[SI-LIST] Re: Interpreting s-params to physical voltage levels.
- From: Istvan Novak <istvan.novak@xxxxxxx>
- To: "Lakshmi N. Sundararajan - PTU" <lakshmi.s@xxxxxxxxxxx>
- Date: Sat, 06 Mar 2010 22:25:11 -0500
Hi Lakshmi,
Valid questions. Not knowing the actual circumstances, my response was
generic. In any particular
situation, as we usually say with my friend Eric, "It depends." There
are a few scenarios, when
simple hand calculations give sufficiently accurate answer. But before
we go there, there is one
more very important thing to point out: you asked about voltage levels,
so implicitly this assumes
that there is a driver and a receiver with some impedance values.
Dependent on the permutations
among source and receive impedance, S21 (assuming reciprocal network, so
S12=S21) and S11
(and S22 if the network is not electrically symmetrical) values, you
can find several simplified
cases.
A few of the cases that you can calculate in a simplified way:
1) everything is ideal: S11=S22=0, S21=1, Zdr=Zrcv=Zo. This is the
obvious case of the ideal
matched interconnect: input and output voltages are the same, equaling
half the source voltage.
If the conditions are true independent of frequency, you could connect
any waveform at the input
and it will appear distortion-free at the output.
2) matched lossy interconnect (S11=S22<<1, S21=S12<1), matched driver
and receiver. Note
that real-life lossy interconnects can not be perfectly matched, that is
why we have S11=S22<<1
instead of =0, but the match can be good enough that the estimate of the
main signal remains
a good approximation. If we further assume sinusoidal excitation (a
single frequency), you
can again calculate the voltages simply based on a 2:1 divider and
attenuation through S21.
3) matched lossy interconnect (S11=S22<<1, S21=S12<1), but assume that
either the driver
or the receiver (but only one of the two) is mismatched AND assume
sinusoidal excitation,
you can still do simple hand calculations as above, plus factoring in
the voltage change due
to the mismatch at one end. (you can do this, because the other end is
matched, so you dont
have multiple reflections that could add or subtract dependent on the
electrical length of
interconnect).
To answer your question: in the general case: if accurate answer is
needed, you need to
go through the full calculation. One straightforward way is to
calculate the transfer matrices
of the driver, channel and receiver blocks and multiple those. In the
general case the
multiplication of S matrices do not work for this. You can then get the
time-domain
result either through Fourier transform or convolution. SPICE is
certainly one tool you
could use, but the free Berkeley SPICE wont have the necessary features:
one of the
commercial versions would be needed. Eventually you could also use any
mathematical
package if linearity can be assumed for the driver and receiver (the
channel is usually
linear). Ultimately you could even use a spreadsheet: one of the
illustrations in my
signal integrity classes uses an Excel spreadsheet with a set of
elaborate macros to go
through the frequency-dependent complex-valued matrices to calculate the
frequency
and time domain response of a causal channel with arbitrary driver and
receiver impedances.
Hope this help.
Regards,
Istvan Novak
Oracle
Lakshmi N. Sundararajan - PTU wrote:
> Hi Istvan,
> Very nicely put.
> I had forgotten the frequency dependency since I was looking at a single
> s-param value within a range of freq where the s11 and s21 was at a max.
>
> Now, given the frequency dependency, is there any way short of using a
> spice tool, to see what would be the max attenuation for a given input
> voltage level on this channel?
>
> I assume that if the specs for this channel were to specify S11 and S21
> for a given range of frequency for valid operation, then one can make a
> judgement straight out of s-param values for the channel.
> But otherwise, to make any sense of a s-param for a channel, is to see
> the time domain graph for a given input signal.
> And this can be made only using some spice tool.
>
> I am curious at this point to understand, what other judgements can be
> made straight out of s-param?
>
> Thanks,
> -LN
>
>
> -----Original Message-----
> From: Istvan Novak [mailto:istvan.novak@xxxxxxx]
> Sent: Friday, March 05, 2010 9:16 PM
> To: Lakshmi N. Sundararajan - PTU
> Cc: si-list@xxxxxxxxxxxxx
> Subject: Re: [SI-LIST] Interpreting s-params to physical voltage levels.
>
> Hi Lakshmi,
>
> This way of calculation would be limited to frequency-independent S
> parameters, which they are definitely not. Keep in mind that in your
> equations the S parameters are in the frequency domain, your voltages
> are in the time domain.
>
> Regards,
>
> Istvan Novak
> Oracle
>
>
> Lakshmi N. Sundararajan - PTU wrote:
>
>> Hi Gurus,
>> Let us suppose I have s-param for a channel.
>>
>> I wanted to figure out from those s-param numbers, assuming I have a
>>
> 1V
>
>> input signal, how much would my receive signal magnitude be?
>>
>>
>>
>> Assuming, s-params are in decibels, then I figure the following
>> definitions for each of them..
>>
>> Sxx_db = 20 Log (Sxx)
>>
>> Sxy_db = - 10 Log ((Sxy ^ 2)/(1 - Syy^2)) /* negative sign is
>>
> normally
>
>> ignored since it is defined as loss */
>>
>>
>>
>> >From the above two equations, I can figure out Sxx and Sxy.
>>
>> And if I assume Vincident,x = 1V
>>
>> Then are the following equations correct?
>>
>> Vreflected,x = Sxx * Vincident,x
>>
>> Vinsertion,y = Sxy * Vincident,x
>>
>>
>>
>> If the above equations are correct, then I can translate manually from
>>
> a
>
>> given set of s-params to a typical voltage levels to see the amount of
>> attenutation,
>>
>> Magnitude wise on the channel, which is what I am looking for.
>>
>>
>>
>> Please correct me here in case my thinking is way off.
>>
>>
>>
>> Thanks,
>>
>> -LN
>>
>>
>>
>>
>>
>>
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