18 



ELEMENTS OF AIRBORNE RADAR SYSTEMS DESIGN PROBLEM 



FREQUENCY (ANGULAR) 



Fig. 1-11 Generated Frequency Spec- 

 trum for 100 Per Cent Sinusoidal Am- 

 plitude Modulation of Carrier. 



as m decreases the power in the side- 

 bands decreases and becomes a lesser 

 fraction of the carrier power. 



A common type of amplitude mod- 

 ulation arises from a modulating 

 signal of the form shown in Fig. 1-12. 

 Essentially, this signal turns the 

 transmitter on and off on a periodic 

 basis. Accordingly the output is a 

 train of pulses of the carrier fre- 

 quency. Since this modulating signal 

 is periodic, it may be expressed as 

 a Fourier series with a fundamen- 

 tal frequency equal to the pulse 



TIME 



Fig. 1-12 Pulse Modulation. 



repetition frequency (PRF — 1 /T^), where Tr is the time between 

 successive pulses.^ Thus, this type of modulation gives rise to a large 

 number of sidebands separated from the carrier frequency by multiples 

 of the pulse repetition frequency. The amplitude spectrum of such a 

 modulated wave is shown in Fig. 1-13. As can be seen, the pulse width r 

 determines the amplitude of each of the sidebands. 



Radar systems employing the type of amplitude modulation just de- 

 scribed are known as pu/se-type radars. Pulse radars, however, are not 

 limited to this type of modulation, as will be described in later paragraphs. 



Frequency Modulation. Another major type of modulation is 

 frequency modulation. In this case, the argument of the cosine function 

 in Equation 1-14 is varied in such a manner as to cause the instantaneous 

 frequency to be altered in accordance with the modulating signal. When 



^Actually, the pulse amplitude modulated AF wave can be represented by a Fourier series 

 with a fundamental frequency equal to the pulse repetition frequency only when the carrier 

 frequency oin is an integral multiple of the PRF. 



