EMC Question of the Week: August 6, 2018

A signal traveling on a 120-ohm wire pair passes through a connector with a characteristic impedance of 50 ohms before continuing along on another 120-ohm wire pair. At frequencies where the connector is short relative to a wavelength, the connector can be accurately modeled with a,

1. series inductor
2. shunt capacitor
3. series resistor
4. shunt resistor

Answer

The correct answer is "b". An electrically short discontinuity in a transmission line can be modeled with a lumped capacitance when the characteristic impedance of the discontinuity is less than the characteristic impedance of the transmission line. The value of this capacitance is,
$$C_{eq}\approx C\mathcal{l}\left[1-{\left(\raisebox{1ex}{${\text{Z}}_{02}$}\!\left/ \!\raisebox{-1ex}{${\text{Z}}_{01}$}\right.\right)}^2\right]$$ where Cl is the capacitance per unit length times the length of the discontinuity.

Similarly, an electrically short discontinuity with a characteristic impedance higher than that of the transmission line can be modeled with a lumped inductance.

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