# A Method for Measuring the Maximum Measurable Gain of a Passive Intermodulation Chamber

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## Abstract

**:**

## 1. Introduction

## 2. PIM Measurement System

## 3. The Method for Evaluating the MMG of a PIM Measurement Chamber

_{0}, its effect can be equivalent to placing an antenna A

_{0}

^{′}that is the same as A

_{0}at a symmetrical position of the metal wall and removing the metal wall at the same time [29]. At this time, the Friis formula can be used:

_{0}is the center of the PIM measurement chamber. In reality, the antenna is usually placed at this position for measurement in order to achieve minimal reflection. It is assumed that the PIM of a directional antenna A

_{0}with a gain of G

_{0}is measured at position P

_{0}, and that the PIM of a directional antenna A

_{1}’ with a gain of G

_{1}is measured at position P

_{1}. The main radiation directions of both antennas are toward the $-x$ direction. Since most of the energy of a directional antenna is concentrated in the main radiation direction, only the reflection from the $-x$ plane needs to be considered, and the reflection from other surfaces can be ignored. Then, Equation (5) can be used in this situation. The following two formulas can be obtained:

_{1}at P

_{1}can be equivalent to the measured result of A

_{0}at P

_{0}. The purpose of replacing the high-gain antenna with a medium-gain antenna can be achieved. In this case, the received power of the PIM signals ${S}_{IM\text{\_}SE}$ and ${S}_{IM\text{\_}AM}$ for a high-gain antenna is also can be replaced by a medium-gain antenna due to the reduced path loss. We can also use Equations (6)–(9) approximately. Regardless of the loading effect of the absorbers, the minimum value of ${d}_{1}$ is the height of the absorbers. Therefore, the highest gain that can be compensated can be approximated as $10\mathrm{lg}\left({d}_{0}/{h}_{ab}\right)$, where ${h}_{ab}$ is the height of the absorbers.

- (1)
- First determine the PIM noise floor target of the chamber. For example, if the required residual PIM level is lower than −160 dBc at 43 dBm, the directional antenna used for measurement must have a PIM below −160 dBc. During the test, if a measurement higher than −160 dBc appears, it is considered not to meet the requirement.
- (2)
- Determine the gain to be measured. The maximum gain to be measured can be directly determined according to the actual application. Generally, a stepping method can be used to determine the MMG. First determine an appropriate gain, and if the measurement results meet the requirements, increase the measurement gain appropriately until a level higher than the target noise floor is detected. Otherwise, decrease the measurement gain until the measurement results are lower than the target noise floor.
- (3)
- Calculate the measurement distance according to the gain to be measured, which can be determined according to Equation (9) or simulation results.
- (4)
- Determine the measurement positions according to the beamwidth and measurement distance of the antenna. The specific method is described above.
- (5)
- If a result higher than the target noise floor appears during the measurement, it is not necessary to continue measuring the remaining positions. It can also be assumed that the results of measurements with an antenna with this gain will be unreliable. Otherwise, the six planes should be measured completely.

## 4. Experimental Validation

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**Selection method of measurement positions for the $-x$ plane. (

**a**) Main lobe projection of the antenna. (

**b**) Sectional view of the $xoy$ plane, and (

**c**) sectional view of the $yoz$ plane.

**Figure 6.**A photograph of chamber A. (

**a**) Appearance of the PIM measurement chamber A, (

**b**) measurement arrangement in PIM measurement chamber A.

**Figure 8.**A photograph of chamber B. (

**a**) Appearance of the PIM measurement chamber A, (

**b**) measurement arrangement in PIM measurement chamber B.

Position | Measurement Distance (m) | Equivalent Gain (dBi) | Measured PIM (dBc) | ||
---|---|---|---|---|---|

