m^ - 32 



FREQUENCY SHIFT TELEGRAPHY 267 



COS ( ^ j (cos (oj — p)t — cos (w + p)t) 

 sin f — ^ j (cos (co — 2p)t + cos (co + 2p)/) 

 cos ( — ^ j (cos (co — 3p)t — cos (co + 3p)i) 



] 



(2) 



u • ^u J • ^- ^- frequency shift 



where w is the deviation ratio = ^ -^ 



2 X signaling speed 



Typical sideband amplitudes calculated from these formulas are shown 

 in graphical form in Fig. 1. In the case of FS keying, the relative ampli- 

 tudes of the sidebands vary considerably as the amount of frequency shift 

 is changed. For miscellaneous signals these Une spectra do not exist but 

 they do indicate the general distribution of energy over the band for a given 

 signaling speed. 



Methods of Modulating the Carrier 



In AM telegraphy the carrier is usually modulated by simply interrupting 

 it for the spacing condition. This is sometimes referred to as **on-off" 

 keying. For low power and low frequencies the carrier may be keyed di- 

 rectly by electrical contacts. A more universally appUcable method is to 

 use vacuum tubes or other nonlinear elements to effectively interrupt the 

 carrier. In some cases it is practical to start and stop an oscillator source 

 of carrier. 



The usual radio telegraph transmitter consists of an oscillator followed by 

 a number of cascaded stages of amplification and frequency multiplication 

 arranged to reach the desired output frequency and power. For on-off 

 keying the carrier is usually interrupted by suitably varying the plate or 

 grid voltage of one or more of the stages. 



There are two general methods of obtaining frequency modulation: (a) 

 The frequency of an oscillator may be modulated directly by suitably vary- 

 ing the frequency-determining circuit, (b) the output of a constant-frequency 

 oscillator may be shifted in phase at such rates of change as to produce indi- 

 rectly the desired frequency variations. In the latter case the marking and 

 spacing intervals of an FS signal would be formed by periods of constant 

 rate of phase change versus time. Square wave reversals would therefore 

 require a triangular shaped wave of phase versus time. Since the transmis- 

 sion of long periods of steady mark or space would therefore involve huge 



