ULTRA-HIGH-FREQUENCY VACUUM TUBES 

 impressed on the diode. This gives from (45) 



2 L 36 



645 



rvi'"(/)^i'"(0 ^ rvi'v(/).^i'v(/) ^ rviv(0y.,v(0 ^ 



[- 



96 



800 



60 

 4032 ' 



180 



rVi'--(/).pr(^) 



224 



+ 



756 



1152 



(46) 



If the first-order voltage which is impressed on the diode is taken to 

 be a single sine wave, it follows from the linearity of the first-order 

 relations that the first-order current is likewise a single sine wave of 

 the same angular frequency, w. Thus, let 



Then 



ipi"'{t) = A sin o:L (47) 



^i'^(0 — ^<^ cos ut, 

 ff-df) = — Aor sin w/, 

 ^r'(0 = — Aoi^ cos wt. 



When these are substituted into (46) it is seen that the right hand 

 side of the equation contains a d.-c. term and a double-frequency term. 

 The left hand side must accordingly contain terms of the same fre- 

 quencies. Hence the most general form which can be assumed for the 

 second-order current (p2"'{t)elkme is: 



<P2"{t) = (ao -i-ai0 + a2^-+ • • •) 



+ (&o + bid + b2d^ + • • ■) sin 2co/ 

 + (co + Cid -f Cid^ -I- • • • ) cos 2ut, 



(48) 



where 6 = coT is the transit angle, and the as have no reference to the 

 symbols previously used for acceleration. 



When (47) and (48) are substituted into (46) it will be seen that the 

 coefficients of the d.-c. term, the sin 2o:t term and the cos lut term 

 respectively may be equated on the two sides of the equation. This 

 gives three equations and in each of these, coefficients of corresponding 

 powers of the transit angle may be equated, thus providing the values 

 of all of the coefficients in (48). 



Without carrying out this procedure in detail it is possible to find the 

 d.-c. component directly from (46) and (47) by noting that time 

 derivatives of the d.-c. component of <p2"{t) are zero. Hence the left 



