imaginary characteristic impedance

hi guys,

I solved a transmission line problem and end up with a quadratic equation of the characteristic impedance are imaginary numbers. I wonder what is the value condition of a characteristic impedance of transmission line? Can it be an imaginary number? negative or positive? what is the physical meaning of an imaginary characteristic impedance?

Thank you!

Transmission line impedance can be a complex number in a form Z=R+JX. The real part R is the resistance, the imaginary X is the inductance (when positive) or the capacitance (when negative).
If you want to know more you should go to the basics and learn about Smith Chart.

A lossless transmission line has a real characteristic impedance Z0 = √L/C, L and C being the line inductance and capacitance per length unit.

With additional loss elements, the characteristic impedance becomes generally complex, but can't be purely imaginary.

I would think that multimode soutions, like waveguides at higher frequency than the fundamental band, would show up as imaginary impedances. the idea that energy can be temporarily stored in these evanescent modes, just like in a capacitor at low frequency, but it is not dissipated there, and eventually returns to the fundamental mode.

A wave guide impedance becomes imaginary below the cut-off frequency. But the question isn't about wave guides.