EC-12.5 Rectifiers, DC-DC Converters and Inverters

What this is and why it exists

This is the topic that connects a wall socket to every device a reader owns.

It is also the one that makes the device material pay. The three basic switching converters are worth learning as one idea in three arrangements, because that is how they are actually derived. It also makes a fourth and fifth arrangement readable without being taught.

The vocabulary

• Rectifier — a circuit converting alternating to direct voltage.
• Ripple — the residual variation left on a rectified output.
• Firing angle — the delay before a thyristor is turned on in each cycle.
• Duty ratio — the fraction of each switching period for which the switch is on.
• Volt-second balance — the rule that an inductor's voltage must average zero in steady state.
• Continuous conduction — operation in which inductor current never reaches zero.
• Discontinuous conduction — operation in which it does.
• Inverter — a circuit converting direct to alternating voltage.
• Pulse width modulation — varying pulse widths so that the average follows a wanted shape.

The mental model

Start with the rectifier, because it is the front of almost everything. Four diodes in a bridge turn an alternating voltage into a pulsating direct one, and a capacitor across the output smooths it.

The capacitor is where the interesting consequences live. A larger capacitor gives less ripple and draws the current in shorter, taller pulses, because it only takes charge near the peak of each cycle.

Those pulses are why an unsophisticated supply has a poor power factor and injects harmonics. They are also why the diodes must be rated far above the average current. It is a good early example of a design choice whose cost appears somewhere other than where the choice was made.

Controlled rectification replaces the diodes with thyristors and delays their firing within each cycle. The later the firing, the lower the average output. It was the standard method of control for decades and works directly from an alternating supply. It also distorts the supply current badly, which is why it is now regulated.

Now the switching converters, and the derivation worth learning once. Take a switch, a diode, an inductor and a capacitor. In steady state the inductor's average voltage must be zero over a cycle, because otherwise its current would grow without limit.

Write that balance and the output ratio falls out in one line. For the step-down arrangement, the output is the input times the duty ratio. That is the whole derivation, and it is more useful than the formula because it works for arrangements you have not seen.

Move the same four parts into different positions and you get a converter whose output exceeds the input. Another arrangement gives an output of the opposite polarity. Deriving each by volt-second balance takes a minute and removes the need to memorise three separate results.

Conduction mode is the complication that catches people out. The derivations above assume the inductor current never falls to zero.

If it does, the diode stops conducting for part of the cycle, and the output no longer depends only on the duty ratio. It now depends on the load as well, which means a converter that behaved predictably at full load behaves differently at light load. Knowing which mode a converter is in explains a good deal of otherwise puzzling behaviour on the bench.

The inverter is the last arrangement and the most satisfying. Switching a direct supply alternately between two polarities produces a square wave, which is an alternating output of a very crude kind.

Varying the width of each pulse across the cycle is what turns it into something useful. Make the pulses wide where the wanted sinusoid is large and narrow where it is small, and the local average follows the sinusoid. A filter then removes the switching frequency and leaves it.

That is pulse width modulation, met earlier as a way of producing an analog output from a microcontroller. It is the same idea at a thousand times the power, and recognising it as the same idea is worth more than either treatment alone.

What you should now be able to explain or do

• Analyse a rectifier with a capacitor filter and explain the shape of its input current.
• Say what controlled rectification achieves and what it costs the supply.
• Derive the output of a switching converter from volt-second balance rather than a formula.
• Recognise the step-down, step-up and inverting arrangements as the same parts rearranged.
• Say what changes when a converter enters discontinuous conduction.
• Explain how pulse width modulation turns a direct supply into a sinusoidal output.

Check yourself