lamp cord audio transmission line REVIEWED

Lamp Code Speaker Transmission Line PhL 6.10.14 See comments at the end. For those reasons, I did not try to include this in lines doc! So ε = 5 or ε = 6 is reasonable! lamp wire 2: d= 1 mm b = 3.0 mm PVC Set G = 0. First compute R from R = 1/(πa2σ) : which is maybe 1 ohm for 45 meters of wire?? Seems low? Well agrees with "std compu power cables" so OK. C = 2πε First get ξ for the left wire: Fine. Now here is C: So C = 79 pF per meter! What about L?? We know that Le = K C = 4πε/K LeC = με = μ0ε0εrel = c-2 εrel so we are talking 0.7 μH/meter which seems OK. This is 700 nH/meter. Lets throw in Lint = 2Li = μ0/4π = 100 nH/m. So ballpark maybe L = 800 nH/m. So we then have G = 0 R = .04 Ω/m for the sum of both wires C = 79 x 10-12 F/m L = 800 x 10-9 H/m for the sum of both wires By one estimate we have So I am getting 100 Ω as Z0 as long as ωL >> R 2πf >> (R/L) f > (R/2πL); Ouch. So at 10 KHz maybe we get this real cable impedance. What is δ? δ ≡ = [ 2/2πfμσ]1/2 = [ 1/πfμσ]1/2 At 1 KHz I get δ = 2 mm while a = 0.5 mm, so not in skin limit. At 4 Khz I get δ = 1 mm while a = 0.5 mm. So I have several problems with this little calculation: (1) the cable impedance is coming out at 100 ohms resistive for f >> 4.4 KHz which does not match an 8 ohm speaker. At lower f the Z0 is not resistive. People would be interested in low f for bass where power is high, but there we don't have a well-terminated transmission line. (2) probably a speaker is an inductive load in general anyway and varying with ω. (3) this is probably a terrible example of a transmission line and I would do well NOT to include it!!!