# Magnetic Communication Using High-Sensitivity Magnetic Field Detectors
## 3 Sensitivity Analysis
### Communication Range for Lossless Transmission Mediums
#### 3.2.5 Transmission Range for Different Core Materials  
Equation (7) shows that the resulting magnitude of the magnetic flux density generated by a transmitter coil directly depends on the magnetic permeability of the core material. This can be explained by the fact that a high-permeability core acts as a flux concentrator inside a coil [19]. According to the Agbinya-Masihpour MI link budget (2), a high-permeability coil core can further be used at the receiver side of a coil-to-coil communication system to enhance the maximum communication distance.  
Subsequently, the influence of the permeability of the coil core material on the transmission range is examined for both communication techniques. For coil-to-coil communication, the transmitter and receiver coil core permeability are adapted simultaneously. For coil-to-AMR communication, only the transmitter coil core permeability can be changed.  
Figure 6 presents the effect of the relative core permeability on the maximum transmission range for coil-to-coil and coil-to-AMR transmission. For both communication techniques, the range increases with the permeability of the coil core. Due to the same slope of the curves in log-log scale, they must follow the same power function.  
Figure 5: Transmission range for coil-to-coil and coil-to-AMR communication depending on the transmitter coil radius (**a**) and receiver coil radius (**b**). Parameters are taken from Table 2.  
Figure 6b shows the maximum coil-to-coil transmission range versus the receiver coil radius for materials with different permeabilities (Table 3). The corresponding coil-to-coil transmission range is compared to the coil-to-AMR communication reference range (dashed line) with different transmitter coil materials and a receiver detection bound of \(B_{\text{min}}=5\) nT for a bandwidth of 1.47 kHz. The maximum transmission distance for coil-to-coil and coil-to-AMR transmission is strictly monotonically increasing with the permeability of the core material by the same factor for both techniques. If for example a ferrite core is used, the maximal distance increases by a factor of 8.6. These numerical results reveal for a variety of different core materials that the influence of the core permeability for coil-to-coil communication and coil-to-AMR communication is the same. The advantage of coil-to-AMR communication is that the change of the transmitter coil core material leads to the same result as changing transmitter and receiver core material in a coil-to-coil communication system. Consequently, increasing the communication range can be realized for coil-to-AMR transmission with less effort than for coil-to-coil transmission.  
However, the enhancement of the possible communication distance by means of increasing the permeability of the core material is limited by a few parameters. Primarily, there are no materials available that exhibit arbitrary high permeabilities. Additionally, the permeability of a material depends on the frequency, so that extremely high permeabilities for high frequencies usually cannot be achieved. Moreover, the saturation flux density B\({}_{s}\) of a core material is a constraint (Table 3). This results in the challenge to choose a core material with a uniformly high permeability for the frequency range which is used for communication and even a sufficiently high saturation flux density. A further restriction of the maximum applicable permeability of the coil core material arises due to the associated increase of the inductance \(L\) according to \(L\sim\mu\). The inductance \(L\) of a coil has a limiting effect on the resonant frequency  
\[f_{0}=\frac{1}{2\pi\sqrt{LC}}, \tag{9}\]  
because the capacity \(C\) of the resonant circuit is lower bounded by parasitic capacitances.  
Figure 6: Transmission range for coil-to-coil and coil-to-AMR communication depending on the permeability (**a**) and the receiver coil radius for different core materials (**b**). Parameters are taken from Tables 2 and 3. The dashed lines are for coil-to-AMR transmission.