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AP3302 Pt3 Contents

AP3302 Pt3 Section 2Contents

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AP 3302 Pt. 3

Section 2

CHAPTER 1

Square Waves

The pulse duration of a wide pulse, on the other hand, is a large fraction of the period of the waveform.

The leading and trailing edges of a pulse are also illustrated in Fig 7. If the leading edge rises from the reference level the pulse is positive-going (Fig 7a). If the leading edge falls from the reference level the pulse is negative-going (Fig 7b).

We have seen in Section 1 that the pulse repetition frequency (p.r.f.) is the number of pulses occurring in one second. In both parts of Fig 7 we have one pulse every 2,000 us. Therefore in one second we have 106/2000 or 500 pulses. This is the p.r.f.

Pulse Shape and Bandwidth

The square waves considered so far have all been ideal waveforms, i.e. with zero rise and fall times and with perfectly flat tops. Such a square wave is made up of sine waves of a fundamental frequency equal to that of the square wave plus an infinite number of odd harmonics, all starting in phase. In practice, of course, no circuit is capable of passing an infinite number of harmonics so that the ideal waveform described cannot exist. However the greater the number of odd harmonics contained in the waveform the more closely it approaches the ideal waveform and the steeper are the leading and trailing edges (see Fig 8).

For accurate timing and synchronization within a radar equipment, and for accurate range measurement, pulses with steep leading edges are essential. This means that the pulse must contain a large number of harmonics. The rise time of the leading edge of the pulse must be short compared with the pulse duration - not greater than about one-tenth of the pulse duration. For a pulse whose duration is 1 us the rise time should not exceed 0.1 us.

To a good approximation this rise time t can be taken as the time of one quarter cycle of the highest harmonic within the pulse. Thus the time of one cycle of the highest harmonic is 4t, giving a frequency of 1/4t cycles per second (Fig 9). If the rise time is 0.1 us the frequency of the highest harmonic within the pulse is:-

1/4t = 1/(4 x 0.1 x 10-6) = 2.5 Mc/s

When a carrier of frequency fe is amplitude-modulated by a sine wave of frequency fm, sidebands fe + fm and fe - fm are produced. A radar transmitter is a sine wave oscillator modulated by a pulse waveform and hence the radiated r.f. pulse consists of the carrier frequency ▒ all the harmonic components of the modulating pulse. In the above example the frequency of the highest harmonic is 2.5 Mc/s so that the band of frequencies in the radiated r.f. pulse extends from fe - 2.5 Mc/s to fe + 2.5 Mc/s.


 

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