On Jun 23, 9:06*pm, lu6etj wrote:
However I can not visualize a simple mechanism to generate
such system in a TL.

I have given the equations for what happens at an impedance
discontinuity in a transmission line. The s-parameter equations are
the same equations in a different format. Simply visualize the voltage
phasors resulting from reflections-from and transmissions-through the
impedance discontinuity. Let's start with voltages instead of power.

source------Z01=50 ohms------+------Z02=300 ohms--------load

measured Vfor1 = 50v, Vref1 = 0v
calculated rho1 = (300-50)/(300+50) = 0.7143

Vfor1*rho1 = 35.7v at zero degrees = portion of Vfor1 reflected by the
impedance discontinuity at '+'.

Vref2*tau2 = 35.7v at 180 degrees = portion of Vref2 transmitted back
through the impedance discontinuity at '+'.

Vref1 = Vfor*rho1 + Vref2*tau2 = 0, measured Vref1. This is the same
as the s-parameter equation (1).

b1 = s11*a1 + s12*a2, all phasor math

These are the two voltage components that superpose to zero volts.
Both of those wavefronts are phasors with phase angles referenced to
the Vfor1 phase angle.

Now let's look at the power in the component phasor wavefronts.

(Vfor1)^2/Z01 = 50^2/50 = 50w, power in the Vfor1 forward wave

(Vref1)^2/Z01 = 0^2/50 = 0w, power in the Vref1 reflected wave

(Vfor1*rho1)^2/Z01 = 35.7^2/50 = 25.49w

(Vref2*tau2)^2/Z01 = 35.7^2/50 = 25.49w

Pref1 = 25.49w + 25.49w + 2*SQRT(25.49*25.49)cos(180)

The corresponding s-parameter power equation is:

b1^2 = (s11*a1 + s12*a2)^2

b1^2 = (s11*a1)^2 + (s12*a2)^2 + 2(s11*a1)(s12*a2)

The two wavefronts that cancel toward the source contain energy before
they superpose to zero. Where does that energy go? Superposing to zero
indicates total destructive interference toward the source. The
conservation of energy principle says that energy cannot be destroyed
so it must appear as an equal magnitude of constructive interference
in the only other direction possible, i.e. toward the load.

The above equations deal only with the destructive interference toward
the source. There is a second complimentary set of voltage/energy
equations that deal with constructive interference toward the load.

I am studying your paper published in World Radio Oct 2005. Have you a
demonstration of the equation cited fro "Optics" book = Pfor=Pi
+P2+2[sqrt(P1P2)]cos(theta)?

See above.
--
73, Cecil, w5dxp.com