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Re: [Amps] Observations on a Pi-L tank

To: nx7u@arrl.net
Subject: Re: [Amps] Observations on a Pi-L tank
From: R@contesting.com;Measures <r@somis.org>
Date: Sat, 11 Mar 2006 03:47:44 -0800
List-post: <mailto:amps@contesting.com>
Scott -- Due to skin effect, the current carrying ability of round 
conductors at HF is c. 20% of that at DC.

On Mar 10, 2006, at 12:15 PM, Scott Townley wrote:

> A rambling set of observations on Pi-L tank design and realization:
> Proposed amp is for 17m/12m, single 3-500Z, 650W output.  It fills the 
> gaps...
> First come up with design values for the Pi-L from TAP.  Then I built 
> a spreadsheet to design the coils using the Nagaoka formulation rather 
> than the Wheeler approximation (in every ARRL handbook since Wheeler 
> published it, no doubt).
> In playing with the proposed inductor diameter I started wondering 
> what the lower limit was.  With a loaded Q of around 12 then I would 
> need the unloaded Qo to be ~200 to keep the tank losses below 0.5dB 
> (70W).  I could accomplish that with 1/4" tubing or with some existing 
> 2" B&W coilstock, but it’s only 14AWG.  Both will easily give me 
> Qo>200.  So what’s the difference?  I’d rather use the coilstock (less 
> work for me).
> Some number-crunching gave inductor losses of 34W and 5.6W (L1 and L2, 
> respectively) for a Qo of 300 (perhaps optimistic).  To get an idea of 
> the temperature rise, I went through a simple DC analogy for the 12m 
> coil:
> Total wire in 12m coil (L1)=71" (of 1/4" tubing)
> DC resistance of the equivalent wire (2AWG)=973micro-ohms
> If it dissipates 34W, then the analogous DC current is 
> sqrt(Pdiss/DCR)=190A!!
> A quick look at a wire manufacturers chart (Alpha and Belden both have 
> nice hookup wire charts) implies the wire temperature reaching 
> 100degC.  This inference made from the published current limit for a 
> 2AWG wire with a rated 100C insulation being 190A or thereabouts.  
> Might be more since tubing has less thermal mass than solid wire.
> A similar run for L2, but using 18AWG for the much smaller inductor 
> required gave an equivalent DC current of 21A and a temperature of 
> 125C.
> This should be the worst case temperature rise, since at lower 
> frequencies, even though Q decreases approximately as the sqrt(f), the 
> total wire required for the same Xl is roughly ~1/f so equivalent 
> currents will decrease roughly 1/sqrt(f).
> Tank inductors get hot!  I can see why Rich mentions forced-air 
> cooling of tank components from time to time.  40W doesn’t sound like 
> much (we don’t force-air cool our house lights, right?).  I’m guessing 
> that the ultimate limit is probably around 180C (solder melting 
> point)…any comments?  Probably less than that given that metal 
> resistance has a positive temperature coefficient.
> I always thought the decreasing inductor wire size with decreasing 
> frequency (e.g., on a B&W850 and many others) was more for compactness 
> when realizing the higher inductances involved…is it as much as 
> thermal consideration?
> Comments?  Flames?  Further observations?  (already hot enough here as 
> it is…)
>
>
> Scott Townley NX7U
> Gilbert, AZ  DM43di
>
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>



Rich Measures, 805.386.3734, AG6K, www.somis.org

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