The three-level SPWM wave can be obtained by the two-level SPWM wave through the phase-shifting and superposition method, as shown in Figure 1. There are two phase-shifting and superposition methods: one is to first shift the phase of the sinusoidal modulation wave by 360°/2=180°, as shown in Figure 1(b), and then compare it with the same carrier triangle wave to obtain two two-phase Flat SP WM wave. And u_{Aa} and u_{Ab}, use u_{Aa}-u_{Ab}=u_{A} to get the three-level SPWM wave; the other is to first shift the carrier triangle wave by 360°/2=180°, as shown in Figure 1(c), and then the same The sinusoidal modulation wave is compared, and two two-level SPWM waves u_{Aa} and u_{Ab} are obtained. Use u_{Aa}-u_{Ab}=u_{A} to obtain the three-level SPWM wave. Comparing Figure 1 (b) and (c), we can see that the three-level SPWM waveforms obtained by these two phase-shifting and superposition methods are exactly the same.

The following specifically introduces an application example of using a sine modulation wave to shift the phase by 180° to obtain a three-level SPWM wave with a dead zone. The working waveform is shown in Figure 2. In order to simplify the analysis, equation (1) can be used, when φ=0, we can get

The Fourier series expression of u_{Ab} is derived as follows.

because

So have

When n=0, there is

When m=0, it is the same as the two-level SPWM wave derivation, when n>1, there is A_{0n}+jB_{0n}=0.

When n=1, there are A_{01}=0, B_{01}=-ME, and we get

because

also because

When n=0 is an odd number, cos(nπ/2)=0, so

Obviously, when n is an even number, sin²(nπ/2)=0; when n is an odd number, sin²(nπ/2)=1. When m is an even number, cos(mπ/2)=(﹣1)^{(m/2)}; when m is an odd number, cos(mπ/2)=0.

It should be noted here that: since the frequency f_{c single }of the unipolar carrier triangle wave is twice as large as the frequency f_{c double} of the bipolar carrier triangle wave, that is, f_{c single }= 2f_{c doubl}e, so the F _{single}, m _{single }and double of the unipolar SPWM The relationship between F _{double }and m _{double }of the polarity SPWM is F _{single} = 2F _{double}, m _{single }= (1/2) m _{double}. Substituting the value of F into the above formula can obtain the double Fourier series expression of the unipolar SPWM three-level SPWM wave as

This formula shows: by the phase-shifting superposition method of subtracting two two-level SPWM waves with a sine modulation wave 180°, one f_{c single} = 2f_{c} _{double}, that is, F _{single }= F _{double}, m _{single }= (1/2) m _{double }(that is, F _{single }is an even number) three-level SPWM wave. In the two two-level SPWM waves, the carrier harmonics, the odd multiples of the carrier harmonics, and their upper and lower side frequencies are all eliminated.

The sine modulation wave is phase-shifted by 180° and superimposed to obtain the control circuit of the three-level SPWM wave, as shown in Figure 3.

If you use a subtractor to output, you use the drive signal for phase-shifting and superposition; if you use a high-speed comparator to output, you use the two bridge arms of the inverter’s main circuit for phase-shifting and superimposing.

In order to obtain the three-level SPWM wave by the phase-shifting and superposition method, the carrier ratio F _{single} must be an even number. Because F_{ single} = 2F_{ double}, F _{double }is an integer, so F _{single }is even.

Equation (10) is an expression of the three-level SPWM wave double Fourier series obtained by the phase-shifting and superposition method considering the existence of the dead zone. Among them, 1+e^{jm△t} increases with the increase of m and △t. When the existence of the dead zone is not considered, △t=0,1+e^{jm△t}=2 in the formula, and substituting this result into the formula (10), the double Fourier series expression without dead zone u_{A} can be obtained as