## 7.6 Switching Regulator for Boost DC-to-DC Converter

### 7.6.1 Boost DC-to-DC Converter Circuit Model

Let us consider the application of the above design methodology to the problem of switching controller design for a boost DC-to-DC converter circuit as shown in Fig. 7.3.

Figure 7.3: Boost DC-to-DC converter circuit.

By Kirchhoff's voltage law we have E = V L when the transistor is ON and E = V L + V out when the transistor is OFF; hence, we get

where the state of the ideal switches (transistor and diode) is represented by the control variable u and u ? {0,1}.

The voltage drop V L across an inductor is given by , where I L is the current through the inductor with inductance L. We have for the voltage drop V C across a capacitor, where I C is the current through the capacitor with capacitance C. By Ohm's law, the voltage drop V R across a resistor is given by V R = RI R, where I R is the current through the resistor with resistance R. By KirchhofF's current law we get I Lu = I C + I R. Denote x 1 = I L, x 2 = V C. By taking into account that V R = V C = V out, we obtain the bilinear switched...

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DC-DC Converter Chips
DC-DC converter chips provide a regulated DC voltage output from a different, unregulated input voltage.&nbsp;
Switching Power Supplies
Switching power supplies are DC sources that use a switching element (normally a power transistor) to generate the desired voltage. Switching power supplies are also called switch-mode products or switching mode power supplies (SMPS).
IC Voltage Regulators
IC voltage regulators are three-terminal devices that provide a constant DC output voltage that is independent of the input voltage, output load current, and temperature. IC voltage regulators are used in power supplies that hold their output voltage constant over a wide range of load variations.
IC Switching Voltage Regulators
IC switching voltage regulators are integrated circuits (ICs) that store energy in an inductor, transformer, or capacitor and then use this storage device to transfer energy from the input to the output in discrete packets over a low-resistance switch.
DC Power Supplies
DC power supplies accept an input power and output the desired form of DC power. Common types of DC power supplies include linear power supplies, switching power supplies, DC-DC converters, and silicon controlled rectifier (SCR) type power supplies.

##### Topics of Interest

7.7 Notes As shown above, the analysis of the realizability of the desired output behavior for the dynamic system given by (7.1) (7.2) requires a more careful investigation of the intrinsic...

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