## EMC Question of the Week: April 15, 2024

Increasing the twist-rate of a certain twisted wire pair from 1.5 twists/cm to 2.0 twists/cm is found to increase the inductance per unit length by 3%. Based on this result, we expect the capacitance per unit length to be

- also 3% higher
- unchanged
- 3% lower
- unpredictable

## Answer

The best answer is “a.” Twisting the wire pair has virtually no effect on the field distribution in a given cross-section. This means the inductance, capacitance, resistance and conductance per unit length of copper wire-pair is not changed. What does change is the lateral distance traveled per wire length. For example, if you start with two straight 1-meter-long wires and twist them together, the length of the resulting transmission line will be shorter than 1-meter. The greater the number of twists, the shorter the line will become.

So, for the wire pair in this example, if increasing the twist rate increased the inductance per unit length, it was because the signal had to travel through more wire to cover the same lateral distance. If the inductance per unit length increased by 3%, then all the per-unit-length parameters increased by 3%.

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This question may have caught some people off-guard, because changes in the cross-sectional geometry of a wire-pair transmission line have a different effect on the per-unit-length parameters. For example, in a homogeneous dielectric, any change in the cross-sectional geometry that increased the inductance per unit length by 3% would decrease the capacitance and conductance per unit length by the same proportion. The change in the resistance per unit length would depend on how the conductor cross-sections changed and would not be predictable based solely on the change in the inductance per unit length.

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