Candidate
Sung Eun Kim
Title
Optimization Algorithm for Antenna Impedance Matching in Digitally Tunable Network
Supervisor
Safieddin Safavi-Naeini
Abstract
In this work, we explore different methods to tune antenna impedance in mobile devices. Mismatch from antenna impedance can cause undesirable effects such as spurious emissions, channel leakages, increased noise floor, degraded receiver sensitivity and so on.
With the advancement in technology, new tunable reactive components are now available. A feedback system with tunable circuitry or aperture tuning are popular choices of solution. In a feedback system, either open or closed loop configuration, a look-up table method is widely adopted in wireless device manufacturing industry. The RF chain is initially calibrated with the tuning circuit and a large look-up table for values of the tunable reactive components (capacitors) for different frequencies and measured G_in(ratio of reflected signal to transmitted signal in dB) is saved in memory for permanent use for the lifespan of the device. In this thesis, in the effort to eliminate the process of creating this look-up table and also freeing up the memory usage, we try to solve the problem analytically – hence, making the procedure a one-time measurement and computing the variables analytically in an open-loop configuration. In Chapter 3, a thorough mathematical analysis has been developed to integrate the Q factors of each component in a pi-network into the solution. However, due to many uncertainties and calibration error from each component of the set-up, we find that the system needs to be a closed-loop configuration that solely relies on the fewest empirical data points to characterize the set-up as a whole and find the most optimized solution through a searching algorithm. The purpose of this thesis is to develop an optimization algorithm for pi-network in impedance matching system. It involves three degrees of freedom using three tunable reactive components, DTCs (Digitally Tunable Capacitors), and the challenge of this research points to inventing a 3D-unconstrained optimization technique that is simple enough to be implemented in a microprocessor without employing complex equation-solving libraries. In Chapter 4, we observe Hill-Climbing algorithm if it provides a suitable approach for finding the global minimum G_in in the 3D space gradient defined by three variables - DTCs. Hill Climbing method, however, will limit its solution to finding only the local minimum from the gradient, and the location of all local minima change with the resolution of the gradient – that is, how coarse the searching steps or increments were used. Hill Climbing algorithm has different solution depending on the increment size of each step in search and the starting location of the search. In Chapter 5, we create a new algorithm that is based on Grid Searching. The main idea is to grasp the picture of the entire gradient of 3D space and zoom-in closer to the global point by iteration. The challenge lies in defining the boundary of zoom-in region without leaking the global point and leaving it behind. Also, the scanning of the reduced region for each iteration must not have too rigorous, since each iteration will multiply the time of search. All pi-network will have its limited region on Smith Chart, of which the load impedance can be matched with. Therefore, selecting the reactive component with the suitable range of capacitance is also important in order to fully utilize the work of this algorithm. Apart from that, the algorithm does not require any information about the antenna, frequency of operation nor the configuration of the DTCs. Overcoming these challenges will guarantee the device to have the best optimized state of impedance match, for the range of capacitance of DTCs. Given that the algorithm is a 3D optimization technique, the work of this research does not only apply to pi-tuner. The three DTCs can be also located as part of aperture tuning system, either fully or partially, integrated in the antenna directly.