Archives

Errata: 1. Chapter 1, Problem 1.1 (Polarity of the voltage across resistor Rshould be the opposite of what is shown in the text, in order to obtain R > 0). 2. Chapter 3, Problem 3.7a (The correct specification of part […]

Chapter 10 1. An LTI circuit has the frequency response H(ω) = 1 1+jω +1 2+jω . What is the system impulse response h(t)and what is the system response y(t) = h(t)∗f(t)to the input f(t) = e−tu(t)? Solution: We can […]

Chapter 11 1. Determine the Laplace transform ˆ F(s), and the ROC, of the following signals f(t). In each case identify the corresponding pole locations where |ˆ F(s)|is not finite. a) f(t) = u(t)−u(t−8) b) f(t) = u(t)−u(t+ 8) c) […]

c) Taking the Laplace transform with zero initial conditions, we obtain 14. If an LTIC system has the transfer function ˆ H(s) = ˆ Y(s) ˆ F(s)=s+1 (s+2)2determine a linear ODE that describes the relationship between the system input f(t)and […]

Chapter 12 1. Derive the transfer function ˆ Ha(s)of the 1st-order active filter circuit depicted in Figure 12.5a. Solution: The equivalent s-domain circuit is + ˆ V+(s) 2. Derive the transfer function ˆ Hb(s)of the Sallen and Key circuit depicted […]

Chapter 2 1. In the following circuits, determine ix: + –ix 6A4 V 1 Ω 1 Ω 1 Ω 2 Ω 2 Ω 1 Ω 3 Ω ix (a) (b) Solution: a) First we label the top left node as […]

Substituting the expressions for vTand RTinto the KVL equation yields 10. In the following circuit, find the open-circuit voltage and the short-circuit current between nodes ato band determine the Thevenin and Norton equivalent of the network between nodes aand b. […]

Chapter 3 1. a) In Figure 3.3a, given that i+≈0, what happens to the current vo RLin the circuit? Hint: the answer is related to the answer of part (b). b) For vs= 1 V, Rs= 50 Ω, and RL= […]

Chapter 4 1. Determine the phasor Fof the following co-sinusoidal functions f(t): a) f(t) = 2 cos(2t+π 3). b) f(t) = Asin(ωt). c) f(t) = −5 sin(πt). Solution: a) The signal b) The signal f(t) = Asin(ωt) =Acos(ωt −π 2), […]

Chapter 5 1. Determine the frequency response H(ω) = Y Fof the circuit shown and sketch |H(ω)| versus ω≥0. In the diagram, f(t)and y(t)denote the input and output signals of the circuit. + – + – 0.05F f(t)y(t) 1Ω 0.2H […]

Chapter 6 1. Plot the following periodic functions over at least two periods and specify their period Tand fundamental frequency ωo=2π T: a) f(t) = 4 + cos(3t). b) g(t) = 8 + 4e−j4t+ 4ej4t. c) h(t) = 2e−j2t+ 2ej2t+ […]

Chapter 7 1. a) Given that f(t) = e−a(t−to)u(t−to), where a > 0, determine the Fourier transform F(ω)of f(t). b) Given that g(t) = 1 a+jt, where a > 0, determine the Fourier transform G(ω)of g(t)by using the symmetry property […]

Chapter 8 1. Verify the frequency-shift property f(t)ejωot↔F(ω−ωo) by taking the inverse Fourier transform of F(ω−ωo). Solution: The inverse Fourier transform formula can be written as 2. Given that f(t)e±jωot↔F(ω∓ωo), determine the Fourier transform of f(t) sin(ωot). Solution: Using Euler’s […]

Chapter 9 1. For the functions f(t)and g(t)sketched as shown, a) Find x(t) = g(t)∗g(t)by direct integration and sketch the result. b) Find y(t) = f(t)∗g(t)using appropriate properties of convolution and the result of part (a). Sketch the result. c) […]