基于小波矩量法的PCB平面螺旋电感研究
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摘要
电子工业的发展,对电子设备的小型化提出更高的要求。PCB平面电感实现了电感器件的片式化,为降低整个电子系统的厚度,减小设备体积提供了保证。PCB平面电感一般工作在射频和微波段,其电感值及等效电阻等参数会随频率改变而发生变化,通过线圈的物理尺寸精确计算其电参数是设计相关电路的关键。此外,在射频和微波段,平面电感的线圈相当于一个小天线,其辐射和散射对其自身及电路周围器件性能的影响也是电路设计中要考虑的问题之一。针对以上问题,本论文主要做了以下几方面的工作。
(1)构造了区间小波。用小波分析解决实际问题时,选择合适的小波函数是十分重要的。本论文采用小波矩量法计算电感导线中的电流分布,需要解积分方程。由于积分区域是有限的,而标准小波是定义在整个实轴上的,因需要构造一个定义在特定区域的小波,以求解积分方程。本文构造了一个分辨率为2~6的4阶Coifman[0,1]尺度函数,用于求解积分方程。
(2)计算了PCB电感的电感和电阻。构成PCB电感的导线是印制电路板上的铜线,其厚度一般接近导体的一个趋肤深度,此时电感的电感值及等效电阻值都会随频率的变化而变化。本论文建立了PCB电感的传输线模型,推导出导线的表面积分方程,用小波矩量法求解该积分方程,得出沿导线横截面的电流分布,进而计算了电感的电感值和电阻值随频率变化的关系。
(3)从理论上分析了PCB电感的辐射特性。当工作频率小于100MHz时,根据天线理论,把电感线圈的每一圈看作是一个小环天线,运用天线辐射和辐射电阻的公式,说明了电感的辐射特性。得出的结论是,当工作频率小于100MHz时,本论文所研究的PCB电感的辐射完全可以不计。频率大于100MHz时,根据Pocklington积分方程,写出PCB电感中导线的积分方程。运用小波矩量法求出导线中的电流分布,进而给出两个尺寸不同的圆形电感在平面入射波作用下的辐射方向图,并进行分析比较。说明PCB电感相当于一个行波天线,其辐射强度随频率增加而增大,辐射方向随频率增加向波传播的方向偏斜。
(4)通过实验验证了PCB电感在工作频率小于100MHz时的辐射特性。通过由PCB平面电感设计的无源滤波器,研究电感的辐射特性。用PCB平面电感分别设计了一个谐振频率为93MHz的简单LC并联谐振回路和一个通带为60-90MHz的带通滤波器。在滤波器工作时,用HP 8753D网络分析仪通过一个探头在电感中心附近测试了各点的辐射强度,并绘制出相应的曲线,说明当电感线度与波长相比较小时,其辐射强度与电路板上的短路线的辐射强度相近。
本论文主要研究了PCB平面电感的参数计算及电磁辐射特性,其结果不仅可以直接用于PCB电路中电感的设计,对于器件封装及集成电感的设计和制造也有一定的指导意义。
The envelopment of electronic industry demands miniaturization for the electronic equipments. PCB planar inductor realizes a flat inductor device, which reduces the thickness of the electronic system and the volume of the equipment. The distributed parameters of PCB planar inductor, such as inductance and resistance, are frequency-dependent in radio and microwave frequency. It is crucial to evaluate the distributed parameters accurately according to the physical dimension of PCB planar for designing relevant circuits. Moreover, the effects on the circumstance due to the radiation and scattering of PCB planar inductor must be considered, because it works as a small antenna in radio and microwave frequency range. Some researches are carried in this dissertation.
(1) Intervallic wavelets are constructed. It is important to choose proper wavelet functions in solving a practical problem using wavelet analysis. Wavelet-MoM is employed to evaluate current distribution, where integral equations need to be solved. The integral ranges are limited while the standard wavelets are defined on the whole real line. The wavelets defined on special intervallic are required. A 4 order intervallic [0,1] Coifman scarlet at level 6 is constructed used to solve integral equations.
(2) The inductance and resistance of PCB planar inductors are calculated. The windings of the PCB inductors are formed by the copper tracks on PCB board which thickness is close to a skin-effect depth. The inductance and resistance are frequency-dependant. Multicoductor transmission model is built for a square PCB inductor. Surface integral equations are derived and solved using wavelet-MoM. The current distribution along the cross section of wires is deduced. The plots of inductance and resistance verses frequency are given.
(3) The radiation characteristics of PCB planar inductors are analyzed theoretically. For frequency range less than 100MHz, the windings of PCB inductor are taken as small antennas. According to the formulae on radiation and radiation resistance in antenna theories, the radiation characteristics are illustrated that the radiation of under considered can be neglected. For frequency over 100MHz, the integral equation on the wires is derived based on Pocklington integral equation. Wavelet-MoM is employed to find the current distribution. The radiation patterns of two circular PCB inductors with different dimensions are given and analyzed. The results show that the PCB planar can be equivalent to a wave antenna, its radiation intensity increase with the frequency increase, and the radiation direction deflect towards along the propagation direction.
(4) The radiation characteristics for frequency less than 100MHz are verified by experiment. A LC parallel resonant circuit with 93MHz resonant frequency and a passive bandpass filter with frequency range 60～90MHz are designed using PCB inductors for studying the radiation characteristic. The radiation intensity around the PCB inductors are measured by HP 8753D network analyzer and the plots are given. The results show that the radiation intensity is similar to a short route on the PCB board.
