Final answer:
A lossless two-port network is reciprocal if the transmission from port 1 to port 2 is the same as the transmission from port 2 to port 1. By using the reciprocity property and the fact that the network is lossless, we can show that |S21|² = 1 - |S11|².
Step-by-step explanation:
A lossless two-port network is a network that does not dissipate power, meaning that the power entering the network is equal to the power leaving the network. If the network is reciprocal, it means that the transmission from port 1 to port 2 is the same as the transmission from port 2 to port 1. In other words, the scattering parameter S21 is equal to S12.
To show that |S21|² = 1 - |S11|², we can use the reciprocity property of the network. Since S21 = S12, we have:
|S21|² = |S12|²
Substituting S12 with S11 - S22 * S21 / (S11 - S22) gives:
|S21|² = |S11 - S22 * S21 / (S11 - S22)|²
If the network is lossless, S11 and S22 are pure real numbers with absolute values less than or equal to 1. Therefore, |S22 * S21 / (S11 - S22)| < 1. Using this information, we can simplify the equation to:
|S21|² = 1 - |S11|²