# How is varying modulation depth achieved by localizer ground transmitters?

An approaching aircraft's navigation receiver uses the difference in depth of modulation between the 90Hz and 150Hz signals which are amplitude modulated onto an RF carrier (on a channel between 108Mhz and 118MHz).

My understanding is that the ground transmitter is formed by several pairs of transmitters forming two interleaved phased arrays to achieved directional beam forming.

My questions is how is the difference in modulation depth achieved by the transmitter system based upon aircraft's position relative to the landing strip's entreline? The beam strength decreases as you move away from it's own centreline, so is it actually that the entire modulated signal strength decreases which when de-modulated is effectively a difference in amplitude modulation depth?

• Possible duplicate of How does ILS (Instrument landing system) work? – Gerry Jan 25 '18 at 13:52
• The 90 Hz and 150 Hz beams are separate beams and the Localizer path is the 'valley' in the middle. – Gerry Jan 25 '18 at 13:55
• The other question has an answer which says "The position of the needle is determined by which lobe of the transmitter is being received stronger than the other", so it doesn't answer the depth of modulation part (amplitude is not modulation depth). – mins Jan 25 '18 at 18:38

The beam strength decreases as you move away from it's own centreline, so is it actually that the entire modulated signal strength decreases which when de-modulated is effectively a difference in amplitude modulation depth?

Your question is very relevant, it can arise naturally if you happen to look at web pages using half correct descriptions (for example this one) to discover the ILS principle.

Let's first look at two oversimplified explanations which are actually dead-ends:

• A precise offset from centerline or glidepath cannot be determined by simply comparing the relative power of two signals. While it's possible in theory, it's also practically imprecise and unreliable. The reason is the final amplitude of a signal depends on many factors which cannot be controlled reliably. So the usual assumption about ILS principle (position is determined by measuring the difference in received power between two signals modulated by two different tones) is not correct, but unfortunately is the one frequently found online.

• ILS use, defined by ICAO, actually refers to sensing the depth of modulation (DM), as you know already. The receiver location relative to the centerline can be found by modulating a carrier with two tones (90 and 150 Hz) and comparing the relative DM at the receiver to find the difference (DDM). However as you correctly noticed, if you use a constant DM for the tones, how can you measure a variable DDM? The answer is you cannot. The DM of the relative tone won't vary when you are closer to or more distant from the transmitter.

Galileo could say: And yet it moves...

The principle relies on mixing signals with a phase difference. When two signals combine (interfere), the phase difference plays a role, e.g.

• When a signal is added to an exact copy of itself, the result is twice the original signal.
• When a signal is added to an inverted copy of itself, the result is zero. A sine signal is inverted by shifting its phase by 180°.
• When a signal is added to a copy of itself which has been phase-shifted by some angle, the result is between zero and twice the signal depending on the relative phase of the signals.

In the ILS, basically one signal is sent for reference and one signal is sent for comparison. On the left side of the runway, the signal to compare is sent in phase with the reference, on the right side the signal to compare is sent in phase opposition with the reference.

The ILS is a combination of a localizer and a glideslope, both systems are very similar. The information provided now on will relate to the localizer, they apply to the glideslope too, with small adjustments. The design involves modulating the amplitude of a carrier. Let's clarify this first.

Amplitude modulation, depth of modulation, sidebands

• A carrier is a constant (usually sine) radiofrequency signal which stay at a given frequency in the whole radio spectrum, with all the wave energy concentrated at this frequency.

• The modulating signal (or modulation) is the signal to transmit, it can have any shape, but in our case its shape is a 90 Hz or 150 Hz sine curve.

• The amplitude modulation process consists in changing the carrier instantaneous amplitude according to the modulation instantaneous amplitude. After it's done, the carrier outer envelope reflects the modulation outer envelope, but the signal frequency is still the carrier frequency.

The modulation process can distort the carrier envelope at variable degrees (create peaks that are taller or smaller), this is the modulation depth (or modulation index). The index value is the peak-to-peak amplitude of the modulation compared to the carrier amplitude before modulation. Example of amplitude modulation at 50%:

The depth of modulation used for the LOC signal is only 20% (40% for the G/S signal). This gentle modulation leaves some room for the LOC carrier to also carry identification tones (on 1020 Hz) and ATC voice used in case of lost communication.

ICAO definition:

The depth of modulation is the ratio of the amplitude of the modulation of the 90 Hz or 150 Hz signal to the carrier amplitude. The DDM is the modulation depth of the stronger signal minus the modulation depth of the weaker signal.

The drawing above describes the modulated carrier in a time-amplitude relationship. Let's look at what happens in the frequency-energy relationship. Before modulation, all energy is concentrated at the carrier frequency (blue bar below). The modulation process creates two variable sidebands (lower and upper sidebands, known as LSB and USB), depicted in magenta:

Spectrum of a carrier AM modulated by a single tone

The modulating signal is a pure sine of constant frequency, each sideband contains its energy at a specific frequency. If the modulation index is 100%, the constant carrier contains 50% of the energy and each sideband 25%. The sideband seats on the frequency axis at a distance from the carrier equal to its own frequency, e.g. when a 100 MHz carrier is modulated by a 150 Hz tone, the LSB is created at 100 MHz - 150 Hz, and the USB at 100 MHz + 150 Hz.

The energy in the sidebands depends on the depth of modulation. The larger the depth of modulation, the larger the energy transferred from the carrier to the sidebands and the lower the energy remaining at the carrier frequency. Sideband energy and depth of modulation are the two sides of the same coin. In the next paragraphs I'll talk about energy rather than depth, but its the same.

Modulating the ILS signal with 90/150 Hz tones

The localizer signal is modulated by two tones, the reference at 90 Hz, the signal to compare at 150 Hz. Therefore each sideband energy is split between two frequencies:

CSB signal spectrum

This signal, known as CSB (carrier and sidebands) will be used as-is in the localizer. However as explained earlier, the in-phase / out-of-phase element must be sent along with CSB.

From 90/150 Hz modulations to CSB/SBO modulations

The localizer transmitter sends an additional signal with an inverted 150 Hz, known as SBO (sidebands only). For this signal the carrier element is removed:

SBO signal spectrum with 150 Hz modulation inverted

The signal is sent so that it is in phase opposition with CSB on the left side of the runway, and in phase with CSB on the right side.

To summarize:

• The localizer transmits CSB on the left and right sides of the array. CSB contains both 150 Hz and 90 Hz with no phase adjustment, and the carrier.

• The localizer also transmits SBO which contains only the sidebands, but where the 150 Hz modulation is phase-shifted by 180° on both sides. The SBO signal itself is sent with a different phase on each half of the antenna array.

How CSB and SBO are sent by the antennas

The actual phase between SBO and CSB is adjusted to compensate for space modulation effects, and SBO is sent with a +90° phase relative to CSB for the antennas on the left of the runway centerline, and with a -90° phase relative to CSB for the antennas of the right of the enterline (the two sides of the array still have a 180° phase difference).

The combination of opposite phases for SBO signal creates a hole in the middle of the SBO radiation pattern, it seems there are two beams for SBO. CSB is radiated centered on this hole:

• CSB radiated power is 15 W.
• SBO radiated power is 0.6 W: It looks tiny compared to CSB, but a large part of the 15 W is used for the information-less carrier. During the demodulation process for SBO the coherent CSB carrier is reused, this process doubles the apparent power of SBO. The difference in power at the end is actually a small one.

In order to achieve this radiation pattern, all the signals must be perfectly coherent (synchronized): 90 Hz and 150 Hz modulations, but also modulations and carrier. If this condition is not met, the resulting radiation pattern is not aligned with the runway and it has a random width.

When spread in space, the three signals mix by space modulation, the principle the ILS is based on and which is more simply known as wave interference.

Space modulation

One signal (SBO) has its carrier suppressed preventing the carrier energy to be increased during the mix CSB+SBO. In contrary when mixing the sidebands from each signal, the space modulation adds the sidebands energy where the sidebands are in phase, and subtract the sidebands energy when they are in phase opposition.

SBO is in phase opposition with CSB on the left side of the runway and is in phase with CSB on the right side of the runway.

• Along the centerline CSB only is present, with equal energy for 90 Hz (green) and 150 Hz (magenta). The LOC indicator will be centered. In order to create a CSB prominent area along the centerline, SBO power is also reduced on the center antennas.

• On the left side, 150 Hz modulation has been shifted by 180° in SBO, and SBO signal has been shifted 180° relative to CSB at antenna level. 150 Hz modulation is therefore in phase for CSB and SBO. Sideband energies are added, while energy for 90 Hz modulation is decreased because 90 Hz modulation in CSB and SBO are out of phase. So there is more energy for 150 Hz (which means there is a larger depth of modulation). This effect is getting stronger as we move away from the centerline.

• On the right side where 150 Hz modulation is out of phase for CSB and SBO, 150 Hz energy is reduced compared to 90 Hz energy in the sidebands, and the difference is getting stronger as we move away from the centerline.

Past 10° from the centerline, CSB cannot be sensed, only SBO can, the LOC indicator will deviate to full scale left or full scale right depending on the phase of SBO. Another signal is used to ensure a full scale deviation past this point (see clearance signal further down).

If you want to do some space modulation simulation, here are the details of the signals to mix (see details here):

$$E_{CSB} = E_C \space \cos \space 2 \pi f_C t + E_{90} \space \sin \space 2 \pi f_{90} t \space \cos \space 2 \pi f_C t + E_{150} \space \sin \space 2 \pi f_{150} t \space \cos \space 2 \pi F_C t$$
$$E_{SBO \space 90} = K \space \sin \space 2 \pi f_{90} t \space \cos \space 2 \pi f_C t$$
$$E_{SBO \space 150} = K \space \sin \space 2 \pi f_{150} t \space \cos \space 2 \pi f_C t$$

We talked about the sidebands energy. Regarding the carrier, which is only present in CSB, the space modulation result always contains the energy of the original CSB carrier until reaching full scale (then the clearance signal provides the carrier because while all modulation information is in the sidebands, the constant carrier is necessary to synchronize and lock the receiver and to retrieve the coherent CSB and SBO from the modulated radiofrequency resulting signal).

Where the DDM finally appears

Now let wrap up:

• The carrier energy is not changed by the space modulation as it is present in only one signal (CSB).
• The sidebands energy is increased or decreased in the resulting signal.

The energy of the sidebands varies relatively to the energy of the carrier, but wait... this is the same than saying the DM is varying (without actually changing anything at the transmitter level).

The DDM between 150 and 90 Hz, is a function of the receiver offset from the centerline (in the range -5° to +5° the function is quasi-linear).

The space modulation actually creates a DDM

The alignment offset is determined by sensing the DDM in the resulting signal.

Antenna array

The LOC antenna is an array system, usually made of a large number of individual log periodic antennas, to form a narrow directional beam.

Localizer array at Melbourne airport, source

CSB and SBO are not distributed equally to all individual antennas of the array. Before reaching the antennas, their amplitude is tuned to form the three sub-beams, and the SBO signal is phase-shifted:

Individual amplifier-phase shifter-mixer

We have now all the basic elements to draw a LOC system:

Components of the ILS LOC system

Example with an array of two antennas (and final answer to the question)

Let's imagine two antennas fed with our earlier CSB and SBO signals with SBO phase being shifted by +90° for antenna 1 and by 270° for antenna 2.

Two antennas with phase shift of 90° and -90° (270°)

Let's see what happens when the receiver is on the centerline at P0, and at any point P1. For this simplified explanation to work, P0/P1 distance to LOC array must be much larger than distance d.

The received signal is the sum of the signals sent by the two antennas. As the distance traveled is the same, the phase at the receiver location is also the same. The signal at point P0 on the centerline is:

$$S_{P0} = K_1 \cdot (CSB - SBO) + K_2 \cdot (CSB + SBO)$$

With $$K_1$$ and $$K_2$$ being the attenuation in free space, as the attenuation is the same for both antennas, this can be simplified:

$$S_{P0} = K_1 \cdot [(CSB - SBO) + (CSB + SBO)] = 2K_1 \cdot CSB$$

In CSB, the 90 Hz depth of modulation is the same than the 150 Hz one (see previous figure) There is no difference in depth of modulation (DDM) between the tones: DDM = 0%.

The distance traveled is shorter for antenna 1, and longer for antenna 2. A phase lead and a phase lag respectively appear for antenna 1 and antenna 2. The phase lead is also equal to the phase lag. After some simplification that can be read in the linked thesis:

$$S_{P1} (\beta) = 2K_1 \cdot (\cos \beta \cdot CSB - \sin \beta \cdot SBO)$$

with $$\beta$$ being the angular distance from the centerline. This formula shows:

• when $$\beta$$ is null (receiver on the centerline), we have the result already seen in the previous case,

• when $$\beta$$ is negative or positive, the SBO signal influence increases and the overall depth of modulation between 150 and 90 Hz tones follows the same trend until reaching -100% or +100%, which correspond to the absence of CSB signal influence at the receiver side.

In the formula above, the system doesn't rely on a difference for the attenuation in free space for the antennas (K1/K2 coefficients are assumed equal).

Instead of relying on amplitude values (two-beam misconception), the system relies on phase difference between SBO and CSB:

Actual principle of the ILS, from this source.

The range of difference of depth modulation obtained must be mapped on the actual standardized values for LOC needle deviation, reducing the full range to a standardized guidance angle. The LOC specification are found in ICAO annex 10 to the Chicago Convention, volume 1, attachment C:

This setting is obtained by tuning the amplifier of the phase-shifter from each individual antenna (the amplifier is actually common to all antennas). This amplifier reduces the SBO signal influence on the DDM.

Clearance signal

So far we have assumed the localizer signal is only composed of the course guidance mixing the two original signals CSB and SBO. But it is very difficult to obtain an actual highly directional beam, like the course beam, without creating unwanted lobes:

Radiation pattern of beam antenna, source

The problem with the secondary lobes is an aircraft approaching aligned with one of them will see it as being the main lobe, and will approach the runway using a wrong course. There are some techniques to minimize these unwanted lobes, but none is practical for large arrays like a LOC system. Alternatives are to block the unwanted waves after they are radiated, or to flood them, the solution used for ILS.

A replica of the course, the clearance signal, is sent with the course signal to outshine the secondary lobes.

The clearance signal has a power level of 10 dB less than the course level (a tenth of the power) and is radiated with a less directional pattern (less individual antennas to form the beam):

Course and clearance

Today's localizers use a dual frequency system, this means the course and clearance signals are sent on separate frequencies.

When an ILS has a published VHF frequency f, the localizer course signal is actually sent on f + 4.75 kHz and the clearance on f - 4.75 kHz. The two signals can use the same aerials or dedicated antennas in the array. Example of signals send to each of the 14 antennas of a Thales LLZ array (refer to above for what are course, clearance, CSB and SBO signals):

Most of the information about ILS come from the 1983 thesis presented by Capt Dennis M. McCollum, B.S.. Respectful thanks to the author.

• From the image it looks like the clearance signal cancels the side lobes but not the back lobe, which would make sense (because back-course approaches, etc.). Also: Amazing answer. – Wayne Conrad Jan 27 '18 at 11:10
• @WayneConrad: Right. If the back lobe needed to be hidden, I believe other ways than flooding by clearance are available, e.g. reflectors on the antennas. Flooding would need more power in the clearance signal, as the back lobe is usually very energized, including for the log periodic antennas used. – mins Jan 27 '18 at 11:26
• That was clear enough that I sorta, kinda, more-or-less understood it! Is this the kind of detail that pilots are expected to know, or is this an area of interest/specialty of yours, @mins? – FreeMan Oct 18 '19 at 18:32
• @FreeMan: Thanks a lot. This is more a topic of electronics engineering than pilot training. However, for a pilot it matters to know that if SBO is down, but CSB is live, the CDI will indicate "aligned" at any location, there was a serious incident based on this condition in July 2000. – mins Oct 18 '19 at 21:06