= Dispersion-limited digital-fibre link length
{title2=$L_{\max}\sim T_r/[|\partial_f(1/v_g)|\Delta f]$}
A pulse's <frequency> components accumulate a differential <group delay> $\Delta t=L|\partial_f(1/v_g)|\Delta f$. If that spread approaches the pulse repetition period $T_r$, neighbouring symbols overlap. The resulting length estimate depends on <bandwidth>, initial pulse width, chirp and the receiver's allowable intersymbol interference. For $n(f)=n_0+\tau(f-f_0)$, the group index is $n_0+\tau(2f-f_0)$ and $\partial_f(1/v_g)=2\tau/c$: differentiating the phase index alone loses a factor of two.
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