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EECS314_W08_HW6

# EECS314_W08_HW6 - EECS 314 Winter 2008 Homework set 6...

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EECS 314 Winter 2008 Homework set 6 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above © 2008 Alexander Ganago Page 1 of 2 Scores for the HW set: Problem 1 2 3 4 5 6 7 Total Score Problem 1 Op Amp Integrator circuit The Big Picture The circuit shown on this diagram is an integrator: its output voltage is V OUT ( t ) = K " V IN ( t ) " dt # Here the constant K does not depend on time and voltage, but it depends on R and C in the circuit. Note that, in order to match the units on the both sides of the above equation, the constant K must have units of (sec) -1 . Also note that there is a typo on page 27 of Chapter 13 in Making sense of EE. One problem with the integrator is that its output signals saturates if it reaches the supply voltage (on this diagram, –10 V or +10 V). To avoid saturation, the capacitor must be discharged (short-circuited with a closed switch, which is usually a MOSFET). The Assignment Part 1 (10 points) For the circuit shown on the diagram, derive the equation for the coefficient K (be careful with its sign!). Your answer: K = _________________ For the circuit shown on the diagram, assume R = 25 k Ω , C = 4 nF, and calculate the numerical value of K (be careful with its sign!). Your answer: K = _________________ Part 1 2 3 Total

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EECS 314 Winter 2008 Homework set 6 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above © 2008 Alexander Ganago Page 2 of 2 Problem 1, continued Part 2 (15 points) Suppose that the input signal is a constant equal to +20 mV, and that the output voltage in the circuit above (with component values as in Part 1 ) was set to zero at time t = 0 . Obtain the equation for the output voltage as function of time. Sketch the output voltage as function of time on the grid. Carefully label the axes and indicate the slope of the linear function. Since the integral of a constant is a linear function, the output voltage would eventually outgrow the source voltage and saturate (clip). Determine at what time t s the output voltage saturates, and whether it saturates at +10 V or at –10 V. Your answer: t s = _________________; saturation occurs at ______________ Part 3 (15 points) Suppose you need to change the circuit so that the saturation occurs at the later time 10 t s [assume that the input is still equal to +20 mV , and V OUT ( t = 0 ) = 0 ]. There are 2 ways of changing the circuit to achieve this goal:
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EECS314_W08_HW6 - EECS 314 Winter 2008 Homework set 6...

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