200 BELL SYSTEM TECHNICAL JOURNAL 



This noise power is transmitted without gain or loss to the output terminals 

 of the repeater circuit. The total noise power at the output terminals is 

 therefore 



SiV^x = 4 X IQ-'^FB — XidlM,) 



2 

 l2 



Assuming the same repeater spacings and fading factors M in. each link and 

 substituting D for nd, 



d\^ ' 



SiV = 4 X 10"'' FBD -J- M Watts (II-3) 



The signal-to-noise ratio at the output terminals is S/^N. The circuit 

 should be designed ibr a signal power, S, as low as possible. Therefore, it 

 is very important to choose values of the several factors in (II-3) which 

 give a low level of output noise. 



Assuming a noise figure F = 20 (13 db) and bandwidth ^ = 10 mega- 

 cycles, eight repeaters of the type described in the above example will have, 



2iV = 2.8 X 10"' Watts 



or, assuming a required minimum output signal to noise ratio of 30 db, the 

 output power must be 5 ^ 0.28 Watts. 



In this example it has been assumed that the signals in all links have 

 faded simultaneously 20 db below the free space value, which may only 

 happen a fraction of a percent of the time. Most of the time the signal-to- 

 noise ratio will be higher than the assumed 30 db and under normal trans- 

 mission conditions it will be 50 db (fading allowance factor M = 1). 



Assuming the same repeater spacings and fading allowances in each link, 

 equation (II-l) and (II-3) give the following formula for the ratio of the 

 output power to noise figure of the repeater amplifier 



5/F = 4 X 10-21 Q 5 (5/2iV)w (II-4) 



Equations (II-l) and (II-4) are the important design equations for the re- 

 peater amplifier. 



The factors in (II-2) and (II-3) will now be discussed briefly. (II-3) 

 shows that the noise figure F should be as small as possible. If by improving 

 the equipment the noise figure could be halved, then the signal power 5 

 could also be halved (unless interference from other microwave circuits 

 predominate). Later on the noise figure will be discussed further. 



The bandwidth B is determined by the characteristics of the signal it is 

 desired to transmit and by the method of transmission. Our aim has been 

 to provide 10-megacycle bands which are sufiicient for transmission of stand- 

 ard television signals by AM or low index FM. 



