Understanding Impedance of Free Space and Its Significance for Antenna Design

[Wannabeagenius]

Hi All,

I understand that the impedance of free space, according to the formula E/H, is 377 ohms. I understand that if the impedance is high, a given electric field is associated with a smaller magnetic field but what does this really mean?

What is being impeded?

Also, what is the significance of this to an antenna? Is there any advantage to designing an antenna with an impedance 377 ohms?

Thank you,

Bob

 

[Bob S]

Hello Bob-
It is useful to review the theory of characteristic impedance in RF (coaxial) cables, and understand why RG-8 and RG-58 are called "50-ohm" cables. Work out the characteristic impedance of a coax cable using the telegraphers equation, and calculate the impedance of RG-8. See
http://en.wikipedia.org/wiki/Transmission_line
The cables have a charactistic impedance even if they are lossless. Nothing is impeded. The geometry of the cable forces the characteristic impedance to be 50 ohms, and free space to be 377 ohms. It is very difficult to design an antenna with an impedance of 377 ohms. The closest that I know of is the folded dipole used for FM radio; it is about 300 ohms, and matches the 300-ohm twin-line lead-in antenna wire. See section on derived electrical parameters in
http://en.wikipedia.org/wiki/Coaxial_cable
Bob S

 

[Wannabeagenius]

Hi Bob,

Thanks for responding but I do understand the characteristic impedance of transmission lines and of antennas and the need to match both (ideally).

I'm having trouble grasping what the impedance of free space is? In free space, what in a traveling wave is impeded? Although for a given electrical field there is a lower magnetic field, I can't see this as a good analogy to current in a wire!

Perhaps I could understand it better if asked a couple of different questions.

What are the consequences of impedance of an antenna not matching that of free space?

And what are the advantages of the impedance of a antenna matching that of free space?

Thank you,

Bob

 

[Bob S]

I'm having trouble grasping what the impedance of free space is? In free space, what in a traveling wave is impeded? Although for a given electrical field there is a lower magnetic field, I can't see this as a good analogy to current in a wire!

There is always a return current for a current in a wire, and the impedance is between the two wires. Rather than impedance, think of it as the ratio of voltage to current, because nothing is "impeded".

What are the consequences of impedance of an antenna not matching that of free space? And what are the advantages of the impedance of a antenna matching that of free space?

There are actually two matches. (1) the electrical input impedance of the antenna should be real at the important frequency, and it should match the characteristic impedance of the coax. (2) The antenna should be optimally designed to radiate efficiently (match to free space) in the correct direction at the right frequency.

remember that Z₀ = sqrt(μ₀/ε₀) = 377 ohms

c= 1/sqrt(μ₀ε₀) =3 x 10⁸ meters per sec

Bob S

 

[Wannabeagenius]

Bob,

If you could easily build an antenna with a characteristic impedance of 377 ohms, how would it be beneficial?

Bob

 

[Born2bwire]

Bob,

If you could easily build an antenna with a characteristic impedance of 377 ohms, how would it be beneficial?

Bob

It wouldn't be, unless your feed network can only be designed to have an output impedance of 377 ohms. The input impedance of an antenna is only in reference to the circuit side of the antenna. We do not talk about the impedance of the antenna with respect to the traveling wave, usually only with respect to the guided wave from the circuit.

EDIT: Should note that impedance is a bit ambiguous. I can have two antennas, both with impedances of 377 ohms but they may not perform the same. If we have an imaginary antenna that has only a real impedance to it, that is the radiation resistance is almost the same as the input impedance, then it will very efficiently radiate incident power. However, antennas have capacitive and inductive properties to them. Ideally we tune the capacitve and inductive properties by modifying the geometry (and in a lazier means adding discrete caps and inductors) so that the inductances and capacitances cancel out at our resonant frequency. Still, we will have power trapped between these elements at resonance, and I would expect that the radiation resistance would suffer as the cycling reactive power is dissipated by the conductive losses and such of the antenna. In addition, the capacitive and inductive elements are dependent upon the operating frequency. Once we deviate from resonance, the antenna becomes reactive which further deteriorates performance. This can affect say bandwidth, radiation efficiency, and impedance mismatch with the feed network among other things. So the impedance at resonance is also not an indicator of how the antenna performs over the wideband unless you have a formula for the impedance as a function of frequency.

