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Old 16th Jul 2019, 3:21 am   #4
Radio Wrangler
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Join Date: Mar 2012
Location: Fife, Scotland, UK.
Posts: 17,869
Default Re: "Matching" transformer.

Just be careful with the word 'Matching'

The technically exact meaning is the connection together of two things where the output impedance of the source is equal to the input impedance of the load. Note that there is an implied halving of efficiency, because as much power must be being dissipated in the source impedance of the source as goes into the load. This is not an ideal situation when your only aim is to stuff power into the load. So, many sources, including radio transmitters, are designed to shove the required power into the specified load, but their output impedance is NOT matched to the load. The freedom is used to be more efficient, use smaller devices, have smaller electricity bills. This either means that the output impedance is appreciably lower than true match, or appreciably higher.

So why the fuss about matching?

The first reason is simple science. If I have a length of cable, it will have a characteristic impedance. If I send a wave down this cable, it temporarily looks to whatever is driving it as Z0. down the cabe go a pair of waves, one voltage, one current. at any point, at any time, the ratio between the voltage and the current are Z0. So that's what flies out the far end and hits the load. IF the load impedance is equal to Z0 (The cable and the load are matched to each other) The load sees the right ratio between the current and the voltage and absorbs the lot. Yummy! IF the load does not equal Z0, then there is either too much voltage for the current, or too much current for the voltage. The load cannot absorb all that hits it. Now the power sent down the line was put in an amount of time earlier and as we aren't about to discover the keys to a time machine, there isn't anything we can do about that. There is only one place for the power the load doesn't accept to go... back up the line. The line will only accept a reverse wave as a voltage/current pair in the magic Z0 ratio, so you have to solve a couple of equations to work out what fraction of the original power gets to the load, and how much turns back. Double entry bookkeeping for the voltages and currents at the point where the line connects to the load shows that the books balance, and from far on high, Mr Kirchoff is smiling. So now we have a smaller wave coming back and hitting the source. The wave sees the source as a new load to try to get off into. If the source is truly matched to the cable, it absorbs the reflected wave totally, and the tale ends here, provided the source can take the applied voltage and current vector-added to the voltage and currents of its intended output. But what if the source isn't matched to the cable? Its output impedance is wrong for the reflected wave hitting it and it's that partial reflection thing all over again. Our reflected energy bounces to-and-fro losing some at each bounce until the level is negligible.

Sounds complicated? It is, but there are tools for handling it. Also, it only needs bothering with if the cable length is a significant fraction of a wavelength at your highest frequency. At audio, this means you are going to need a very very large lounge to justify those immensely expensive speaker cables

The second reason is that in some uses of cables you don't want the hall-of-mirrors thing going on. Good RF measuring instruments need to suppress it because it upsets their accuracy with ripply frequency responses. Sig gen designers do an output amp with as low a Zout as they can, then pad it up to 50 Ohms with a resistor. True matching makes delivery of calibrated power levels possible.

There is something called "The maximum power transfer theorem" It's dead simple. It says that if you have a power source, with an output impedance of Zout, driving a load of Zload, then adjusting Zload to equal Zout will extract the maximum power it is mathematically possible from that theoretical source.

Sounds good, dunnit?

It's what we came across earlier where our cable met its load, so we want to do it in some places.


The max power transfer theorem cares not at all about efficiency and the size of your power bills.

The max power transfer theorem cares not at all about whether your source can stand the voltages and currents it sets, or if the thing goes up in smoke. Your source is a real world one and not quite the same as an idealised mathematical model. Real world ones are much more expensive.

So in a hifi setup, the speaker cables are negligible, The speaker impedance should be within the amplifier's happy region. The amplifier is under no obligation to present that value as an output impedance. Damping factor is a measurement of how FAR it is away from a true match. If all is well, your amp is loaded within its capabilities and there is no matching going on. Matching is a two-way thing. It takes two to Tango...

In an amateur radio setup, you want to adjust your antenna so its feed impedance matches your feeder cable, so there is no reflection back to the transmitter. Where the transmitter output is marked "50 Ohms" read that as "Please connect me to 50 Ohms" but don't assume that the output looks like its from a 50 Ohm source, it could be a long way different.

So there you have it. "Matching" is a very special word with a precisely defined meaning in the electrical world. Unfortunately it gets used a lot in places where matching is not going on. This causes so much confusion, that whenever you spot it, you should question it.

Sometimes, what's going on is loading, not matching.

Can't afford the volcanic island yet, but the plans for my monorail and the goons' uniforms are done
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