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W09 314 HW 03 extra credit Schmitt trig solution

W09 314 HW 03 extra credit Schmitt trig solution - EECS 314...

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EECS 314 Winter 2009 Homework set 3 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) HW problem for extra credit Schmitt trigger – a better comparator © 2009 Alexander Ganago Page 1 of 5 The Big Picture The greatest disadvantage of comparators is so-called chattering (isn’t it a highly scientific term ;), which means that even the slightest variations of the difference between the sensor voltage V 1 and the set voltage V 2 would lead to abrupt changes of the output voltage. For example, variations of temperature by a small fraction of a degree would make (V 1 – V 2 As in any comparator, the Schmitt trigger’s output voltage saturates either at a certain high level V ) vary only by a millivolt or so – but it would be enough to turn on and off a powerful air conditioner every few seconds, without due reason (and with possible damage to its motor, etc.), the big switch would close and open very often, making a chattering sound. A better circuit solution would involve a “comfort zone” in which nothing should be done. For example, in temperature control, you turn on the heater if the room air gets cooler than 68 ˚ F, you turn on the air conditioner if the temperature rises above 72 ˚ F, but the range of temperatures between 68 ˚ and 72˚ F is your comfort zone: you are comfortable and do need to control the temperature until it goes beyond this range. An improved comparator, which has a comfort zone, is called the Schmitt trigger , based on an Op Amp whose non-inverting (+) input terminal is connected to the output terminal (this is called positive feedback). OUT, HIGH which is smaller than the positive supply voltage (shown on this diagram as +12 V) or saturates at V OUT, LOW which is higher than the negative supply voltage (shown on this diagram as –12 V, but it can equals zero = ground in other circuits). For simplicity, we may assume that saturation occurs at the supply voltages such as -12 and +12 V. The change of the output voltage from V OUT, HIGH to V OUT, LOW and back from V OUT, LOW to V OUT, HIGH is abrupt: it occurs as the difference (V IN – V + ) changes its sign: If V IN > V + then V OUT = V OUT, LOW , for example = –12 V If V IN < V + then V OUT = V OUT, HIGH , for example = +12 V To begin our analysis of the Schmitt trigger circuit, let us to calculate V + . Note that V + can take only two possible values: one is obtained when V OUT = V OUT, HIGH and the other when V OUT = V OUT, LOW . We label these two values V +, HIGH and V +, LOW Since we may neglect the input current I , respectively.
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