Electronics > Beginners
Does cable impedance add to source or load impedance?
macboy:
--- Quote from: fonograph on February 15, 2019, 04:02:27 am ---So cable impedance adds up to and counts as source output impedance? I expected it will add up to load impedance.
--- End quote ---
Actually it is both.
From the perspective of the load (speaker), the source has an additional 2 ohms. From the perspective of the amplifier, the load has an additional 2 ohms.
unitedatoms:
--- Quote from: macboy on February 16, 2019, 12:59:44 pm ---
--- Quote from: fonograph on February 15, 2019, 04:02:27 am ---So cable impedance adds up to and counts as source output impedance? I expected it will add up to load impedance.
--- End quote ---
Actually it is both.
From the perspective of the load (speaker), the source has an additional 2 ohms. From the perspective of the amplifier, the load has an additional 2 ohms.
--- End quote ---
For completeness of model, you may choose to consider 4 impedances of 3 devices. Single port source Zs, two port cable with Zin and Zout, and single port load Zl.
My estimate is that typical speaker cable (two thick wires as air line) is about hundred ohms. With insertion loss of -0.00x dB at low Hz frequencies.
edit: I looked up for formulations.
For 1 meter loslsess cable with characteristic impedance of 100 Ohm, 4 Ohm active load the cascade at 1000Hz will look like 4 Ohm plus 0.002 imaginary ohms.
http://www2.ece.ohio-state.edu/~johnson/311/week3.pdf
https://www.wolframalpha.com/input/?i=z%3D100*((4%2B0.002096i)%2F(100%2B0.0000838i))
https://en.wikipedia.org/wiki/Vacuum_permittivity
lost link to value of mu, it is 1.257e-6Henries/meter
The reactance value can be represented as lumped component , inductance about 300nanoHenries
So to answer the topic. You may choose to add very small inductance to load impedance.
Also equally valid to add inductance to source impedance instead.
But to be absolutely correct, the cable should be considered a lossy line and must be not added to either and model should be of 3 devices.
edit 2: Coming from VNA metrology lingo. It looks like for cables with load there is a general intuitive rule. The loads lower than characteristic impedance of line will make input of a cable to look like inductance, the matching loads will look like active load and the loads higher than characteristic impedance will look like capacitance. That sounds very intuitive and with agreement to calibration standards story for VNAs.
With assumption that line is very short. Lines longer than some portion of lambda will look very different.
Zero999:
--- Quote from: fonograph on February 16, 2019, 11:47:56 am ---This is excellent answer, thank you very much Zero999.
--- End quote ---
Except for the fact I made a mistake, which I've corrected.
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