I'm curious to know how the turn rate of a twisted pair affects the frequency of crosstalk interference rejection.
It's clear that an untwisted pair has no inherent rejection. Alexander Graham Bell figured out in 1881 that twisting is good, so we now twist wire to reduce crosstalk.
As twisted pair communication has evolved, cabling has started to be specified with more and more twisting (cat5 is around 50-70 twists/meter). Ostensibly this is to ensure we can reduce crosstalk at higher frequencies of communication.
I understand the principle of why twisting is good. I'm looking for a mathematical or rule-of-thumb explanation for the relationship between the twist ratio and the bandwidth I get from crosstalk rejection.
The Internet is not yielding such an explanation for this. Am I missing something?
Best Answer
As I recall from doing this 40 yrs ago, twisted pair was about 240 to 120 Ohms differential impedance depending mostly on the insulation thickness. The closer the conductors the more capacitance and lower impedance while increasing the number of twists per unit length increases both the capacitance and inductance so the change is less significant, where \$Z= \sqrt \frac{L}{C}\$ .
Meanwhile the crosstalk is the result of a coupled input signal. The attenuation ratio of E field in free space to impedance of the cable and the tolerance of wire mismatch will be effectively cause poor CMRR similar to a say 1% resistor (-40dB CMRR) unlike a -100 dB CMRR in an INA (INstrument Amp). As you go to "far field" this imbalance can improves.
When that cable has a differential signal it is easy to understand the induced crosstalk is greater when the load impedance is mismatched and thus \$V(F)=I(f)*ΔZ(f)\$.
Wire Inductance per m depends slightly on L/D ratio from 0.5uH to 1 uH /m Wire Pair Capacitance per m length depends on gap of insulations. Both L,C increase with twists per cm or inch.
I would expect (but never measured) insulation thickness of 2 strands is approx equal to wire diameter to get the rated impedance of the twisted pair.
Ribbon cable I recall was 200 to 220 Ohms.
As I recall each twist adds about 1 pF but I am not sure about L.
But it is harder to visualize say a 0.2% mismatch in coupling capacitance or inductance unless you have perfect uniformity and it the twists are far away from the interfering source.
For an E field in [V/m] the coupling is capacitive and for a B field it is inductive [A/m] while the bandwidth of the signal is limit by the 0~90% risetime \$BW_{-3dB} = 0.35 /T_r\$
Since CAT 5 uses matched impedance applications, I suspect the number of twists is far more tolerant than the insulation thickness to wire thickness ratio.
Beyond 1GHz you need a shielded pair for adequate SNR even with the best BALUNs. That's my hand-waving argument for today.