# Re: [SI-LIST] : Trace Impedance Selection

From: Larry Miller ([email protected])
Date: Mon May 08 2000 - 13:43:53 PDT

Long ago in my E&M course among other things they looked at an antenna as a
way of matching a 50 ohm (or whatever) transmission line to free space (377
ohms).

There was a memorable picture of a coaxial cable as a matching section: it
looked like a regular coax cable at one end but at the other end the outer
conductor was flared out like a trumpet (theoretically to infinity), and
the inner conductor flared out for a while and then came back to zero
diameter, sort of like a bulb. The distance between the inside of the outer
conductor and the outside of the inner conductor constantly increased. Very
like an exponential horn loudspeaker.

A graphical way of showing what an antenna does....

Larry Miller

At 10:24 AM 5/8/00 -0700, you wrote:
>Can free space be modeled as a network of transmission lines, arranged in
such
>a manner that the impedance seen looking into any two points in space, is 377
>ohm?
>
>Thanks,
>Vinu
>
>
>Neven Pischl wrote:
>
>> Here's my \$0.02.
>>
>> The scenario doesn't work because it roughly assumes that if you have a 377
>> Ohm source, and a 377-Ohm resistor somewhere in free space, that you will
>> have max power transfer (even without any other connection). That's what
you
>> are saying when you say that half power would go through the space (at
least
>> it seams to me so).
>>
>> It mixes the wave-guiding concept in which there is at least two-conductor
>> structure that guides EM-waves, and it is characterized by its
>> characteristic impedance, with the free-space EM-wave propagation in which
>> the intrinsic impedance of the medium (not characteristic impedance of a
>> waveguide) is 377 ohm. There is an analogy between these two ways of
>> propagation, in terms of mathematical description, but the terms do not
have
>> the same meaning.
>>
>> Same as a 377 ohm line will not radiate half power to the space, when
>> immersed into the EM field, it will not couple half power of the field
>> (which should happen if the concept is right).
>>
>> It can be seen that the concept does not work also if you examine a 50-Ohm
>> air- microstrip. If you assume the concept of splitting power between the
>> line and the air, 50/377 of the total power which is about 0.13 (or 13%)
>> would always be lost to the space, even in a perfectly matched 50-Ohm
>> system. We know that it does not happen when you connect a matched load,
>> source and a line.
>>
>> Neven
>>
>> ----- Original Message -----
>> From: Vinu Arumugham <[email protected]>
>> To: <[email protected]>
>> Sent: Friday, May 05, 2000 5:55 PM
>> Subject: Re: [SI-LIST] : Trace Impedance Selection
>>
>> > If you were able to connect a transmitter to a receiver using a 377 ohm
>> > transmission line, this line would be in parallel to the "transmission
>> > line" between the two formed by free space. Therefore, one half the
>> > transmitted power would go through free space and the other half through
>> > the line. As the line impedance is lowered, more power would be
>> > transmitted through the line and less through space.
>> >
>> > What's wrong with this scenario?
>> >
>> > Thanks,
>> > Vinu
>> >
>> > Mary wrote:
>> >
>> > > Somone recently claimed that higher impedance transmission lines
>> > > radiate more because their impedance is closer to the 377-ohm
>> > > impedance of free space. This is not true. It is not possible
>> > > to judge anything about the radiation from a transmission line
>> > > based on the value of its characteristic impedance.
>> > >
>> > > Characteristic impedance is the ratio of voltage to current in a
>> > > forward traveling wave. The ratio of electric to magnetic field
>> > > strength in a free-space transmission line is approximately
>> > > 377 ohms regardless of what the characteristic impedance is.
>> > > Even if you were to build a transmission line with a 377-ohm
>> > > characteristic impedance, there is no reason to believe it would
>> > > radiate any better or worse than a 300-ohm or a 400-ohm line.
>> > >
>> > > Mary
>> > >
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