33 dBm | 40 dBm | 43 dBm | |||

P1 | 1.6 | 10.5 | −169.0 | −166.8 | −160.3 |

P2 | 1.05 | 12.3 | −168.5 | −164.6 | −158.4 |

P3 | 0.95 | 12.7 | −168.6 | −164.4 | −156.3 |

P4 | 0.85 | 13.2 | −168.2 | −164.4 | −155.7 |

P5 | 0.75 | 13.8 | −168.0 | −164.1 | −154.8 |

P6 | 0.65 | 14.4 | −164.5 | −160.2 | −150.3 |

Low PIM load | - | - | −172.5 | −171.1 | −170.6 |

Position | Measurement Distance (m) | Equivalent Gain (dBi) | Measured PIM (dBc) | ||
---|---|---|---|---|---|

33 dBm | 40 dBm | 43 dBm | |||

P1 | 1.6 | 8 | −169.0 | −167.6 | −166.2 |

P2 | 1.05 | 9.8 | −168.9 | −166.4 | −161.4 |

P3 | 0.95 | 10.3 | −168.8 | −166.6 | −162.2 |

P4 | 0.85 | 10.7 | −168.6 | −166.4 | −162.2 |

P5 | 0.75 | 11.3 | −168.3 | −166.2 | −161.3 |

P6 | 0.65 | 11.9 | −166.7 | −163.6 | −154.3 |

Low PIM load | - | - | −170.5 | −169.9 | −169.1 |

Position | Measurement Distance (m) | Equivalent Gain (dBi) | Measured PIM (dBc) | ||
---|---|---|---|---|---|

33 dBm | 40 dBm | 43 dBm | |||

P1 | 1.6 | 10.5 | −167.9 | −167.2 | −166.8 |

P2 | 0.95 | 12.7 | −168.2 | −167.2 | −165.8 |

P3 | −168.0 | −167.9 | −166.3 | ||

P4 | 0.65 | 14.4 | −168.4 | −167.2 | −166.5 |

P5 | −168.7 | −167.5 | −167.2 | ||

P6 | −168.2 | −167.2 | −166.4 | ||

Low PIM load | - | - | −169.5 | −168.9 | −168.5 |

Average(P1~P6)-Low PIM load | - | - | 1.3 | 1.5 | 2.0 |

Position | Measurement Distance (m) | Equivalent Gain (dBi) | Measured PIM (dBc) | ||
---|---|---|---|---|---|

33 dBm | 40 dBm | 43 dBm | |||

P1 | 1.6 | 8 | −167.6 | −166.5 | −165.8 |

P2 | 0.95 | 10.3 | −167.9 | −167.1 | −165.5 |

P3 | −167.7 | −167.0 | −166.0 | ||

P4 | 0.65 | 11.9 | −168.0 | −167.7 | −166.7 |

P5 | −168.0 | −167.4 | −166.0 | ||

P6 | −168.3 | −167.5 | −166.3 | ||

Low PIM load | - | - | −168.6 | −168.2 | −167.1 |

Average(P1~P6)-Low PIM load | - | - | 0.7 | 1.0 | 1.1 |

PIM Measurement Chamber | Position | Measurement Distance (m) | Gain (dBi) | Measured PIM at 900 MHz (dBc) |
---|---|---|---|---|

A | P1 | 1.6 | 16 | −152.1 |

B | P1 | 1.6 | 16 | −161.5 |

Outside the chamber | - | - | 16 | −134.8 |

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**MDPI and ACS Style**

Cai, Z.; Zhou, Y.; Liu, L.; de Paulis, F.; Qi, Y.; Orlandi, A.
A Method for Measuring the Maximum Measurable Gain of a Passive Intermodulation Chamber. *Electronics* **2021**, *10*, 770.
https://doi.org/10.3390/electronics10070770

**AMA Style**

Cai Z, Zhou Y, Liu L, de Paulis F, Qi Y, Orlandi A.
A Method for Measuring the Maximum Measurable Gain of a Passive Intermodulation Chamber. *Electronics*. 2021; 10(7):770.
https://doi.org/10.3390/electronics10070770

**Chicago/Turabian Style**

Cai, Zhanghua, Yantao Zhou, Lie Liu, Francesco de Paulis, Yihong Qi, and Antonio Orlandi.
2021. "A Method for Measuring the Maximum Measurable Gain of a Passive Intermodulation Chamber" *Electronics* 10, no. 7: 770.
https://doi.org/10.3390/electronics10070770