This paper mainly studied the circuit parameter calculation theory and the methods based on damped oscillations in transient signals. The methods can be used for the location and origin of faults by calculating the circuit parameters of transient fault signals' path when the fault occurs in the power system transmission lines. It is important in theoretical and practical engineering to locate faults in powerlines by calculating circuit parameters based on damped oscillations which are the main component of the transient signals. In R-L and R-C circuits, relations of the characteristic parameters in damped oscillation voltage and current in time domain, with the circuit parameters as well as the component parameters are deduced. And the impedance characteristic of the circuit under damped oscillation is analyzed, which is defined as a pseudo-impedance based on the definition that impedance is steady and sinusoidal. Relations between the pseudo-impedance and circuit parameters are also found. Relations between component parameter and pseudo-impedance in series or parallel are also analyzed. So methods for circuit parameter calculation are proposed separately based on the characteristic parameters and pseudo-impedance, each of which is a kind of characteristic of the damped oscillation signal. Specific calculation methods are also proposed combining with the state-of-the-art signal analysis for damped oscillation signal. Analyses in this paper may lay an important foundation for practical engineering application. The proposed theory and methods are verified based on simulation of fault signals produced by MATLAB. The equivalent circuit of an actual distribution system is simulated by using PSCAD/EMTDC. Actual fault signals reappear in the simulation. Location of single-line-to-ground fault using damped oscillation signal proposed in the paper is proved feasible.