Question

Find the transfer function between the output inductor voltage vl(t) and input voltage v(t) for the following system? R w + v(t) + 0000 vi(t) iſt)

Answer 1

A transfer function is used to analyze Series RL circuit. It is defined as the ratio of output of a system to the input of a system, in the laplace domain VR ww R Vin r VL I jie. HCS) = H Cs) out H(s) in consider R-L circuit in which resistor and inductor are connected in series with each other Vin = input supply voltage VL voltage across inductor VR = Voltage across resistor I = cument flowing through circuit. To find transfer function apply voltage or potential divider rule. This voltage divider rule is a simplest rule used for determine the output voltage across any element in circuit It states that voltage divided between resistors is in direct proportion to their respective resistance

Vl(s) Using Voltage divider rule, the voltage across inductor vL is Ls Vince) Rt Ls voltage across the resistor VR is R Vincs) R+ Ls The transfer function CHL) for the inductor Hacs VL (s) Ls Vin (s) R+Ls VRCS) - Also, The transfer function CHR) for the resistor HRCS) = VRCS) R Vincs) R+Ls Also current since the current is in series so the current in resistor and inductor are same and is given by : Ics) Vincs) Rt Ls