IMPEDANCE CONCEPT AND APPLICATION 37 



where 



P = P\P^, q = 21^2, K = K+K-. 



The same formula appHes of course to / provided we interpret the 

 p's, q's and /c's as referring to the variable / rather than the variable 

 V. If the inserted piece is electrically long, we have approximately 



T = pK+. 



In many practical applications the inserted piece is a uniform trans- 

 mission line, so that 



/c+ = /c~ = e~^^, K — e~'^^^, 



where T is the propagation constant and / is the length of the piece. 

 In this case 



P „-rz 



T = 



1 - oe-2r' 



Power Absorption and Radiation 



The power transferred from left to right across P is the real part 

 of the following function '^ : 



^P = iVpIp* = hZpIpIp*, (18) 



where the asterisk denotes the complex number conjugate to the one 

 represented by the letter itself. The power absorbed by the imped- 

 ance Zt is 



^r = iZ,/g/Q*. (19) 



The difference between (18) and (19) represents the power absorbed 

 by the section PQ. 



The power absorbed by a shield is calculated in a similar manner. 

 The energy flow per unit area of the shield is given by an expression 

 closely analogous to (18) ; the tangential component of H appears in 

 the place of / and Zp is to be interpreted as the impedance in the 

 direction normal to the shield. The formula is derivable from the 

 Poynting expression for energy flow. Thus the power flow per unit 

 area is \ZnHtHt* where lit is the tangential component of // and Z„ 

 is the impedance in the direction normal to the shield. 



