Good explanation.

You might add that this applies to coaxial libes whose fields do not
interact. For open wire line the picture is considerably different
because the eleccctric and magnetic fields overlap.

Jim

On Wed, 01 Jun 2005 07:50:06 -0500, Cecil Moore
wrote:

Asimov wrote:
This is a hypothetical question, if one needs to send more power down
a line than its capacity can 2 or more lines be paralleled? Is the
equivalent characteristic impedance of the combined lines the same as
that of a single individual line?

Let's say we parallel two pieces of lossless 50 ohm coax such
that the voltages at the load (V1 and V2) are equal magnitude
and phase. The currents at the load (I1 and I2) will be equal
magnitude and phase.

For matched line operation, V1/I1 = V2/I2 = 50 ohms.
Pload = (V1*I1)+(V2*I2) = 2*(V1*I1)
Vload = V1 = V2
Iload = I1 + I2
Rload *for matched line operation* = V1/(I1+I2) = V1/(2*I1).
Rload = 1/2(V1/I1) = 50/2 = 25 ohms. So 25 ohms is the
equivalent Z0 of two pieces of 50 ohm coax in *parallel*.

Conversely, if you use one piece of 50 ohm coax going to the
load and one piece of 50 ohm coax coming back from the load
to achieve a shielded balanced feedline, the Z0 of that
feedline is 2*Z0 = 100 ohms and the two lines are in *series*.