# Impedance of a half-wave dipole antenna

• xopek
Yes, that is correct. The reactive part is usually very small and can be ignored when speaking about impedance. At RF frequencies, the impedance of an antenna is a function of antenna size and of operating wavelength. The multimeter is not tuned to the resonant frequency of interest. In summary, the active resistance of a half-wave radiating antenna is not a DC resistance, and it can only be measured as a ratio of AC current to AC voltage.f

#### xopek

73 + j42 means it has an active resistance plus reactance. But this "active" resistance is not a DC resistance, right? We can't just measure 73 ohm with a multimeter since the circuit is open. What closes it then? Let's say the reactive part is zero. How do we measure 73 ohm? By measuring current and voltage? But what causes resistance and what kind of resistance is that since it is only measurable as a ratio of AC current to AC voltage but cannot be measured as a DC resistance?

73 + j42
You need to define your half-wavelength correctly. In free space, or at the radiating antenna? You trim your radiating antenna to have a real radiation impedance, otherwise you have a terrible SWR feeding your antenna... https://en.wikipedia.org/wiki/Dipole_antenna Last edited:
I am asking about a resistance of a half-wave radiating antenna as measured at the feed point. I am not asking how to make it resonant and how to get rid of reactance.

What I am trying to ask is a really silly question, if the resistance is 73 ohm or whatever, why can't it be measured with a multimeter? I am just trying to understand the physical meaning of a resistance (radiation resistance). What physical phenomena makes it infinity at DC (because there is obviously a gap between the two parts) but it measures ~73 ohm as a ratio of AC current to AC voltage. Just trying to understand Ohm's law as applied to antennas.

Oh. The antenna radiation "resistance" or "impedance" is at RF frequencies, not at DC. Impedances vary over frequency, for a number of different reasons.

Where are you in your learning about elecronics and E&M so far? That will help us to tailor our responses to give you the best learning links and resources... • DaveE and Tom.G
Think of it this way: Drive the antenna at it's feed point with 73 vac. It will draw one ampere from the voltage source with the current and voltage being exactly in phase (resonant). 100 percent of the power from the source will be radiated if we ignore resistive losses in the conductors. If we move slightly off frequency a portion of the power will be radiated but since we no longer are resonant, the voltage and current will no longer be perfectly in phase. Part of the power is reflected back into the source.
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The fact that we cannot measure this at DC is not really that hard to grasp if we think about driving a plain old resistor through a suitable capacitor. Assume the capacitance is large enough so that it offers very little to no impedance. Current and voltage will be in phase. But if the frequency drops far enough this changes due to the capacitor. Drop it to DC and you have the same result as trying to measure the feed point of antenna with an ohmmeter.

What I am trying to ask is a really silly question, if the resistance is 73 ohm or whatever, why can't it be measured with a multimeter?
The impedance of the antenna is a function of antenna size and of operating wavelength. The multimeter is not tuned to the resonant frequency of interest.

You need a "Vector Network Analyzer" to measure antenna RF impedance at the other end of a transmission line. The equivalent of a multimeter for RF today would now be something like a low cost NanoVNA-H.

• Averagesupernova
Every antenna is a complete circuit. For example, a loop antenna is clearly a circuit. For a dipole, this circuit is formed by the two wires and the capacitance between them. Due to the capacitance, it only works as a circuit for high frequency alternating current. If we have an Ohmmeter for high frequency AC then we will see the resistance figure. Of course, as it is alternating current we also can have reactance in the circuit and some test equipment can measure resistance and reactance separately.
The reason we see resistance is that, due to the large size of the antenna, the electrons are being accelerated back and forth each cycle. This causes a loss of energy due to radiation, and it is necessary to do work to accelerate them. This energy loss is seen as resistance in the antenna.

driving a plain old resistor through a suitable capacitor. Assume the capacitance is large enough so that it offers very little to no impedance. Current and voltage will be in phase. But if the frequency drops far enough this changes due to the capacitor.
So if I understand correctly, it is a high-pass filter and its transfer function is usually Vout/Vin, but we can think of it as impedance I/U which is R - j/wC. As frequency goes up, the reactive part diminishes and the phase approaches zero and the magnitude is approaching R. Strictly speaking, current and voltage will never be exactly in phase since there is no resonance but we can assume they are in phase at really high frequencies.

