# Slot, notch, and rectangular loop antennas

Antennas notes.

## Transmission line model.

We start by considering a length of parallel wire transmission line along which is running radiation of wavelength lambda. The development of this model into a slot antenna proceeds as shown in the figure below:-

(If you click on the small .jpg image you will get a 90kB .gif version for more detail.)

• In the first frame we show the parallel wire line.
• In the second frame we show the parallel wire line shorted at each end of a lambda/2 section.
• In the third frame we show the voltage on this line; it is zero at each short circuit (the "nodes") and maximum in the middle, (the "antinode"), where it oscillates up and down at the wave frequency.
• In the fourth frame we show the current on this line; it is zero at the node in the middle, and maximum in the two short circuits at the end. We notice that the current is oppositely directed in the top and bottom wires of the transmission line.
• In the fifth frame, we fill in the entire plane outside the transmission line wires with a conducting ground plane, to realise a slot antenna. The currents are again oppositely directed in the edges of the slot. However, they are no longer confined to the transmission line wires (of assumed negligible thickness) but spread out over the surface of the ground plane.

### The slot antenna

Now thinking about the fifth frame in more detail, we have drawn the maximum and minimum values, along the line, of the right-hand-directed current in the top wire of the two wire line. When the current at the left hand node is maximally positive (ie to the right), the current (again in the top wire) at the right hand end is maximally negative (ie to the left). Thus in both the end short circuits, the currents are in phase and are flowing upwards. There is more information on waves on transmission line.

Thus the current elements in the shorts at the end are in phase, and spaced by a half-wavelength. The array pattern for such a distribution of elements is shown in the notes on array antennas , and we see that the main lobe is at right angles to the plane of the slot.

Since these currents are vertical (on the diagram) we readily see that the horizontal slot antenna produces a vertical linearly polarised E field direction.

The currents in the horizontal edges, being equal and oppositely directed, give very little radiation (one cancels the other) until the height of the slot (which equals the distance between the opposing currents) becomes an appreciable fraction of a half wavelength.

### Notch antennas

Since the currents are zero at the middle of the slot, we may cut the ground plane here to make a notch antenna.

In, for example, the wing or fin of an aircraft it is possible to make a folded notch, as is shown in the figure. The area of current which radiates is not limited to the dimensions of the notch; thus, such an antenna can be a reasonably efficient radiator for its size.

### Rectangular loop antennas

The same arguments may be used to analyse a rectangular loop antenna, whose long dimension is comparable to a half-wavelength. In a non-radiating shorted transmission line the half-wave resonances are very sharp as the Q factor is high, there being only limited conductor loss and no radiation damping. However, in a radiating loop the energy stored compared to the energy radiated per radian of oscillation need not be that large, so the loaded Q may be small and the fractional bandwidth reasonably large. Under these circumstances it is no longer necessary to have the long loop length accurately tuned to a half-wavelength.

Now, if we consider a rectangular loop where the long dimension lies between a quarter and a half wavelength, and the short dimension is a bit less than a quarter wavelength, the currents in the short sides will be co-directed whereas the currents in the long sides will be contra-directed. Thus the antenna radiation (normal to the plane of the loop) will be polarised parallel to the short sides of the loop.