Dear Sir:

I am new to microwave fixture de-embedding and I am in the process of learning

scattering transfer parameters T-parameters). I have read conflicting accounts with

regard to how transfer scattering parameters are defined. For example, if you go to this

link I have provided below and scroll down to the section entitled "scattering transfer parameters":

[ http://en.wikipedia.org/wiki/Scattering_parameters ]

There one will see two equations that define the T matrix differently. This is not the only

example that I have read online where the T parameter matrix is defined differently. There

exist many definitions of T parameters.

Therefore, to avoid any confusion, the T parameter matrix equations that I will be

referencing are found in Agilent Application Note 1364-1 (see Appendix for the reference

equations). For your convenience I have provided a link to this application note:

[ http://anlage.umd.edu/Microwave%20Measurements%20for%20Personal%20Web%20Site/5980-2784EN.pdf ]

I would like to be provided the 2x2 T matrix for two (2) lossless cables (each cable

is a separate T matrix, cable 1 = 1/4 wavelength and cable 2 = 1/8 wavelength) connected to

a fixture T matrix. The two matrices are configured in this equation below:

{ Tmeasured } = { T-cable 1} * {T-fixture} * {T-cable 2 }* {T-load=Zo}

If you see page 5 of AN 1364-1, a fixture is modelled as an ideal tline in a 2x2 S

matrix in this form:

{ 0 e^(-j*theta) }

{ e^(-j*theta) 0 }

I would like to be provided the 2x2 transmission scattering matrix (T-matrix) for each

cable matrix, both, { T-cable 1 } and { T-cable 2 }, such that the multiplication of these

matrices will be mathematically consistent with the { T measured } matrix found in the

equation above.

Can someone please provide me with an explicit answer to this question in matrix form?

Thank you for your consideration.

Edited by: SOLT_guy on May 28, 2015 8:24 AM

Edited by: SOLT_guy on May 28, 2015 8:25 AM

Edited by: SOLT_guy on May 28, 2015 8:31 AM

Edited by: SOLT_guy on May 28, 2015 8:33 AM

I am new to microwave fixture de-embedding and I am in the process of learning

scattering transfer parameters T-parameters). I have read conflicting accounts with

regard to how transfer scattering parameters are defined. For example, if you go to this

link I have provided below and scroll down to the section entitled "scattering transfer parameters":

[ http://en.wikipedia.org/wiki/Scattering_parameters ]

There one will see two equations that define the T matrix differently. This is not the only

example that I have read online where the T parameter matrix is defined differently. There

exist many definitions of T parameters.

Therefore, to avoid any confusion, the T parameter matrix equations that I will be

referencing are found in Agilent Application Note 1364-1 (see Appendix for the reference

equations). For your convenience I have provided a link to this application note:

[ http://anlage.umd.edu/Microwave%20Measurements%20for%20Personal%20Web%20Site/5980-2784EN.pdf ]

I would like to be provided the 2x2 T matrix for two (2) lossless cables (each cable

is a separate T matrix, cable 1 = 1/4 wavelength and cable 2 = 1/8 wavelength) connected to

a fixture T matrix. The two matrices are configured in this equation below:

{ Tmeasured } = { T-cable 1} * {T-fixture} * {T-cable 2 }* {T-load=Zo}

If you see page 5 of AN 1364-1, a fixture is modelled as an ideal tline in a 2x2 S

matrix in this form:

{ 0 e^(-j*theta) }

{ e^(-j*theta) 0 }

I would like to be provided the 2x2 transmission scattering matrix (T-matrix) for each

cable matrix, both, { T-cable 1 } and { T-cable 2 }, such that the multiplication of these

matrices will be mathematically consistent with the { T measured } matrix found in the

equation above.

Can someone please provide me with an explicit answer to this question in matrix form?

Thank you for your consideration.

Edited by: SOLT_guy on May 28, 2015 8:24 AM

Edited by: SOLT_guy on May 28, 2015 8:25 AM

Edited by: SOLT_guy on May 28, 2015 8:31 AM

Edited by: SOLT_guy on May 28, 2015 8:33 AM

If your cable is 1/4 wavelength at F0, then, S21(F) is

S21=e^-(j(2*Pi*F/(4*F0))

And the T matrix is

{S21 0 }

{ 0 1/S21 }

or

{ e^-(j(2*Pi*F/(4*F0)) 0 }

{ 0 e^j(2*Pi*F/(4*F0)) } If I did my complex exponetials correct.

1/8 wavelength is

S21=e^-(j(2*Pi*F/(8*F0))

{ e^-(j(2*Pi*F/(8*F0)) 0 }

{ 0 e^j(2*Pi*F/(8*F0)) }

Or at least I think so. This gives the mag as 1 and the phase as Pi/2 for F=F0 for 1/4 wave, which I think is the definition of 1/4 wave. I developed this by saying e^-j(2*piF/F0) is the full wavelength case for S21 at F=F0 and just divided by 4 or 8.

Edited by: Dr_joel on Jun 1, 2015 12:40 PM

Clean up matrix where tabs didn't show and added explicitly the two cases.