Drop it to DC and you have the same result as trying to measure the feed point of antenna with an ohmmeter.
Yes, but I can open the "black box" that is RC and find R and measure it with an ohmmeter.
Where is that R for the antenna? Or another example, let's say we have a power line that has an inductive load. That load can be modeled as R + jwL, so it has an active/real winding resistance and imaginary/reactive inductance due to L. We can measure its power factor and correct it if we want to, but still that real R is what causes the active power dissipation due to RI^2 and that power does real work and the reactive part gets reflected back to the grid. So I am trying to think of an analogy with an antenna that also has an impedance that can be modeled as R + jX, and that X can be capacitive or inductive or it could be zero. But what is that R? Clearly it is not a "resistor". Apparently it is called radiation resistance. Does it depend on frequency? If it depends on frequency, then it has a reactive component so it is not really resistance? I looked up the equivalent circuit of a typical antenna and they vary but generally speaking it seems to be a bunch of RLC in series and in parallel. I imagine some of the reactances get canceled out at resonance. But there still should be the "active" real R there somewhere that measures 73 ohm.

The reason we see resistance is that, due to the large size of the antenna, the electrons are being accelerated back and forth each cycle. This causes a loss of energy due to radiation, and it is necessary to do work to accelerate them. This energy loss is seen as resistance in the antenna.
So that's actual real resistance, not reactance? So is this some kind of an "AC resistance"? Because if we push DC current through a resistor, there is also a loss of energy as it is dissipated as heat. I am just trying to wrap my mind around this magical "AC resistance" that cannot be directly measured even though it is not a reactance.

Perhaps it is some kind of a lumped element that is "seen" as active resistance by the circuit at AC? I looked up the formula for radiation resistance and it is mind bogglingly complicated and seems to depend on the antenna geometry.

Impedance = resistance + signed reactance; Z = R + j X .
As the frequency is swept across the resonant frequency of a tuned circuit or antenna, the reactance passes through zero, and at that frequency the antenna is purely resistive. XC + XL = 0 at resonance.

You can think of an antenna as a leaky transmission line. The antenna terminals have a characteristic impedance, just like a transmission line. The antenna impedance, at the test frequency, is simply the ratio of voltage to current on the line or antenna.

I looked up the formula for radiation resistance and it is mind bogglingly complicated and seems to depend on the antenna geometry.
Radiation resistance is a more difficult concept to understand for resonant antennas.

Found this in the wikipedia article:

Radiation resistance is an effective resistance due to the power carried away from the antenna as radio waves. Unlike conventional resistance, radiation resistance is not due to the opposition to current (resistivity) of the imperfect conducting materials the antenna is made of.

So I am getting closer to understanding the "AC resistance" that is a function of frequency but it is not really a reactance.

So I am getting closer to understanding the "AC resistance" that is a function of frequency but it is not really a reactance.
No, you are not. You are contaminating simple AC impedance with other concepts.

No, you are not. You are contaminating simple AC impedance with other concepts.
But it is not about a simple AC impedance. It is the resistance of an antenna that I am asking about. I understand simple AC impedance. It has a real and an imaginary part. The imaginary part is a simple reactance that depends on frequency. And the real part is a simple "conventional resistance" aka the opposition to current or resistivity. It doesn't depend on frequency. Its value can be measured with an ohmmeter. And the antenna's radiation resistance is not a simple conventional resistance. It does depend on frequency and the antenna geometry. I think the contamination occurs in the opposite direction: there is no need to consider the reactive part in this case as it is just a distraction.

It has a real and an imaginary part. The imaginary part is a simple reactance that depends on frequency. And the real part is a simple "conventional resistance" aka the opposition to current or resistivity. It doesn't depend on frequency.
The Real resistance component does depend on frequency when there is any time delay such as a transmission line, which is what an antenna looks like to a signal.

