[TowerTalk] Amplifier Impedance Matching

[Jim Brown]

On 10/27/2013 7:14 AM, Jim Lux wrote:
> In the audio world, I don't think people much care about optimum 
> Thevenin power transfer, and there's no real reason why we should do 
> so in the RF world, except if there's some external constraint. 

Right. Further, let's remember the specific problem on which the maximum 
power transfer theorem is based -- a LINEAR circuit in which the SOURCE 
resistance is FIXED and the load resistance is the variable. In that 
circuit, maximum power will be transferred to the load when the load 
resistance is made equal to the source resistance.

But that does NOT apply at all to a non-linear circuit in which the load 
affects the linearity, nor does it apply to the opposite condition, 
where the load resistance is fixed and the source resistance is the 
variable.  In THIS circuit, maximum power transfer can occur when the 
source resistance is much smaller than the load resistance.

In general, impedance matching for power amplifiers is simply a matter 
of providing a resistive load (with minimal reactance, or with load 
reactance any conjugate of source reactance) to the amplifier that 
allows the amplifier to operate in a dynamic region (i.e., operating 
voltage and current) where it is both linear and efficient, and where 
efficiency is a function of bias, drive level, and those operating 
conditions. There is nothing in this that suggests that the source Z and 
load Z should be equal -- indeed, they were, half the power produced in 
the output devices would be dissipated within the amplifier itself, 
limiting efficiency to 50%, with further reductions in efficiency due to 
class of operation.

The fact is simply that because 50 years ago when the first solid state 
ham rigs were designed they were designed to be happy with a 50 ohm load 
was nothing more than a good design choice given available devices and 
commonly used transmission lines. And I suspect that 50 ohms might have 
been chosen over 75 ohms because the first solid state amps (and their 
output devices) were likely made for use in 2-way radio, which was 
almost exclusively a vertical ground plane that matched 50 ohm coax.  
When I got started in ham radio in the mid '50s, we mostly used dipoles, 
which we learned were a closer match to 75 ohm coax than to 50 ohm coax. 
What we missed in those days was that height affects feedpoint Z, and 
that low antennas tend to be a closer match to 50 ohms. So 50 ohms 
wasn't as dumb a choice as it first looked.  :)

Bottom line -- when we match the antenna to an output stage, we are NOT 
applying the maximum power transfer theorem, we are simply providing the 
output stage an impedance that makes the amplifier happy. That matching 
may be within the amplifier in the form of matching networks, or in an 
external tuner. And in most practical amplifiers, the source Z is less 
than the load Z.

73, Jim K9YC