Topband: Re: Coax capacitor losses (summary)

Peter Wardenier Peter.Wardenier at asml.com
Wed Jan 5 07:22:59 EST 2005


Summary:
- coax stubs make acceptable capacitors @ 1.8 MHz 
- example 10m RG58A Ri=0.69 ohm, Q~110; loss<0.1 dB when used as series 
  cap for a slightly long quarter-wave vertical)
- Q scales with (~1/stub length) 
- theory and experiments are in agreement(again)

Thanks to Kevin, W9CF the 'mystery' has been fully solved 
(refer to my 30 Dec 2004 posting). 

Here's Kevin's full answer that I got by e-mail:
> The transmission line equations are fine. The problem with Peter's
> analysis is the incorrect assumption that the characteristic impedance
> is purely resistive. Making this approximation assumes that the loss
> is equally in series resistance of the conductors and in the parallel
> resistance of the dielectric. This approximation has little effect
> if the line length is a multiple of a quarter wave length (or if it
> is so long that it is many wavelengths) or nearly matched. However,
> this resistive Z0 approximation is completely inaccurate for short
> runs of coax at high SWR, which is exactly the case when using an open
> circuited line as a capacitor. Both my applet and TLA use a complex
> Z0 and therefore correctly give the increase of Q when the line gets
> short. This is because, as Tom mentioned, there is less affect from
the
> series resistance for short lengths, and the series resistance of the
> conductors is the dominant loss mechanism.

The effect has recently been illustrated on this forum by the example 
given by David, WX7G.

Finally, some noteworthy remarks made by various commentators:
- resistive losses in coaxial cables dominate; dielectric loss can
safely 
  be ignored in the calculations (esp. at these low frequencies)
- Zo is not your 50 ohms, but may turn into something complex (as stated
above
  by Kevin); examples: RG58 @ 1.8 MHz Zo=50-j1.7 ohm, RG213 Zo=50-j0.79
ohm 
  ref. http://fermi.la.asu.edu/w9cf/tran/
- ignoring the additional imaginary component in Zo leads to
overestimating the 
  value of Ri for short stubs
- for the mathematically inclined reader: if g=0 (no dielectric losses),

  Zo = sqrt[(r+jwl)/jwc], or after some manipulation:
  Zo = Ro(1-j*alpha/beta) with 
   -   alpha [Neper/m] = attenuation per unit length [dB/m] / 8.686 
   -   beta [radians/m] = 2*pi / (free space wavelength [m] * coax
velocity factor)
   -   Ro [ohm] = sqt(l/c)
 
73, Peter PA3AUC


-- 
The information contained in this communication and any attachments is confidential and may be privileged, and is for the sole use of the intended recipient(s). Any unauthorized review, use, disclosure or distribution is prohibited. If you are not the intended recipient, please notify the sender immediately by replying to this message and destroy all copies of this message and any attachments. ASML is neither liable for the proper and complete transmission of the information contained in this communication, nor for any delay in its receipt.



More information about the Topband mailing list