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5. [20 marks Consider the RC series circuit shown in Fig. 3. Determine the overall output...
The Bode diagram below relates the input u(t) to the output y(t): Bode Diagram 20 2...
The Bode diagram below relates the input u(t) to the output y(t): Bode Diagram 20 2 -40 -60 o-45 2 -90 O-135 -180 10 10 10 Frequency (rad/s) Find the steady state response of the system y$s (t), results from the sinusoidal input as: u(t) -2 sin(3t) Find the steady state response of the system yss (t), results from the sinusoidal input as: u(t) - 5 sin(10t) a) b) c) Find the input u(t) that results into a sinusoidal steady...
14. Problem For the circuit in figure below, find the steady-state output voltage vo (t). The inp...
14. Problem For the circuit in figure below, find the steady-state output voltage vo (t). The input signal is v (t) and C = 5 μF 4-2 cos 100t, R 1 kΩ Do C R 12 U)
14. Problem For the circuit in figure below, find the steady-state output voltage vo (t). The input signal is v (t) and C = 5 μF 4-2 cos 100t, R 1 kΩ Do C R 12 U)
2.7. Consider the differential equation for the RC circuit in Fig. P.2.12: Figure P. 2.12 R=1...
2.7. Consider the differential equation for the RC circuit in Fig. P.2.12: Figure P. 2.12 R=1 r(t) =tu(t) C=1/4F y(t) (b) dy(t)dt+4y(t)=4x(t) Let the input signal be a unit step, that is, x(t) = u(1). Using the first-order differential equation solution technique discussed in Section 2.5.1 find the solution y(t) for t2 0 subject to each initial condition specified below: a. y (O) = 0 b. y (O) = 5 c. y (0) = 1 d. y (0) = -1...
Q.2 ICO2]10 Marks] The signal g(t) forms the input to the LPF circuit shown in the figure, where R l,and y(Dis the output. If the power spectral density (PSD) of the signal ge) is (a) The autoc...
Q.2 ICO2]10 Marks] The signal g(t) forms the input to the LPF circuit shown in the figure, where R l,and y(Dis the output. If the power spectral density (PSD) of the signal ge) is (a) The autocorrelation of g(t) (b) The 3-dB bandwidth of the LPF (c) The power of g(t) and y(t) (d) Based on your answers above, will it be better if the signal has more or less bandwith? (e) If a white noise of PSD No/2 is...
Exercise 4) Consider the RC network shown, where v(t) is the input voltage and ve(t) is...
Exercise 4) Consider the RC network shown, where v(t) is the input voltage and ve(t) is the circuit output voltage. R is the same for all resistors (4a) Write differential equations of the circuit in terms of the currents. Convert the equa tions to the Laplace domain (5 marks)v(oO 4b) Find the transfer function Ve(s)/V(s) (5 marks) (4c) Using the final value theorem, calculate the steady-state value of ve(t) for an unit step input of u(t), i.e., u(t)-1 V (2.5...
(please explain your answers). for the following transfer function, a) determine if the associated system is...
(please explain your answers). for the following transfer
function,
a) determine if the associated system is BIBO stable
b) if BIBO stable systems in question a). For these systems,
determine the steady state output Yss(t) given
- an input u(t) = 2step(t) → Yss(t) = lim t→+∞ (y(t)) = constant
value
-an input u(t) = 3 sin(t) → Yss(t) = sin function
c) if non BIBO stable systems in question a). For these systems,
find a bounded input that makes...
3) Given x1 = x2 with kER, find the forced output response y(t) and steady state...
3) Given x1 = x2 with kER, find the forced output response y(t) and steady state output response yss(t) to an input u(t) = 1 + sint and find values of k E R such that ly(t) - a 0.05 for allt 10-2sec. yss
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t)...
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t) x(t) The input to this circuit is given as x(t) s(t)+ny (t), where the noise component of input, n(t), is a sample function realization of white noise process with an autocorrelation function given by Rpx(t) 8(T), and s (t) cos(6Tt) is the signal component of input. IS(fOI df, where S( a. Find the power of the signal component of input, Ps is the Fourier...
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t)...
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t) x(t) The input to this circuit is given as x(t) s(t)+ny (t), where the noise component of input, n(t), is a sample function realization of white noise process with an autocorrelation function given by Rpx(t) 8(T), and s (t) cos(6Tt) is the signal component of input. IS(fOI df, where S( a. Find the power of the signal component of input, Ps is the Fourier...
