RECEIVING 



29 



Figure 9. Circuit equivalent to a long line. 



quency band ol 1 cycle and a temperature of L'O C ii 



has the value 



1.6] x 10--")- , 



(11) 



where i\. is the equivalent series resistance of the 

 device. 



In the practical case there are two distinct condi- 

 tions to be considered: calculated threshold and meas- 

 ured threshold. 



Calculated Threshold 



In the case of low-impedance hydrophones, usually 

 of the electrodynamic or magnetostrictive type, the 

 active unit usually is directly connected to a line. 



II this line has appreciable length, its impedance 

 must be matched at both terminals, since otherwise 

 irregularities in response are introduced due to reflec- 

 tions in the line itself. Neglecting attenuation, the 

 circuit may then be represented as in Figure 9. 



Here e g is the generated open-circuit signal voltage, 

 e nX is the generated noise voltage in the resistance of 

 the hydrophone r, and e n2 is the generated noise volt- 

 age in the terminating resistance r T . Reactances in the 

 circuit are omitted for the sake of simplicity. V n is the 

 noise voltage and V s is the signal voltage applied to 

 the input of the measuring circuit, assumed to be the 

 grid of the amplifier. 



The noise voltage applied to the grid due to e nl is 



The noise voltage applied to the grid due to e n2 is 



v., = (-Sa_V- 



" V rf r T J 



The nns noise voltage V „ applied to the grid due to 

 both e„i and e„ 2 ' s obtained by adding the two fluc- 

 tuating noises at random phase, thus 



V'' + »V/ V + ' '■;■/ 



(12) 



When the line impedance is matched at the two ter- 

 minals, r T = r. Then by equation (1 1) above, e nJ = 



>'„- = ('„. so that 



v, - (I) 2 + (|) 2 



\ -' 



(13) 



The signal voltage V s applied at the grid is then one- 

 hall the voltage generated by the hydrophone, 



v — e ° 



From the above relation V s , the signal voltage gen- 

 erated by the hydrophone, equals V„, the noise volt- 

 age in the matched circuit, when 



1.41 e„ 



(14) 



The other possibility, instead of matching the circuit, 

 is to connect the hydrophone to a very high impe- 

 dance. In that case r T is very large relative to r(r y— »oo). 

 Hence from equation (12) 



(15) 



and the signal voltage f' s applied to the grid becomes 



so that 



V, = e g 



<■„ = c, 



(16) 



It is seen by comparing equations (14) and (16) that 

 there is a theoretical gain in the signal-to-noise ratio 

 of 3 db in terminating the hydrophone in a high im- 

 pedance as compared to matching it. Where the leads 

 are sufficiently short it is therefore advantageous to 

 use a high-impedance termination. This applies espe- 

 cially to the internal connection between the active 



