This is the simplest configuration, as shown in Figure 3 , using a single switching cell with two complementary switches [3] .

The diodes are placed in parallel with the transistors. Their role is to ensure current continuity. This is because an inductive load cannot withstand a sudden interruption in current. So, after Q₁ has blocked, the I_ch current continues to flow through the D₂ diode, which conducts spontaneously.

When transistor Q₁ conducts, the load sees a voltage V_ch = E/2. The current Ich grows exponentially according to a time constant.

When transistor Q₁ is blocked, diode D₂ starts conducting to ensure current continuity. The load then sees a voltage V_ch = E/2. The current Ich then decreases. When the current passes through 0, a control signal is sent to the base of Q₂. The 𝐷₂ diode blocks and the I_ch current continues to increase in the opposite direction. When Q₂ blocks, diode D₁ takes over and the load again sees a voltage V_ch = E/2.

When the current passes through 0, Q₁ is made to conduct and the cycle resumes.

When the current passes through 0, Q₁ is made to conduct and the cycle resumes.

Its structure is simple and economical, with only two controlled switches and two diodes, a single switch passing at each instant so reduced voltage drop.

Its main disadvantage is that the switch blocking voltage is twice the maximum voltage at the load terminals. In addition, the power can only be adjusted by pulse width modulation; the switching frequency is then 6 to 10 times that of the fundamental of the load.

The voltage-controlled inverter configuration shown in Figure 4 consists of a stable DC bus, full-bridge switches, an LC low-pass filter and a resistive load R representing the power consumers. Unipolar SPWM (sinusoidal pulse width modulation) signals are generated by the controller and applied to drive the full bridge switches.

Mathematically, this DC-AC inverter can be modelled as a second-order system.

Given that the voltage across the inductor is given by the relation:

$V_L=L\frac{\text{d}{i}_L}{\text{d}t}$ (1)

In steady state, the output voltage V in can be expressed as follows:

Since the voltage V in is equal to VL + V₀, we can write

$V_0=L\frac{\text{d}\left(\frac{V_0}{R}+C\frac{\text{d}{V}_0}{\text{d}t}\right)}{\text{d}t}+V_0$ (2)

$LC\frac{{\text{d}}^2{V}_0}{\text{d}t}+\frac{L}{R}\frac{\text{d}{V}_0}{\text{d}t}+V_0=V_{in}$ (3)

On the basis of Equation (3), a representation of the state space of this dynamic system can be obtained using a function in the form of a state vector

$\left[\begin{array}{c}{\stackrel{\dot{}}{V}}_0\\ \cdots \\ {\ddot{V}}_0\end{array}\right]$ (4)

So the equation describing the complete bridge is:

$\left[\begin{array}{c}{\stackrel{\dot{}}{V}}_0\\ \cdots \\ {\ddot{V}}_0\end{array}\right]=\left[\begin{array}{cc}0& 1\\ -\frac{1}{LC}& -\frac{1}{CR}\end{array}\right]\left[\begin{array}{c}{V}_0\\ {\stackrel{\dot{}}{V}}_0\end{array}\right]+\left[\begin{array}{c}0\\ \frac{1}{LC}\end{array}\right]V_{in}$ (5)

As mentioned previously, single-pole SPWM signals are applied to control this inverter. According to the control scheme, the switches of each branch of the full-bridge inverter are switched separately. Four combinations of switch activation states and corresponding voltage levels are expected as follows:

1) S₁ et S₃ sont ON: $V_{in}=0$;

2) S₁ et S₄ sont ON: $V_{in}=+V_{dc}$;

3) S₂ et S₃ sont ON: $V_{in}=-V_{dc}$;

4) S₂ et S₄ sont ON: $V_{in}=0$;

The input voltage pulse is represented in the equation and this three-valued switched voltage Vin can be expressed as follows [4] :

$V_{in}=\{\begin{array}{ll}\pm V_{dc}\hfill & \text{insides of perid}\Delta T\hfill \\ 0\hfill & \text{outside the period}\Delta T\hfill \end{array}$ (6)