[TowerTalk] Bazooka 1/4 wave balun

[Jim Lux]

At 01:04 PM 7/7/2005, Tom Rauch wrote:
> > If you can put it into a resonant circuit, then you can
>measure Q by
> > measuring 3dB points, turning the measurement problem into
>one of
> > accurately matching levels (at the two points), and
>measuring frequency
> > accurately (which is fairly easy).
> >
> > A resonant circuit with a Q of 500 at 14MHz would have a
>3dB bandwidth of
> > 28 kHz. The challenge would be accurately knowing when
>you're really at
> > 3dB. And, how would you couple in the power in a
>consistent way? A single
> > turn link coupling probably wouldn't cut it.
>
>I don't think so.
>
>The 3dB point method assumes you have a perfect lumped
>capacitor whose reactance changes as calculated by formula
>and the inductor does the same. Large components don't do
>that, especially as we approach a frequency where the
>components are changing fast. Far away from self-resonance
>everything changes normally and with lumped components that
>would work fine assuming you could measure 3dB points.


Ideally, one would be far from the inductor's self resonance (i.e. you'd 
need that lumped C to form the resonant circuit)  (this may not be 
reasonable for inductors that hams might want to measure, though, in, for 
instance, traps, where self C is considerable).  Likewise, the C would need 
to be far from self resonance (substantially easier, since it can be 
physically small.. it doesn't need to handle significant power, so any 
decent low loss RF capacitor should do)

Just to put some numbers to the discussion...
a coil 2 inches in diameter, 10 inches long, with 10 turns per inch (100 
turns all told) has an approximate inductance of 86 uH and a self C of 
about 4.1 pF  (Wheeler and Medhurst approximations used, respectively).

 From this, self resonant frequency would be about 8.4 MHz.  Say you wanted 
to use it at 3.7 MHz, so you want to measure it at that frequency. To get 
it to resonate, you'd need to add about 17 pF in series.  Assume you can 
get a lossless air dielectric capacitor (something like a moderate sized 
toroid or sphere, working against a ground plane, might do).

The reactance of the 86 uH inductance at 3.7 MHz would be real close to 
2000 ohms.  If the Q (of the system) were, say, 500, then you're looking 
for 4 ohms of resistance.

Now, looking at the challenge of measuring 3dB points.  Say you drive this 
from a 50 ohm signal generator, and measure the voltage.  At resonance, the 
voltage will be lowest (i.e. 4/54 * open circuit voltage).  At the 3 dB 
point, the reactance should also be 4 ohms, so the voltage will be 
(4+4j)/(54+4j)

If the open circuit voltage of the signal generator is 1V, then at 
resonance, the voltage across the RLC would be 0.0741.  At the 3dB point 
(going up in freq) it would be .079+.068j, or 1.41V magnitude....

I guess this is where the problem lays, in a practical sense. It's hard to 
determine the 3dB points with a simple measurement (since the source 
impedance of the generator figures into it, and you don't know the loss 
term until you've done the bandwidth measurement.  If you had a very high 
impedance current source(or an accurate impedance meter that could read low 
impedances).

Seems, though, that one should be able to work out a scheme using a 
standard SWR bridge (like an antenna analyzer) that gets the values into a 
range where the swr bridge is reasonably accurate.  Clearly, measuring 4 
ohm impedances (a VSWR of 12:1) is out of the question.


>If I add stray capacitance across an inductor by using a
>poor inductor design and place that inductor in a series
>resonant circuit, 3dB BW becomes narrower while the Q based
>on loss resistance is actually reduced!
>
>Some of my  narrowest mobile antennas have the highest coil
>ESR.
>
>73 Tom
>
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