# Small single turn un-tuned shielded loop

 This article explores the operation of the feed arrangement of a typical small single turn un-tuned shielded loop using transmission line concepts.

# Coaxial transmission line properties

Before examining operation of the loop, lets us refresh the properties of coaxial transmission lines.

Practical transmission lines at radio frequencies have an outer conductor that is much thicker than the skin depth. For that reason, the current that flows on the outside of the outer conductor  can be quite different to the current that flows on the inside of the outer conductor.

In the normal mode of operation of a coaxial cable (TEM), there are three currents to consider:

1. the current flowing on the outside of the inner conductor;
2. the current flowing on the inside of the outer conductor, and which is equal in magnitude to the current flowing on the outside of the inner conductor, but opposite in direction; and
3. the current flowing on the outside of the outer conductor.

# Shielded loop antenna

## Loop Basics Fig 1 shows what is meant by the term "single turn shielded untuned loop" in this article. The inner conductor travels from the feed tee around the loop and is connected to the outer conductor adjacent to the feed tee. The shield is continuous at all places except at the gap which is opposite the feed tee. The coaxial feedline from the feed tee must be routed symmetrically away from the loop to preserve loop balance.

An incident EM wave will induce voltage in the conductor formed by the outer surface of the outer conductor. Where the shield in continuous, resultant current is confined to the outer surface of the outer conductor by skin effect. At the gap, something else happens.

## Analysis at the gap Fig 2 shows the detail at the gap in the outer conductor.

In the case considered, the single turn shielded loop with a single turn inside the loop can be simply described by transmission line theory.

A two way node is formed by the LH end of the outer conductor, there are two current paths, the outer surface of the outer conductor and the inner surface of the outer conductor.

The Current I1 (on the outer of the outer conductor) flows into that node and current Ia (on the inner of the outer conductor) flows out of that node, so Kirchoff's current law  is satisfied.

By virtue of property 2 above of a coaxial transmission line, current Ib (on the outside of the inner conductor) is equal to (and opposite in direction) to current Ia.

Current Ic is in fact Ib, so they are equal.

Similarly, current Id (on the inner of the outer conductor on the RH side) is equal to and opposite in direction to Ic.

A two way node is formed by the RH end of the outer conductor, there are two current paths, the outer surface of the outer conductor and the inner surface of the outer conductor.

The Current Id (on the inner of the outer conductor) flows into that node and current I2 (on the outer of the outer conductor)  flows out of that node, so Kirchoff's current law  is satisfied.

Currents I1, Ia, Ib, Ic, Id, and I2 are equal in magnitude.

The impedance Z1 is the ratio of V1/Ia and is determined by the impedance presented between the outer of the inner conductor and the inner of the LH outer conductor. This is in fact a s/c stub (The inner conductor is connected to the outer conductor at the opposite side of the loop, so it will be a small loss resistance in series with an inductive reactance.

The impedance Z2 is the ratio of V2/Ia and is determined by external load impedance as transformed by the length of transmission line. In the simple case where the external load is the same as Zo, the Z2 would be Zo.

The impedance presented by the load at the gap is V/I1, which is (V1+V2)/I1 or Z1+Z2.

The loop formed by the outer surface of the outer conductor has an equivalent series source impedance that is a small radiation resistance, and small loss resistance and the inductive reactance of the loop.

The voltage induced in the loop by the incident plane wave easily can be calculated.

The current I1 is the induced voltage divided by circuit impedance (sum of source impedance and load impedance at the gap), and so in turn the power delivered to the external load can be calculated having regard to impedance transformations and loss.

## Feedline current

Any current induced for flowing on the outer conductor of the feedline divides equally at the tee because of the symmetry of the antenna and feedline, and the components arriving at the gap are equal and opposite and so cancel.

## Conclusions

The gap in the shield provides a means of coupling current on the outer of the outer conductor to the transmission line formed by the outer surface of the inner conductor and the inner surface of the outer conductor. The inner conductor is not directly subject to incident EM wave because it is effectively shielded by the outer of the outer conductor.

The source of the current flowing on the inner conductor is entirely the current flowing on the outer of the outer conductor at the gap, coupled through the gap as described above.

The antenna is no more or less subject to the influence of electric and magnetic field components than an equivalent loop with the load connected directly at the gap.

The advantage of this feed arrangement is that the coaxial feed typically enters the loop opposite to the gap, and if attention is paid to symmetry of the loop and feed, the balance that is achieved. Best balance yields the deepest null which is important in direction finding applications for instance.

