# How does the ADF null positions find where the NDB is?

I understand how it operates for the most part, although I don't understand how the null positioning works. This image below doesn't include the sense antenna that limits it to one null position, however how is the null position created? Wouldn't the signal still be received at that position, how does it become null?

Also does the null positioning tell you where the NDB is? If it's null wouldn't that mean no signal is being received so the beacon wouldn't be in that direction? Or do you find the null position, the assume it's 90 degrees from the beacon?

Do you find the null position, then assume it's 90 degrees from the beacon?

That's correct. For the antenna pattern shown in the question, the angle between direction of nulls and peaks is 90°. When sensing a null (or a peak) there are two possible and opposite directions for the beacon. This ambiguity has to be removed. This could be done by triangulation, with a second reading of the angle of arrival after the receiver has moved a bit, but in the modern ADF antenna this is not required, a sense antenna is added to the loop antenna to change the radiation pattern (i.e. the sensitivity vs. the transmitter relative bearing):

Radiation pattern of the loop antenna, and loop + sense antenna system (measured in a horizontal plane)

With the sense antenna, the null is at 180° of the peak, and there is no ambiguity. However the performance of the system is degraded by the sense antenna, thus usually two measures are done, without the sense antenna (for maximum accuracy) and with the sense antenna (for ambiguity removal only). See further down for the details.

The reason we prefer to sense the null direction is the signal received is fading at the larger rate near the null than it is increasing in intensity near the peak. The change being sheer near the null, sensing the null is easier and gives a better accuracy.

Details follow. I added a section about electromagnetic waves details at the end of this answer for those who are interested.

The ADF receiver uses a small-loop antenna (the circumference is small compared to the wavelength), which principle is to sense the magnetic field of the wave, the antenna is actually a coil with a single turn, ensuring it is unsensitive to the electric field.

This loop antenna is unusual in the sense receiving antennas generally couple with the electric field of the wave. However sensing the magnetic field is efficient at lowest frequencies and for direction finding applications.

How is the null position created? Wouldn't the signal still be received at that position, how does it become null?

Correct, the signal reaches the antenna with the same mean intensity, regardless of the orientation.

The loop antenna reacts to the combined result of instantaneous magnetic field at all points of the antenna. According to the law of induction, two points of the loop receiving the signal with a phase difference due to the difference of distance from the transmitter (left side below) will be at a different potential, creating a current in the conductor between these points:

ADF antenna sensing NDB magnetic field (not to scale)

On the other hand (right side), when the loop plane is normal to the direction of the wave, each point of the loop receives the magnetic field with the same intensity, no back-emf is created, no difference of potential is measured, no current circulates, this is a null.

### Rate of variation of gain

We mentioned earlier the radiation pattern of an antenna, which is a representation of its relative gain according to the direction. For the loop antenna:

Radiation pattern of the loop antenna (dotted line for the vertical plane). Source

The gain is provided in decibels, which is a handy way to express a ratio, here the ratio between the intensity in the direction considered, and the maximum intensity found when varying the direction. A decibel value is the logarithm of the ratio, a logarithmic scale being more usable than a linear one when the values vary by several orders of magnitude. By principle the maximum is 0dB (100%, a ratio of 1/1) and other values are negative (less than 100%, a ratio smaller than 1/1).

When looking at the indications in green, The dip in received energy (the null) near +/- 90° is narrower than the peak near 0°/180°. This tells us about the rate of variation of the sensitivity:

• Signal is maximum at 0°, but varies only by less than 2 dB (1.2x) on a range of 60° around the maximum.

• Signal varies by more than 30 dB (31x) for only 30° around the minimum/null.

It means it will be more accurate to determine the direction of the null rather than the direction of the peak (which is the direction of the transmitter). This is the case of many types of antenna: Nulls are more pronounced than maximums.

### Loop antenna with sense antenna

There is a problem with the loop antenna: It has a symmetrical radiation pattern, when a null is found, there are still two possible opposite bearings for the transmitter. The solution is to use an additional antenna, the sense antenna, which is an antenna with the same sensitivity regardless of the bearing. It is said to be omnidirectional and is usually coupling with the electric field.

A wave creates some current in each antenna which instantaneous amplitude is $$A \sin 2 \pi f t$$, where $$A$$ is the maximum amplitude.

• In the loop $$A$$ depends on the antenna gain, thus varies with the transmitter bearing.

• In the sense antenna $$A$$ is constant, regardless of the transmitter bearing. This $$A$$ in the sense antenna is made equal to the $$A$$ in the loop antenna by a trivial adjustment.

Now the polarity of the signals:

• In the loop the sign is positive when the bearing is in [270..(0)..90] and negative in [90..(180)..270].

• In the sense antenna the sign is always positive.

The polarity in each antenna indeed depends on how we measure the signal and can be inverted, but the important point is the polarity is inverted in the loop and constant for the sense antenna. Whatever they the actual signs, we get the same result if we sum the two signals when the loop is aligned on the transmitter bearing and $$A$$ is maximum:

• On one side $$A \sin 2 \pi f t + A \sin 2 \pi f t = 2 A \sin 2 \pi f t$$

• On the other side $$-A \sin 2 \pi f t + A \sin 2 \pi f t = 0$$

The 180° ambiguity has been removed. For other bearings, when the loop is not aligned with the transmitter, $$A$$ for the loop won't have the maximum value and the result will be between 0 and $$2A$$, a heart shape curve (cardioid):

Radiation pattern of the loop antenna combined with sense antenna

In the figure above, the red curve denotes a negative polarity (a 180° phase shift). Both the loop and sense antennas have a power peak of 0dB, they are equal. The null is now opposite to the maximum, and the maximum is +3dB, meaning twice the power of the loop alone. It is easy to determine the null direction. When the null direction has been determined, the NDB direction is the exact opposite.