U Question 8 3 pts Consider a series RC circuit as in the figure below for...
U Question 8 3 pts Consider a series RC circuit as in the figure below for which R-SMOhms, C-81F, and -50V. с w R $ a) Find the time constant of the circuit. 18.18 sec 0 0 44 sec O 40 sec None of the above
The Bode diagram below relates the input u(t) to the output y(t): Bode Diagram 20 2 -40 -60 o-45 2 -90 O-135 -180 10 10 10 Frequency (rad/s) Find the steady state response of the system y$s (t), results from the sinusoidal input as: u(t) -2 sin(3t) Find the steady state response of the system yss (t), results from the sinusoidal input as: u(t) - 5 sin(10t) a) b) c) Find the input u(t) that results into a sinusoidal steady...
14. Problem For the circuit in figure below, find the steady-state output voltage vo (t). The input signal is v (t) and C = 5 μF 4-2 cos 100t, R 1 kΩ Do C R 12 U)
14. Problem For the circuit in figure below, find the steady-state output voltage vo (t). The input signal is v (t) and C = 5 μF 4-2 cos 100t, R 1 kΩ Do C R 12 U)
2.7. Consider the differential equation for the RC circuit in Fig. P.2.12: Figure P. 2.12 R=1 r(t) =tu(t) C=1/4F y(t) (b) dy(t)dt+4y(t)=4x(t) Let the input signal be a unit step, that is, x(t) = u(1). Using the first-order differential equation solution technique discussed in Section 2.5.1 find the solution y(t) for t2 0 subject to each initial condition specified below: a. y (O) = 0 b. y (O) = 5 c. y (0) = 1 d. y (0) = -1...
Q.2 ICO2]10 Marks] The signal g(t) forms the input to the LPF circuit shown in the figure, where R l,and y(Dis the output. If the power spectral density (PSD) of the signal ge) is (a) The autocorrelation of g(t) (b) The 3-dB bandwidth of the LPF (c) The power of g(t) and y(t) (d) Based on your answers above, will it be better if the signal has more or less bandwith? (e) If a white noise of PSD No/2 is...
Exercise 4) Consider the RC network shown, where v(t) is the input voltage and ve(t) is the circuit output voltage. R is the same for all resistors (4a) Write differential equations of the circuit in terms of the currents. Convert the equa tions to the Laplace domain (5 marks)v(oO 4b) Find the transfer function Ve(s)/V(s) (5 marks) (4c) Using the final value theorem, calculate the steady-state value of ve(t) for an unit step input of u(t), i.e., u(t)-1 V (2.5...
(please explain your answers). for the following transfer
function,
a) determine if the associated system is BIBO stable
b) if BIBO stable systems in question a). For these systems,
determine the steady state output Yss(t) given
- an input u(t) = 2step(t) → Yss(t) = lim t→+∞ (y(t)) = constant
value
-an input u(t) = 3 sin(t) → Yss(t) = sin function
c) if non BIBO stable systems in question a). For these systems,
find a bounded input that makes...
3) Given x1 = x2 with kER, find the forced output response y(t) and steady state output response yss(t) to an input u(t) = 1 + sint and find values of k E R such that ly(t) - a 0.05 for allt 10-2sec. yss
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t) x(t) The input to this circuit is given as x(t) s(t)+ny (t), where the noise component of input, n(t), is a sample function realization of white noise process with an autocorrelation function given by Rpx(t) 8(T), and s (t) cos(6Tt) is the signal component of input. IS(fOI df, where S( a. Find the power of the signal component of input, Ps is the Fourier...
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t) x(t) The input to this circuit is given as x(t) s(t)+ny (t), where the noise component of input, n(t), is a sample function realization of white noise process with an autocorrelation function given by Rpx(t) 8(T), and s (t) cos(6Tt) is the signal component of input. IS(fOI df, where S( a. Find the power of the signal component of input, Ps is the Fourier...
U Question 8 3 pts Consider a series RC circuit as in the figure below for which R-SMOhms, C-81F, and -50V. с w R $ a) Find the time constant of the circuit. 18.18 sec 0 0 44 sec O 40 sec None of the above
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