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Per-unit-length series impedance and shunt admittance are extracted from electromagnetic analysis of a transmission line at a few discrete frequencies. Compact models are synthesized from the per-unit-length extraction. The lumped models are then used to rapidly calculate characteristic impedance, effective dielectric constant, and RLGC parameters at all frequencies, including dispersion and loss. The resulting models are perfectly physically (i.e., speed of light) causal, a critical consideration for time-domain analysis. To demonstrate feasibility, the models are parameterized as a function of transmission linewidth. Total error is carefully quantified and is typically less than 1%. The process is demonstrated for several planar transmission lines. New concepts, ??modal?? and ??environmental?? sensitivity, are introduced and quantified.