In practical applications, in addition to the resistive loads mentioned in the previous article, inductive loads are often encountered, such as excitation windings of various motors, various inductive coils, etc. An inductive load contains both an inductance and a resistance, so it can be represented by an inductance L and a resistance R in series. Since the inductance hinders the change of the current, the current in the inductance cannot change abruptly. When the current flowing through the inductance changes, an induced electromotive force is generated at both ends of the inductance to prevent the current from changing. When the current increases, the polarity of the induced EMF prevents the current from increasing; when the current decreases, the polarity of the induced EMF prevents the current from decreasing. Therefore, the working conditions of the controllable rectifier circuit with an inductive load and a resistive load are quite different.

**Working principle and waveform**

The circuit diagram and waveform diagram of the single-phase half-wave controllable rectifier circuit with inductive load are shown in Figure 1.

When ωt_{1}=α, the thyristor VT is triggered and turned on, the AC voltage u_{2} is immediately added to the load (L_{d} and R_{d}), and the rectified output voltage u_{d} appears on the load immediately. However, due to the action of the inductance L_{d}, an induced electromotive force (the polarity of which is up positive and down negative in Figure 1a) is generated, which hinders the current change. The current in the inductance (that is, the load current) cannot be abruptly changed, but can only gradually increase from zero. When the current rises to a maximum value, the induced EMF is zero, and then when the current decreases, the induced EMF also changes polarity (up negative and lower positive in Figure 1a). When the AC voltage u_{2} drops to zero, due to the induced electromotive force of the inductor, the thyristor VT is still turned on by the positive voltage, even if the AC voltage u_{2} changes from zero to negative, as long as |e_{L}|>|u_{2}|, the thyristor VT is still subjected to the forward voltage, the thyristor will continue to conduct, and the rectified output voltage ud on the load will have a negative value. Until the anode current of the thyristor is less than the holding current, the thyristor VT is turned off and bears the reverse voltage immediately.

From the above analysis, a basic analysis method of power electronic circuits can be summarized. In fact, there are nonlinear power electronic devices in power electronic circuits. If the turn-on and turn-off processes are ignored, the device can be idealized, and the circuit can be simplified as a piecewise linear circuit, and each state of the device corresponds to a linear circuit topology. The above method is used for the analysis of single-phase half-wave circuit, that is, when VT is in an off state, it is equivalent to the circuit being disconnected at VT, and id=0; when VT is in an on state, it is equivalent to a short circuit at VT.

As can be seen from the waveform diagram in Figure 1, with an inductive load, the waveforms of the rectified output voltage u_{d} and current id are very different from those of a resistive load. Due to the action of the inductance L_{d}, the rectified output voltage u_{d} will have a negative voltage for a period of time, which reduces the average value of the rectified output voltage U_{d}. The larger the inductance L_{d} is, the larger the negative voltage part is, and the more the average value U_{d} of the rectified output voltage decreases. When the inductance L_{d} is large and meets the condition of ωL_{d}>R_{d} (usually ωL_{d}>10R_{d}), the positive and negative areas of the rectified output voltage ud waveform on the load are nearly equal, and the average value of the rectified output voltage U_{d}≈0. It can be seen that when a single-phase half-wave controllable rectifier circuit is used for a large inductive load, no matter how α is adjusted, the average value of the rectified output voltage U_{d} is always small, so this circuit is not actually used. When the actual single-phase half-wave controllable rectifier circuit has an inductive load, a freewheeling diode is connected in parallel at both ends of the load.