Impedance, 1/4 wavelengths & energy

If you have a wave travelling from a medium of impedance (Z1) to a medium of similar impedance (Z2), then putting a 1/4 wavelength bit of material of impedance = sqrt(Z2*Z1) at the boundary causes the reflected waves to interfere destructively. Also, if Z1 and Z2 are really different, you can insert a whole load of quater-wave layers to cause the reflected waves to all interfere destructively.

Questions:
1) Is that right?
2) What's the proper name for the quarter wave layer things?
3) If you get all the reflected waves interfering destructively, how does the transmitted wave have 100% of the energy of the original wave? [by the conservation of energy, I don't see what else could happen, but I don't understand how this actually works.]

I'm probably most likely to understand explanations referring to waves on string, rather than anything based on sound waves or electricity. Thanks in advance :smile:

Reply 1

Morbo

1 & 2) Right, pretty much....

I'll imagine the incident wave if travelling left to right.

If you have transmission material (A) of impedance Z1 connected to another material (C) of impedance Z2 by another piece of material (B) of impedance SQRT(Z1*Z2) and length 1/4-wavelength, then the two lines Z1 and Z2 are said to be impedance matched.

Because a wave reflected at the B-C boundary interferes destructively with the wave reflected at the A-B boundary, then no reflected wave is seen in material A.

However, this impedance matching only works at the particular frequency of wave for which material B is 1/4 of its wavelength. (Because the wavelength of the incident wave changes in each material, we refer instead to a particular wave in the system as having a particular frequency, which generally remains constant no matter which material the wave is in.)

Zero reflection will be seen in A when the wave is at this particular frequency. However, if you put a wave of frequency different to that which matches the 1/4-wavelength material, then this will not have complete destructive interference at the A-B boundary, and some of this non-matched wave will be reflected.

In order to minimize reflection of waves in a certain bandwidth (i.e. if you incident waves have a certain range of frequencies) is to stack up a few of the intermediate anti-reflection materials in order to cover a broader frequency range. This has the advantage that the reduced reflection works for a greater bandwidth, but it also means that any waves outside this bandwidth will probably be totally reflected. It makes a kind of bandpass filter.

In transmission lines, material B has no particular name apart from an "impedance matched" connection. In optics (i.e. light in glass), it can be called an anti-reflection coating.

3) I believe a standing wave is set up inside the anti-reflection material which you can imagine as passing the energy directly from material A to material C. With no damping (of which there is little in electromagnetic waves), this standing wave pretty much conserves energy, although in practice not 100% of the light is transmitted.

Impedance, 1/4 wavelengths & energy

Related discussions

Latest

Trending

Trending

Articles for you