 

[Wannabeagenius]

It wouldn't be, unless your feed network can only be designed to have an output impedance of 377 ohms. The input impedance of an antenna is only in reference to the circuit side of the antenna. We do not talk about the impedance of the antenna with respect to the traveling wave, usually only with respect to the guided wave from the circuit.

EDIT: Should note that impedance is a bit ambiguous. I can have two antennas, both with impedances of 377 ohms but they may not perform the same. If we have an imaginary antenna that has only a real impedance to it, that is the radiation resistance is almost the same as the input impedance, then it will very efficiently radiate incident power. However, antennas have capacitive and inductive properties to them. Ideally we tune the capacitve and inductive properties by modifying the geometry (and in a lazier means adding discrete caps and inductors) so that the inductances and capacitances cancel out at our resonant frequency. Still, we will have power trapped between these elements at resonance, and I would expect that the radiation resistance would suffer as the cycling reactive power is dissipated by the conductive losses and such of the antenna. In addition, the capacitive and inductive elements are dependent upon the operating frequency. Once we deviate from resonance, the antenna becomes reactive which further deteriorates performance. This can affect say bandwidth, radiation efficiency, and impedance mismatch with the feed network among other things. So the impedance at resonance is also not an indicator of how the antenna performs over the wideband unless you have a formula for the impedance as a function of frequency.

Thank you

Bob

 

[tiny-tim]

I'm having trouble grasping what the impedance of free space is? In free space, what in a traveling wave is impeded? Although for a given electrical field there is a lower magnetic field, I can't see this as a good analogy to current in a wire!

Hi Bob W!

I think the confusion here is that there are two different things both called characteristic impedance.

The characteristic impedance of a transmission line is:

$$Z_0\ =\ \sqrt{\frac{R_x+j\omega L_x}{G_x+j\omega C_x}}$$

while the characteristic impedance (or intrinsic impedance) of a medium is the wave impedance of a plane electromagnetic wave in the medium:

$$Z\ =\ \sqrt{\frac{j\omega\mu}{\sigma+j\omega\varepsilon}}\ =\ \sqrt{\frac{\mu}{\varepsilon-j\sigma/\omega}}$$

(which is $Z_0\ =\ \sqrt{(\mu_0/\varepsilon_0)}\ =\ \mu_0c\ =\ 1/\varepsilon_0c$ for free space).

I can't really see any analogy either, except that they're both measured in ohms: the first is voltage/current along a line, while the second is electric field (E)/magnetic intensity (H), or volts per metre/amps per metre.

 

[Bob S]

If you could easily build an antenna with a characteristic impedance of 377 ohms, how would it be beneficial?

If we had a metal rod a half-wavelength long, a TEM signal could set up a standing wave in it, with current nodes and voltage maxima at the ends, and a current maxima at the center. The normal half-wave dipole splits this rod in the center, and inserts a 72-ohm load, across which the standing-wave current is measured. By putting two symmetrical taps on the rod, the ratio of voltage and current of the standing wave can be varied. This is equivalent to changing the output impedance of the antenna. As the taps get closer to the ends, the voltage gets higher and the current lower; so the output impedance is increased. A delta-match network can match this to a balanced line, such as the 300-ohm twin line. See
http://www.ycars.org/EFRA/Module%20C/AntMatch.htm
Sorry; I don't have formulas for designing delta matches. There is no unique advantage to having a 377-ohm antenna input/output impedance. The antenna itself is just an impedance matching network, from the balanced line electrical signal to free space.
Bob S.