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.The voltage on the negative termi-nal of the op amp is:Rs Rs + R Rs- ------------------V- = Vout----------------- E" Vin-----------------f - = Vin = V+Rs + R Rs Rs + Rf fIn fact, the positive and negative inputs on the op amp had better be about equal.Ifthis were not the case, the output of the real op amp would be pegged near one ofthe supply rails.Basically, the feedback is doing all that it can to try and make thevoltages on the plus and minus inputs as close to equal as possible.All negativefeedback op amp circuits should have this characteristic.This suggests a fast way of solving op amp circuits.If the op amp is setting the twoinputs equal, why don t we just assume that has happened, and solve from there!Applying this technique to the previous circuit, we see that V- = Vin.If no currentgoes into the op amp inputs, than the current through the two resistors must beequal.This gives:Vout  Vin VinI = Is = ---------------------- = --------fR RsfA Pragmatic Introduction to the Art of Electrical Engineering 43Guess the NumberCollecting terms gives:Vout1 1---------- = Vinëø ----- + -----öøíø øøR Rs Rf fSolving for Vout yields:R + R Rf-Vout = Vin-----------------s = Vinëø 1 + -----föøíø-Rs RsøøAssuming the inputs are equal turns out to be equivalent to saying that A is verylarge.Before we leave this section, there is one more thing to say about high gain differ-ential amplifiers.If you look at the input versus output characteristic for an op amp,you will note that if the positive input is bigger than the negative input, the outputquickly saturates near the positive rail.Similarly, if the situation is reversed, theoutput dives down near the negative rail.An op amp without feedback to keep it inthe tiny linear region is a comparator.A comparator is a device which tells you ifone input is bigger than another.While real comparators are differential amplifiersthat have been optimized for the comparison task, a generic op amp will workalmost as well for our low speed applications.In fact, the symbol for a comparatoris exactly the same as that for an op amp.How do you build an Analog to Digital Convertor?At this point, we return to our original objective - building an analog-to-digital con-vertor, or ADC.There are many different ways of creating an ADC.For now, wewill use a classic technique called successive approximation.Have you ever played a game called  Guess the Number ? One person thinks of anumber within some range.The other person tries to guess it.After each wronganswer, the guesser is told whether the guess was too high or too low.Eventually,the guesser zeros in on the correct number.This is exactly how a successive approximation analog-to-digital convertor works.You have some unknown input voltage.Using a DAC, you generate a guess.Then acomparator tells you whether you were high or low.You modify the guess, and con-tinue the game until you home in on the value of the input.44 A Pragmatic Introduction to the Art of Electrical EngineeringHow do you build an Analog to Digital Convertor?If you are very smart, you play the game cleverly.For example, if you know thenumber is between 0 and 100, your first guess should be 50.This evenly splits therange, giving you the maximum amount of information from the guess.If you splitthe remaining range every time, it will take you log2n guesses to find the correctneighborhood of n numbers.For your assignment, you are to build an ADC which reads a 0V - 5V input, andtells you which of eight ranges it is in.These ranges should be equally spaced andare shown below.0V.625V 1.25V 1.875 2.5V 3.125 3.75 4.375 5V0 1 2 3 4 5 6 7The input will be created with a potentiometer.That s a big name for a variableresistor.Sometimes you ll hear the older generation refer to them as rheostats.Per-sonally, we prefer to just call them pots.In any case, these are resistors with con-nections at the two ends, plus a third connection, called a wiper, which can beadjusted from one end to the other.You should have two 10k&! trim pots.(Thesesmall ones are usually used to trim, or make small corrections to a circuit, hence thename.) The wiper is the middle terminal.You will connect this as a variable voltagedivider as shown below.10k&!5VpotVoutBy the way, there are many types of potentiometers.Most are rotary, but some aremoved linearly, and are sometimes called sliders.On some pots, the resistanceschange linearly with angle.On others, the resistances change logarithmically.Theselater ones are used to control volume levels, and are audio tapered, as opposed lin-ear tapered.When buying potentiometers, make sure you get the right type - bothare very common!(Hearing, like most human senses, is inherently logarithmic.For example, the justnoticeable increases in volume from a given level increase proportionally with theA Pragmatic Introduction to the Art of Electrical Engineering 45Guess the Numbervolume level.Audio taper pots allow equal increments on a volume control tosound like equal increments in loudness, even though the power has to increase dra-matically more with each further setting.)So, without further ado, here s the big picture:5VVout10k&!pot5V+9V1/4 LMC660 1N4007DAC amp1k&!1N400735V10k&!StampThe idea here is that you will use the Stamp to choose DAC outputs.These will beamplified up to give the appropriate comparison voltages.(You will have to designthis amplifier.Use a noninverting amplifier as discussed in the previous sectionwith resistor values on the order of 10k&!.) The output of the amp is compared withthe potentiometer output.After some protection circuitry, the output of the compar-ator is sent to a Stamp input.Unfortunately, another nonideality of op amps is that they will only function prop-erly when the inputs are within the common-mode input range.For the LMC660,this extends below the negative rail up to about 2.5V below the positive rail [ Pobierz caÅ‚ość w formacie PDF ]