FreeLists / si-list / [SI-LIST] Re: Conversion from dB to ohm

[Larry Smith <larry.smith@xxxxxxx>]

Bob - I've been away for a few weeks but I wanted to comment on this 
thread of emails.  S parameters can come in 3 formats:
        
        1) real and imaginary numbers.
        2) magnitude and phase with magnitude expressed as a number.
        3) magnitude and phase with magnitude expressed in dB.

And then of course, phase can be either in degrees or radians.
Anytime we make calculations with S parameters, we must be certain of
their numerical format.  For passive systems, the real and imaginary
numbers must be between -1 and +1, the numerical magnitude must be between
0 and 1; and the dB magnitude must be between 0 and minus infinity.  If an
S parameter is outside of these bounds, this implies that more power was
measured than was given to the system, which is not going to happen with
a passive system.  

When we convert S21 to Z21, the formula to use is |Z21| = (Z0/2) * |S21|, where
Z0 is the instrumentation reference impedance and S21 is in numbers, either 
real and imaginary or magnitude and phase.  The magnitude symbol |x| indicates
that we want the magnitude only and not the phase.  Real and imaginary numbers
must be converted to magnitude and phase and the phase dropped.

The formula that you are using below applies when S21 is in dB rather than 
numerical format.  You must convert from dB to numbers before finding Z21.
The negative sign in the -60dB is part of the magnitude because S21 is in 
dB format.  We drop the phase part of S21 before dividing by 20 and raising
10 to that power.  But we don't want to drop the negative sign because that is
part of the dB magnitude.  Confusing isn't it...  But once you trace through the
possible formats of S21, it becomes clear what you have to do to make the
conversion.  The notation does seem a bit ambiguous.  Perhaps somebody has
a better way of writing this equation.

regards,
Larry Smith
Sun Microsystems

Bob Patel wrote:
> 
> Hi! The formula for conversion from ohm to dB is :
> Ztrans=25*10^(|S21|/20).
> So if S21=-60dB then Ztrans=25000, what is this value
> in i.e. units is in ohm but do I need to divide it
> with some factor to get in ohms.
> I am trying to convert and it is not corelating.
> Any inputs appreciated.
> Thanks
> Bob
> 
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