** 1-phase voltage source inverter** produces square shaped output voltage for a 1-phase load. Such inverters have very simple control logic and the power switches need to operate at much lower frequencies compared to switches in some other types of inverters. The first generation inverters, using **thyristor** switches, were almost invariably square wave inverters because thyristor switches could be switched on and off only a few hundred times in a second.

Present-day switches like **IGBT**s are much faster and used at switching frequencies of several kilohertz.**1-phase voltage source inverters** mostly use half bridge or full bridge topologies. Power circuits of these topologies are redrawn.

1-phase square voltage source inverter is divided into two types

**1- Phase Half Bridge Voltage Source Inverter****1- Phase Full Bridge Voltage Source Inverter**

## 1- Phase Half Bridge Voltage Source Inverter

In half-bridge voltage source inverter the single-phase load is connected between the mid-point of the input dc supply and the junction point of the two switches these points are marked as ‘O’ and ‘A’ respectively. For ease of understanding, the switches Sw1 and Sw2 may be assumed to be controlled mechanical switches that open and close in response to the switch control signal.

If the switches Sw1 and Sw2 are turned on alternately with a duty ratio of each switch kept equal to 0.5, the load voltage (V_{AO}) will be a square wave with a peak-to-peak magnitude equal to input dc voltage (E_{dc}).

Fig shows a typical load voltage waveform output by the half-bridge inverter. V_{AO} acquires a magnitude of +0.5 E_{dc} when Sw1 is on and the magnitude reverses to -0.5 E_{dc} when Sw2 is turned on.

**The** **fundamental frequency component of the square wave voltage, its peak-to-peak magnitude= 4/π E _{dc}.**

The two switches of the inverter leg are turned on in a complementary manner. For a general load, the switches should neither be simultaneously on nor be simultaneously off. The simultaneous turn-on of both the switches will amount to short circuit across the dc bus and will cause the switch currents to rise rapidly. For an inductive load, containing an inductance in series, one of the switches must always conduct to maintain continuity of load current.

**Harmonic Analysis of The Load Voltage And Load Current Waveforms**

The load voltage waveform shown in Fig can be mathematically derived in terms of its Fourier’s components as:

where ‘n’ is the harmonic order and w /2π is the frequency (f) of the square wave. ‘f’ also happens to be the switching frequency of the inverter switches.

Fundamental frequency component has a peak magnitude = 2/π E_{dc}

**For n ^{th} harmonic voltage has a peak magnitude = 2/nπ E_{d}**

The current waveforms in such loads have less higher-order harmonic distortion than the corresponding distortion in the square-wave voltage waveform. A simple time-domain analysis of the load current for a series-connected R-L load has been presented below to corroborate this fact. Later, for comparison, frequency domain analysis of the same load current has also been done.

## 1-Phase Full Bridge Voltage Source Inverter

The single-phase full-bridge circuit can be thought of as two half-bridge circuits sharing the same dc bus. The full-bridge circuit will have two pole-voltages (V_{AO} and V_{BO} ), which are similar to the pole voltage V_{AO} of the half-bridge circuit. Both V_{AO} and V_{BO} of the full-bridge circuit are square waves but they will, in general, have some phase difference shows these pole voltages staggered in time by ‘t’ seconds.

It may be more convenient to talk in terms of the phase displacement angle ‘Φ’ defined as below

where ‘t’ is the time by which the two pole voltages are staggered and ‘T’ is the time period of the square wave pole voltages.

**Harmonic Analysis of The Load Voltage And Load Current Waveforms**

The pole voltage V_{AO} of the full-bridge inverter may again be written as given below, used earlier for the half-bridge inverter. Taking the phase shift angle ‘Φ’ into account, the pole-B voltage may be written as

The difference between V_{AO} and V_{BO} gives the line voltage V_{AB}. In full-bridge inverter, the single-phase load is connected between points ‘A’ and ‘B’, and the voltage of interest is the load voltage V_{AB}. Taking the difference of the voltage expressions given by

The n^{th} harmonic component in V_{AB} may similarly be written as

As the phase shift angle changes from zero to 1800 the width of voltage pulse in the load voltage waveform increases. Thus the fundamental voltage magnitude is controlled by pulse-width modulation.

It may be seen that the line voltage distortion due to higher order harmonics for pulse width modulated waveform (except for Φ = 180^{0}) is less than the corresponding distortion in the square wave pole voltage. In fact, for some values of phase shift angle (Φ) many of the harmonic voltage magnitudes will drastically reduce or may even get eliminated from the load voltage. For example, for Φ = 60^{0} the load voltage will be free from 3rd and multiples of third harmonic.