Binary search algorithm for adaptive impedance matching network

Abstract

A novel design strategy for adaptive impedance matching network which consists of two tunable components is presented. The input resistance is controlled by the first tunable component and independent of the second tunable component. Additionally, the proposed strategies ensure that the input resistance is proportional to the first tunable component and input reactance is proportional to the second tunable component. Therefore, the binary search algorithm is employed to calibrate the tunable matching network. In contrast to the single-step method, the convergence speed is improved from O(N) to O(log N).Introduction: The antenna impedance is sensitive to the nearby objects and human bodies. The antenna impedance variation leads to an impedance mismatch, which reduces the transmit power and link quality. As a result, an antenna tuning unit that can calibrate the tunable matching network in real time is highly desired [1]. The simplest and fastest tuning algorithm is single-step method [2]. However, this algorithm is easily trapped into a local optimum point. The impedance matching domain of Π-type network is analytically represented in [3]. The impedance variation located in the matching domain is likely to be calibrated. To secure reliable convergence, a cascade of two control loops is proposed for independent control of the real and imaginary parts of input impedance [4].A novel design strategy for T-type and Π-type networks with two tunable components is proposed in this Letter. The antenna impedance variation is covered by the matching domain of proposed network. The input resistance is independent of the second tunable component. Hence, this Letter utilises the first tunable component to calibrate the input resistance, and then utilises the second tunable component to calibrate the input reactance. In contrast to [4], the proposed matching network only employs three components. Furthermore, the proposed design strategies ensure that the input resistance is proportional to the first tunable component and the input reactance is proportional to the second tunable component. Hence, the binary search algorithm is employed to accelerate the convergence speed. In contrast to [2], the convergence speed is improved from O(N) to O(log N).

Design strategy of tunable matching network and prototype verification

“…In the case of TMN with fixed X 1 or fixed X 2 , the binary search tuning algorithm can be used to accelerate convergence speed. For more detailed information, please see [3].…”

“…To minimise the reflection coefficient, a set of unimodal criteria are proposed in [2], which converge to the neighbourhood of the global optimal point. Once the unimodal criteria are satisfied and the input impedance is detected, the convergence speed is accelerated from O(N ) to O(log N ) by binary search algorithm in [3]. Take a further step, this Letter details the design procedures of TMN, which are compatible with [2,3].…”

“…Once the unimodal criteria are satisfied and the input impedance is detected, the convergence speed is accelerated from O(N ) to O(log N ) by binary search algorithm in [3]. Take a further step, this Letter details the design procedures of TMN, which are compatible with [2,3]. In addition, the bandwidth and parasitic parameters of TMN are analysed.…”

Unimodal criteria of tunable matching network

“…The trajectories of input impedance point tuned by X 2 and X 1 are illustrated in Figs. 2 and 3, respectively [3].…”

“…If Z L and X 1 are constants and X 2 is a variable, (1) is written as (2). Similarly, if Z L and X 2 are constants and X 1 is a variable, (1) is written as (3). The trajectories of input impedance point tuned by X 2 and X 1 are illustrated in Figs.…”