Microwave Circuit Theory

Abstract

The electric current \(\dot{I}\) and the volage \(\dot{V}\) on the imagined surface S are defined by \(\dot{I}\textbf{\itshape F}=\textbf{\itshape H}^{t}\), \(\dot{P}=\dot{V}\tilde{I}\) or \(\dot{I}\textbf{\itshape F}=\textbf{\itshape E}\), \(\tilde{P}=\dot{V}\tilde{I}\), where H t , E t are tangential magnetic and electric field components on S , and F is a vector function depending only on the distribution of H t and E t on S and \(\dot{I}\) is a scalar complex constant depending only on the total strength of H t or E t , \(\dot{P}\) is the apperent power flowing through S , and∼expresses the conjugate value of the quontity. It is proved that \(\partial\dot{Z}/\partial\lambda\) is positive and ∥∂ Z k h /∂λ∥ ispo sitive definite form in reactive case, where λ= j ω, \(\dot{Z}\) and \(\dot{Z}_{kh}\) are impedance and impedance matrix element respectively, and \(Q=(1/r)\sqrt{L/C}\) in resonant case, werer r , L , C are resistance, inductance, and capacity.