How to sum up S11 return loss ?

[mauloftin]

Hi,
can you tell me, if I have first return loss S11A dB and somewhere next second return loss, S11B dB, what will be S11 in sum ? Yes, of course depends on phase, but if the phase between S11A and S11B will be 2*Pi, the S11 will be "maximum", can you tell me how i can do sum return loss ?

Thank

 

[biff44]

return loss, log

So lets say you have a long transmission line, with two discontinuities, one at x=a, and one at x=b. A unity travelling wave goes down the line and hits the discontinuity at x=a. Some of the wave bounces back (as described by S11a), and some of the wave continues on down the line. However, the remaining wave t travelling down the line is no longer unity in amplitude, since some of the initial wave has been reflected. You have 1=|s11a|²+t².

This new wave magnitude travels down the line some more and a x=b the remaining wave is reflected by S11b, so the reflected wave at x=b is S11b*t.

Now, the wave returns towards x=a, where it again is partially reflected back to b, and partially tansmitted to a. IF they are in-phase (distance between a and b is n*Π), then the final reflected signal is the sum of |s11a| +|s11b*t|*t. That is most of it, but there is still a little more from additional round trip travels of bounces.

Check my math, it is still early in the morning!

Of course, if the wave reflected at b returns to a in anything but exactly the same phase, you have to do vector math to figure out the answer.

These sort of problems get complicated in a hurry. One way to figure it out is to convert your S parameters into something called T matrixes--one for the discontiuity at a, one for the transmission line in between, and one for the discontinuity at b. You then multiply the 3 T matrixes together, and the composite reflection coefficient is obvious.

Rich

 

[mauloftin]

log returns summation

Hi, thank you much.

Of course, all is true. OK

so I have return loss (RL). The formula is

RL = 20log(S11)

And sum RL will be 20*log(|s11a| +|s11b*t|*t) , OK ?


and now I have formula:

RL = 10 log(Pr/Pin) - Pin incident, Pr - reflected. It is true too ? So what will be sum RL in this case ?

for example, p = Pr/Pin, pA = 10^RL-A/10, and pB pB = 10^RL-B/10

and sum = RL = 10log(pA+ pB*t*t) OK ?

And note: RL= -20dB => t = 0.995, I think, that you can write t = 1 (Yes of course, it is not exactly, but approximately: S11 = S11A+ S11B, OK ?)

 

[biff44]

return loss formula s11 real

Actually, read this, it is probably clearer:
**broken link removed**

 

[mauloftin]

formula for return loss

btw - T matrixes is wonderfull, but there is another problem, may be later - It is in my topic "S parameter - Is it so hard ?"