MICROWAVE PARAMAGNETIC RESONANCE ABSORPTION 453 



We define the coupling coefficient /3 = Qx/Qa such that: 



Critically coupled cavity j8 = — ^ = -^— = 1 (9) 



Overcoupled cavity ^ > 1 VSWR = /3 = ^ (10) 



Undercoupled cavity ^ < 1 VSWR = 1 = -^, (11) 



We will see that the coupling coefficient for maximum output depends 

 on the characteristics of the detecting element. Two cases will be treated: 

 the power (square law) detector and the voltage (linear) detector. 



1. Detector Output Proportional to Incident Power 

 Power into the cavity at resonance 



r 



Vn V 



^' \\/2) (Ron^ + ry 

 Max. power available from source (in arm 1) 



(VnY „ „ 2Ronr 



Pc = P 







" 4/?on2 " {R,n^ + rf 



The change in reflected power APr equals the change in the power inside 

 the cavity APc (since the incident power stays the same). 



AP. = ^ Ar = 2Pon^Po ,g"^' ~ ' Ar (12) 



dr {Ran + ry 



We want to optimize APc with respect to the coupling parameter n^ 



(or Rm^), i.e., 



.-. ^ = 2 ± V3 



r 



the positive sign being associated with the overcoupled, the negative 

 with the undercoupled case. The experimentally measured quantity 

 is the voltage stanchng wave ratio VSWR = 2 + \/3 = 3.74 correspond- 

 ing to a reflection coefficient of 0.58. Putting this value into (12) we get 

 for the maximum signal 



^ = ± 0.193 - = =F 0.193 ^ = T (0.193)(47r)x"7?Qo (14) 

 Po r Qo 



