RECEIVING 



27 



In connection with these measurements, reference 

 should be made to the discussion at the beginning 

 of this chapter where are stated certain precautions 

 that must be observed in taking the data in order to 

 obtain a precise determination of the efficiency. 



It is shown later in this chapter that, when the 

 device is linear, the projector efficiency is the same 

 on transmitting and on receiving. This further illus- 

 trates the fundamental nature of this quantity. 



41 - 5 Selectivity 



The above quantities relate to the transmitting 

 performance of the device at any one frequency. In 

 general, however, the performance over a range of 

 frequencies is of interest. In that case, the response 

 and efficiency are determined over the frequency 

 range and plotted versus frequency to provide re- 

 sponse or efficiency characteristics. Directivity pat- 

 terns may also have to be taken at several frequencies. 



The response characteristic in particular is used to 

 study the selectivity of the device. For this purpose 

 use is frequently made of the equivalent series reso- 

 nant circuit. This circuit is one in which the current 

 varies with frequency in the same way that the re- 

 sponse does. Assume this circuit to have resistance r 



and reactances Lu> and — L (where <•> = 2-n-f). Its impe- 



dance then is 



r + j 



(- - B 



Since at resonance . 



l/LC, 



— o)„- 



z = r + j La 



w 



The ratio of the resistance r to the reactance x in 

 this circuit is 



U(±jl*f 



L(o _ I x I / or \ 

 r \r\ \u> 2 — a> V 



There are two values, o^ and <i> 2 , one on each side of 

 resonance a> , where x = r. Then \z x \ = |z 2 | = r\/2. 

 At resonance, that is, at a> , we have x = 0, so that 

 z = r. In addition because of symmetry o> = \/o>i<B2. 

 so that 



LlOg 



r 



U 



For constant applied voltage e, the currents then are 



and i n = -■ 



Hence 



20 log U 



20 log ^ = 20 log ~ = -3 db. 



V^ 



The symbol Q has been used for the ratio Lu> /r. 

 Usually in a resonant circuit the resistance is asso- 

 ciated with the coil. The Q of the coil then is its qual- 

 ity or figure of merit. 8 - To obtain the Q of a response 

 curve, first the frequencies f 1 and f 2 , at which the re- 

 sponse is 3 db below the peak, and the resonant 

 frequency f„ are found; then Q is found from these 

 three frequencies by means of the above relation: 



fo 



fx-h 



(9) 



4.2 



RECEIVING 



An underwater acoustic device which is used only 

 for receiving is called a hydrophone. The measure- 

 ments on receiving usually involve determination of 

 the following factors: 



1. The voltage delivered by the device. This is re- 

 ferred to the condition in which the unit is in a 

 uniform, plane sound field of reference pressure 

 (1 dyne per sq cm). 



2. The variation of this voltage with direction of 

 sound incidence. 



3. The variation of the voltage with frequency. 



These factors are analogous to those tested on trans- 

 mitting. There is another quantity of interest on re- 

 ceiving, the threshold pressure. This denotes the pres- 

 sure on the face of the hydrophone that generates a 

 voltage equal to its inherent noise voltage. This is re- 

 lated to the minimum signal that can be measured 

 with the particular instrument. Of these quantities 

 only the receiving response and the threshold are con- 

 sidered in detail, since the other items have been 

 covered on transmitting. 



4.2.1 



Receiving Response 



«n 



U -h 



The receiving response of a hydrophone or a pro- 

 jector is expressed in terms of the open-circuit voltage 



