# High-Performance Magnetoinductive Directional Filters

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Magnetoinductive Waveguides

#### 2.2. Impedance and Power Flow

#### 2.3. Magnetoinductive Directional Filters

#### 2.3.1. Frequency Response

#### 2.3.2. Bandwidth

#### 2.3.3. Frequency Tuning

#### 2.4. Advanced Filters

#### 2.4.1. Infinite Rejection

#### 2.4.2. Multiple Bandstop Frequencies

#### 2.4.3. Three-Port Filters and Multiplexers

## 3. Results and Discussion

#### 3.1. Single-Notch Filter

#### 3.2. Single-Notch Filter with Infinite Rejection

#### 3.3. Double-Notch Filters

#### 3.4. Double-Notch Filter with Improved Rejection

#### 3.5. Applications

#### 3.6. Frequency Scaling

_{C}, and loss factor. The main difference between groups is the maximum usable frequency F

_{max}. Following Snoek’s limit [52], ${\mu}_{i}$falls as F

_{max}is raised. High-frequency performance is therefore accompanied by a reduction in magnetic field confinement and an increase in loss. Small toroids may be used to minimise the volume of magnetic material. However, careful design will be required to optimise performance, power handling will be reduced, and automated coil winding may be required for construction [53]. Despite this, the data suggest that response may be extended to the low UHF band. Above this, air-cored inductors may be used, but non-nearest-neighbour coupling and radiation will inevitably complicate the design and reduce performance.

#### 3.7. Future Work

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Magnetoinductive (MI) waveguide: (

**a**) equivalent circuit; (

**b**) frequency dependence of ${k}^{\prime}a$ and ${k}^{\u2033}a$ for $\kappa =\left\{\pm 0.6,\pm 0.3\right\}$ and $Q=200$. Crosses show measured points for $\kappa =0.3$.

**Figure 2.**(

**a**) MI directional filter equivalent circuit; (

**b**) lumped element terminations: (1) magnetoinductive, (2) resistive, and (3) broadband resistive.

**Figure 3.**MI directional filter performance for $\kappa =0.6$ and ${\kappa}_{c}=0.3$: (

**a**) scattering parameters for lossless and lossy ($Q=200$ ) resonators with MI terminations (1) and real narrowband terminations (2); (

**b**) variation of ${Q}_{bp}$ with $\kappa $ and ${\kappa}_{c}$ for a lossless filter with MI terminations (1); (

**c**) scattering parameters for lossless resonators with MI terminations (1) for ${\omega}_{0}^{\prime}/{\omega}_{0}=0.9,\text{}1.0,\text{}\mathrm{and}\text{}1.1$.

**Figure 4.**(

**a**) Variation of $\lambda $ with $\mu $ for different unloaded resonator Q-factors with $\kappa =0.6$. (

**b**) Frequency dependence of scattering parameters for infinite rejection filter with lossy MI and resistive narrowband terminations with $\kappa =0.6$, ${\kappa}_{c}=0.3$, and$\text{}Q=200$.

**Figure 5.**(

**a**) Multiple bandstop MI directional filter; (

**b**) frequency dependence of S-parameters for multiple passband filter with lossless MI terminations (1) for $\kappa =0.6$, ${\kappa}_{c}=0.3$,$\text{}N=2$, and $N=5$.

**Figure 6.**MI directional filter: (

**a**) mechanism for tuning of magnetic coupling (LH–maximum coupling; RH–minimum coupling); (

**b**) complete PCB with labelled port numbers.

**Figure 7.**Experimental (solid) and theoretical (dashed) frequency dependence of scattering parameters for MI filter with resistive narrowband terminations (2) with ${\omega}_{0}=13.56$ MHz, $Q=200$, and ${Z}_{0M}=50\text{}\mathsf{\Omega}$. (

**a**) ${\kappa}_{c}=0.28$ and $\lambda =1$; (

**b**) infinite rejection with ${\kappa}_{c}=0.25$ and $\lambda =$ 0.79.

**Figure 8.**Experimental (solid) and theoretical (dashed) frequency dependence of S-parameters for double passband MI filter with resistive narrowband terminations with ${\omega}_{0}=13.56$ MHz, $Q=180$, ${Z}_{0M}=50\text{}\mathsf{\Omega}$, and ${\kappa}_{c}=0.3$. (

**a**) No improved rejection; (

**b**) improved rejection.

**Figure 9.**Power spectral densities of (

**a**) input signal to port 1 of MI single-notch directional filter; (

**b**) output signal at port 2 normalised by the input carrier power ${P}_{c}$. Dashed lines: filter bandwidth; red: harmonics at multiples of carrier frequencies; green: harmonics at message sidebands. (

**c**) Attenuation of sidebands and carrier.

Parameter | Value | Range of Adjustment |
---|---|---|

${L}_{T}$ | 1.16 μH | N/A (not applicable) |

${L}_{c}$ | 460 nH | N/A |

${L}_{s}$ | 710 nH | N/A |

$\kappa $ | 0.725 | 0.51–0.92 |

${\kappa}_{c}$ | 0.28 | 0.19–0.34 |

${\omega}_{0}$ | 13.56 MHz | DC to 50 MHz |

$Q$ | 200 ± 10% | N/A |

Manufacturer | Model | OD (mm) | ID (mm) | Height (mm) | Initial μ_{i} | F_{max} (MHz) | T_{C} °C | Material | Loss Factor |
---|---|---|---|---|---|---|---|---|---|

Ferroxcube | - | - | - | - | 125 | 20 | >350 | 4C65 | 130 @ 10 MHz |

Fair-Rite | 5961001801 | 22.10 | 13.70 | 06.35 | 125 | 25 | >300 | 61 | 10 @ 10 MHz |

Ferroxcube | - | - | - | - | 25 | 100 | >400 | 4E2 | - |

Fair-Rite | 5968001801 | 22.10 | 13.70 | 6.35 | 16 | 150 | >500 | 68 | 300 @ 100 MHz |

National Magnetics | - | - | - | - | 7.5 | 400 | >320 | M5 | <3500 @ 100 MHz |

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**MDPI and ACS Style**

Voronov, A.; Syms, R.R.A.; Sydoruk, O.
High-Performance Magnetoinductive Directional Filters. *Electronics* **2022**, *11*, 845.
https://doi.org/10.3390/electronics11060845

**AMA Style**

Voronov A, Syms RRA, Sydoruk O.
High-Performance Magnetoinductive Directional Filters. *Electronics*. 2022; 11(6):845.
https://doi.org/10.3390/electronics11060845

**Chicago/Turabian Style**

Voronov, Artem, Richard R. A. Syms, and Oleksiy Sydoruk.
2022. "High-Performance Magnetoinductive Directional Filters" *Electronics* 11, no. 6: 845.
https://doi.org/10.3390/electronics11060845