load the tuned circuit

[reset]

OK
so are you saying if the impedance is not matched it wastes power?

Sometimes Z matching can be confusing because of the rule of thumb being used out of context. To get the maximum power from a battery we would match the battery internal resistance but in the process we would waste power heating the battery and if it is a wet cell boiling it dry. The better rule of thumb is to maintain a 10 to 1 ratio of load to source resistance. With the 10:1 ratio the source would not be as likely to be burned out. With the battery supply we need to know our maximum available but we don't need to load to it. What is the cranking current for your car battery? Don't you want the battery to be able to produce more than is needed?

Check out this little excursion into transformer action. Note the datasheet says the transformer matches 10K to 200 AND 25K to 500. Now which is it? The simple answer is the turns ratio sets the Z tranformation but the transformer has to be suitable for the service. It is obvious I can't wind a transformer with 100 turns primary and 10 turns secondary and expect it to power a tube filament. it is obvious the inductance of the primary must be able to limit the primary current with no load BUT it is less obvious that it must still be able to limit the primary current when loaded. So what they are saying is the primary will produce 25KOhms at the design frequency with a 500Ohm load or 10KOhms at 200Ohms load. You can see as I adjust the load the primary inductance changes.

http://radio.radiotrician.org/2016/02/mu...ormer.html


In the test I ran above the source sees a load reflected back on it because the secondary is drawing power. If I short circuit the secondary the wire resistance limits the load. When you buy headphones they maybe rated 3KOhms. That is to say the winding resistance is 3KOhms. This would imply a large number of turns of fine wire. The magnetic field would be rated in amp turns of electromotive force. So you would have a win-win situation. High Z to prevent loading the system and high amp turns to make a very sensitive headset. Sadly some less than professional folks would wind the coil with German Silver wire. The resistance of the wire would allow fewer turns to give the desired resistance but not the electromotive force.

You can apply the transformer loading to a tuned circuit. As you load the tank you draw power and it in turn loads the antenna. Because the antenna circuit is power limited you have to load it as lightly as possible while still drawing enough power to drive the phones. The tank is complicated because of the reactive loading producing a voltage or current gain(series voltage gain parallel current gain). Q = Xl/R so we get a gain factor based on Q. The good news is that just as we can wind a transformer to produce more inductance than will limit the current we can build tanks to produce high Qs.

WARNING: I'm going a little crazy to make a point.
Suppose I have a tank with a Q of 100 and I need a a 5Khz bandwidth at 500Khz Fo. BW=Fo/Q=500K/100=5Khz. That is good except I can't load the tank without reducing Q and broadening the BW. Now assume the resistance of the tank is 1OHM (just a round number). So Xl=100 and R=1 giving the Q=100. Now use a larger wire and make R=.1Ohm. Now Q=100/.1=1000 but what happened to BW? BW=Fo/Q=500Khz/1000=.5Khz. Unless I'm receiving CW that is to small a bandwidth But when I load the tank and draw power from it my Q goes down and BW increases so the Higher Q allows me to draw power from the tank and still maintain my desired BW. In effect I transfer the resistance of the load back into the tank and I can load .9Ohm reflected load to have the 1Ohm I had in the first example BUT in the latter case I'm using the power that was being dissipated in the coil winding.
.END crazy