Editing RL circuit (section)

===Transfer functions===
The [[transfer function]] to the inductor voltage is

:<math> H_L(s) = \frac{ V_L(s) }{ V_\mathrm{in}(s) } = \frac{ Ls }{ R + Ls } = G_L e^{j \phi_L} \,.</math>

Similarly, the transfer function to the resistor voltage is

:<math> H_R(s) = \frac{ V_R(s) }{ V_\mathrm{in}(s) } = \frac{ R }{ R + Ls } = G_R e^{j \phi_R} \,.</math>

The transfer function, to the current, is

:<math> H_I(s) = \frac{ I(s) }{ V_\mathrm{in}(s) } = \frac{ 1 }{ R + Ls }  \,.</math>

====Poles and zeros====
The transfer functions have a single [[pole (complex analysis)|pole]] located at

:<math> s = -\frac{R}{L} \,.</math>

In addition, the transfer function for the inductor has a [[zero (complex analysis)|zero]] located at the [[origin (mathematics)|origin]].