The State-Based Method

The State-Based Method

Ô non-uniform: samples cluster where waveform changes rapidly

Ô dynamic: sample points move to track waves travelling through line during simulation

m Voltages, currents inside line are sampled

Ô uses analytical impulse responses, but eliminates convolution

m New mathematical formulation: combines strengths

of the convolution and lumped RLC methods

Ô simulates line interior, but eliminates lumping and segmenting

m Computation increases linearly with

simulation length

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Notes:

The convolution technique is based on the convolution of the line's terminal variables with its impulse-responses.The impulse-responses characterise the behaviour of the line.

The simple lossy line has three basic impulse responses.

The char. imp. response is a generalization of a lossless line's char. impedance; an example is shown on the lower left. This response describes the voltage-current relationship at each end of the line.

The delay response is a generalization of the delay in a lossless line, and is shown on the lower right. This response describes signal transfer from one end of the line to the other.

A third response, the convolved response, is the convolution of these two responses.

Note that there are sharp discontinuities in the impulse responses.