24 



ELEMENTS OF AIRBORNE RADAR SYSTEMS DESIGN PROBLEM 



Fig. 1-19 Product Obtained from a Nonlinear Impedance. 



input sine-wave, the output consists of only the positive half-cycles as 

 shown. 



It is interesting to observe that this process may be put into the form 

 of the generic device of Fig. 1-18 merely by considering the output to be 

 the product of the input and a reference square wave of the same frequency 

 and phase as the input. Such a representation is shown in Fig. 1-20. 



Thus, the input may be defined as 



:rLrLn 



TT 2ir 3ir Att Stt 



Fig. 1-20 Nonlinear Impedance as a Product-Taking Device. 



Ei = A sin CO/. 

 The reference signal may be expressed by a Fourier series 



sin Sco/- , sin 5a)/ 



Er 



H (sin co/ 



+ 



+ -) 



and the product has the Fourier series form 



zr w r^ A , A . lA V 



Ei X /t,. = - + ;r- sin a)/ ) 



Inixit 



An' 



(1-21) 

 (1-22) 



(1-23) 



The consequences of this product process are quite evident from Equation 

 1-23. Although the input contains only one frequency, the output has a 

 d-c component, an input-frequency component, and components at all 

 the even harmonic frequencies of the input. 



Now, if the amplitude of the incoming wave A, instead of being constant 

 as implied, were amplitude-modulated at a frequency aj;„, such that 



