Question 6.15: An RC High-Pass Filter A passive, analog, first-order high-p...
An RC High-Pass Filter
A passive, analog, first-order high-pass filter can be realized by an RC circuit (see Figure 6.62), which passes high-frequency signals but attenuates signals at low frequencies. Assume that the resistance is R=100 \Omega and the capacitance is C=10 \mu \mathrm{F}. The circuit is connected to an \mathrm{AC} voltage source, which has an amplitude of 1 \mathrm{~V} and a frequency varying from 1 to 1000 \mathrm{~Hz}. Build a Simscape model of the physical system and find the output voltage v_{o}(t) when the frequency of the input voltage is 1,10,100, and 1000 \mathrm{~Hz}.
The Simscape block diagram of the RC high-pass filter is shown in Figure 6.63, in which the AC Voltage Source block outputs a sinusoidal voltage. To better understand high-pass filtering, two Voltage Sensor blocks are included to measure the input and output voltages. They are displayed on the same scope through a Mux block, which can be found in the Simulink library of Signal Routing. Double-click on the AC Voltage Source block, type 1 for the Peak amplitude, and choose the unit as V. Vary the Frequency from 1, 10, 100, to 1000 \mathrm{~Hz} and run the simulations. The comparison between the input voltage and output voltage is given in Figure 6.64, in which solid lines are the output voltages and the dashed ones are the input voltages. It is obvious that the filter passes high-frequency signals but attenuates signals at low frequencies. The reader can derive the transfer function of the system and build a Simulink block diagram as an exercise.