A transmission line rotates the impedance vector once for each λ of line travelled. That cyclically changes R with X by rotating the vector represented by the complex impedance.

If you measure or model the impedance of a real antenna, you will see a frequency dependence in the resistance component. An ideal theoretical dipole is probably the only exception, but that is unreal.

The imaginary part is a simple reactance that depends on frequency. And the real part is a simple "conventional resistance" aka the opposition to current or resistivity.
You're overdoing it with your choice of words. In place of "is", try using "can be modeled as."

You fell into a language trap caused by use of the verb "to be" in its many forms. See:

https://en.wikipedia.org/wiki/E-Prime
Kellogg and Bourland describe misuse of the verb to be as creating a "deity mode of speech", allowing "even the most ignorant to transform their opinions magically into god-like pronouncements on the nature of things".

• sophiecentaur
The Real resistance component does depend on frequency when there is any time delay such as a transmission line, which is what an antenna looks like to a signal.
But that time delay in a transmission line is due to reactance since a transmission line is modeled as a bunch of repeating RLC segments? So it is not really "the real" resistance?

Electromagnetic waves are radiated by electric charges when they are accelerated. In a transmitting antenna radio waves are generated by time varying electric currents, consisting of electrons accelerating as they flow back and forth in the metal antenna, driven by the electric field due to the oscillating voltage applied to the antenna by the radio transmitter. An electromagnetic wave carries momentum away from the electron which emitted it. The cause of radiation resistance is the radiation reaction, the recoil force on the electron when it emits a radio wave photon, which reduces its momentum. This is called the Abraham–Lorentz force. The recoil force is in a direction opposite to the electric field in the antenna accelerating the electron, reducing the average velocity of the electrons for a given driving voltage, so it acts as a resistance opposing the current.

I am not trying to understand every detail of that but it sounds satisfactory as it confirms that "there is this certain *other* type of resistance" blah-blah which ends up with "electrons being slowed down" for whatever reason => slower electrons => less current => higher resistance. Is there a way to reconcile this explanation with the transmission line based theory you referred to?

You can think of an antenna as a leaky transmission line. The antenna terminals have a characteristic impedance, just like a transmission line. The antenna impedance, at the test frequency, is simply the ratio of voltage to current on the line or antenna.
I didn't notice this post. Does that apply to both transmitting and receiving antennas? Can a receiving antenna be though of as a voltage source with a leaky transmission line attached to it so the load "sees" 73 ohm or whatever?

@xopek just because a resistor will have the voltage across it in phase with the current through it does not mean that every component that exhibits this specific behavior has to also exhibit all other behavior of a resistor.

Lets try getting back to a 'simpler' text explanation... oops, even though the following turned out a bit difficult visualize, give it a few tries. (maybe try drawing a few sketches as we go along. (I'm a cra*py artist, so I'm leaving the sketches to you! )

• Consider an antenna to be a series-resonant circuit, that is an inductor in series with a capacitor.
• As you likely know, a series-resonant circuit has the lowest impedance at its resonant frequency.
• Just to make the following a bit easier to follow, assume the inductor to be a coil, and the capacitor made of several capacitors in series.
• Now imagine a large value resistor connected to each turn of the coil and the other resistor end connected to 'something' (Ground?) at an infinite distance.
• The several series capacitors also have a resistor connected to each of their junctions and to that 'something' at infinity.
• At resonance, the inductance and capacitance cancel each other out (if considered from the end points of the assembly, they act like a solid wire).
• What is left is this whole bunch of resistors connected in parallel between that antenna and that 'something' at infinity.
• Now an antenna radiates energy as electromagnetic waves. This is an energy loss from the antenna. That loss is what occurs thru all those resistors we connected above... and the resultant equivalent resistance is 73 Ohms for a halfwave dipole.

Further Info:
Essentially those resistors connected to 'something' above, is the resistance of the antenna coupled to the whole Universe. In the real world there are other things much closer to the antenna, causing the radiation resistance to be somewhat lower.

Hope this helps a little!

Cheers,
Tom

if the resistance is 73 ohm or whatever, why can't it be measured with a multimeter?