Notions that the shielded loop is not sensitive to E-field by virtue of an electrostatic shield formed of the outer conductor are not based on fact.

## Extension to other loops

The principles above apply also to a loop where the inner conductor is more than a single turn, but the transmission line analysis becomes much more complex.

A loop could be tuned for better impedance matching, better efficiency, and better Antenna Factor of the antenna system. Tuning does not affect the way the outer conductor and gap operate, it just presents a different load impedance at that point. The tuning could be done with:

• a shunt capacitor at the gap (not a good idea as it is challenging to preserve balance);
• a shunt capacitor on the feedline located in a shielded box opposite the gap;
• some other place; or
• a combination of these.

# ARRL

The Antenna Handbook 18th Edition has a number of treatments of "shielded" loops but are of questionable accuracy. Fig 3 is from the ARRL Antenna Handbook 18th Edition p14-2 Fig 2 and shows a shielding arrangement that is not at all effective in balancing the loop. The gap in the shield is adjacent to the feedline entry, so any current flowing on the outside of the feedline flows into one side of the loop where  it is coupled to the inner conductor. Further, there is no support for the statement that the shield is effective against electric fields, and there is no reason to believe that it is, this just serves to perpetuate myths.

Another figure in the ARRL Antenna Handbook 18th Edition, p5-6 Fig 8 contains the note "capacitance from shield to conductor is uniform around circumference". The capacitance from the inner of the outer conductor to the outer of the inner conductor acts entirely inside the transmission line and has no effect on the external balance of the loop. The conditions on the inside of the loop outer conductor are isolated from the outside of the conductor due to skin effect as described above. The ARRL Antenna Handbook 19th Edition has a change to this diagram, but is is still in error in suggesting that a shielded loop overcomes unbalance due to environmental asymmetry.

## A worked example

The following example shows that the operation of the loop, untuned and impedance matched can be solved using transmission line analysis.

A loop constructed as in Fig 1, but a square loop, has the following characteristics at 7MHz:

• RG-58C/U coaxial cable used for feedline and loop;
• loop sides = 600mm;
• Zloop = 0.7+j101Ω;
• Zstub = 0.5+j13.7Ω;
• Zrx = 50Ω
• Zload = Zrx + Zstub =50.5+j13.7Ω

Note that the loss resistance of the loop outer conductor assumes a solid copper conductor, the braid of RG-58C/U will be a little worse.

The Antenna Factor is 0.9dB higher (worse) than if the loop were terminated with a 50 ohm receiver load at the gap. The reason for this is the introduction of the stub impedance in the series circuit. (In fact, for a single turn loop, there is no reason to not connect the inner conductor to the RH side outer conductor at the gap.)

This loop is not impedance matched to the feedline. One place where it is practical to place a matching network is in a shielded box at the tee. The impedance of the antenna at the tee is Zloop + Zstub transformed by 1.2m of RG58C/U, which gives 12.45+j345Ω.

If a shunt capacitor was used to tune out the reactance as in Fig 3, the load would become ~10kΩ, so that is not practical (though often suggested). Fig 4 is from the ARRL Antenna Handbook 18th Edition p5-24 Fig 34 and shows another feed arrangement. The solution to this configuration is found by developing a transmission line model of the configuration. It is not impedance matched to a 50Ω load. Another author suggests the behaviour of this configuration "depends on capacitance inside cable for coupling", an explanation that denies the transmission line behaviour. The load can be transformed to 50Ω load using an L network, in this case a capacitor of about 800pF in shunt with the load, an a capacitor of about 70pF in series, the 70pf would be adjusted for best match. Fig 5 shows the matching network that would be employed in the Minbox pictured in Fig 3.

Examining the loss of this arrangement and assuming lossless capacitors, the radiation resistance of the loop is 1.3mΩ and the series loss resistance of the loop and stub is 1.2Ω, so there is 29.7dB of loss in the loop and stub, and a further 1.3dB of loss from the tee to the gap, so the total loss is 31dB (about 0.08% efficiency). The directivity of a small loop is 1.8dB, so the gain of the impedance matched loop is 1.8dB - 31dB or about -29dBi.

# References

From R. W. P. King, H. R. Mimno and A. H. Wing, Transmission Lines, Antennas and Waveguides (New York: Dover Publications, Inc, 1965), footnote 1 on p 235 is relevant:
"The operation of the shielded loop is explained popularly by first stating that the desired loop current is due to the magnetic field, and then maintaining that the metal shield cannot be penetrated by the electric field but can be penetrated by the magnetic field. All these arguments are incorrect in the light of fundamental electromagnetic principles."