Root Mean Square Voltage in dBV and dBm Given x(t) = 1.5 cos(2Tt x 500t), -...

  

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Root Mean Square Voltage in dBV and dBm Given x(t) = 1.5 cos(2Tt x 500t), - Fourier coefficients of rectangular pulse trains Given the following time domain periodic pulse trains x(t) 1. Rectangular pulse train, Vp/p=3V, Vp=1.5V, To=2ms, duty cycle=1/2 2. Rectangular pulse train, Vp/p=3V, Vp=1.5V, To=2ms, duty cycle=1/3 3. Rectangular pulse train, Vp/p=3V, Vp=1.5V, To=2ms, duty cycle=1/4 4. Rectangular pulse train, Vp/p=3V, V-1.5V, To=2ms, duty cycle=1/5 The Fourier series representation of x(t) is given by 2n x(t) Xneinwot = co + En=1 Cn cos(nwot + 0n), wo = То Plot the first five periods of x(t) as a function of time t. Derive the complex exponential and trigonometric Fourier coefficients magnitude and phase expressions Xn & Cn of x(t) for duty cycle=1/4. i. ii. iii. Plot in two graphs Cn (dBV) & 0, (degrees) for n = 0 to 10 & duty cycle=1/2, 1/3, ¼, 1/5 color coded. Root Mean Square Voltage in dBV and dBm Given x(t) = 1.5 cos(2Tt x 500t), - Fourier coefficients of rectangular pulse trains Given the following time domain periodic pulse trains x(t) 1. Rectangular pulse train, Vp/p=3V, Vp=1.5V, To=2ms, duty cycle=1/2 2. Rectangular pulse train, Vp/p=3V, Vp=1.5V, To=2ms, duty cycle=1/3 3. Rectangular pulse train, Vp/p=3V, Vp=1.5V, To=2ms, duty cycle=1/4 4. Rectangular pulse train, Vp/p=3V, V-1.5V, To=2ms, duty cycle=1/5 The Fourier series representation of x(t) is given by 2n x(t) Xneinwot = co + En=1 Cn cos(nwot + 0n), wo = То Plot the first five periods of x(t) as a function of time t. Derive the complex exponential and trigonometric Fourier coefficients magnitude and phase expressions Xn & Cn of x(t) for duty cycle=1/4. i. ii. iii. Plot in two graphs Cn (dBV) & 0, (degrees) for n = 0 to 10 & duty cycle=1/2, 1/3, ¼, 1/5 color coded.

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