[TowerTalk] Liberal Arts Major and Antenna Theory

[Jim Lux]

At 01:48 PM 6/20/2005, Lee Buller wrote:
>Can someone direct me to a web site that explains antenna input impedance 
>for a Liberal Arts Major with a smattering of college algebra some 35 
>years ago?  I've never understood imaginary numbers.  I am working on yagi 
>design here and the program defines input inpedance in imaginary 
>numbers...such as 41.3 -j .9 ohms.  OK.  I am trying to interpret that stuff.
>
>Lee - K0WA
>

What that tells you is that the current is out of phase with the voltage:

E = Z*I

Think of the feedpoint impedance as a resistor in series with either a 
capacitor or an inductor (or nothing).  If the j part is negative (as you 
have with 41.3-0.9j ohms), then it's a capacitor.  If the j part is 
positive, it's an inductor.

If you want to turn the imaginary part (the j) into pF or uH, you use the 
equation:

X = 2*pi*f*L  (for positive X)  OR  L = X/(2*pi*f)
X = -1/(2 * pi* f * C)  (use for negative X)  OR  C = -1/(2*pi*f*X)

if f is in MHz, then L is in uH and C is in uF.

There's a theorem that says that maximum power transfer occurs when the 
source has an impedance that's the complex conjugate of the load 
impedance.  Complex conjugate means flipping the sign of the imaginary (j) 
term.  So,  in your case, the optimum source impedance would be 41.3 + 
0.9j  (a so called conjugate match).

If your source and your load aren't matched (as above), some of the power 
gets reflected from the interface. This may or  may not be a bad thing.  If 
the amount of power reflected is small, then you don't care.  If the amount 
of power reflected is large, then it IS a problem, because reflected power 
isn't necessarily being radiated (at least from the antenna).  Note well 
that even a purely resistive load can reflect power (that is, a 25 ohm load 
will reflect power back to a 50 ohm source)

Since most ham gear is made to work with a 50 ohm impedance, in general, 
you want your antenna impedance to be as close to 50 ohms as is 
practical.  This presents a practical problem, because most antennas have 
an impedance (particularly the imaginary part) that varies with frequency. 
So what people do is compromise by having a mismatch that isn't "too bad" 
over the range you want to operate over (i.e. 1.5:1 VSWR bandwidth)



>Common sense is in short supply - get some and use it.
>If you can't find any common sense, ask for help from
>somebody that has some common sense. - Lee Buller
>_______________________________________________
>
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>Weather Stations", and lot's more.  Call Toll Free, 1-800-333-9041 with 
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>
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