The usual procedure to determine the direction is:

• First find a null with the sense antenna off, because the sense antenna smooths out the null dip in the radiation pattern. This give the direction with 180° ambiguity.

• Do a second but rough measure with the sense antenna on to remove the ambiguity.

On modern ADF, the antenna doesn't rotate to determine the direction of the NDB. Instead the antenna system is a combination of multiple fixed antennas. The signal direction of arrival is determined by sensing the time of arrival at the different individual antennas. As the time of arrival is actually difficult to determine without an accurate clock, the difference of signal phase is used, as explained in this other question:

A practical realization:

### Electromagnetic waves simply

The very common representation of an EM wave:

Electric and magnetic components of an EM wave. Source

A radio wave, synonymous for an electromagnetic field, propagates in 3D space and its electric and magnetic fields are not dissociable, they are the two sides of the same coin. The classical high-level principles behind EM waves, explaining how the loop antenna can work, are quite easy to summarize, at least in the far field, the area where they actually propagate as we know:

• When a current flows in a wire, a magnetic field exists around the wire as well as an electric field. If these fields vary they creates in turn another varying magnetic/electric pair, and so on. The wave propagation is just the result of electric and magnetic fields expanding from the wire.

• The condition is the first magnetic field must vary, which implies the current in the wire has to be variable, it cannot be a constant DC.

Said otherwise feeding a wire with AC automatically creates a wave. Fortunately if the wire is not tweaked to resonate at the AC frequency, the wave energy is tiny. We can use electric devices on 50/60Hz without creating significant waves because a resonant antenna for this frequency has to be 6 000km long.

Electric current in an open circuit

A NDB transmitter is an AC current generator feeding, e.g., a basic vertical dipole which length is tweaked to make it resonant, like a piano string is tweaked to produce a specific sound. You may wonder how electrons can circulate in an open circuit. The truth is they don't exactly circulate, they oscillate around a fixed position:

• It's well known currents are created by the drift of electrons, but what is actually the velocity of this drift? Surprisingly it is very low: In a DC flashlight it takes about 24 hours for electrons to travel the 10 cm wire connecting the battery to the LED. It's exactly like water traveling from the pumping station to the kitchen.

• An antenna can be seen as a capacitor, mutual capacitance effects exist between the two elements of the antenna. Electrical loads can move on a small distance without leaving the conductor, increasing a bit the local loads density, said otherwise the wire can store some energy at different locations.

• If the antenna is fed with AC, electrical loads are moved back to their initial location after half a cycle, and are pushed in the opposite direction during the next half cycle, their mean position is constant. Electrons oscillate in the open circuit without leaving it, still an AC current is created.

Wave propagation

When a current is created in an antenna, the propagation of the wave can be described by the laws of electromagnetism:

• Ampère-Maxwell's law says 1/ a sinusoidal current creates a magnetic field around the antenna (Ampère's initial idea). The field intensity follows the variation of the current, 2/ the same happens with an electric field instead of a current (Maxwell addition).

• Faraday's law of induction says a varying magnetic field creates an electric field. This field opposes the magnetic flux which created it according to Lenz's law. Lenz's law is to electric field what inertia is to mass (and therefore links both fields like mass is linked to inertia).

When a magnetic field varies a variable electric field is generated and when an electric field varies a variable magnetic field is generated. This leads to an infinite process:

Source: Wikipedia.

The energy of the electric field comes from the magnetic field, as postulated in Lenz's law: The electric field opposes the magnetic field changes, therefore it is a force, aka the back electromotive force (back-emf).

The wire (antenna) is only required to accelerate electrons and generate the initial magnetic field. The subsequent expanding magnetic fields are strictly due to electric fields, electrons and conductors play no role:

The two fields, normal to each other, are the two inseparable aspects of the electromagnetic field. They exist at the same time, and the repeating process leads to their propagation as wave. As fields have no mass, they can travel at the speed of light.

The wave crosses conductors while expanding. A conductor acts as a reception antenna. Depending on the conductor ability to couple more or less strongly with the electric and/or magnetic fields, a given portion of the energy from the fields is converted back into current, by virtue of the same reversible laws.

• What a great upgrade of your answer mins! I would like to upvote it once more, but that's not allowed unfortunately. Oh wait... Commented Apr 14, 2020 at 18:53
• Perhaps I am an expert in the area of surveillance, but in the field of navigation and antenna design I am not. You clearly put a lot of effort in writing this answer; it's well structured and contains a lot of well researched background information. I enjoyed reading it and I learned something new. It's answers like this that make aviation.stackexchange great. Thank you! Commented Apr 14, 2020 at 20:58
• Still I don't understand how the sense antenna works and how the combined effects of loop and sense antenna works. Can you please elaborate on that? Commented Mar 12 at 17:33
• Sorry, not clear to me Commented Mar 13 at 15:37
• @mins, sorry not clear to me. Commented Mar 17 at 23:39