Editing Power electronics (section)

=== Single-phase half-bridge inverter ===

[[File:The AC Input for a Standard Adjustable Speed Drive.jpg|thumb|left|'''Figure 8:''' The AC input for an ASD]]
[[File:Single-Phase Half-Bridge Voltage Source Inverter.jpg|thumb|left|'''FIGURE 9:''' Single-phase half-bridge voltage source inverter]]

The single-phase voltage source half-bridge inverters are meant for lower voltage applications and are commonly used in power supplies.<ref name=Rashid3 /> Figure 9 shows the circuit schematic of this inverter.

Low-order current harmonics get injected back to the source voltage by the operation of the inverter. This means that two large capacitors are needed for filtering purposes in this design.<ref name=Rashid3 /> As Figure 9 illustrates, only one switch can be on at a time in each leg of the inverter. If both switches in a leg were on at the same time, the DC source would be shorted out.

Inverters can use several modulation techniques to control their switching schemes. The carrier-based PWM technique compares the AC output waveform, v<sub>c</sub>, to a carrier voltage signal, v<sub>Δ</sub>. When v<sub>c</sub> is greater than v<sub>Δ</sub>, S+ is on, and when v<sub>c</sub> is less than v<sub>Δ</sub>, S− is on. When the AC output is at frequency fc with its amplitude at v<sub>c</sub>, and the triangular carrier signal is at frequency f<sub>Δ</sub> with its amplitude at v<sub>Δ</sub>, the PWM becomes a special sinusoidal case of the carrier based PWM.<ref name=Rashid3 /> This case is dubbed sinusoidal pulse-width modulation (SPWM).For this, the modulation index, or amplitude-modulation ratio, is defined as '''{{math|m<sub>a</sub> {{=}} v<sub>c</sub>/v<sub>∆</sub> }}'''.

The normalized carrier frequency, or frequency-modulation ratio, is calculated using the equation '''{{math|m<sub>f</sub> {{=}} f<sub>∆</sub>/f<sub>c</sub> }}'''.<ref>{{Cite book|last=Kiruthiga|first=Murugeshan R. & Sivaprasath|url=https://books.google.com/books?id=KDRlDwAAQBAJ&q=mf+%3D+f%E2%88%86%2Ffc&pg=PA918|title=Modern Physics, 18th Edition|date=2017|publisher=S. Chand Publishing|isbn=978-93-5253-310-7|language=en}}</ref>

If the over-modulation region, ma, exceeds one, a higher fundamental AC output voltage will be observed, but at the cost of saturation. For SPWM, the harmonics of the output waveform are at well-defined frequencies and amplitudes. This simplifies the design of the filtering components needed for the low-order current harmonic injection from the operation of the inverter. The maximum output amplitude in this mode of operation is half of the source voltage. If the maximum output amplitude, m<sub>a</sub>, exceeds 3.24, the output waveform of the inverter becomes a square wave.<ref name=Rashid3 />

As was true for Pulse-Width Modulation (PWM), both switches in a leg for square wave modulation cannot be turned on at the same time, as this would cause a short across the voltage source. The switching scheme requires that both S+ and S− be on for a half cycle of the AC output period.<ref name=Rashid3 /> The fundamental AC output amplitude is equal to '''{{math|v<sub>o1</sub> {{=}} v<sub>aN</sub> {{=}} 2v<sub>i</sub>/π }}'''.

Its harmonics have an amplitude of '''{{math|v<sub>oh</sub> {{=}} v<sub>o1</sub>/h}}'''.

Therefore, the AC output voltage is not controlled by the inverter, but rather by the magnitude of the DC input voltage of the inverter.<ref name=Rashid3 />

Using selective harmonic elimination (SHE) as a modulation technique allows the switching of the inverter to selectively eliminate intrinsic harmonics. The fundamental component of the AC output voltage can also be adjusted within a desirable range. Since the AC output voltage obtained from this modulation technique has odd half and odd quarter-wave symmetry, even harmonics do not exist.<ref name=Rashid3 /> Any undesirable odd (N-1) intrinsic harmonics from the output waveform can be eliminated.