For matched junction S parameters, which of the following is correct?

Explanation:

Matched Junction S-parameters

Definition: In RF and microwave engineering, S-parameters (scattering parameters) are used to characterize how RF signals behave in a network. For a matched junction, the term refers to a system where the impedance of the ports is perfectly matched, minimizing reflections.

• S₁₁ = 0: This indicates no reflection occurs at Port 1 due to perfect impedance matching.
• S₂₁ = 1: This indicates complete transmission of the signal from Port 1 to Port 2 without any loss.

In the case of a matched junction, the input signal is fully transmitted to the output port without any reflection or loss. This ideal condition is represented by S₂₁ = 1, meaning the transmission coefficient is unity (100% transmission). Matched junctions are often used in high-frequency systems to ensure maximum signal transfer and minimal signal degradation.

Derivation of S₂₁:

For a matched junction, the reflection coefficient S₁₁ is zero, which implies no signal is reflected back to the source. Consequently, all the power is transmitted to the output port, leading to the transmission coefficient S₂₁ being equal to 1.

The S-parameters are governed by the energy conservation principle:

• |S₁₁|² + |S₂₁|² = 1

For a matched junction:

• S₁₁ = 0
• |S₁₁|² = 0
• Thus, |S₂₁|² = 1
• S₂₁ = 1

This confirms that the correct option is S₂₁ = 1.