在這幾年各式電感已經被研發很多年了，線圈除了可以當成電感使用，也可以感應磁場，由於磁場通過線圈的截面積。透過這個方法，我們也可以得知該處的輻射磁場，並討論最佳化線圈的所有參數以及其等效電路。其優點為不需破壞電路，且方便製造及測量。

在這篇論文使用Ansoft HFSS （ High Frequency Structure Software ）來模擬使用製程以及ＦＲ４電路板製作的磁場感測器，而影響感測的主要原因來自於線圈所圍的面積，以及集膚深度所造成的電阻值等等效應，因此，各線寬、線距、線高等等參數之間的改變，對感測器就十分重要。論文中，我們將會介紹一個使用新的線圈來測量主機板，量測ＰＣＢ板上的１００ＭＨｚ到４ＧＨｚ訊號，它的好處是有一個很大的輸出訊號，減少影響電路的部份至最低，且可應用於解決電磁干擾的問題。

In the last decade, the progress of personal computer is growing very fast. The frequency of signals on mother boards applies between 33MHz and 1GHz. Due to the high operating frequency, the radiation from the microstrip lines on PCB should be noticed when designing the PCB’s layout. The solution is using solenoidal and rogowski coils which have been investigated for many years. Coils, however, not only can be used in RF inductors, but also induce currents due to magnetic field through the cross section wound in turns. Therefore, coils may be used to induce magnetic field. Using this phenomenon, intensity of currents on DUT(Device Under Test) could be measured as well. In order to make more extensive use, optimization routines on the basis of the model were found.

This thesis shows that magnetic field sensors on silicon and PCB can be studied in a better model, simulated by the software, Ansoft HFSS. Simple accurate expressions, an equivalent circuit model, and the transfer impedance are presented. As a result, induction of magnetic field on silicon is demonstrated in the area enclosed by turns, the parasitic capacitance or inductance, and conductor resistance, which is due to the skin effect in the high frequency. Hence, coils can induce large current because of big cross section. We can use it to measure the magnetic field and the currents radiated by the microstrip on PCB. In this thesis, I will show a novel PCB sensor which can measure 100MHz to 4 GHz signals and it has large output signal as well. The advantages of these coils are less disturbing DUT and easy to produce. It proves that we can use these magnetic field sensors to help solving the EMI problems.

Contents
Acknowledgement………………………………………………i
Abstract………………………………………………………..iii
摘要……………………………………………………………iv
Contents………………………………………………………..v
List of Figures and Tables……………………………………viii
Chapter 1 – Introduction …………………………...................1
1.1 Background……………………………........1
1.2 Statement of motivation…………………….2
1.3 Contents of this thesis………………………2
Chapter 2 - Theory of coils on silicon and PCB………………3
2.1 General analysis of coils……………………3
2.2 Antenna mode…………………………........5
2.3 Inductance calculation methods…………….6
2.4 Near field calculations……………………...8
2.4.1 Electrostatic solution for a microstrip line……………………………………….8
2.4.2 Near-field calculations for a rectangular loop…….…………….........................12
2.5 Coupling between a coil and a microstrip line……………………………………….13
2.5.1 Inductive Coupling………………...13
2.5.2 Capacitive Coupling……………….16
2.6 Special cases – sensors fabricated on silicon……………………………………17
Chapter 3 - Simulations and the design of rogowski coils on silicon…………………………………………20
3.1 Simulation foundation……...…………….20
3.2 Simulation results……………….…..…....21
3.3 Inductance calculation of spiral inductors
...……………………………….…..……..29
3.4 Summary………………………………….31
Chapter 4 - Simulations and measurements of coils on PCB…………………………………………..32
4.1 The foundation of the microstrip and coil..32
4.2 Implementation of closed loop coils……..33
4.3 Analysis of closed loop coils…………….38
4.4 Implementation of Rogowski coils………40
4.5 Analysis of Rogowski coils……………....43
4.6 Coupling effects between the sensor and DUT……………..……………………….44
4.7 Coil implementation with a coplanar waveguide…………………..……………45
4.8 A Survey of the SI issue by magnetic field sensors..…………………………………..49
4.9 Summary…………………………………52
Chapter 5 – Conclusions……………………………………54
Reference……………………………………………………55

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