# Antennas and Impedance Matching

Discussion in 'Wireless & RF Design' started by PRS, Jun 3, 2014.

1. ### PRS Thread Starter Well-Known Member

Aug 24, 2008
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Now that I have gotten back into radio design I am wondering what gives rise to an antenna's impedance. It couldn't just be the dc resistance as measured by an ohm meter and so it must be reactance.

And I would guess it's a matter of capacitive reactance in that: the longer a wire is, the more capacitance it displays. With this in mind, reactance displays different amounts at different frequencies.

And yet there must be more to it in that Yagi arrays are geometric, not just a length of conductor. Or are they?

This question came up when I pondered making a transmitter to feed a 75 ohm coaxial cable and I realized this fed a 50 ohm antenna which then requires a resistor pad to match them, but the big question then came up: Why is an antenna 50 ohms in the first place?

Last edited: Jun 7, 2014
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2. ### Sparky49 Well-Known Member

Jul 16, 2011
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My understanding is that antenna impedance simply relates voltage and current at the input. The real part is the radiated or absorbed energy, which the imaginary part is the energy in the near field, or non-radiated energy. Hence why an antenna with a real impedance is resonant, which is logical as impedance varies with frequency.

3. ### Papabravo Expert

Feb 24, 2006
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Reactance has both an inductive component and a capacitive component. Any antenna that you construct will work better at some frequencies than others. If you take an instrument called an "Antenna Analyzer" you can measure the "feed point impedance of an antenna which will depend on it's geometry and height above ground.

As you know impedance as has real part measured in ohms and an imaginary part also measured in ohms. The magnitude of this complex impedance is how we determine that a match exists between the antenna and a transmission line.

The locus of all points in the complex plane with a magnitude of 50 ohms is a semi-circle, centered at the origin with a radius of 50, in the right half plane. So the following impedances all have a magnitude of 50 Ohms

50 + j0
35.35 + j35.35
0 +j50
0 - j50

If you connect you 75 Ohm tranmission line to an antenna that has an impedance with a magnitude of 50 Ohms you will have a mismatch. At the mismatch a portion of your transmitted signal will propagate through the discontinuity and a portion will be reflected back toward the source. This can be calculated or measured by the Voltage Standing Wave Ratio or the Return Loss.

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4. ### KL7AJ AAC Fanatic!

Nov 4, 2008
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The electrical model for an antenna is a series resonant circuit. The resistive part is the radiation resistance, plus any "ohmic" resistance. An antenna at resonance looks like a pure resistance. If it's shorter than resonance it looks capacitively reactive; if it's longer it has inductive reactance.

An antenna that's very very short (relative to wavelength) such as a whip antenna on a car used for AM broadcast reception has a radiation resistance of a fraction of an ohm and a HUGE capacitive reactance.

A normal antenna has a purely resistive impedance at any harmonic of its fundamental frequency

5. ### t_n_k AAC Fanatic!

Mar 6, 2009
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It might be worth looking at an antenna modelling software package such as MMANA-GAL which is free for private (amateur radio) use.

6. ### nsaspook AAC Fanatic!

Aug 27, 2009
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An antenna at it's heart is a matching device (a transformer) to the impedance of free space ~377 ohms. This resistance (Z0) of free space is a consequence of the limited speed (c0) of electrical signals in vacuum that give it the equivalent electrical properties of capacitance (electrical constant) and inductance (magnetic constant) similar to a transmission line and sets the ratio of electric to magnetic fields as they move in space. If you alter the electrical geometry of space with conductors or other materials of the correct shape and size near those waves you can change the energy balance (lower impedance) of those fields to more magnetic (current) than electrical (voltage) but still have the same amount of energy overall in the wave as it moves from point to point until it leaves the antenna as EM radiation.

How to explain and maximize the amount of radiation of EM energy into free space for each type of antenna structure is another complex subject that deals with face that fields generated by moving charges in the antenna at one instant in time are not in sync with fields that have moved away from the antenna so you have a time varying potential across space away from the source.

Near field.

To far field.

Last edited: Jun 3, 2014
7. ### alfacliff Well-Known Member

Dec 13, 2013
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I suggurst one of the many ARRL books, hams have been working on antennas for many years, and have compiled a lot of information. feed point impedance is determined by a lot of things, and can actually be designed into an antenna. a folded dipole antenna has a higher feed pint impedance than a regular dipole, for instance, around 70 ohms.

8. ### t_n_k AAC Fanatic!

Mar 6, 2009
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Presumably you mean the regular dipole has a resonant impedance of ~70 ohms.

9. ### alfacliff Well-Known Member

Dec 13, 2013
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no, the follded dipole has an impedance of 70 ohms. the regular dipole under ideal conditions runs about 52.

Apr 5, 2008
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11. ### t_n_k AAC Fanatic!

Mar 6, 2009
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I'm curious as to the conditions under which this would be the case.

12. ### alfacliff Well-Known Member

Dec 13, 2013
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most real world conditions. I have been building antennas for over 40 years and find that to wrok for me.

13. ### t_n_k AAC Fanatic!

Mar 6, 2009
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Which is an important matter that can lead people to be confused with observations in RF systems. So many factors effect the variation from expected ideal performance and practical outcomes.
However I expect that closer ageement with the ideal can be achieved under well controlled laboratory conditions such as one might encounter in RF certification environments.

