User:Abduselam Hamid/sandbox

Random pulse width modulation is a modulation technique introduced for mitigating electromagnetic interference (EMI) of power converters by spreading the energy of the noise signal in to wider bandwidth so that no significant peaks of the noise could exist. This is achieved by randomly varying the main parameters of the Pulse Width Modulation signal.

Description
Electromagnetic interference (EMI) filters are widely used for filtering out the conducted emissions generated by power converters. However, when size is a great concern like aircraft and automobile applications one of the practical solutions to suppress conducted emissions is to use random pulse pidth Modulation (RPWM). In conventional pulse width modulation (PWM) schemes, the harmonics power is concentrated on the deterministic or known frequencies with a significant magnitude, which leads to mechanical vibration, noise, and EMI. However, by applying randomness on the conventional PWM scheme, the harmonic power will spread out so that no harmonic of significant magnitude exists, and peak harmonics at discrete frequency are significantly reduced.

In RPWM, one of the switching parameters of the PWM signal, such as switching frequency, pulse position and duty-cycle are varied randomly in order to spread the energy of the PWM signal. Hence, depending on the parameter which is made random, RPWM can be classified as Random Frequency Modulation (RFM), Random Pulse Position Modulation (RPPM) and Random Duty-Cycle Modulation (RDCM).

The properties of the RPWM can be investigated further by looking at the power spectral density (PSD). For conventional PWM, the PSD can be directly determined from the Fourier Series expansion of the PWM signal. However, the PSD of the RPWM signals can be described only by a probabilistic level using the theory of stochastic processes such as wide-sense stationary (WSS) random processes.

RFM
Among the different RPWM techniques, RFM is the most common one which is being used in many power converter topologies to pass the electromagnetic compatibility (EMC) test. In this type of modulation, the switching frequency of the PWM signal is varied randomly in order to spread the noise coming out of power converters. RFM is very easy to implement and it offers significant reduction of the noise peaks compared to conventional PWM. However, application is limited to power converters which does not require fixed switching frequency for their normal operation. Besides, higher switching frequency variation can affect the proper functioning of the devices and components inside the power converter circuit.

RPPM
RPPM is also commonly deployed in power converters to pass the EMC compliance tests. This modulation techniques also offers significant reduction of the conducted emission and hence radiated emission of power converters. However, compared to RFM, RPPM is less effective in EMI reduction. This is because, the PSD of RPPM contains both the density and harmonic parts and the spectrum can not be fully spread unlike that of RFM where the spectrum has only density part. However, in this modulation scheme, both the switching frequency and the pulse width are fixed so that the converter components like inductors and capacitors can function properly.

RDCM
In RDCM, the pulse width or the duty cycle of the PWM signal is varied randomly in order to spread the noise spectrum. This kind of modulation is less common compared to the previous ones. This is because RDCM is less effective at spreading the noise. Moreover, randomly varying the duty cycle may cause output voltage fluctuations and ripples. Besides, in some power converter topologies, duty cycle is being used for controlling the input-output voltages and currents using closed loop control systems.

Coexistence issue
RPWM techniques are very effective in reducing the EMI of power converters. However, when power converters with this special type of modulation coexist with communication systems, there may be a severe electromagnetic interference and coexistence issue to the communication system. This detrimental effect can be observed in power line communication (PLC) systems, where both power converters and communication system coexist. Indeed, recent studies confirmed that RPWM, applied to power converters to minimize conducted emissions, detrimentally interfere with the PLC system. The interference can be worse when the switching frequency and the bandwidth of the PLC system overlaps. Practically, most of power converters switching frequency is below 150 kHz. This could cause coexistence issue mainly in narrow band PLC systems, specially PLC protocols which are being used for smart grid application, like Prime PLC and G3-PLC, in frequencies below 150 kHz. In conventional PWM, the noise from power converter overlaps with the PLC frequency band at discrete multiples of the switching frequency only. This results less interference to the PLC system. However, In RPWM, the noise is more spread and both the PLC and the noise from power converter shares wider bandwidth. This creates more disturbance to the PLC system. Therefore, it is recommended to choose non-overlapping switching frequencies for randomly modulated power converters in application where PLC systems coexist.