So I am getting closer to understanding the "AC resistance" that is a function of frequency but it is not really a reactance.

I am not trying to understand every detail of that but it sounds satisfactory as it confirms that "there is this certain *other* type of resistance" blah-blah which ends up with "electrons being slowed down" for whatever reason => slower electrons => less current => higher resistance. Is there a way to reconcile this explanation with the transmission line based theory you referred to?
Ouch! You seem to be intent on using your own definition of Resistance that implies Resistance is a different kind of thing, depending on the circumstances. That would be a very risky sort of quantity to be dealing with and it will take you nowhere.

In the model we use for describing the behaviour of electrical circuits and components Resistance is the real part of a complex quantity called Impedance. The other part is the Reactance. Impedance (Z) is the sum of Resistance (R) and jX (X is the Reactance).
So Z = R +jX.
The X component will always be frequency dependent and, for anything but a 'small' component, the R will also be. This Z quantity is just the Ratio of the Complex Volts and the Complex Current. That is one way of describing both the Amplitudes and Phases of V and I.

Forget about dodgy 'explanations' involving Electrons going Slower because that is a very faulty model. The speed of electrons in solid conductors is in the order of a mm per second; no significant Kinetic Energy involved at all. Just treat Current and Volts as quantities that can (sometimes) be measured and avoid, at this stage, trying to discuss what is 'really happening'. That's beyond the scope of EE and just tends to waste time.

Found this in the wikipedia article:

Radiation resistance is an effective resistance due to the power carried away from the antenna as radio waves. Unlike conventional resistance, radiation resistance is not due to the opposition to current (resistivity) of the imperfect conducting materials the antenna is made of.

So I am getting closer to understanding the "AC resistance" that is a function of frequency but it is not really a reactance.

-For the dipole antenna there is a frequency dependence in the processes but the requirement that the dipole be half-wave makes them cancel and so the "resistance" is frequency independent. The energy radiates away
--Feynman derives the impedance of a semi-infinite cable. where coax having only L and C can look like a resistance because the energy is transported "away" below resonance. See section 22-6. I very much like this chapter of the Lectures

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so the "resistance" is frequency independent.
Not 'independant' but slowly varying across the band. (Wikipedia figure) As the wavelength increases (shorter and shorter dipole) the radiation resistance gets embarrassingly low, which is why there's a very practical limit to how small y our transmitting aerial can be. So much so that the (series resistance) losses in the transmitter and matching network make it very inefficient.

Not 'independant' but slowly varying across the band. (Wikipedia figure)
Perhaps I was unclear. The real impedance (i.e.resistance) of a truly halfwave antenna is always 73 ohms. If one changes the frequency without concurrently changing the length it is no longer a half wave antenna.

.

• sophiecentaur
it is no longer a half wave antenna.
Thing is, an antenna is not a lot of use for most purposes if it only operates at one frequency. (There are relatively few single frequency beacons.) so the frequency dependence of both X and R tends to be important if your required bandwidth is significant. But, as with a lot of these 'simple' questions, the practical answer is a long as a piece of string. For anything but a 'thin' dipole, the impedance characteristic is different. The actual length, for best, won't be a half wavelength and the radiator can be very thick - if you want to transmit multiple TV signals, for example.
We should try to limit things to the basics that the OP was wanting (needing) and that is all about the notion of Impedance, a complex quantity and how the Energy Flow from the dipole into space shows itself as a Resistance because of the Real Part of the Impedance..

We should try to limit things to the basics that the OP was wanting (needing) and that is all about the notion of Impedance, a complex quantity and how the Energy Flow from the dipole into space shows itself as a Resistance because of the Real Part of the Impedance
Yes. The first timeI I understood how this happens was long ago first reading the Feynman lectures on transmission lines which I referenced. Much easier for me to understand than the dipole although the physics is really the same. Good stuff.

• sophiecentaur
Much easier for me to understand than the dipole
It's a matter of choice but . . . . . people tend to be obsessed with the resonant dipole when, in fact, of course most antennae are not resonant and the feed contains elements that match as best as they can, the varying impedance of the radiator over the operating band with the source of power (at 50 Ohms usually).

