EMC Question of the Week: December 18, 2017

A signal traveling on a 50-ohm cable passes through a connector with a characteristic impedance of 150 ohms before continuing along another 50-ohm cable. 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 "a". An electrically short discontinuity in a transmission line can be modeled with a lumped inductance when the characteristic impedance of the discontinuity is greater than the characteristic impedance of the transmission line. The value if this inductance is,
$$L_{eq}\approx L\mathcal{l}\left[1-{\left(\raisebox{1ex}{${\text{Z}}_{01}$}\!\left/ \!\raisebox{-1ex}{${\text{Z}}_{02}$}\right.\right)}^2\right]$$ where Ll is the inductance per unit length times the length of the discontinuity.

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

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