page_title: Power electronics
section_title: Single-phase half-bridge inverter
hierarchical_section_title: Power electronics / DC/AC converters (inverters) / Single-phase half-bridge inverter
caption_attribution_description: Single-Phase Half-Bridge Voltage Source Inverter
context_page_description: Power electronics is the application of solid-state electronics to the control and conversion of electric power.
  The first high power electronic devices were mercury-arc valves. In modern systems, the conversion is performed with semiconductor switching devices such as diodes, thyristors, and power transistors such as the power MOSFET and IGBT. In contrast to electronic systems concerned with transmission and processing of signals and data, in power electronics substantial amounts of electrical energy are processed. An AC/DC converter is the most typical power electronics device found in many consumer electronic devices, e.g. television sets, personal computers, battery chargers, etc. The power range is typically from tens of watts to several hundred watts. In industry a common application is the variable speed drive that is used to control an induction motor. The power range of VSDs start from a few hundred watts and end at tens of megawatts.
  The power conversion systems can be classified according to the type of the input and output power
  AC to DC
  DC to AC
  DC to DC
  AC to AC
context_section_description: The single-phase voltage source half-bridge inverters, are meant for lower voltage applications and are commonly used in power supplies. 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. As Figure 9 illustrates, only one switch can be on at time in each leg of the inverter. If both switches in a leg were on at the same time, the DC source will be shorted out.
  Inverters can use several modulation techniques to control their switching schemes. The carrier-based PWM technique compares the AC output waveform, vc, to a carrier voltage signal, vΔ. When vc is greater than vΔ, S+ is on, and when vc is less than vΔ, S- is on. When the AC output is at frequency fc with its amplitude at vc, and the triangular carrier signal is at frequency fΔ with its amplitude at vΔ, the PWM becomes a special sinusoidal case of the carrier based PWM. This case is dubbed sinusoidal pulse-width modulation (SPWM).For this, the modulation index, or amplitude-modulation ratio, is defined as mₐ = vc/v∆ .
  The normalized carrier frequency, or frequency-modulation ratio, is calculated using the equation mf = f∆/fc .
  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, mₐ, exceeds 3.24, the output waveform of the inverter becomes a square wave.
  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. The fundamental AC output amplitude is equal to vₒ₁ = vaN = 2vᵢ/π .
  Its harmonics have an amplitude of vₒₕ = vₒ₁/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.
  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. Any undesirable odd (N-1) intrinsic harmonics from the output waveform can be eliminated.
caption: FIGURE 9: Single-Phase Half-Bridge Voltage Source Inverter
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