The truth about coaxial cables at high frequencies

[htg]

High inductive impedance and low capacitive impedance of coaxial cables make it unbelievable that with proper resistive termination R such a coaxial cable behaves like a lossless line with the resistance R at the end.
Do HF probes in oscilloscopes brutally amplify signals to make up for attenuation introduced by coaxial cables?

 

[FvM]

Which "HF probes" are you specifically asking about? No coaxial cable is completely lossless, but short cables (e.g. a few meters long) have fairly low losses up to GHz range. You didn't mention a frequency range and a cable impedance.

Not sure if you understand the role of inductive and capacitive impedance of a coaxial cable. Characteristic impedance Z = √(L/C), e.g. 250 nH/m and 100 pF/m results in 50 ohms impedance.

 

[htg]

Which "HF probes" are you specifically asking about? No coaxial cable is completely lossless, but short cables (e.g. a few meters long) have fairly low losses up to GHz range. You didn't mention a frequency range and a cable impedance.

With the specific inductance of the order of 1 microHenry/m and specific capacitance 100 pF/m it is hard to believe low attenuation at GHz range. To get a brutal estimate, consider length = 1m and ω = 6 Grad/s - then we are dealing with 6kΩ of inductive reactance and with 1.66 Ω of capacitive reactance. Regarding active HF probes I am asking a general question

 

[KlausST]

Hi,

Let's say 10GHz....and a cable with signal speed of 200.000km/s.
Then one fullwave is just 0.02m.

Thus the 10GHz signal never will "see" full inductance of 1m nor will it see full capacitance of 1m.

The 0.02m wave is travling through the cable of random length.
And the Cs and Ls of this 0.02m are very lossless, thus almost full injected energy is pushed continously further through the cable.

Imagine throwing a stone into a lake.
You will see a wave (ring) traveling from center.
The amplitude of the wave does not depend on the size of the sea.
Nor does traveling speed or damping depend on the size of the lake.

But in opposite to a "linear" cable ... the diameter of the wave is increasing ... thus the area of water under the wave is increasing ... and because of the energy does not increase, the amplitude needs to decrease.

But have a look into videos where a water wave travels in a canal with concrete walls. The amplitude of the wave may be about constant for many kilometers.

Klaus

 

[FvM]

See attenuation of commonly used RF cables. An active oscilloscope probe might e.g. use RG-174, 1 dB/m @ 1 GHz.



Reactive impedance (specific L and C) doesn't cause cable losses, only resistive impedance components, series R (conductor resistance with skin effect) and shunt G (dielectric losses).

 

[volker@muehlhaus]

With the specific inductance of the order of 1 microHenry/m and specific capacitance 100 pF/m it is hard to believe low attenuation at GHz range. To get a brutal estimate, consider length = 1m and ω = 6 Grad/s - then we are dealing with 6kΩ of inductive reactance and with 1.66 Ω of capacitive reactance. Regarding active HF probes I am asking a general question

You misunderstand the concept of RF lines. The L' and C' are distributed across the length, which behaves completety different from a simple low pass of 1µH and 100pF. The line that you describe has a line impedance of Zline = sqrt(L'/C') = 100 Ohm which can be properly terminated by 100 Ohm load. That can be very wideband, the line just introduces a delay but no low pass behaviour.