[Elecraft] : Resonance

[Stephen W. Kercel]

Don:

Your points are well taken.

TNX & 73,

Steve
AA4AK


Don Wilhelm wrote:
> 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.  
>