A thinking exercise on Jacobi Maximum Power Transfer #3

At A thinking exercise on Jacobi Maximum Power Transfer #2 I posed the question of a metric for the mismatch at the L2L1 junction in the following network where the calculated values L2L1_lZ is the load impedance at the L2L1 junction (looking left as Simsmith is unconventional), and L2L1_sZ is the source impedance at the L2L1 junction (looking right). The left three components are the fixed antenna representation.

Common practice is to speak of a “source VSWR” to mean the VSWR calculated or measured looking towards the source, and very commonly this is taken wrt 50+j0Ω which may be neither the source or load impedance but an arbitrary reference.

If neither of the adjacent elements are real Zo=50+j0Ω transmission lines as is so often the case, then the value of VSWR is diminished. Often a calculated Mismatch Loss from that VSWR will be invalid.

The complex reflection coefficient at each Zo discontinuity is relevant and gives the correct value of reflected wave in a wave based analysis. Accuracy depends on use of the actual value of Zload and Zo for the calculation.

A better metric for some purposes in this type of scenario may be the (Kurokawa 1965) Power Reflection Coefficient |s|^2 of the actual source and load impedances. (Note that calculator input field Zref is not used in this calculation.)

Above calculation for this scenario (L2L1 junction) gives |s|^2 of -35dB.

Note that making changes that affect the mismatch at this point will probably affect the generator match.