Basic Power Conversion Examples | Power Circuits

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Basic Power Conversion Examples

February 6, 2015 admin Leave a comment

Let’s look at a few examples of power electronic systems.

Consider the circuit shown below. It contains an AC source, a switch, and a resistive load. It is therefore a simple but complete power electronic system.

Just to get an idea of how power conversion might take place, let us assign some kind of control to the switch. What if the

switch is turned on whenever , and turned off otherwise? The input and output voltage waveforms are illustrated

below. The input has a time average of 0, and an RMS value equal to . The output has a nonzero average

value given by

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Basic Power Conversion Examples | Power Circuits

A very simple power electronic system described in the first example.

and an RMS value equal to . The output has some DC voltage content. The current can be thought of as an AC-DC converter

Input and output waveforms for the example circuit.

The circuit example above is a half-wave rectifier with a resistive load. A diode can be substituted for the switch. The

example shows that a simple switching current can perform power conversion functions. But, notice that a diode is not, in

general, the same as the switch. A diode places restrictions on the current direction, while a true switch would not. An ideal

switch allows control over whether it is on or off, while a diode’s operation is constrained by circuit variables. Consider a

second half-wave circuit, now with a series L-R (inductor-resistor) load, shown below.

Half-wave rectifier with R-L load described in second example.

A series D-L-R (diode-inductor-resistor)

circuit has AC voltage-source input. This

circuit operates much differently than the half-

wave rectifier with resistive load. Remember

that a diode will be on if forward biased, and

of if reversed biased. In this circuit, an off

diode will give . Whenever the diode

is on, the circuit is the AC source with R-L

load. Let the AC voltage be %latex V_0 cos(\omega t)$. From Kirchoff’s Voltage Law,

Let us assume that the diode is initially off (this assumption is arbitrary, and we will check it out as the example is solved). If the diode is off, , and the

voltage across the diode . The diode will become forward-biased when becomes positive. The diode will turn on when the input voltage makes

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Basic Power Conversion Examples | Power Circuits

a zero-crossing in the positive direction. This allows us to establish initial conditions for the circuit: . The differential

equation can be solved with conventional methods. Though one is able to solve such equations in closed form by hand, it is generally much simpler to evaluate

with modern symbolic computer programs such as Mathematica. Other, more complex problems, must be solved numerically. In this case, the somewhat

complex result is

where is the time constant . What about diode turn-off? One first guess might be that the diode turns off when the voltage becomes negative, but this is

not correct. We notice from the solution that the current is not zero when the voltage first becomes negative (check this for yourself!). If the switch attempts to

turn off, it must drop the inductor current to zero instantly. The derivative of current in the inductor, , would become negative infinite. The inductor

voltage similarly becomes negative infinite – and the devices are destroyed. What really happens is that the falling current allows the inductor

to maintain forward bias on the diode. The diode will turn off only when the current reaches zero. A diode has very definite properties that determine the

circuit action, and both the voltage and current are relevant.

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Basic Power Conversion Examples | Power Circuits

● Background● Goals and Methods● History● Switches● Waveforms

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● Overview of Switching Devices● Review of Fourier Series● Characteristics of Power Semiconductor Devices● Kirchhoff’s Voltage and Current Laws● Introduction to Switches

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