## 1 Introduction  
A system that includes a power semiconductor based on a wide bandgap (WBG) device has the advantages of high di/dt, dv/dt, efficiency, and a fast-switching speed, compared to conventional silicon devices [1, 2]. Therefore, WBG devices are attracting much attention in the industry and related research pursuing small size and low-cost devices; in particular, GaN devices have remarkably fast switching characteristics among WBG devices; hence, the issues of stability and system protection in transient response situations are major issues that need to be resolved in the development and use of GaN devices [3, 4, 5, 6]. At this time, the stability of a system is based on accurate and fast measurement information during the switch operation. Therefore, it is necessary to follow the step change of the current well. Otherwise, when measuring current, excessive peak current may cause malfunction of the already established protection operation. To measure the switch current of the power semiconductor embedded in the PCB [7, 8], current sensor technologies based on sensor evaluation criteria such as a minimum area with sufficient bandwidth, insulation, and sufficient sensitivity are required. The toroidal Rogowski coil is a representative insulation sensor and can be a viable current sensor candidate for WBG devices based on its relatively wide bandwidth, small size, and linear characteristics. Basically, in toroidal Rogowski coils, which are a type that wraps the conductor of the primary current in all directions [9, 10, 11], the position between the coil and the conductor has a great influence on the measurement accuracy [12, 13], and the study conducted in [14] minimizes the position error between the sensor and conductor. In the paper of [15, 16, 17], a PCB-based Rogowski coil model that can minimize the position error between the sensor and the conductor was proposed; [18; 19; 20] described the application of this PCB-based toroidal Rogowski coil for system protection. However, the PCB-based Rogowski coil discussed in this paper was only applied to the power semiconductor of module type, and [20] demonstrated higher performance than DeSat protection. The shape of the Rogowski coil and the different design structures in the PCB circuit can have a significant influence on the bandwidth, sensitivity, and external noise that appear through different magnetic properties. Accordingly, studies on various coil shapes and designs have been studied to increase bandwidth and improve sensitivity and noise immunity, and their influence has been analyzed [21; 22]. In [23; 24; 25], a differential Rogowski coil with insulation characteristics was proposed to reduce the coupling capacitance noise of the conventional Rogowski coil. In [26], a current sensor with a rolling trace was proposed to maximize the bandwidth of the Rogowski coil in the PCB. In [27; 28], a spiral-type Rogowski coil structure was proposed to improve the sensitivity of the coil. Moreover, a guideline for the optimal coil shape was presented through the analysis of the mutual inductance, according to the coil type [29]. However, it is impossible to embed a conventional toroidal-type Rogowski coil in a PCB, including a non-modular power converter; hence, a pickup coil was proposed in [30; 31; 32; 33; 34]. The pickup coil uses the same sensor method as the existing Rogowski coil in a large category and, according to Maxwell-Faraday law, an electromotive force (EMF) is induced at the output end of the coil loop through the coil structure in which a part of the magnetic flux generated by the primary current flows into the closed-loop area of the coil. The current sensor configuration of the rolling structure shown in [26] can secure a higher bandwidth than a conventional sensor configuration, and hence a pickup coil with such a rolling structure is proposed in [30].