[Elecraft] : Resonance

[Don Wilhelm]

David,

You are correct, this *is* a common point of misunderstanding.  You 
referred to the driving "source impedance" in your statement, and I 
believe that is the source of the misunderstanding.

What you say is true about the driving generator.   Amplifiers are 
designed for some efficiency into some load - in our case, usually 50 
ohms, and whatever the amplifier designer must do to make that happen is 
up to the designer.  However, to obtain maximum power transfer *into* 
the antenna, the antenna and feedline must have an impedance that 
matches the output impedance of the amplifier - we all strive to match 
our antennas to a 50 ohm load (or an SWR of 1:1 based on a 50 ohm system).

We typically adjust the parameters of an antenna system to have an input 
impedance of 50 +j0 ohms in order to obtain the maximum power into the 
antenna (because that the the load the amplifier needs to see for proper 
in-spec operation).  To accomplish that, we might have a tuner of some 
nature between the transmitter and the input of the feedline.  If the 
antenna feedline has an impedance of (for example) 120 +j30. then the 
matching network will have an input impedance of 50 +j0 and an output 
impedance of 120 - j30 -- that is as far as it goes.  I stand on my 
statement (but will not extend it to the internals of amplifier design) 
- it is only related to feedline and antenna matching.

Consider that if one builds a matched antenna system at some frequency 
as I described above and terminates it at the transmitter end with a 50 
ohm pure resistive dummy load.  Now split the feedline at any point and 
measure the impedance of both the open ends created by the split - you 
will measure an R+jX impedance in one direction and an R-jX impedance in 
the other direction - that is a conjugate match.  If it is something 
other than that, there will be significant loss in the antenna system.

Yes, if we put a theoretical (equivalent circuit) generator on that 50 
ohm feedpoint, that theoretical generator must have an internal 
resistance of 50 +j0 ohms to achieve maximum power transfer between that 
theoretical generator and the antenna feed - and the power dissipated by 
that theoretical resistance on the theoretical generator will be the 
same as that delivered to the load.  However, real amplifiers are not 
usually built the same way we create equivalent circuits.  We do know 
that amplifier efficiencies can be much higher than 50%.  When we 
replace the real amplifier with an equivalent circuit, that will contain 
a driving generator of zero loss and a series resistance of 50 ohms, but 
we never analyze the internals of an equivalent circuit, it is only the 
*representation* of the driving source which makes the system being 
analyzed behave as though the real generator (amplifier) were driving it.

73,
Don W3FPR

>
> Although I agree with most of the preceding, the above statement hints 
> at a common misunderstanding.  In general, you do not want to feed an 
> antenna from a source impedance that is the the complex conjugate of its 
> impedance.  Doing so guarantees that you cannot exceed 50% efficiency.
>
> Whilst such matching will give you the highest power for any given open 
> circuit voltage, it will not give you the highest output power for a 
> given input power.
>
> When one says is a transmitter is matched to 50 ohms, one actually means 
> that its output network presents the optimum load to the finals when 
> feeding a 50 ohm load.
>   
>