14. ### vk6zgo Active Member

Jul 21, 2012
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Sorry,I've been around a long time,too,& folded dipoles have always been around 300Ω.
Simple dipoles?-----Yes,in practice,they are often closer to 50,rather than 70Ω.

Remember,they are talking about single folded dipoles- with no other elements----------if used as the driven element of a Yagi,fhey may well have a much lower impedance.

15. ### PRS Thread Starter Well-Known Member

Aug 24, 2008
989
35
Thanks everyone for your replies. I'll look into the question using the ARRL handbook and online sources then maybe I'll know something about it, but more than likely I'll just have more questions.

I had planned to ask about my plan to match a transmitter to an antenna but I got caught up in personal happenstance that took me away from home for a while. Well, now that I'm back I'd like to continue with the question, but in a more specific form:

I'm putting a 1496 or 1596 into a box tomorrow and that box is going to drive a transmitter that basically consists of an NPN common emitter. All I want is 1/4 watt into a 75 ohm coax to drive a 50 ohm antenna through a matching pad. I calculate, from V^2/75 = .25 that I need 4.33 volts rms and this means 12.2 volts peak to peak.

The collector of my CE output amplifier will be a 2:1 step down transformer with no capacitor to create a BP filter, for I want to broadcast any frequency from 300kHz to 30 MHz. The 2:1 ratio should decrease the impedance seen by the load (the 75 ohm coax) by a factor of 1/4 since N^2 = 4. Therefore I need 200 ohms from the primary winding and this will be at a 1MHz frequency (chosen as the center of the AM broadcast band). From XL=2*pi*f*L, L is computed as 32 uH. Therefore the coax will see 50 ohms and the capacitance across the secondary. Am I right so far?

P.S.

This L is just the first of six I plan to wind and switch into the circuit in order to get incremental frequency bands. Since the AM broadcast band is the simplest to test I'm going after that one first.

On edit, 6-7-14, the computed L was based on 50 ohms, not 75 ohms as it should have been. But you get the idea, I hope. I'll add the point that calculating transformers this way yields good results. The output impedance can be found experimentally by putting a resistor in parallel with the output and causing the voltage to go down by 1/2. I have done this with many other circuits and so I believe the transformer calculation works. Incidentally, this is book learning. I didn't make it up.

Last edited: Jun 7, 2014
16. ### Papabravo Expert

Feb 24, 2006
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What is your understanding of the law regarding the unfettered transmission of RF signals in the 300 kHz to 30 MHz region of the RF spectrum. The reason I ask is to alert you to the possibility that you may be subject to fines and penalties of which you may not be aware.

17. ### PRS Thread Starter Well-Known Member

Aug 24, 2008
989
35
I understand it is illegal to broadcast at any frequency without a license and I don't have one yet. Until then my plan is to keep the signal strength down so it stays in my house -- an aluminum skinned mobile home with that skin grounded with a copper rod driven into the earth. The output amplifier will have variable gain -- a center tapped potentiometer at the emitter of a CE stage. I'll take a receiver outside and make sure the signal is undetectable. That's the plan, anyway.

On edit, P.S. At my work bench there are two antennas -- the one going outside through a coaxial cable, and the one inside, consisting of a thin magnetic wire travelling across the ceiling for about 40 feet. I plan to use the latter until I get my license. And when I do use the outside antenna and step up the gain it will be within a spectrum that I'm qualified to broadcast on using my license. But thanks, I appreciate your concern.

Last edited: Jun 7, 2014
18. ### Lestraveled Well-Known Member

May 19, 2014
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Paul
You have asked a question that can be mind numbing. I started a technical reply and stopped after two paragraphs. I realized that an understanding of transmission line theory is not needed to make an antenna system work really well. Here are my suggestions:
- Match the impedance between your transceiver and your cable.
- Use good cable.
- Match the impedance between your cable and your antenna.
- If you have to transform from 50 ohms to 75 ohms use a balun. Do not use resistors.
- Get an SWR meter. Do not spend too much. Cheap ones do the job.
- Measure the SWR at the output of your transmitter and at the input to your antenna. If both numbers are low, you are good to go.

When you are bored and want to be put to sleep, read transmission line theory.

Mark

19. ### PRS Thread Starter Well-Known Member

Aug 24, 2008
989
35
Hello Mark. Actually I don't have a transceiver yet. I'm developing radio circuits just out of curiosity right now. I haven't ever developed a transmitter but I'm considering it at the moment. This brought up the question of matching the output and antenna impedances. I'm trying for a wide band -- from 300 kHz to 30 MHz -- and this means the avoidance of reactance's as far as I am able. Thus my choice of a resistor pad over a balun. But I agree with you about using 50 ohm coax instead of 75 ohm in order to avoid this issue. I'll just make the transmitter have a 50 ohm output and get a new cable. As far as the antenna goes I'm considering a loop antenna built on a square wooden frame and clamping this to a mast. Its direction could then be changed by loosening the clamps. However, this is all just an idea at the moment. I'll have to buy an SWR meter. Do they make them for MF and HF? The ones I've seen on EBay are all higher frequencies than that.

20. ### Lestraveled Well-Known Member

May 19, 2014
1,957
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One of my best performing wide band antennas was a 385 foot loop in the shape of a Triangle. I used ladder line and a Johnson matchbox to feed it. It was also the cheapest. There was not a HF band it would not match up to.

Mark
KG7VH