# Can we draw analogy between em power flow through free space and ac power flow through a transmission line?

Knowing that the free space has a characteristic impedance (which is purely resistive, measured in ohms) I was wondering if I can model the free space as an infinitely long transmission line- comprised of distributed inductors and capacitors.

We know, a lossless transmission line model of infinite length supplied by an AC source at one terminal looks:

If we consider the direction of changing electric field across the capacitance (say X axis) and that of changing magnetic field inside the inductance (say Y axis), we find the poynting vector directing outward of the plane of transmission line (Z axis)-- which seems weird, since power flow direction is certainly along Y axis.

However, if I adjust the orientation of the inductors in following way:

It seems that the problem regarding to power flow direction is solved apparently. However, I am not still convinced with this depiction. Firstly, I have considered only the magnetic field inside the inductors. But H has a non zero curl, it ends upon itself. So if I take the total H field (around the inductor) into account, I end up with a zero power flow -- which is definitely not what is happening. Moreover, the power flow, irrespective of the orientation of inductors, must be along transmission line (not outward of the plane containing TX line).

At this point, I wonder where I am making mistakes. (i.e.- is it because I am ignoring current through the capacitor and electric field across the inductor? )Or is it a crap idea to model the free space as transmission line ?

• Why would you want to do this? Commented Dec 4, 2013 at 15:41
• Its because I think there should exist a generalized model for power transmission in a medium, so that the same model can be used in both AC power propagation in transmission line and electromagnetic power propagation in free space.
– Joy
Commented Dec 4, 2013 at 16:18
• The whole point of a power line is that it's a conductor, with different propagation properties and a boundary. You could probably use the free space model for transmission within a big metal body (planetary core?) Commented Dec 4, 2013 at 16:27

We usually draw the inductor symbol as a coil of wire which can be very misleading. You have to take a look at the B-field around a straight wire then all the sudden your analogy makes perfect sense.

I have answered a question about transmission line models already here: Transmission Line Inductance Some background information for you on the subject. It is not an answer to your question though.

Knowing that the free space has a characteristic impedance (which is purely resistive, measured in ohms) I was wondering if I can model the free space as an infinitely long transmission line- comprised of distributed inductors and capacitors.

If free space is purely resistive, then it is not accurate to model free space as a transmission line because a transmission line is not purely resistive, especially at long lengths. Here is a response about why conductors are not purely resistive. Where does a straight conducting wire get its capacitance?

If we consider the direction of changing electric field across the capacitance (say X axis) and that of changing magnetic field inside the inductance (say Y axis), we find the poynting vector directing outward of the plane of transmission line (Z axis)-- which seems weird, since power flow direction is certainly along Y axis.

In your third image you have drawn your inductors perpendicular to your capacitors. Which coincides with your convention that the electric field is in the X direction and the magnetic field in the Y direction. You state the poynting vector should be in the direction of the the Z axis. This is correct for the electromagnetic wave.

Then you have drawn a conductor after each capacitor-inductor node. This conductor makes a 180 degree "turn" with respect to the direction of the magnetic field travelling through the inductor. Meaning your Y axis shows negative and positive values. I can understand that perhaps you want to show the magnetic wave as a changing magnetic field. Although you do not show the changing electric field in this respect. So this is one indication that we cannot evaluate vectorially, the circuit elements which are modelled to represent the way they operate and connect in terms of arithmatic (series & parallel). In general, it's better to use phasors to model circuit elements for various reasons, see Phasor Wikipedia.

• No resistance in the model DOES NOT mean real power cannot flow. Commented Dec 8, 2018 at 11:13