Characteristic Impedance and RC Filters

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Posted by Maxamillion (A) on April 23, 2010 at 11:04:37

I have been reading up on the subject of RC filters and came across the concept of characteristic impedance of a cable. A post from Al back in 2006 notes that if you know the characteristic impedance of your cables, a resistor value matching that value will give better results in an RC filter than the generic 10ohm resistor often specified.

I read up on characteristic impedance as defined in infinitely long transmission lines, and it turns out there is a relatively simple formula for calculating this at high frequencies such as the RF we are concerned with here:

Z(0) = sqrt(L/C) where L = series inductance per unit length and C= shunt capacitance per unit length of the cable.

Fortunately for me, Zu cables publishes the L and C values for their Ibis speaker cables, which I own, and the values are L=3uH and C=600pF. Plugging these in, I get a Z(0) = 70.7ohms.

Now that I know the Z(0), I can use a standard 68R resistor to better match my speaker cables. To keep approximately the same RC time constant I will need to use approximately 1400pF of capacitance in the filter.

Sound about right to the experts?

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Topic - Characteristic Impedance and RC Filters - Maxamillion 11:04:37 04/23/10 (17)

RE: Just use a resistor. - rick_m 14:10:20 04/24/10 (0)

Yes, but... - Al Sekela 14:40:56 04/23/10 (13)

Yes about those Parallel Networks... - Maxamillion 07:11:52 04/24/10 (11)

Procrustes' Bed - Al Sekela 15:32:56 04/24/10 (8)

I'm easily confused.... - rwiley 21:51:56 04/25/10 (7)

Yes, that's correct, but - Maxamillion 05:36:13 04/26/10 (6)

I've had good results with... - rwiley 08:00:30 04/26/10 (1)

RE: I've had good results with... - Maxamillion 13:31:47 04/26/10 (0)

Without the theory, in practice - bartc 06:15:09 04/26/10 (3)

Thanks, Bart. Have you tried... - Maxamillion 07:35:05 04/26/10 (2)

Yes, Max, I tried that too - bartc 07:41:29 04/26/10 (1)

I will try multiple combos - Maxamillion 08:30:32 04/26/10 (0)

That is a nature of capacitors after all... - Tweekeng 13:21:15 04/24/10 (1)

RE: That is a nature of capacitors after all... - Maxamillion 13:50:38 04/24/10 (0)

RE: Yes, but... - Maxamillion 19:31:40 04/23/10 (0)

Applies only to R-C filters on SPEAKER cables - bartc 11:22:38 04/23/10 (1)

RE: Applies only to R-C filters on SPEAKER cables - Jack D II 13:14:30 04/27/10 (0)

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