[SI-LIST] Re: S11 and S21 for PCB trace with different dielectic think

  • From: "Brad Brim" <bradb@xxxxxxxxxxx>
  • To: <shlepnev@xxxxxxxxxxxxx>, "'Ralph Wilson'" <wilson@xxxxxxxxxxxxxxxxxx>, <si-list@xxxxxxxxxxxxx>
  • Date: Thu, 15 Jan 2009 12:34:33 -0800

hello John, Ralf and Yuriy,

There are a number of independent issues that interact to make the topic of
reference impedance seem more complex that it really is. First considering
the issues independently leads to a more clear overall view, rather than
first trying to consider the topic in total.

best regards,
 -Brad Brim
  bradb@xxxxxxxxxxx


Theoretically:
S-parameters are defined by the S-matrix *and* the Z-vector of reference
impedances. If the Z-vector changes (e.g. renormalization) then the
corresponding S-matrix must also change. Regardless of the reference
impedances applied, the combination of S-matrix and Z-vector contain exactly
the same fundamental information
 
Circuit Simulation:
Few, if any, commercial circuit simulators work at their core directly with
S-parameters. Even though at a netlist/schematic level you may interact in
terms of S-parameters, they are internally converted to Y-parameters and
applied to implement classical modified-nodal circuit analysis in either
time or frequency domain.

Conceptually:
It is common to intuitively judge the performance of an interconnect in
terms of small reflection (small Smm,Snn) and low loss (large Smn,Snm). This
typically assumes the driver and receiver are "matched" to the interconnect.
If the reference impedance of measurement probes or simulation ports do not
conform to this matched impedance condition then renormalizing supports your
quick intuitive interpretation. However, if your Tx/Rx are mismatched you
may wish to renormalize to their impedances rather than to the line
impedance of the interconnect before you judge the performance. You can do
this renormalization prior to exporting S-parameter in most simulation tools
and some VNAs, or after export in a math program and some circuit parameter
viewers . or simply use the S-parameters directly in a circuit simulator and
specify whatever port impedance you wish to get the circuit simulation
results you want.

Numerically:
The S-parameter renormalization process is a relatively simple matrix
operation. When a diagonal matrix term is large (Snn=1) this transformation
becomes numerically illconditioned. This is common when the input impedance
at a port is dramatically different from that port's reference impedance.
For example, a 50 ohm probe looking into a power delivery network. The PDN
impedance at low frequency is very low/high (whether or not VRM is
attached). Any measurement/numerical noise or even too few significant
digits for such Snn significantly affects the input impedance value derived
from the S-parameter. As Yuriy explained, selecting a reference impedance Zn
on the same order of magnitude as the expected input impedance at port n
will minimize such numerical sensitivities.
 

