Question

Prelab Preparation: For the RC circuit shown in Figure 1, derive the modeling equation relating the output volta ge Vout to the input voltage vin. What is the transfer function? What is the time constant of the system? Vout Figure 1: RC Circuit What is the analytical step response solution in terms of vin, Rand C? For assumed values of R 1 K, and C 6.8 uF, perform a simulation using Matlab/Simulink assuming an input square wave signal of 5Vpp, 2.5V offset, and a frequency of 10 Hz. Adjust the display of the Scope block of the Simulink model and screen capture the resu lt. Modify the input in the Simulink model to make it a sine wave of 5Vpp, no offset, and a frequency of 10 Hz. Adjust Page 15 of 16 the display of the Scope block of the Simulink model and screen capture the result. Change the frequency to 200 Hz. Adjust and then record the display of the Scope Add a noise block to the sine wave input. Set the frequency of the sine wave to 5 Hz. Adjust the time constant to filter out the noise from the output signal. Again, adjust and then record the display of the Scope. Figure 2: R-C circuit Prototype

Answer 1

below Laplacu domain The Carai traneev funchon The Var Vvs) igiven by 0- VauT ) 1/cs VINC) R T(S) Time onstant エ= RC. aphe the respons of The step y T) SCRCS ctomain sCIKx st) s(68A 6.S S S147. o6 apply ng apluTrans form 3NIAU YC+) Va)

Simulation in SIMULINK is given below. block diagram is given below.

untitled File Edit View Simulation Format Tools Help 0.5 Normal 2.5 offset 1 6.8e-3s+1 0O0 Scope Transfer Fcn square wave generator Ready 100% ode45 LO

the response Vout(t) for square wave input is given below.

Scope 4 2 -1 2 -3 -4 -5 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time offset: 0 . .

Now simulation without offset.

untitled File Tools Edit View Simulation Format Help 0.5 Normal 2.5 offset 1 6.8e-3s+1 Scope Transfer Fcn square wave generator Ready 100% ode45

Simulation result:

X Scope 3 7 -1 -3 -4 -5 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time offset: 0 17

Now change the frequency to 200 Hz.

Source Block Parameters: square wave generator Signal Generator Output various wave forms: Y(t) Amp*Waveform(Freq, t) Parameters Wave form: square Time (t): Use simulation time Amplitude: 2.5 Frequency: 200 Units: Hertz Interpret vector parameters as 1-D Cancel Help OK

Simulation result:

Scope 1.5 1 0.5 -0.5 wwwwWW -1 -1.5 -7 -2.5 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Time offset: 0 . . IC

signal filtering:

simulation block diagram

X Source Block Parameters: square wave generator untitled Source Block Parameters: Band-Limited White Noi.. Band-Limited White Noise. (mask) (link) Format Tools Help Signal Generator File Edit View Simulation 10 Output various wave forms: Y(t) Amp *Waveform(Freq, t) Normal The Band-Limited White Noise block generates normally distributed random numbers that are suitable for use in continuous or hybrid systems. Parameters Parameters Wave form: sine Noise power: Band-Limited White Noise Time (t): Use simulation time [0.01] Amplitude: (12pi-5)s+1 Sample time: innnn Transfer Fan Scope 2.5 0.01 ve Frequency: Seed: 5 [23341] Units: Hertz Interpret vector parameters as 1-D Interpret vector parameters as 1-D Cancel Help OK Ready 100% ode45 Cancel Help OK

simulation result:

Scope 4 3 2 0 -1 -2 -3 -5 2 3 7 10 Time offset: 0 LC t

from the above figure, it is observed that the noisy signal (yellow color) is fitered and the output signal (pink color) is free of noise.