Although the distributed parameters and radiation characteristics of PCB planar inductors are researched in this dissertation, the results can be used for inductors design and manufacture in integrated circuits.
(1)构造了区间小波。用小波分析解决实际问题时,选择合适的小波函数是十分重要的。本论文采用小波矩量法计算电感导线中的电流分布,需要解积分方程。由于积分区域是有限的,而标准小波是定义在整个实轴上的,因需要构造一个定义在特定区域的小波,以求解积分方程。本文构造了一个分辨率为2~6的4阶Coifman[0,1]尺度函数,用于求解积分方程。
(2)计算了PCB电感的电感和电阻。构成PCB电感的导线是印制电路板上的铜线,其厚度一般接近导体的一个趋肤深度,此时电感的电感值及等效电阻值都会随频率的变化而变化。本论文建立了PCB电感的传输线模型,推导出导线的表面积分方程,用小波矩量法求解该积分方程,得出沿导线横截面的电流分布,进而计算了电感的电感值和电阻值随频率变化的关系。
(3)从理论上分析了PCB电感的辐射特性。当工作频率小于100MHz时,根据天线理论,把电感线圈的每一圈看作是一个小环天线,运用天线辐射和辐射电阻的公式,说明了电感的辐射特性。得出的结论是,当工作频率小于100MHz时,本论文所研究的PCB电感的辐射完全可以不计。频率大于100MHz时,根据Pocklington积分方程,写出PCB电感中导线的积分方程。运用小波矩量法求出导线中的电流分布,进而给出两个尺寸不同的圆形电感在平面入射波作用下的辐射方向图,并进行分析比较。说明PCB电感相当于一个行波天线,其辐射强度随频率增加而增大,辐射方向随频率增加向波传播的方向偏斜。
(4)通过实验验证了PCB电感在工作频率小于100MHz时的辐射特性。通过由PCB平面电感设计的无源滤波器,研究电感的辐射特性。用PCB平面电感分别设计了一个谐振频率为93MHz的简单LC并联谐振回路和一个通带为60-90MHz的带通滤波器。在滤波器工作时,用HP 8753D网络分析仪通过一个探头在电感中心附近测试了各点的辐射强度,并绘制出相应的曲线,说明当电感线度与波长相比较小时,其辐射强度与电路板上的短路线的辐射强度相近。
本论文主要研究了PCB平面电感的参数计算及电磁辐射特性,其结果不仅可以直接用于PCB电路中电感的设计,对于器件封装及集成电感的设计和制造也有一定的指导意义。
The envelopment of electronic industry demands miniaturization for the electronic equipments. PCB planar inductor realizes a flat inductor device, which reduces the thickness of the electronic system and the volume of the equipment. The distributed parameters of PCB planar inductor, such as inductance and resistance, are frequency-dependent in radio and microwave frequency. It is crucial to evaluate the distributed parameters accurately according to the physical dimension of PCB planar for designing relevant circuits. Moreover, the effects on the circumstance due to the radiation and scattering of PCB planar inductor must be considered, because it works as a small antenna in radio and microwave frequency range. Some researches are carried in this dissertation.
(1) Intervallic wavelets are constructed. It is important to choose proper wavelet functions in solving a practical problem using wavelet analysis. Wavelet-MoM is employed to evaluate current distribution, where integral equations need to be solved. The integral ranges are limited while the standard wavelets are defined on the whole real line. The wavelets defined on special intervallic are required. A 4 order intervallic [0,1] Coifman scarlet at level 6 is constructed used to solve integral equations.
(2) The inductance and resistance of PCB planar inductors are calculated. The windings of the PCB inductors are formed by the copper tracks on PCB board which thickness is close to a skin-effect depth. The inductance and resistance are frequency-dependant. Multicoductor transmission model is built for a square PCB inductor. Surface integral equations are derived and solved using wavelet-MoM. The current distribution along the cross section of wires is deduced. The plots of inductance and resistance verses frequency are given.
(3) The radiation characteristics of PCB planar inductors are analyzed theoretically. For frequency range less than 100MHz, the windings of PCB inductor are taken as small antennas. According to the formulae on radiation and radiation resistance in antenna theories, the radiation characteristics are illustrated that the radiation of under considered can be neglected. For frequency over 100MHz, the integral equation on the wires is derived based on Pocklington integral equation. Wavelet-MoM is employed to find the current distribution. The radiation patterns of two circular PCB inductors with different dimensions are given and analyzed. The results show that the PCB planar can be equivalent to a wave antenna, its radiation intensity increase with the frequency increase, and the radiation direction deflect towards along the propagation direction.
(4) The radiation characteristics for frequency less than 100MHz are verified by experiment. A LC parallel resonant circuit with 93MHz resonant frequency and a passive bandpass filter with frequency range 60～90MHz are designed using PCB inductors for studying the radiation characteristic. The radiation intensity around the PCB inductors are measured by HP 8753D network analyzer and the plots are given. The results show that the radiation intensity is similar to a short route on the PCB board.
Although the distributed parameters and radiation characteristics of PCB planar inductors are researched in this dissertation, the results can be used for inductors design and manufacture in integrated circuits.
引文
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