A visual approach to investigating the bandwidth of transmission lines with non-Z0 impedance

In electrical engineering education, there is currently no way to graphically study the bandwidth of transmission lines with arbitrary characteristic impedance. For the first time, this paper presents a visual approach to investigating non- Z₀ transmission lines, with a particular emphasis on bandwidth considerations. By plotting the Smith-chart locus of input impedance as a Z₀ generator is moved closer and farther from a load, insight is gained into the bandwidth of the circuit. The visual approach can be performed with a single Smith chart and back-of-the-envelope calculations in three steps: i) finding the λ 4 point, ii) drawing the locus, and iii) determining points of reference along the locus. A detailed explanation of each step is provided, along with example plots and additional analytical insights based on mathematical analysis. Three rules of thumb are discussed, and example applications are investigated. Finally, a visual analysis tool is presented (including MATLAB code) for students and educators to gain an intuitive understanding of non- Z₀ transmission lines.