Time domain reflectometry method and time domain reflectometers are used to monitor the state of continuity for transmission lines. The method is based on probing the transmission line with short voltage pulses and return stream signal registration. Functionality of existing TDRs can be enhanced by the use of digital processing TDR traces. The digital processing should be based on adequate models of a transmission line with discontinuities and return stream signal (TDR trace). This paper presents the improved mathematical model of TDR trace for a transmission line with discontinuities. The model allows for the complex character and frequency response of the particular impedance. The paper also comes up with the results of theoretical and experimental studies. The results demonstrate the need of the model refinement and validity of the proposed formulas.