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What is the definition of "signal to ground capacitance" of a coaxial cable. I know what capacitance is, but I'm not sure whether it is just the same thing.

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It's exactly the same thing. It is the capacitance from the signal wire on the inside to the shielding on the outside.

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Yes. Both are the same thing.

To fully understand this, you can view a coaxial cable as a cylindrical capacitor:

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capcyl.html

The inner conductor of the coaxial cable serves as one capacitor "plate" while the conducting shield of the coaxial cable serves as the other capacitor "plate". Therefore, signal to ground capacitance refers to the capacitance between the inner conductor and the conducting shield.

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