Research On The PCB Planar Spiral Inductors Based On Wavelet-MoM

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.