# Franklin antenna – how does it work?

(Franklin 1924) described a technique to cophase sections of a long antenna by “concentrating alternating half wave length portions of the wire within a small space, by winding such portions as inductance coils or by doubling such portions back on themselves so that there is practically no radiation from these portions”.

Let’s explore his second option, as unlike the first, it does work reliably.

Above is an NEC-4.2 model with current shown (magnitude and phase). The stubs conductors are all defined from top to bottom.

The S/C stubs are capable of supporting both common mode and differential mode currents.

Let’s take the current in each conductor of one of the stubs and calculate the magnitude of the common and differential mode transmission line currents.

Above is a plot of the common mode and differential mode current calculated from the NEC model. Note that |Ic| is not zero, so any analysis of how the stub works that has ignored this element of its characteristic, and as it happens a really important element, is incomplete.

Let’s look at a device that provides the differential mode behavior, but without clearly simulating the common mode behavior.

The figure above shows such a coaxial implementation from (King et al, 1945) Fig 22.3(b). (King et al, 1945) notes “their operation is, however, much less satisfactory than with the open wire stubs”. They also state “It is important to note that the inside diameter of the coaxial sleeves must be large compared with the diameter of the antenna and their length considerably less than λ/4 if a sufficient phase shift is to be achieved”.

This is all a bit nebulous, and they are struggling with this phase shift explanation, giving little guidance for effective designs. Nevertheless, these designs are not uncommon and rarely provide evidence of cophase operation.

## A better model?

Lets consider this firstly from the desired charge distribution on the horizontal wires of the cophased antenna.

Taking another figure from (King et al, 1945), we can see that between each half wave section, we need some device that:

• accommodates a large charge difference between the conductors on each side of it; and
• minimises the common mode component of charge on its terminals.

If the antenna was not cophased, there would be a large common mode element of charge at the device terminals, and so spoiling that condition is a path to preventing that undesired mode exciting successfully.

The quarter wave S/C stub (as in the diagram above) fulfills these functions as:

• the differential input impedance of the quarter wave section is high, so permitting the high charge difference required for cophase mode; and
• the stub in common mode acts as a common mode charge sink, the charge maximum in common mode being at the outboard common mode open end of the stub.

There may be other devices that work effectively, for example forming the quarter wave stub into a spiral about the horizontal conductors can make a more compact form which has advantage in a vertical collinear.

But there are many devices employed in published designs that are unlikely to work, and either have not been measure to prove co phasing, or the inventor’s measurements demonstrate they are not cophased (eg the W5GI Mystery Antenna).

## References

• Franklin C. Aug 1924. Improvements in wireless telegraph and telephone aerials GB Patent 242342.
• King, Minmo and Wing 1945. Transmission Lines Antennas and Waveguides. New York: McGraw-Hill.