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4. (15 points - PA.3) Consider the RLC circuit shown below, where the input and output...
Consider a causal LTI system implemented as the RL circuit shown below. In this circuit, v(t) is the input voltage. The current i(t) is considered the system output. i(t) R L wwwm v(t) (a) Find the differential equation relating v(t) and i(t). (b) Determine the frequency response of this system (H(jw)). (c) Determine the output it) if v(t) = sin(t), R=10 and L=1. (d) Sketch Bode plot of H (jw) for R=10 and L=1. (e) Determine if the system is...
Using () as the input and vo(t) as the output of the system, calculate the transfer function H(s), the impulse response h(t) vi Vo and the frequency response H(ia for the system shown in Figure 1 below. Plot (by hand or in Matlab) the asymptotic gain and phase of H(jw) Figure 1: Circuit for problem 1
Consider a causal LTI system with frequency response H(jw) = 1 2 + jw For a particular input x(t) this system is observed to produce the output y(t) = e-ºut) - e-stutt) i) Determine x(t). ii) Is this system stable? Explain your reasoning. iii) Plot the magnitude and phase responses of H (jw).
4s +1 2s2 +13s 20 H(s) = 1- Use MATLAB to plot the magnitude and phase responses of this filter. Label 2- What is the type of this filter type (lowpass, highpass, bandpass,.. .? Plcase 3- Derive the partial fraction expansion of H(s) using the residue command in 4- Determine the impulse response h(t) of the system and plot it using MATLAB. the axes completely. explain. MATLAB and write the expression.
Consider the following circuits connected in series. The input is the voltage x(t), the output to system Si is the voltage y(t), and the output of system S2 is the voltage y(t). The differential equation relating the input X(t) to the output yı(t) was found in Homework #3. S2 x(1) y(t) | X(t) 6+ R yce) .66) (1) + y(t) Let L = 0.01, C1 = 0.01, R = 100, C2 = 0.002, and R2 = 50. a) Find the...
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n) as shown in Figure 1, where K 6 (constant), system #1 is described by its impulse response: h(n) = -36(n) + 0.48(n- 1)+8.26(n-2), and system # 2 has the difference equation given by: y(n)+0.1y(n-1)+0.3y(n-2)- 2a(n). (a) Determine the corresponding difference equation of the system #1. Hence, write its fre- quency response. (b) Find the frequency response of system #2. 1 system #1 system #2...
Clear steps, please. Consider the following LTI system where, Q -5, and w 2000m rad./sec. a) Use MATLAB to determine magnitude response and phase response of the filter. b) What type of filter is it? c) What will be the output of this filter if input xio- 5Cos(1000). Show all calculations step by step as shown in Lecture-21 . d) Verify your answer of part (e) by using Simulink model. Attach the snapshot of Simulink model and output. e) What...
I just need help with question 4 only: Consider the RLC circuit where R = 5, C = 1, L = 4 and Vs = 8. 1. Use circuit analysis laws to show that the resistor's voltage and induc- tor's voltage can be modelled as the system of ODEs VR 0 R RC L 2. Solve the eigenvalues and eigenvectors of the coefficient matrix in the system of ODEs. 3. Verify your answer for question (2) by using the eig...
Consider the simple series RLC circuit shown in figure below, the circuit has the following parameters, R=12, L = 0.2 Henry, and C = 0.05 Farad, R 1000 Vs The system is governed by the following equations: V = VR + V + V VR = IR V = Vc S(t)dt Or I = CM Construct a Simulink model for this system such that the input is the supply voltage Vs and the output is the voltage across the resistor...
For MATLAB users. Can you please type the answers for the MATLAB sections. Consider the RLC circuit where R - 5, C- 1, L- 4 and Vs - 8 1. Use circuit analysis laws to show that the resistor's voltage and induc- tor's voltage can be modelled as the system of ODEs Vi VL RC 2. Solve the eigenvalues and eigenvectors of the coefficient matrix in the system of ODEs. 3. Verify your answer for question (2) by using the...