figure 2.8 The development of the reluctance model for a simple inductor with an air gap. Figure 2.9 is the reluctance model that represents the magnetic structure at the top of Fig. 2.8. Now we need to convert this reluctance model to an equivalent electric circuit model, but before we can do that, it will help to briefly review the duality transformation. We can then proceed to convert the reluctance model. An example of a duality transformation is given in Fig. 2.10. A node is placed within...

## Constructing a Transformer

As a final exercise in this chapter, we will combine the core model which we just completed, along with the turns subcircuit, and model a two-winding transformer. To make a transformer model that more closely represents the physical processes, it is necessary to construct an ideal transformer and Figure 2.37 A complete transformer model. The saturable core may be combined with the ideal transformer, XFMR, and some leakage inductance and series resistance to create a complete model of a...

## Rw

Figure 2.40 Winding resistance model. Figure 2.40 Winding resistance model. Figure 2.41 HF winding resistance, normalized to 1 (Rjc) at frequency where the layer is 1 skin depth thick. Figure 2.41 HF winding resistance, normalized to 1 (Rjc) at frequency where the layer is 1 skin depth thick. The winding resistance is also dependent upon the shape of the current waveform. Figure 2.42 is an example of a three-layer winding with a symmetrical bipolar PWM current waveform. Note that all square...

## Saturable Core Modeling

It would be difficult to accurately model power circuits without the ability to model magnetics. This section details the SPICE 2 and SPICE 3 methods that are used to simulate various types of magnetic cores including molypermalloy powder (MPP) and ferrite. The presented techniques can be extended to many other types of cores, such as tape wound, amorphous metal, etc. Figure 2.20 The completed forward converter shows how the reluctance derived transformer is integrated into the circuit. Figure...

## Software Included with This Book

The CD that is included with this book contains some of the models, circuits, schematics, and graphs found within the book. The schematics utilize the OrCAD Capture PSpice format. Capture is a schematic entry program that has been specifically designed for use with the PSpice simulator. Probe is a postprocessor, which is used to analyze SPICE output files by way of waveform graphs and powerful signal processing functions. An evaluation version of OrCAD PSpice is available free of charge from...

## Z Zn Zo

Where Zo is the filter characteristic impedance defined by If we combine the above equations, we have The filter Q is generally maintained below a value of 2. If we set Q 2 and solve for Zo we obtain If we use this impedance and the calculated resonant frequencies, we can define both inductors and both capacitors. As shown in the previous example, we can use the .Step command to sweep the values of the damping capacitor and the damping resistor. If we use a range of 3 to 5 times the value of...

## Defining the Negative Resistance

The negative resistance of the power circuit can be defined by looking at the following conditions The input resistance is negative because as the input voltage increases, the input current decreases. As a simple example, we can use PSpice to analyze the input resistance of the power circuit. PSpice can analyze the input resistance in a number of ways. The simplest method is the transfer function (.TF) analysis, which calculates the DC gain and the small signal input and output impedance. The...

## SPICEBased Analyses Types Used in This Book Operating point analysis

Produces the operating point of the circuit, including node voltages and voltage source currents. The DC analysis determines the quiescent DC operating point of the circuit with inductors shorted and capacitors opened. A DC analysis, Figure 1.1 The transfer function for the PSpice switch with hysteresis (selem), voltage-controlled resistor (switch), and the PSpice smooth transition switch (PSW1). Figure 1.1 The transfer function for the PSpice switch with hysteresis (selem), voltage-controlled...

## Using and Testing the Saturable Core

.PRINT TRAN V(3) V(6) I(VM1) V(4) R1 4 3 100 RL 2 0 50 X1 1 0 6 CORE Params VSEC 25U IVSEC -25U LMAG 10MHY + LSAT 20UHY FEDDY 25KHZ X3 3 0 2 0 XFMR Params RATIO .3 VM13 1 * Use the above statement for Square wave excitation * Use the above statement for Sin wave excitation * Adjust Voltage levels to insure core saturation .END Figure 2.27 Saturable core test circuit schematic. I(V3) I(VM1). The test circuit shown in Fig. 2.27 can be used to evaluate a saturable core model. Specify the core...

## 2n R6C3

The DC gain of the modulator is approximated by The regulator is configured as an open-loop model in order to measure the Bode response. Inductor L2 is set to 1 H in order to effectively open the loop. The plots in Figs. 4.4, 4.5, and 4.6 show the modulator gain (VM(10) VM(9) and VP(10) - VP(9), where VM is the magnitude and VP is the phase), the error amplifier gain (V(9)), and the overall loop gain (V(10)), respectively. In the next simulation, the loop is closed in order to simulate the...

