DEPENDENCE OF SIGTNAL POWER ON PARAMETERS 



199 



mulh. Scaimiiig conditious may be included if de- 

 sired. Some factors which affect the signal threshold 

 power will now be enumerated, and the magnitude of 

 their effects described. 



The first such factor is the noise figure of the re- 

 cei\er. In brief, this is simply a multiplicative factor 

 wliich would go with any of the other determinations 

 made. The noise figure of the receiver specifically 

 measures the amount by which that receiver is noisier 

 than the best theoretical receiver. Ordinarily this noise 

 figure runs to the order of 10 db, which means that 

 the recci\er is something like 10 times as noisy as 

 the theoretically perfect receiver. As we are dealing 

 with signal threshold power in terms of the receiver 

 noise power (the latter being a universal parameter) 

 it is only necessary to determine the noise figure of a 

 given receiver in the field to determine what sort of 

 input signal power is necessary. 



The second factor affecting the signal threshold is 

 the intermediate frequency or the radio frequency 

 bandwidth B of the receiving system. B represents 

 specifically the narrower of the two. This bandwidth 

 will affect the signal visibility in a way which will be 

 discussed presently. The third quantity is the video 

 bandwidth & of the receiver. At one time it was thought 

 that the video bandwidth and the i-f bandwidth were 

 equivalent, but this is not at all true. Between the 

 i-f and the video systems there is a second detector 

 which is a nonlinear element, wliich causes frequency 

 conversion to take place. This causes the video band- 

 width to ha\e an entirely different action from that of 

 the i-f bandwidth. A third factor is the sweep speed 

 of the scope, denoted by small s. The sweep speed has 

 an important eff'ect which is nearly equi\alent to that 

 of video bandwidth. Another parameter is the time 

 interval during which the signal is actually presented 

 to the observer. This quantity will be represented by 

 the letter T and called the signal presentation time. 

 In addition to these there are several other factors 

 connected with contrast effects in the presentation 

 and the scanning variables. 



The first four variables mentioned apply to the 

 geometry of the system, and geometrical scaling argu- 

 ments can be applied to these quantities. One of these 

 variables can thus be eliminated at the start by using 

 not the pulse length t, but the product s X t as a 

 variable. Similarly, the other variables are B X r, 

 b X T, and N X t. These quantities have a definite 

 physical significance. The sweep speed multiplied by 

 the pulse length is simply the length of the signal on 



the scope and can be expressed in millimeters if de- 

 sired. 5 X r is the i-f bandwidth times the pulse 

 length and turns out to be a simple number. This is 

 a number which will affect the signal visibility curves. 

 Similarly the video bandwidth & X t is another num- 

 ber. The signal power multiplied by the pulse length 

 is simply the energy of the signal per pulse, and so 

 on. These variables are essentially geometrical para- 

 meters. The pulse repetition frequency and the signal 

 presentation time are statistical parameters and must 

 be treated in a statistical way as will be shown. 



The first geometrical factor to be considered is the 

 i-f bandwidth. The interesting factor is the behavior 

 of signal and noise. Independently, these are known 

 quite well. With respect to noise the power response 

 is proportional to the bandwidth. However, the re- 

 sponse to a signal of a particular length, once there 

 has been obtained a bandwidth which is adequate for 

 the transmission of the pulse, will be essentially in- 

 dependent of the bandwidth. AVheu the bandwidth is 

 very narrow the voltage of the output pulse is propor- 

 tional to the bandwidth of the receiver. A curve can 

 be drawn which is essentially the signal-to-noise power 

 response curve, which for wide bandwidth will be 

 proportional to the signal threshold power, while for 

 narrow bandwidth it will be inversely proportional to 

 the bandwidth. This is exactly the form of curve ob- 

 tained experimentally. The optimum bandwidth is 

 found to be approximately 1.3 times the reciprocal of 

 the pulse length. The noise power in the receiver is a 

 very poor single criterion as to how small a signal can 

 be seen. For example, with a bandwidth of 1 mc for 

 l-/iisec pulse a signal about 3 db below the noise 

 can be seen. But if the i-f bandwidth is 10 mc for a 

 1-yiisec pulse, a signal is visible 7 db below noise. If 

 the i-f bandwidth is too small, even a signal equal to 

 noise power is invisible. In general, therefore, signal 

 threshold power is rated in decibels above the receiver 

 noise power for a particular value of B (usually B 

 = 1/t), since this provides a universal scale. 



For the video bandwidth the situation is more com- 

 plicated. A good deal of theoretical work can be done 

 on this problem, but the experimental data do not 

 confirm the theory. The reason is that the video band- 

 width is already effectively narrowed by the effect of 

 sweep speed. Video bandwidth effects can be observed 

 when the sweep speed is very fast, where s X t (the 

 pulse length on the scope) is of the order of a milli- 

 meter or so. Under these conditions video bandwidth 

 narrowing always reduces the signal visibility and in- 