> -----Original Message-----
> From: Yuriy Shlepnev [mailto:shlepnev@xxxxxxxxxxxxx] 
> Sent: Thursday, January 15, 2009 6:40 AM
> To: 'Ralph Wilson'; bradb@xxxxxxxxxxx; si-list@xxxxxxxxxxxxx
> Subject: RE: [SI-LIST] Re: S11 and S21 for PCB trace with 
> different dielectic think
> 
> Ralph and John,
> 
> The S-parameters normalization was discussed earlier in the 
> thread on "3D-em simulation and terminations". Though, the 
> thoughts on the normalizations were probably lost in a lot of 
> details. So, let me summarize it.
> 
> Normalization does not matter: In case if you write your 
> S-parameters in a Touchstone file and/or use it directly with 
> a system-level solver that converts S-parameters to 
> "un-normalized" admittance parameters for instance (it 
> usually does). Re-normalization or de-normalization is 
> practically accurate if all normalization coefficients are 
> close to the termination impedances within the order of 
> magnitude. Obviously, S-parameters look different with 
> different normalization, but it does not matter for the final 
> analysis of the system.
> 
> Normalization does matter: If you create a behavioral 
> macro-model of S-parameters (using rational approximation for 
> instance) or your system-level solver uses S-parameters 
> directly as provided. In such cases the normalization 
> impedances should be as close as possible to the termination 
> impedances or to the characteristic impedances of t-lines to 
> increase the quality of the macro-model.
> 
> Best regards,
> Yuriy Shlepnev
> www.simberian.com 
> 
> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx 
> [mailto:si-list-bounce@xxxxxxxxxxxxx] On Behalf Of Ralph Wilson
> Sent: Thursday, January 15, 2009 4:45 AM
> To: bradb@xxxxxxxxxxx; si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Re: S11 and S21 for PCB trace with 
> different dielectic think
> 
> OK, the details of this have had me pondering for some 
> time.... (my transmission line theory class was waaaayyyyy to 
> long a go). When we say "renormalize the S-parameters", what 
> is really going on?  and when do I need to renormalize?
> If I have a 50 ohm system under test (SUT), and a 50 ohm test 
> system (VNA), and the results I want are for 50 ohms, I 
> assume no renormalization is necessary.  If, however, as 
> suggested below, I have a 75 Ohm SUT and a 50 Ohm VNA I get 
> reflections at the connection between the two, and my S11 / 
> S21 measurements get discombobulated due to the mismatch.  
> Now, if I really want a 75 Ohms system, do I renormalize the 
> results (since the VNA was 50 Ohms)?  To which - 50 Ohms  or 
> 75 Ohms - in this case, which value is the "base" 
> (non-normalized) and which would I normalize to?
> Can I use the results in a 75 Ohm system simulation?
> 
> Thanks,
> Ralph Wilson
> Alcatel-Lucent
> 
> Brad Brim wrote:
> > hi John,
> >
> > You'll see the same thing if you use a 50 ohm network analyzer to 
> > measure
> a
> > 75 ohm system :-)
> >
> > Yes, you are seeing impedance mismatch from your ports/probes to the
> system
> > you are simulating. Simply renormalize the S-parameters to the 
> > impedance
> of
> > the nets. You can simulate a single net in isolation to extract its 
> > impedance or simply get the impedance of the lines from the field 
> > solver, available in some simulators for certain port setups.
> >
> > cheers,
> >  -Brad
> >  
> >   
> >> -----Original Message-----
> >> From: si-list-bounce@xxxxxxxxxxxxx
> >> [mailto:si-list-bounce@xxxxxxxxxxxxx] On Behalf Of John Kwan
> >> Sent: Wednesday, January 14, 2009 9:15 PM
> >> To: si-list@xxxxxxxxxxxxx
> >> Subject: [SI-LIST] S11 and S21 for PCB trace with 
> different dielectic 
> >> think
> >>
> >> Hi,
> >>  
> >> I am trying to extract the S11 and S21of some PCB traces 
> using one of 
> >> the field solver tools. The traces are running on top of a solid 
> >> ground plane, and I run the simulation for two different 
> dielectric 
> >> thickness settings. In one case, the Zo for the trace is around 
> >> 50-ohm, and the other case the Zo is around 80-ohm. The 
> S11 and S21 
> >> for the two case is quite different. The insertion loss 
> S21 is much 
> >> less and smoother through out the frequency range in the case of 
> >> 50-ohm. The reflection coefficient S11 is also much closer 
> to zero in 
> >> the case of 50-ohm.
> >>
> >> Is it because the port reference is set to 50-ohm for the 
> simulation, 
> >> so the result for the 50-ohm case is much better?
> >> If so, how can we use the result if the system is not 
> 50-ohm in the 
> >> real case?
> >>
> >> Regards,
> >> John

------------------------------------------------------------------
To unsubscribe from si-list:
si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field

or to administer your membership from a web page, go to:
//www.freelists.org/webpage/si-list

For help:
si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field


List technical documents are available at:
                http://www.si-list.net

List archives are viewable at:     
                //www.freelists.org/archives/si-list
or at our remote archives:
                http://groups.yahoo.com/group/si-list/messages
Old (prior to June 6, 2001) list archives are viewable at:
                http://www.qsl.net/wb6tpu
  

Other related posts: