# Signal demodulation

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Demodulation refers to the extraction of information from a carrier wave. The extracted information is either digital or analog in nature. For example, Wifi transmits digital information on 2.4GHz and 5GHz frequencies, while a typical FM radio transmits analog signals in the form of sound at carrier frequencies between 80-100MHz.

In the case of Anser EMT, the carrier signals are those transmitted by the eight field emitter coils in the field generator. The extracted information are the magnitudes of each of the received frequency components. The sensor coil detects these carrier frequencies as described in section (5b) and produces a composite signal representing the sum of the received carrier frequencies. Following amplification and sampling, the magnitudes of these carrier signals are extracted using asynchronous demodulation techniques. The position and orientation algorithm compares these magnitudes with the system magnetic field model in order resolve a unique sensor position and orientation.

## Demodulation theory

Two modulation schemes are discussed in this section, synchronous and asynchronous methods are discussed. Asynchronous demodulation is the chosen scheme as it provides more information regarding the orientation of the sensor.

In order to calculate the amplitude of the AC magnetic field experienced by the sensor many techniques are available. Generally, the signals of interest are small in amplitude with relatively large noise levels as well as interference from the other transmitting channels. The most common method to extract the signals of this type is synchronous demodulation, also known as synchronous detection or lock-in amplification

### Synchronous demodulation

Synchronous demodulation is a method for extracting information from an AC carrier signal. Although asynchronous demodulation is used in Anser, synchronous demodulation illustrates basic concepts that are used in the asynchronous design.

The amplitude and phase of an AC signal can be calculated through multiplication by a reference signal that is locked in frequency with the original signal. The multiplication by the reference signal, shifts the signal down to a lower frequency, typically DC, which is then easier to accurately measure. The "locking" of frequencies can be implemented in many ways although the simplest is to use the source of the signal as a reference.

Consider an input signal:

${\displaystyle v(t)=V\sin(\omega t+\varphi )}$

where ${\displaystyle V}$ is the modulating signal we wish to extract. The amplitude and phase of this signal can be determined by multiplying by two reference signals at the same frequency:

${\displaystyle Y(t)=\sin(\omega t)}$
${\displaystyle X(t)=\cos(\omega t)}$

This multiplication result in two quadrature signals:

${\displaystyle v_{y}(t)=v(t)Y(t)={\frac {V}{2}}[\cos(\varphi )-\cos(2\omega t+\varphi )]}$
${\displaystyle v_{x}(t)=v(t)X(t)={\frac {V}{2}}[\sin(\varphi )-\sin(2\omega t+\varphi )]}$

The DC component of the signal is extracted by using an appropriate low-pass filter. The resulting DC values are:

${\displaystyle v'_{y}(t)={\frac {v}{2}}\cos(\varphi )}$
${\displaystyle v'_{x}(t)={\frac {v}{2}}\sin(\varphi )}$

The amplitude of the modulating signal $V$ can be found using:

${\displaystyle V=2{\sqrt {(v'_{x}(t)^{2}+v'_{y}(t)^{2})}}}$
The phase of the signal can be found using:
${\displaystyle \varphi =\arctan \left({\frac {v'_{y}(t)}{v'_{x}(t)}}\right)}$

Demodulating using this technique requires ${\displaystyle Y(t)}$ and ${\displaystyle X(t)}$ be generated from the reference source. This requires each of the eight coil voltages (20.5kHz, 21.5kHz...) to be individually sampled for processing, requiring an analogue to digital converter with a very high aggregate sampling frequency. Instead, simulated reference signals may be used to generate ${\displaystyle Y(t)}$and ${\displaystyle X(t)}$which results in asynchronous demodulation.