Wes Stewart wrote:
All of the S-parameters I've ever measured were referenced to the ends
of the cables used to connect the DUT to the test equipment.

Where the signal generator was connected?

b1 = s11*a1 + s12*a2

The HP S-parameter Ap Note 95-1 sez:

|a1|^2 = Power incident on the input of the network
= Power available from a source impedance Z0

What was |a1|^2 referenced to?
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73, Cecil http://www.qsl.net/w5dxp