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Matching at 1000 Ohm to 50 Ohm.

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Georgy.Moshkin

Georgy.Moshkin

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I found this interesting example:
Suppose that the impedance of the antenna is very far from 50 ohms and very reactive, say 1 − j × 1000 ohms, which is not uncommon for nonoptimal antennas. To match it and cancel the 1000-ohm capacitive reactance, you need to add a serial inductor with a reactance of 1000 ohms. Unfortunately, you can't buy an ideal inductor. Good inductors may have a quality factor Q of, say, 200, which means that their parasitic resistance will be 200 times less than their reactance (here 1000/200 = 5 ohms). If you compare this value with the 1-ohm resistance of this antenna at resonance, you can see that five times more energy will be dissipated in the matching inductor than radiated by the antenna, which is not optimal. This is only an example, but it is significant. If you have an antenna with an impedance far from the source impedance, building a matching network will often be practically impossible, even if it is always theoretically possible.
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It states that building matching network will be practically impossible. What if it is sqrt(1000*50)=223 Ohm quarter-wave transformer? Or frequency is too low and transformer will be impractical (length and cable losses, narrowband)?
 

He said well... Even 223 Ohms Transmission Line will be very thin that is practically not reliable in manufacturing.
 
The antenna load assumed in the quote can't be matched by a quarter wave transformer, even if the line impedance would be feasible. 1000:50 ohms real impedance matching is well possible with LC networks (medium bandwidth) or real transformers (wide bandwidth). We should talk about frequency band and bandwidth first.
 
What is "theoretically possible" solution author talking about:
1) putting inductor to transform 1 − j × 1000 Ohm to 1 Ohm.
2) And then? 1 Ohm to 50 Ohm transformer?

About "five times more energy will be dissipated in the matching inductor than radiated by the antenna, which is not optimal".
What would be practical solution for this "nonoptimal antenna" example? Does it makes sense to make "partial" matching using different inductors with lower parasitic resistance? Or only solution is to re-design this antenna to be more optimal?
 

Basically if your antenna has a given Q (1000 in this example) then in order to exchange power efficiently with it you will need matching components with an even higher Q.

Matching 1 ohm to 50ohm, or 1000ohm to 50ohm, is not too difficult. But matching 1-j1000 ohm to 50ohm, or 50-j50000, or 0.05-j50 to 50 ohms is very difficult without extremely high Q inductors.
 
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