Harmonic series analysis of digital clock distribution circuits

A transmission line model that can be used to analyze clock distribution nets on computer circuit boards is derived. This model uses a finite Fourier series expansion of a square wave clock signal with finite rise and fall times. Complex transmission and reflection coefficients are found for each harmonic at each termination and branch point in the net. Steady state solutions consisting of an infinite number of reflections of each harmonic are then found at any desired point in the circuit, and a time-domain waveform can be reconstructed at that point. This allows the designer to accurately predict such parameters as clock skew, waveshape, and ringing anywhere in the net. This information can then be used to decide the necessity of items, such as termination resistors and their optimum locations. The model has been programmed in FORTRAN, and compares well with actual laboratory data