Solution:
HW 2-1. For the RLC circuit in HW 1-2, with the voltage source x(t) as the...
HW 2-1. For the RLC circuit in HW 1-2, with the voltage source x(t) as the 'input' and the loop current y(t) as the 'output' (20 pts) L=11 R=3.12 X(t) To-"000) 1) find its frequency response function H(w). (5 pts) 2) then, find its response to the following input signals, respectively 2-a) x(t)=8(t), (2 pts) 2-b) x(t)=u(t), (3 pts) 2-c) x(t)=sin(10t), (3 pts) 2-d) x(t)=2sin(10t)+cos(20t+1), (3 pts) 3) For the signals in 2), calculate the energy or the average power...
HW 2-1. For the RLC circuit in HW 1-2, with the voltage source x(t) as the 'input' and the loop current y(t) as the 'output' (20 pts) L-11 R=3.22 yo 1) find its frequency response function H(w). (5 pts) 2) then, find its response to the following input signals, respectively 2-a) x(t)=8(t), (2 pts) 2-b) x(t)=u(t), (3 pts) 2-c) x(t)=sin(10t), (3 pts) 2-d) x(t)=2sin(10t)+cos(20t+1), (3 pts) 3) For the signals in 2), calculate the energy or the average power (whichever...
4. (15 points - PA.3) Consider the RLC circuit shown below, where the input and output x(t) and y(t) are the input voltage vi(t) and capacitor voltage vc(t) respectively, and R = 1 K12, C = 0.1 mF, L = 100 H. i(t) + (i) Determine the frequency response of the system H (jw), as well as its magnitude and phase responses. What type of filter does it correspond to? (ii) Sketch its magnitude and phase response in Matlab. You...
Problem 2 In each step to follow the signals h(t) r (t) and y(t) denote respectively the impulse response. input, and output of a continuous-time LTI system. Accordingly, H(), X (w) and Y (w) denote their Fourier transforms. Hint. Carefully consider for each step whether to work in the time-domain or frequency domain c) Provide a clearly labeled sketch of y(t) for a given x(t)-: cos(mt) δ(t-n) and H(w)-sine(w/2)e-jw Answer: y(t) Σ (-1)"rect(t-1-n)
Problem 2 In each step to follow...
For a continuous time linear time-invariant system, the
input-output relation is the following (x(t) the input, y(t)
the
output):
, where h(t) is the impulse response function of the
system.
Please explain why a signal like e/“* is always an eigenvector
of
this linear map for any w. Also, if ¥(w),X(w),and H(w) are
the
Fourier transforms of y(t),x(t),and h(t), respectively.
Please
derive in detail the relation between Y(w),X(w),and H(w),
which means to reproduce the proof of the basic convolution
property...
၀ရ R - + vo(t) v(t) C Figure Q7 (a) 07 (a) A second order RLC circuit is given in Figure Q7 (a). Determine; (i) the time domain input-output relationship of the RLC circuit, (3 marks) (ii) the frequency response, H(W) of the circuit, (3 marks) (iii) the impulse response, h(t) given that R = 12, C = 1 F and L = 2 H. (4 marks) (b) An input vi(t) = e-ztu(t) is passed as the input to the...
In each step to follow, the signals h(t), a(t), and y(t) denote respectively the impulse response, input, and output of a continuous-time LTI system. Accordingly, H(w), X(w) and Y(w) denote their Fourier transforms. Hint: Carefully consider for each step whether to work in the time domain or frequency domain. (b) (25 points) On the axes below, provide a clearly labeled sketch of y(t) for all t given Σ H(w)-( ) sine? (w/8) j2Tt r(t)-e δ(t-n/2) and with sinc(t) = sin(t)/t...
5.37 The current source in the parallel RLC circuit of Fig. P5.37 is given by is (1) = [10+5 cos(100t + 30°) _ cos(200t-30°)] mA. Determine the average power dissipated in the resistor given that R = 1 kQ, L = 1 H, and C = 1 μF. h(t) Figure P5.37: Circuit for Problem 5.37. 1. Fourier series and Parseval's theorem: Problem 5.37 from the textbook. Hint:Use the complex impedances of the elements to analyze the parallel circuit, determine the...
b) A periodic voltage vs(t) is applied to a RLC circuit shown in Figure 1 (b) with R=10012, L=100mH and C=1pF. The first four nonzero terms in the Fourier series is given by the following: v:(t) = 10 +2 sin(10’t)-1sin(2x10't)+sin(3x10°r) v Find the first four nonzero terms in the Fourier series of the steady-state current iſt). (20 marks) R M v.(t) Tv.(t) Figure 2(b): Circuit for Question 2
4 a. y(t)-x(t)cos(t/2 b. y(t)-x(t)cos(') x()cos(21) c. X (ju) 5. The signals y(t) in 4a-4e are passed through a filter with unit impulse response h(t) so that the output is z(t)-h(t)*y(t) . Ifthe frequency response of the filter is sketch by hand the Fourier transforms Z(j for 4a-4e Fromjust observing your sketches of Z (jo), which z(1) if any in a-e equal to the original