{'fraction_non_alphanumeric': 0.011530398322851153, 'fraction_numerical': 0.0, 'mean_word_length': 5.496598639455782, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Time domain analysis of transmission lines

A simple numerical method is developed for the determination of the transient response of lossy transmission lines with a general impedance loading to a general voltage excitation. First, the transient response of the lossless transmission line with a load impedance to a voltage excitation is formulated. The steady state response of the line is then derived from its transient response. A recursive relation for determining the transient response is also given. Reflection coefficient at the load is determined by deriving differential equations directly and also by the use of the Thevenin's equivalent circuits. A computer program for the implementation of the numerical method together with several examples of the transient response of lossless/lossy transmission lines with passive/reactive loadings are presented. This numerical method has both practical engineering applications and pedagogical value.