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ABCD vs T Parameters

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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 transfer parameters) 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 for cascade analysis (embedding/deembedding), then convert from ABCD back to S params for the cascaded network? I knowwe can do this with T params, and am trying to understand if they are two paths to the same end result, of if there aresituations where using ABCD params would be more appropriate than T params. Thanks, Andy
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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)embedded voltages and currents at another location.These ABCD values can be calculated starting 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.pdf It states the ABCD and T matrices are adept at cascaded networks
Greetings,Frans
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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 linear combinations. As such one can use any of them to perfor m cascading, embedding or de-embedding. Depending on the
description one can use a matrix multiplication (e.g T-par for wave formalism or ABCD for VI formalism). Using the other type 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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