Fall 2009 EE40 Homework 6 Due Oct 15 Thursday 12 00 noon in Cory 240 Reading Assignments Chapter 5 of Hambley textbook Section 5 7 on Three Phase circuit is optional Sections 6 1 6 5 of Hambley textbook Problem 1 Power Calculation Hambley P5 72 The voltage across a load is v t 10 4 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 terminals Problem 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 ca pacitance 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 si nusoidal 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 func tion 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 circuits Hambley 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 Filter Hambley P 6 63 Consider 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 Filter Hambley P 6 67 Consider 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
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