Question

prove that it is not possible to construct to perfectly matched lossless reciprocal three port junction

Answer 1

Answer:

Explanation:

Consider a 3-port device. Such a device would have a scattering matrix :

■(S11 S12 S13

   S21 S22 S23

  S31 S32 S33)

Assuming the device is passive and made of simple (isotropic) materials, the device will be reciprocal,

S12=S21

S31=S13

S23=S32

Likewise, if it is matched, we know that S11 = S22 = S33=0;

As a result, a lossless, reciprocal device would have a scattering matrix of the form:

■(0 S12 S13

 S21 0 S23

S31 S32 0)

Due to these zeros, it is not possible to construct to perfectly matched lossless reciprocal three port junction because reciprocal of zero lead to infinity