OPERATION OP THERMIONIC VACUUM TUBE CIRCUITS AA7 

 we have, from (88), for second order effects 



'"'^^'^^'^[(^^+,ir-)(-,^-)''.+-') 



2jhC A'- ^., 



+ -. ^— "ti ^— T -^ cos 2/z/ 



V''^ jhc) y'^2jhc) 





+ /f^ ^ fcos2./ 



(39) 



+ jVi+^ _ ^^ ^Qg {h+k)t 



-\ ^^-j AB cos {h-k)r\ 



While most of the frequencies in this expression are unimportant 

 in relation to any practical case on hand, they are included here to 

 show the complete result for a given simple case. The last term of 

 the above expression results in what is known as detection. 



Let us consider this component in more detail as regards detection 

 of an incoming modulated radio wave of the form 



g=^ (1+5 cos g/)cos^/. (40) 



They may be written 



A Ti A Ti 



e=A cos pt-\- -^ cos {p-\-q)t-{- -^ cos (p — g)t. (41) 



If we identify the "/>" frequency with "h," and let "^" have the 

 values ip-\-q) and ip — q) in turn, the detection term of (39) gives 



1 , / At \ r~ i?p 



_('■''- lie) ('•''+ i(#T^)('''+^''> 



+ - T-^. '—, r K-coss/. (42) 



(^.+,.,cj('-J(^^c)('«+^«U 



2 



