PWM Signal Analyzer
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PWM Spectrum
For a PWM signal, the information is represented by variations in the pulse width (duty cycle) according to the message signal. The PWM signal can be represented as a periodic pulse train whose pulse width varies with time.
\[ s_{PWM}(t) = \sum_{n=-\infty}^{\infty} A\,\mathrm{rect} \left( \frac{t-nT_c-\tau(t)}{T_p} \right) \]
For a sinusoidal message, the PWM spectrum contains the carrier frequency and its harmonics, together with sidebands produced by the message signal.
\[ f = kf_c \pm nf_m \]
Frequency Components
Therefore, the PWM spectrum can contain components around integer multiples of the carrier frequency:
\[ \boxed{f = kf_c \pm nf_m} \]
where \(k = 0,\pm1,\pm2,\ldots\) and \(n = 1,2,3,\ldots\)
Here, \(f_c\) is the carrier (pulse) frequency and \(f_m\) is the message frequency. Unlike PAM, where the message information is carried by pulse amplitude, PWM carries the information through variations in pulse width. The spectrum therefore consists of the carrier and harmonic components with sidebands spaced by the message frequency.