[AMPS] Another arc question

Ian White, G3SEK G3SEK@ifwtech.demon.co.uk
Sun, 10 May 1998 12:23:42 +0100

Rich Measures wrote:

>In a parallel circuit, E is constant, and I is variable.  In a series 
>circuit, I is constant and E is variable.  The "normal units" are 

They don't have to be. The choice between working in impedance and
admittance units is completely optional, and based solely on

>>>>>Then on to Part II:  what is the parallel-equivalent resistance of 200nH 
>>>>>in parallel with 200 ohms at 100MHz?  (presumably using the method 
>>>>>described below)
>>>>200 ohms, at ANY frequency, by definition - no calculation is required.
>>>.....not the definition of Rp in Wes' measurements.  
>>Or rather... not in your interpretation of "Rp" in Wes's measurements. 
>>Wes - the guy who made the measurements - emphatically disagreed with
>>your interpretation, and he made the measurements.
>How could Wes' have possibly measured 166 ohms of Rp for a suppressor 
>that uses a 109 ohm resistor?  

Easily - the effect is due to a small series lead inductance external to
the parallel R-L network.

Let's assume that 109 ohms was an accurate value at all frequencies, and
the parallel inductance that Wes used was exactly 100nH (the target
value for all the samples measured). Let's also assume that the
inductance of straight #14 wire in free air is about 20nH per inch (from
standard formulae, and it's not very dependent on wire diameter).

It turns out that lead lengths of only 0.3in between the parallel R-L
network and the binding posts of the impedance analyser would be enough
to push the measured Rp value up to nearly 140 ohms at 10MHz - which is
almost exactly what Wes DID measure (140.85). The computed Q at 10MHz is
19.4; Wes measured 19.7.

So there's your answer. Even a very small amount of stray series
inductance can push the measured Rp way above the physical value of the
resistor in the network.

I chose 10MHz because the components are more likely to behave in an
ideal way down there. At 100MHz this very simple model requires a little
more lead inductance to fit the data - but that's still only about
0.5-inch leads. A model with better representations of the values and
stray reactances in the main resistor and inductor would fit Wes's data
at all frequencies.

I said:
>>2. My terminology and analysis agree exactly with Wes's. 
 - and they still do.

Rich replied:
>If 109 ohms = 166 ohms.  

Or rather, if a 109 resistor can be made to LOOK LIKE 166 ohms at the
terminals of the impedance analyser - which clearly it can. Even a very
small lead inductance is enough to do it.

BTW, that was all done with standard R-X transformations - not an
admittance in sight.

73 from Ian G3SEK          Editor, 'The VHF/UHF DX Book'
                          'In Practice' columnist for RadCom (RSGB)

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