## SPICE 3 Compatible Core Model

A magnetic core model has three major elements permeability, hysteresis, and core loss. Unfortunately, both the permeability and the core loss are nonlinear functions. The models in this chapter properly represent the nonlinear permeability and the hysteresis. 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....

## Calculating Core Parameters

The saturable core model is defined 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 final 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, i, and Bm, and would be more useful for studying previously designed...

## Switch Elements SW Elements

Switches are a key part of most power electronics simulations. Switches are frequently used to replace a semiconductor in order to speed the simulation. PSpice includes three different switches whose characteristics make them suitable for different applications. One of the most frequently used is the switch with hysteresis. If your simulator supports all the standard Berkeley SPICE 3 elements, then this switch can be used without any syntax changes. This type of switch has only recently been...

## Nonlinear Dependent Sources B E and G Elements

The arbitrary dependent source B element allows an instantaneous transfer function to be written as a mathematical expression. This B element is a standard Berkeley SPICE 3 element. The expressions, EXPR , given for V and I may be any function of node voltages, currents through any element, or a variety of traditional math functions. In PSpice, the E- and G-controlled source elements are utilized Format BnameN N - I EXPR V EXPR SPICE 3 Examples B1 0 11 sqrt cos v 1 v 2,3 B4 outp outn V exp i...

## EMI Filter Design

Nearly all power circuits contain an input electromagnetic interference EMI filter. The main purpose of the EMI filter is to limit the interference that is conducted or radiated from the power circuit. Excessive conducted or radiated interference can cause erratic behavior in other systems that are in close proximity of, or that share an input source with, the power circuit. If this interference affects the power circuit, it can cause erratic operation, excessive ripple, or degraded regulation,...

## SPICE 2 Compatible Core Model

A saturable reactor is a magnetic circuit element consisting of a single coil wound around a magnetic core. The presence of a magnetic core drastically alters the behavior of the coil by increasing the magnetic flux and confining most of the flux to the core. The magnetic flux density, B, is a function of the applied MMF, which is proportional to ampere turns. The core consists of many tiny magnetic domains that are made up of magnetic dipoles. These domains set up a magnetic flux that adds to...

## Ferrite Cores

The same principles apply to ferrite cores as well as MPP cores. In this example, a model is generated for ferrite F material. Again, trial-and-error and curve-fitting techniques may be used in order to obtain a closed-form expression of percent permeability versus magnetizing force. Graphical data are provided in the Magnetics Ferrite Data Book. 2 5 10 20 50 100 200 H - Oersteds in Volts 55121 MPP Core with 21 Turns Figure 2.30 Permeability versus magnetizing force. 2 5 10 20 50 100 200 H -...

## Ideal Components in SPICE

The built-in models in SPICE provide reasonable first-order approximations for circuit behavior. Unfortunately, most circuits must be designed to be tolerant of second-order effects, at a minimum, and must occasionally provide compensation in order to achieve a desired performance level. Most frequently, the parasitic and second-order effects are related to changes in frequency. It may not be clear, especially to novice SPICE users, that when you use a passive component, such as an inductor or...

## Low Dropout Linear Regulator

Power converters typically have multiple outputs. In some cases, the regulation is good enough, so that postregulation is not required. In many applications, the regulation requirement demands the use of postregulators for the secondary outputs. Simple three-terminal regulators may be used in the vast majority of applications however, many applications are sensitive to the efficiency of the converter. A good example of this can be seen in the notebook computer and other battery-powered...

## PSpice SPICE 3 and Other Spice Extensions

The majority of the models and circuit elements in this book utilize SPICE 2G.6 syntax. Wherever possible, generic syntax is used so that the models can be adapted to various simulators. However, some key elements are modeled using PSpice specific and or Berkeley SPICE 3 syntax extensions. In particular, SPICE 3 has an arbitrary dependent source, or B element, that allows mathematical expressions of voltages, currents, and other quantities to be used. PSpice extends the syntax of the E- and...

## Flyback Converters

The flyback converter has long been popular for low-power applications. The major attraction of the flyback topology is its low component count. At higher power levels, the output capacitor ripple current is often too great to deal with using conventional, low-cost capacitors. Dynamic response is also limited in continuous conduction mode, because of a right-half-plane RHP zero in the transfer function. In the flyback topology, energy is stored in a power inductor which often has multiple...

## Buck Topology Converters

Many power converters in use today are based on buck topologies. The buck topology includes all converters that produce an output voltage which is proportional to a controlled duty cycle. The switched voltage is averaged by an L-C filter, which results in a DC voltage. Examples of buck topologies include buck regulators, forward converters, and push-pull converters. The circuit shown in Fig. 4.1 is the simplest form of a buck regulator. The circuit was popular in the 1970s because of its...