8/11/2019 [Discussion] ABCD vs T Parameters
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2158 Views 2 Replies Latest reply: Jul 24, 2013 1:41 PM by
MarcVB
Jul 23, 2013 12:44 PM
ABCD vs T Parameters
It seems ABCD and T parameters can both used for cascaded
two-port network analysis, and from what I read, seem toserve the
same basic purpose.Their main difference seems to be that T
parameters relate incident and reflected waveforms (i.e. scattering
transferparameters) when ports are terminated with characteristic
impedances, whereas ABCD parameters relate port voltagesand
currents in short/open circuit conditions.
So my question is, if Z, Y, H, ABCD, S, etc... parameters all
completely describe a two-port network, and conversionformulas are
readily available, if we use a VNA to acquire S parameters, could
we also convert to ABCD params forcascade analysis
(embedding/deembedding), then convert from ABCD back to S params
for the cascaded network? I knowwe can do this with Tparams, and am
trying to understand if they are two paths to the same end result,
of if there aresituations whereusing ABCD params would be more
appropriate than T params.Thanks,Andy
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1. Jul 24, 2013 1:00 AM (in response to Andy_Hinde)
Re: ABCD vs T Parameters
In fact ABCD matrices can be used to embed/de-embed in a
large-signal context given voltages and currents at each portin
order to calculate the (de)embeddedvoltages and currents at another
location.These ABCD values can be calculatedstarting from
S-parameters.
Cascading is typically done using T-parameters (if their
convention is chosen such that they can be cascaded)I didn't give
cascading a thought using ABCD matrices, but mathematically it
should be possible (taking into account theproper current sign
convention) and consistent with using T-parameters.Here's a link
which confirms this consistency:
http://home.sandiego.edu/~ekim/e194rfs01/sparm2.pdfIt states "the
ABCD and T matrices are adept at cascaded networks"
Greetings,Frans
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2. Jul 24, 2013 1:41 PM (in response to fransv1963)
Re: ABCD vs T Parameters
S-par, Z-par, T-par, ABCD etc ... describe linear networks and
the voltage / current and waves at a port are linearcombinations.
As such one can use any of them to perform cascading, embedding or
de-embedding. Depending on thedescription one can use a matrix
multiplication (e.g T-par for wave formalism or ABCD for VI
formalism). Using the othertype of parameters, e.g. S-parameters,
cascading can be done by solving the set of equations.But one
cannot perform cascading without any pre-caution.Suppose one has a
network of which S12 = 0. Intuitively it can be seen that by
knowing a1 and b1, one cannot know a2and b2. Of course, a
consequence of the S12=0 is that b1/a1=S11. But one needs to know
the reflection of the terminationto be able to determine a2 and b2.
In reality S12 will not be zero but very small and will be
influenced by the noise andsystematic calibration errors.
Determining the T-parameters will result in ill conditioned
T-matrix. Using the S-par would bemore adequate but requires the
knowledge of the termination.Suppose one has a network of which S21
= 0, one faces a similar problem. At that moment at port 2, one
knows thatb2/a2=S22. As such a2 and b2 (and equally v2 and i2) are
not related to what happens at port 1. Indeed, the ABCD matrixis
not adequate and will be ill -conditioned when calculated from
measured S-par.In fact to be able to calculate from one port to the
second port, one must make sure that both quantities at the first
portcontain enough "power" of both quantities at the second
port.
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Andy_Hinde
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MarcVB
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