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# AE_Lecture4_PartD2_Line Spectrum of a Pulse Train.

Module by: Bijay_Kumar Sharma. E-mail the author

Summary: This Lecture4_PartD2 analyzes the line spectrum of a pulse train with an offset voltage, pulse duration TAU ,pulse period 'T' and pulse height Vo.

Analog Electronics_Lecture4_PartD

Experimental Methods of measuring

the Frequency Band-Width of an Amplifier.

1. FREQUENCY SPECTRUM OF A PULSE TRAIN.

Let us look at the spectrum of a pulse train

Figure 6. A pulse train, offseted with respect to the time axis.

In the above Figure we represent a pulse train of Pulse Repetition Frequency = 1/T

and duty cycle of (τ/T)×100 percent and pulse duration of τ secs and pulse height of Vo.

Let us find out the FOURIER SERIES EXPANSION of the pulse train shown in the above figures.

FOURIER SERIES METHOD states that :

Any time periodic function contains a D.C. component , contains a fundamental frequency fo =(1/T) and its harmonics.

In terms of phasors(a rotating vector)

Figure 7. Two oppositely rotating vectors are shown. These rotating vectors are known as Phasors.

Here an = a-n are magnitudes of the nth Harmonic oppositely rotating phasors.

This gives the double sided spectrum.

Figure 8. Frequency Spectrum of a pulse train.

A signal has a frequency spectrum. For a periodic signal we use FOURIER SERIES techniques. For a non-periodic signal we use FOURIER-TRANSFORM techniques.

If a signal passes through an infinite Band Width system we are able to maintain 100% FIDELITY in reproducing the signal on the output of the system. This is why a wide-band musical system is called a Hi-Fi System. Here Hi-Fi is HIGH FIDELITY. But if we pass a complex signal through a finite B.W. System inevitably there will be suppression of frequency on the high frequency end of the spectrum as well as on the low frequency end of the spectrum .This leads to FREQUENCY DISTORTION as well as PHASE DISTORTION.

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