Wavelength and length of wire limitation?

[likephysics]

Can someone explain, why the wavelength(frequency) of a signal limits the length of the transmission wire?
Also, how come we see thru microwave oven, but microwaves cannot get out of the mesh door.

thanks.

 

[xez]

The frequency being high does NOT limit the practical
length of a transmission wire, though when the wavelength
of the frequency traveling on the wire becomes
an appreciable fraction of the wire length, you will not be
able to use simple 'circuit theory' with quite so many
short-cuts of assumptions to model the flow of energy
along the wire.

It is possible for the wire to start radiating propagating
electromagnetic waves away from itself, like an antenna.

It is also possible that the wire itself in its environment
will have an high frequency complex impedance
that is relevant to consider when looking at how waves
of high frequency flow down the wire.

When the lengths of the conductors exceed around
1/10th of a wavelength of the frequency of the signal
flowing, it is a good time to start using the techniques
of transmission line design and modeling to ensure that
your wire (or transmission line) will behave as desired.

That is why there are transmission lines like coaxial cable,
twin-axial / flat two-conductor, microstrip, wire above
a ground plane, et. al. because those kinds of lines can
propagate signals over many wavelengths efficiently
without much radiation, loss, or impedance mismatch
when they're used properly.

The microwave oven has a screen of metal with holes
in it along the front door. The holes are perhaps less than
2mm in diameter, which is a huge number (4000 or so)
of wavelengths for light, but it is only 1/61st of a
wavelength at the 2.4GHz frequency that a typical
microwave operates at.

When an electromagnetic wave encounters a
uniform metal screen with performations of a diameter
less than 1/40th of a wavelength, and with good thick
metal webbing around the holes, the wave energy will
reflect off of the metal screen and only a very small
fraction of the electromagnetic field energy from the wave
will exist for any significant distance beyond the wall
of the screen.

Light, of course, passes through such a 2mm hole very
easily since the hole is 4000 wavelengths wide.

 

[likephysics]

xez, thanks for the reply.
What exactly happens when the microwave sees the mesh window? Can't it pass thru the 2mm hole?

In case of the wire, why does the conductor start radiating?

 

[xez]

Well at the surface of a good conductor the electric
field of the wave stimulates a current in the metal
that causes a wave of opposite electric field polarity
to be emitted, so the electric field at the surface
of the metal cancels out due to the incoming wave and
the addition of the outgoing wave.

The overall result of a very conductive boundary condition
is that the incoming wave reflects off the metal sheet,
like a mirror, at an angle of reflection (relative
to the surface normal) equal to the angle of incidence.

Small amounts of magnetic and electric fields pass through
the holes for a very small length, but the fields are
insignificantly small and generally are just local fields that
don't turn into propagating E/M waves.