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Fall 2009EE40 Homework #6Due Oct 15 (Thursday), 12:00 noon in Cory 240Reading AssignmentsChapter 5 of Hambley textbook. Section 5.7 on Three-Phase circuit is optionalSections 6.1-6.5 of Hambley textbookProblem 1: Power Calculation Hambley P5.72The voltage across a load is v(t)=104 sqrt(2)cos(wt+100) and the current through the load is i(t)=20sqrt(2) cos(wt-200). A. The reference direction for the current points into the positive reference for the voltage. Determine the power factor, the power, and the apparent power for the load. Is this load inductive or capacitive?Problem 2 : Phasor Equivalent Circuits (Hambley 5.91)Draw the Thevenin and Norton equivalent circuits for the figure below,labeling elements and terminalsProblem 3 Maximum power transfer (Hambley 5.93)The Thevenin equivalent of a two terminal network is shown below. The frequency is f=60Hz. We wish to connect a load across temrinals a-b that consists of a resistance and a capacitance in series such that the power delivered to the resistance is maximized. Find the value of the resistance and the value of the capacitance. Problem 4 Simple Transfer Function Calculation (Hambley 6.15)The figure below shows the input and output voltage of a certain filter operating in steady state with a sinusoidal input. Determine the frequency and the corresponding value of the transfer function.Problem 5 Transfer Function of a differentiator (Hambley P.6.18)Consider a circuit for which the output voltage is the time derivative of the input voltage as illustrated in figure below.The input voltage is given by vin(t)=Vmaxcos(2 pi f t).Find an expression for the output voltage as a function of time. Find an expression for the transfer function of the differentiator. Plot the magnitude and phase of the transfer function versus frequency. Problem 6 db and log frequency practice(a) Hambley P.6.41 What frequency is halfway between 100 and 3000Hz on a logarithmic scale? And on a linear scale?(b) Hambley P6.42 What is the decibel equivalent for |H(f)|=0.5 ? Repeat for |H(f)|=2, |H(f)|=2-1/2 =0.7071, |H(f)|=2+1/2=1.4142(c) Hambley P6.43 What frequency is one octave higher than 500Hz ? Three octaves lower ? Two decades higher? One decade lower?Problem 7 Bode Plot of circuitsHambley P.6.60 Solve for the transfer function H(f)= Vout/Vin and draw the asymptotic Bode magnitude and phase plots for the circuit shown in figure below.Problem 8 Low Pass FilterHambley P.6.63Consider the circuit shown in figure below. Sketch the asymptotic Bode magnitude and phase plot to scale for the transfer function H(f)= Vout(f)/Vin (f).Problem 9 High Pass FilterHambley P.6.67Consider the circuit shown in figure below. Sketch the asymptotic Bode magnitude and phase plot to scale for the transfer function H(f)= Vout(f)/Vin


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Berkeley ELENG 40 - Homework

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