RECEIVEK SENSITIVITY 



17 



2.2.J 



The Reciprocity Principle 



So far in this chapter the radiation and reception 

 of power by antennas have been treated separately. 

 Actually, many of the properties of an antenna are 

 the same for either reception or radiation ; in partic- 

 ular, the current distribution, the effecti\'e length, 

 and the gain are unchanged. The reciprocity prin- 

 ciple, from which these propositions may be pro\-ed, 

 may be stated as follows : If an electromotive force 

 V, inserted in antenna 1 at a point Xi, causes a cur- 

 rent / to flow at a point x^ in antenna 2, then the 

 voltage V applied at x^ \\ill produce the same cur- 

 rent I at Xi. 



From this principle the statement of the eciuiva- 

 lence of current distribution, effective length, and 

 gain follow readil^^ 



This theorem does not hold when the propagation 

 of a wave takes place in an ionized medium in the 

 presence of a magnetic field (the ionosphere), but it 

 does hold for all cases of transmission discussed in 

 this A'ohmie. 



2.3 



RECEIVER SENSITIVITY 



The sensitivity of a radio receiver is that charac- 

 teristic which determines the minimum strength of 

 signal input capable of causing a desired value of 

 signal output. In high-frequency receivers the 

 limiting factor for reception is usually set noise, 

 that is, noise produced in the tubes or other ele- 

 ments, such as crystals, of the receiver itself. At 

 frequencies below about 100 mc, atmospheric dis- 

 turbances sometimes exceed the set noise in intensity, 

 but at higher frequencies atmospheric static is 

 negligible. Man-made noise (automobiles, etc.) 

 may be a source of serious trouble, but such inter- 

 ference can often be eliminated b.v proper siting. 

 Conseciuently, for high-frecjuency receivers, sensi- 

 tivity may be expressed, at least approximately, in 

 terms of set noise only. 



Although set noise has an important bearing on 

 sensitivity of radar receivers, there are other factors 

 which must be considered for this type of ecjuipment. 



There are several types of set noise. Though all 

 noise sources in a well-designed recei^•er are mini- 

 mized with the exception of the thermal noise whose 

 magnitude is independent of equipment construction, 

 the total set noise is usually several times the purely 

 thermal noise. 



^•'•' Thermal Noise 



Thermal noise is generated by the random 

 (temperature) motion of electrons in a conductor; 

 it is, therefore, a universal property of matter and 

 independent of the design features of the receiver. 

 The rms thermal-noise voltage that appears across 

 the terminals of any circuit element is a function of 

 the frequency interval (receiver bandwidth) over 

 which the noise is averaged ; it is given by 



V„ = V4/.'7'A/ . H, 



(30) 



where R is the resistance across which the noise 

 voltage is measui'ed, Af the bandwidth in cycles 

 per second, 7' the absolute temperature, and k, 

 the Boltzmann constant, is equal to 1.38 X 10"^^ 

 watt-second per degree. The noise voltage is inde- 

 pendent of the leactance components in the circuit. 

 Consider now, for the purpose of definition, a 

 receiver without internal noise, that is, let all the 

 noise be generated in the receiving antenna of re- 

 sistance Ra- If Ri designates the load resistance 

 (that is, the resistance of the receiver exclusive of its- 

 antenna), the average noise power delivered to the 

 receiver will be 



T' 2/?, 

 ^ _1jlJ^ (31) 



(Ra + RiY 

 where V„ is the rms \-alue of the noise generated in 

 the antenna. 



The noise power is maximum when the receiver is 

 matched to its input; this maximum is 



JV 



■iRa 



by equation (30). Assuming equivalent temperature 

 T = 290 degrees alssolute, and measuring A/ in 

 megacj'cles, 



p„ = 4 X W^^Af watt. (33) 



This result means that in an idealized receiver,, 

 noise is the thermal noise of an antenna of equivalent 

 temperature T = 290 degrees absolute, and the 

 minimum detectable signal would he approximately 

 equal to 4 X 10"'"A/ watt. 



Pn = 



kTAf watts 



(32) 



2.3.2 



Noise Figure 



The sensitivity of a set cannot be described in 

 terms of the thermal noise alone, because the set 

 noise is usually several times the purely thermal 

 noise. For this purpose another quantitj^ called the 



