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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)...
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...
Consider a causal LTI system with frequency response H(jw) = 1 2 + jw For a...
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).
Using () as the input and vo(t) as the output of the system, calculate the transfer...
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 series RLC circuit where the output voltage y(t) is taken across the resistor and...
Consider a series RLC circuit where the output voltage y(t) is taken across the resistor and the input is the voltage x(t). (a) Find the transfer function of this filter. (b) What is the type of this filter?
Consider a series RLC circuit where the output voltage y(t) is taken across the resistor and...
Consider a series RLC circuit where the output voltage y(t) is taken across the resistor and the input is the voltage x(t). WHAT TYPE OF FILTER IS THIS?
Consider the following circuits connected in series. The input is the voltage x(t), the output to...
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...
4s +1 2s2 +13s 20 H(s) = 1- Use MATLAB to plot the magnitude and phase...
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.
Question Systems: Consider the following system for the questions below (indicate relevant transition points and peak...
Question Systems: Consider the following system for the questions below (indicate relevant transition points and peak values when drawing frequency domain representations). Note that X (jw) is the frequency domain representation of the input and both filters use a scaled version of the filter, H(jw). y(t) x(t)- H(w) H(jw) cos(2w.t) H(w) W(0) -Wo Wo X(jw) -2wo-WOW O 2w, a) Draw the frequency response of the output of the first signal path, Y. (jw) b) Draw the frequency response of the...
Problem 2 An RC circuit ( with an active component) has the following transfer function (where...
Problem 2 An RC circuit ( with an active component) has the following transfer function (where R and Care positive) H(s) - Vout(8) _R|| R/10k12 Vin(8) 10KN 1 + $RC Where s = jw Find the value of the resistor and the value of the capacitor so that: for w = 0 rad/s, H(jw)lde = +12dB at f = 1kHz, |H(jw)lab = +9dB Problem 3 The transfer function of a circuit is given by H(S) = Vout(s) Vin(s) Where s...
Clear steps, please. Consider the following LTI system where, Q -5, and w 2000m rad./sec. a)...
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...
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...
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).
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 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...
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.
Question Systems: Consider the following system for the questions below (indicate relevant transition points and peak values when drawing frequency domain representations). Note that X (jw) is the frequency domain representation of the input and both filters use a scaled version of the filter, H(jw). y(t) x(t)- H(w) H(jw) cos(2w.t) H(w) W(0) -Wo Wo X(jw) -2wo-WOW O 2w, a) Draw the frequency response of the output of the first signal path, Y. (jw) b) Draw the frequency response of the...
Problem 2 An RC circuit ( with an active component) has the following transfer function (where R and Care positive) H(s) - Vout(8) _R|| R/10k12 Vin(8) 10KN 1 + $RC Where s = jw Find the value of the resistor and the value of the capacitor so that: for w = 0 rad/s, H(jw)lde = +12dB at f = 1kHz, |H(jw)lab = +9dB Problem 3 The transfer function of a circuit is given by H(S) = Vout(s) Vin(s) Where s...
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...
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