The choice of the PWM-switching frequency (or referred in some literature as carrier frequency) \$F_{PWM}\$ is of utmost importance in an inverter, especially in a setting where non-electrical factors may be significant as well.
- The switching frequency determines the rate at which on-off processes of the switches (MOSFETs, IGBTs, etc.) in an inverter will occur. This frequency is decided by multiple factors and is also limited by the kind of switches employed.
- \$F_{PWM}\$ can be imagined as the frequency at which the reference signal (which in the case of a 3-phase inverter may be a sinusoidal wave) is sampled. As one may deduce, a higher \$F_{PWM}\$ would correspond to a more accurate sampling of the reference signal with minimal loss of the signal.
- The average output voltage \$\bar{U_{u,0}}\$ of a Phase U w.r.t to a middle neutral (generally GND) point \$0\$can be termed as: \$ \bar{U_{u,0}} = \bar{s_u} \cdot \frac{U_{DC}}{2} \$ where \$s_U\$ is the switching function, which can assume the value +1 when the high-side switch is on and -1 when the low-side switch is on.
- In terms of the switch on time, the output voltage can be seen as: \$ \bar{U_{u,0}} = (\frac{2\cdot t_{on}}{t_{PWM}} -1) \cdot \frac{U_{DC}}{2} \$. This equation may invoke a false impression that the order of these times may not really come to play since when the reference signal is sinusoidal, irrespective of the switching frequency the fundamental WILL be sinusoidal as well.
- However, one must also consider the effects of harmonics on the output voltage, which contribute to the block-like nature of the output voltage. Had there not been any harmonics except the fundamental, the output voltage would be perfectly sinusoidal and we could solve all the world's problems. This is unfortunately not the case.
- A general equation of the output voltage can be seen as:
\$[ U_{u,0}(t) = \frac{U_{DC}}{2} \cdot \sum_{n=-\infty}^{\infty} c_{n} e^{j2\pi n f_{REF} t} \$]. In this equation, the amplitude \$c_n\$ of the nth harmonic, is inversely proportional to \$F_{PWM}\$. The occuring higher order harmonics start reducing with increasing PWM-frequency. This leads to a smoother output voltage. The illustration below shows the Fourier spectrum when \$ F_{PWM} = 6 \cdot F_{REF}\$:
Similarly, the illustration below shows the Fourier spectrum when \$ F_{PWM} = 30 \cdot F_{REF}\$:
As may be evident, the spectrum is fairly widely or rather evenly distributed in the second case, with higher harmonics having lower amplitudes in the Frequency range around the reference signal. Moreover, the higher order harmonics can be safely filtered out via a low-pass filter, thereby leading to a potentially highly sinusoidal output voltage with a lot less disturbance. This filtering is harder in the first illustration since the unwanted harmonics are so close to the actual output frequency.
- The above results can be even enhanced by employing a ratio \$q\$ (\$ F_{PWM} = q \cdot F_{REF}\$)in the multiples of 3, which will cancel out multiple out of phase harmonics amongst the three phases. The exact working of such mechanisms is out of scope of this answer.
- Finally, it must be noted that a discretionary high switching frequency may not be chosen since a higher switching freqeuncy leads to a higher switching loss due to the non-idealness of the switch. Moreover, in the case of inverters in an automobile, the switching frequency must be chosen so that it is not in the hearing range of the human ear (which may go upto 20KHz) otherwise during a drive, a switching buzz can be audible which may lead to an unpleasant driving experience.
Wrapped up, a higher switching frequency is essential in building up an output signal faithful to the reference signal. The switch on times of the MOSFET will play a major role in the value of the output votlage, with a higher carrier signal frequency resulting in a magnitude-wise smaller switch-on time per period of the PWM. This factor may not be directly evident in the output signal or even in the equation of the output signal, however is brought to light once the fourier Analysis of the outptu waveform is observed. The choice of this switching frequency is controlled by multiple factors such as losses and use case.
