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Propagation constant of a microstrip transmission line on FR4 from ABCD-Parameters

时间:04-04 整理:3721RD 点击:
Hi,

I am trying to calculate the propagation constant (γ=α+jβ) of a microstrip transmission line from the measured S-parameters (ABCD-parameters).
The relationship seems to be given by the equation:
γ=acosh (A)/d
where d is the length of the transmission line (0.15 m) and A is the complex A-parameter.

The measured S parameters (S11 & S21) at 3 frequencies were:
At 1 GHz, S11=-0.013+0.022i, S21=0.80+0.50i
At 1.5 GHz, S11=-0.0069+0.016i, S21=-0.88-0.23i
At 2 GHz, S11=-0.036+0.022i, S21=0.40+0.79i

The A parameter at 3 frequencies are as below (these are converted from the above S-parameters):
At 1 GHz, A=0.85-0.032i
At 1.5 GHz, A=-0.97+0.024i
At 2 GHz, A= 0.45-0.11i

According to the transmission line equation, γ at these frequencies are as below:
At 1 GHz, γ=0.40-3.7i
At 1.5 GHz, γ=0.62+19.19i
At 2 GHz, γ=0.82-7.39i

Since α and β never becomes negative, am I calculating wrong?
Or, is that from my measurement error?

Also, I would typically expect to observe the imaginary part of the propagation factor (β) increases with the frequency.

Without going into the calculation details, obviously the micro strip length is larger than lambda for some frequencies and calculating propagation constant from S21 phase is ambiguous.

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