Answer Happy

The diagram below shows an RC low pass filter: VR I R Vin C: vcl Analysing the system in the s-domain, let: • Vr(s) denote the voltage across the resistor R • Vels) denote the voltage across the capacitor C • Vin(s) denote the input voltage • S denotes the complex frequency The transfer function from the input voltage to the voltage across the resistor is given by: VR(S) RCS VIN (s) 1+ RCS a) Show that the above formula has one horizontal and one vertical asymptote. b) Show that the graph of VR against s passes through the origin. VIN (5) c) By attempting to find the turning points of the above function, show that there aren't any. d) Sketch the graph of VR(S) VIN (S) against s. e) From the resulting sketch, find: i) the value that VR(S) VIN (5) approaches to whenever s increases to a very large number. VR(S) ii) the value of the time constant RC if, as the value of increases, s is required to VIN (8) approach the value - 500