wave digital filters (wdfs) transform an analog network into a topologically equivalent digital structure. a natural application of wdf is the simulation of electric circuits since measurements of any desired node voltages and branch currents are available during all time-steps in wdf structures. wdf structures tend to preserve most of the good properties of their analog counterpart. in this work, wdf techniques applied to transient simulation are studied. after a review o f the basic theory of wdfs and the treatment of nonlinear elements in wdfs, wdf simulations for different circuits, including a simple rc circuit, an anharmonic oscillator and a cmos lc voltage controlled oscillator (vco), are presented. special detail is put on the design and modeling of the lc vco. the lc vco was designed and fabricated using the tsmc (taiwan semiconductor manufacturing co., ltd) cmos 0.1 sum technology. the linear frequency tuning range of the lc vco is from 2.526 ghz to 3.015 ghz for control voltages from 0 to 1 v with a 1.712 ma tail current. wdf simulation results are compared with the exact solution if possible or otherwise with the results obtained with other simulation methods. the comparison shows that wdf techniques are efficient for the simulations of linear circuits and circuits with one nonlinear element. the potential of wdf for the simulation of large networks with many nonlinear elements is also discussed in this thesis.