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F07 HW 03 all

# F07 HW 03 all - EECS 314 Fall 2007 HW 03 Problem 1...

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EECS 314 Fall 2007 HW 03 Problem 1 Student's name ___________________________ Discussion section # __________ (Last name, first name, IN INK) © 2007 Alexander Ganago Page 1 of 2 The big picture The circuit shown on this diagram is known as an inverting summer, or summing amplifier, a.k.a. adder. This summer is inverting, because the signals are fed into the inverting (-) input terminal of the Op Amp. Its output signal V OUT is a sum of the two input signals V OUT = K 1 V S1 + K 2 V S2 where the coefficients K 1 and K 2 can be individually – and independently! – changed if the resistances R 1 and R 2 are varied. This is a great advantage of the inverting summer: in its twin brother – the non-inverting summer, where the signals are fed into the non-inverting (+) input terminal of the Op Amp – changing one of the resistors results in a change of both gain values thus independent adjustment of gains is nearly impossible. The inverting summer circuit has many applications; one of the most obvious is the mixer at an audio recording studio, where the signals V S1 and V S2 come from two microphones. In control systems, a similar circuit with 3 inputs can play the role of the adder (such as needed for P + I + D control, which we will discuss later in the course). For conditioning of sensor signals, one input V S1 might be used for the sensor signal itself (to be amplified with the desired gain) while the other input V S2 might be used for compensation of DC offset (see Part 2 of this problem. Problem (Assume an ideal Op Amp and use the “Golden Rules” in all derivations; show your work on additional pages) Part 1 (10 points) For the circuit shown on the diagram above, write a complete node voltage equation for node A; then simplify the equation by applying the “Golden Rules” and derive the coefficients K 1 and K 2 (since the circuit is based on an inverting amplifier, both are negative).

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EECS 314 Fall 2007 HW 03 Problem 1 Student's name ___________________________ Discussion section # __________ (Last name, first name, IN INK) © 2007 Alexander Ganago Page 2 of 2 Part 2 (15 points) Assume that you measure temperature with a voltage divider based on a thermistor, as in problem 3 of homework 02, and the voltage signals V S1 from your temperature sensor linearly depend on the temperature and equal V S1, 0˚F = 4.0 V at 0˚ F, and V S1, 100˚F = 3.2 V at 100˚ F (these values are similar to what you obtain in the circuit of HW 02 problem 3). For your application, you need to obtain the output voltage of the circuit equal to V OUT, 0˚F = 0.0 V at 0˚ F, and V OUT, 100˚F = 10.0 V at 100˚ F . To achieve this goal, you have to design an inverting adder with R F = 100 k Ω and V S2 = –2 V, a DC source, which remains the same at all temperatures.
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F07 HW 03 all - EECS 314 Fall 2007 HW 03 Problem 1...

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