A Method to Determine the Appropriate Section Number of Exponential Nonuniform Transmission Lines

The exponential nonuniform transmission line (ENTL) is commonly used in pulsed power accelerators. The circuit model, which treats the ENTL as a cascaded combination of many small uniform transmission line sections, is usually adopted for study. In previous studies, there is a lack of a method to estimate the appropriate section number for the circuit model. This article analyzes the frequency responses of the circuit model and the ENTL through theoretical analysis and compares them. Then, the formula that can estimate the maximum error between the circuit model and the ENTL is derived. Based on the formula, a method is proposed to determine the appropriate section number under an arbitrary error limit. The correctness of the proposed method is verified by simulation. This work provides a theoretical basis for establishing the circuit model of the ENTL, which can help researchers develop the circuit model faster and more accurately.