To measure the transient current of very fast switching circuits, sensors with a high frequency bandwidth are needed. For such an accurate current sensor, the voltage measured from the two ends of the sensor conductor must be proportional to the passing current in all conditions. The main problem of these sensors is the change in the impedance of this conductor at different frequencies. In this way, the relationship between the measured voltage and the desired current is not linear and the measured value is not valid. Also, the change of conductor resistance due to skin effect can also be the cause. In this article, it is shown that based on coaxial shunt sensors and the selection of the thickness of the sensor conductors, the effect of internal conductor inductance and skin effect can be eliminated in the desired bandwidth. The conductor of the inner pipe of the sensor is divided into several parallel parts, which causes a greater increase in the ratio of ohmic resistance to inductance. Also, the inductance of this conductor has been calculated analytically. To design the sensor based on the frequency bandwidth and current pulse characteristics, the sensor design flowchart was proposed and based on that, a current sensor for the MHz frequency bandwidth and a sensor for the GHz frequency bandwidth were designed and then a sample current sensor was made. And by that, the flat current pulse with the amplitude of 146A and the width of 2.5ms and the standard current pulse of 20.8µs with the amplitude of 2kA and the width of 32µs have been accurately measured.