[Elecraft] : Resonance

[Don Wilhelm]

Guy and Steve,

AFAIK, the condition of zero reactance *defines* resonance whether that 
be a dipole or a tuned circuit using lumped components.

On a dipole of any length (whether resonant or not), the current must be 
zero at the ends (there is no place for it to go - it is an open 
circuit).  If that dipole is less than 1/2 wavelength long, the current 
will be a maximum at the center - lets restrict the discussion to 1/2 
wave or less for simplicity.  The thing which changes as the feedpoint 
is moved along the antenna is the feedpoint impedance - it can be fed at 
any point - the impedance will be lowest in the center and highest at 
the ends.
If you plot both the voltage and the current along an antenna, you can 
get an *idea* about the feedpoint impedance at any point by dividing the 
voltage by the current (there are other factors like the radiation 
resistance, so that is not exact) - in the center, the voltage is low 
but the current is high, so the impedance (V/I) is low and it becomes 
larger as you move toward either end of the dipole.
If the reactance is zero at any feedpoint, it will be zero no matter how 
the feedpoint is moved - that fact only occurs if the wire is resonant - 
if there is any reactance, the values of resistance and reactance will 
move about the constant SWR circle on a Smith chart.

Steve, your analogy of a guitar string is OK, but what you are stating 
only applies at resonance - and is thus comparable only to a half wave 
dipole.  The fact is that a wire of any length can be made to take power 
at any frequency by feeding it with the conjugate of its feed impedance 
- and a transmission line section can easily provide that at certain 
lengths and characteristic impedances (or a lumped element network like 
a tuner).  I cannot think of an easy analogy to that for a vibrating 
string feedpoint.  Maybe the MEs in this group can provide that 
mechanical analogy.

73,
Don W3FPR


Guy Olinger, K2AV wrote:
>> I was always of the impression that the definition of resonance of a
>> half wave radiator is the condition in which the current at the center
>> is a maximum and the current at the ends is at zero.
>>     
>
> This would also be true of a 1/4 wave dipole fed in the center, or any 
> dipole less than a 1/2 wave.  The current would be higher in the center of a 
> less than 1/2 wave dipole, than it would be for the same power fed to the 
> center of a 1/2 wave dipole. No one to my knowledge considers a 1/4 wave 
> dipole "resonant".
>
> I'm not aware of any standard reference that does not define as resonant a 
> 1/2 wave dipole having zero reactance at a center feed. The classic Terman's 
> shows overall circuit current at "resonance" as being entirely resistive. 
> {p.46, Electronic and Radio Engineering 4th Edition, F E Terman, McGraw 
> Hill, 1955}
>
> For the dipole this would be the point that the undissipated power from 
> prior excitation returns exactly in phase with incident excitation.  This is 
> your grid dip meter case of maximum accepted power, hence maximum dip, and 
> also where a center feed displays zero reactive current.
>
> Perhaps a better definition of a wire resonant at a given frequency would be 
> *if there exists* a point on the wire where a feed so placed would not 
> exhibit any reactance. This takes in other cases than center fed 1/2 wave 
> dipoles.
>
> 73, Guy. 
>   
>