• hutchphd
We should try to limit things to the basics that the OP was wanting (needing) and that is all about the notion of Impedance, a complex quantity
The imaginary part wasn't really my question (pun unintended).

and how the Energy Flow from the dipole into space shows itself as a Resistance because of the Real Part of the Impedance..
Yes, that's what I asked about, the real part. About Radiation resistance and why it depends on frequency despite being a real active resistance. And if I understand you correctly, you are basically telling me "it just happens, don't worry about it, the nature of that resistance doesn't matter, it is a "black box" as EE is only concerned with R as a result of V/I with V and I also being in phase, and not with what is really happening". And you and perhaps some other posters seem to reject the explanation given in the wiki article I quoted (and found satisfactory) as being "faulty" and "dodgy". Which begs the question of what is the right explanation then, and most importantly should we even ask that question or should we be satisfied with "let's not worry about that, it is just V/I that happen to be in phase".

-For the dipole antenna there is a frequency dependence in the processes but the requirement that the dipole be half-wave makes them cancel and so the "resistance" is frequency independent. The energy radiates away
--Feynman derives the impedance of a semi-infinite cable. where coax having only L and C can look like a resistance because the energy is transported "away" below resonance. See section 22-6. I very much like this chapter of the Lectures

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Funny that you mention Feynman. Some of the responses in this thread remind me of this video :)

@xopek do you know what a hairpin match is on an antenna? And do you have doubts about how a transmission line can drive a dead short for DC but the proper impedance appears at the feed point of the antenna at the designed frequency?
No, I don't know what that is. And no I don't have any doubts for that reason. I agree with what you said earlier that if some black box behaves like a resistance with U and I being in phase, that doesn't mean it is a resistor. I just thought of some other examples, for example JFET in a linear mode can be used as a VCR (though I didn't have much luck with that). Or even a vacuum tube. There is a plate "resistance" between the cathode and the anode due to space charge and negatively charged grid etc. It also depends on the plate voltage and the cathode temperature and perhaps other factors. Yet it is not a "resistor" that can be measured with an ohmmeter. I think I am satisfied with the idea of an antenna as a lumped element that may have I and U in phase and therefore presents an active resistance under certain circumstances.

Yes, that's what I asked about, the real part. About Radiation resistance and why it depends on frequency despite being a real active resistance.
If the dipole was a real 73 ohm resistance, it would get hot. But the dipole does not get hot because it is part of a transmission line. The dipole is a coupler that connects the transmission line to the space around the dipole.

If rather than λ/2, you cut the dipole to a length of λ/3, it will not have a resistance of 73 ohms.

If you use wire thicker than a filament for a λ/2 dipole, it will not have a resistance of 73 ohms.

If you have a dipole with a resonant frequency of 100 MHz it will not have a resistance of 73 ohms at 99 MHz, nor at 101 MHz.

• hutchphd and sophiecentaur
you are basically telling me "it just happens, don't worry about it, the nature of that resistance doesn't matter, it is a "black box" as EE is only concerned with R as a result of V/I with V and I also being in phase, and not with what is really happening"
I can see why that could make you cross. However, 'we' have been trying to present you with a number of opinions about the meaning of Resistance. A piece of solid carbon with wires at each end is a very straightforward example of resistance which will present the same value of resistance over a wide range of frequencies and currents. That resistance value here is just a description of Energy Transfer; Electrical to Thermal. The same thing happens in a radiator of EM waves.

There is another example which might help you and that is an electric motor. When you are lifting a load with an electric motor, you will be able to measure the V and the I and it will present a Resistance to the power supply. There is (ideally) no thermal dissipation in the motor (or in the wires of an antenna) and the resistance that's presented will vary with the load (or the gearing mechanism / motor speed). These are similar in essence to the matching network on an antenna.

I think you are needing too much 'carbon' in your mental model of resistance. The power supply will know no difference between a resistor, an antenna or a motor, if it's supplying the appropriate Volts and Current.

• hutchphd and Averagesupernova