# Annual Day Script

Topics: Transformer, Diode, Transistor Pages: 27 (7342 words) Published: April 11, 2013
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Fig. 1: Buck converter circuit diagram.
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Fig. 2: The two circuit configurations of a buck converter: On-state, when the switch is closed, and Off-state, when the switch is open (Arrows indicate current as the conventional flow model). [pic]

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Fig. 3: Naming conventions of the components, voltages and current of the buck converter. [pic]
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Fig. 4: Evolution of the voltages and currents with time in an ideal buck converter operating in continuous mode. The operation of the buck converter is fairly simple, with an inductor and two switches (usually a transistor and a diode) that control the inductor converter. In the idealised converter, all the components are considered to be perfect. Specifically, the switch and the diode have zero voltage drop when on and zero current flow when off and the inductor has zero series resistance. Further, it is assumed that the input and output voltages do not change over the course of a cycle (this would imply the output capacitance as being infinite).

Concepts

The conceptual model of the buck converter is best understood in terms of an inductor's "reluctance" to allow a change in current. Beginning with the switch open (in the "off" position), the current in the circuit is 0. When the switch is first closed, the current will begin to increase, but the inductor doesn't want it to change from 0, so it will attempt to fight the increase by dropping a voltage. This voltage drop counteracts the voltage of the source and therefore reduces the net voltage across the load. Over time, the inductor will allow the current to increase slowly by decreasing the voltage it drops and therefore increasing the net voltage seen by the load. During this time, the inductor is storing energy in the form of a magnetic field.

If the switch is opened before the inductor has fully charged (i.e., before it has allowed all of the current to pass through by reducing its own voltage drop to 0), then there will always be a voltage drop across it, so the net voltage seen by the load will always be less than the input voltage source.

When the switch is opened again, the voltage source will be removed from the circuit, so the current will try to drop. Again, the inductor will try to fight against it changing, which it does by reversing the direction of its voltage and acting like a voltage source. Put another way, there is a certain current flowing through the load due to the input voltage source: in order to maintain this current when the input source is removed, the inductor will have to take the place of the voltage source and provide the same net voltage to the load. Over time, the inductor will allow the current to decrease gradually, which it does by decreasing the voltage across itself. During this time, the inductor is discharging its stored energy into the rest of the circuit

If the switch is closed again before the inductor fully discharges, the load will always see a non-zero voltage. The capacitor placed in parallel with the load helps to smooth out voltage waveform as the inductor charges and discharges in each cycle.

Continuous mode

A buck converter operates in continuous mode if the current through the inductor (IL) never falls to zero during the commutation cycle. In this mode, the operating principle is described by the plots in figure 4:

• When the switch pictured above is closed (On-state, top of figure 2), the voltage across the inductor is [pic]. The current through the inductor rises linearly. As the diode is reverse-biased by the voltage source V, no current flows through it; • When the switch is opened (off state, bottom of figure 2), the diode is forward biased. The voltage across the inductor is [pic] (neglecting diode drop). Current IL decreases. The energy stored in inductor L is

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Therefore, it can be seen that the energy stored in L increases during On-time (as IL increases) and then decreases...