ECE 2100 Lecture notes Wed, 1/22/03

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1 HW #4, due, /24 Ch : 34, 37, 43 ECE 0 Lecture notes Wed, /22/03 Exercises: 2., 2.2, 2.4, 2.5 Stu or hints etc., see lecture notes or, /7 Problem Sessions: W, :50-2:40 am, WBB 22 (tall brick geology building), 0:45 - :35 am, MEB 8 (by SW entrance) Clean up some loose ends Bode Plots The Bode plots that we've covered in class are the simplest types and will do or our purposes. We are primarily interested in the design o ampliiers and analysis o the low and high corner requencies. The poles and zeroes are usually ar apart. When poles and zeroes are too close to each other they can interact or even result in complex poles. Complex poles result in resonance eects like those shown at right. I poles and zeroes are simply close but not complex, the eects o each simply add or subtract. That can throw o your assumptions (like the -3dB) around the corner requency, etc.. I asked in a uture classes i you have "covered" Bode plots, answer only a qualiied "yes" or you may be expected to know more than you do. db deg phase HW #5, due W, /29 Ch.2: problems 6, 8a-e, 0, 5, Ex2.4 - Ex2.9 Ans: 6: -, -3.00V, -2.7V to -3.3V HW #6, due, /3 Ch.2: Ex2.0 - Ex2.6, problems 2.22, A. Stolp //03 rad sec Clipping v All real ampliiers will clip the output signal i the input is too big. in Only one part in the model can possible account or the s o clipping-- a nonlinear A vo. in v. out A vo 0 positive "rail" ut L A vo "active" region Clipping level at the output (ut ) is less than that o A vo (+ 0V) because o the o, L voltage divider. The maximum allowable v 0. V in A vo negative "rail" 0 The maximum allowable v s is greater than this because o the S, in voltage divider. Operational Ampliiers (Op amp) Chapter 2 o the textbook Start with lecture or, /7 It's very diicult to make v a & v b close enough without using some negative eedback. Negative eedback makes the op-amp maintain v a ~ v b or itsel. With the proper negative eedback the op-amp keeps v a ~ v b so close that you can usually assume that v a v b. Without this negative eedback the op-amp output will almost certainly be at one o its limits, either high or low, i.e. NOT in its active, or linear, range. Incidentally, circuits without negative eedback are also useul, but the output is either high or low (digital) and not linearly related to the input. These types o circuits are called nonlinear circuits. ECE 0 Lecture notes Wed, /22/03, p

2 The op-amp has very high input impedance. The input currents are almost zero. As long as you use reasonable resistor values in your circuits (say 00Ω to MΩ), you can neglect the input currents. The output impedance o IC op amps is not that great, but negative eedback makes it look much smaller than it really is, and it's oten neglected. Op-amps ampliy DC as well as AC. Active (Linear) Op amp Circuits Voltage ollower Negative eedback, the entire is ed back. v a ~ v b O: v a Normally the approximate equal sign is let out. Also known as a buer. This is very useul as a current ampliier. Very little (usually negligible) current lows in and signiicant current can low out. Notice that he power supply connections are not shown. They are "understood" to exist. Negative eedback What i: v. a V & v. o 0 V because they're connected: v. b 0 V v a v b V So the op amp wants to make the output 00000V, and will "turn up" the output voltage as ast as it can. Very soon the output will reach V and the process will stop. What i: v. a V & v. o 3 V v b v a v b 0000 V Now the op amp wants to make the output -0000V, and will "turn down" the output voltage as ast as it can. Again, the output will soon reach V and the process will stop. This is how negative eedback works. Negative eedback is an important concept. It is used in almost all systems, including all natural systems. A very simple example is the heating system in your house. I the air temperature is too low the thermostat detects a dierence between its setting and the air temperature and turns on the heater. When the air temperature reaches the set temperature the thermostat turns o the heater negative eedback. Incidentally, a real op amp does have a limit as to how ast it can change its output voltage. This maximum is called the "slew rate" (S) o the op amp and is generally speciied in V/µs. Noninverting Ampliier Same type o negative eedback, but now only a raction o is ed back. v a ~ v b. O:. You can get whatever gain you want just by selecting the right resistor values.. emember the + These calculations are only valid I the op amp is in its active region. I is too big, the output will be clipped and v a will NOT equal v b. It is only reasonable to assume that the circuit might be in the active region i there is negative eedback. Look or a connection rom the output to the inverting (-) input. This ampliier is called "noninverting" because the output is not inverted with respect to the input. You can tell this at a glance i you see that the input is connected to the noninverting (+) input. Inverting Ampliier You still have negative eedback, but now the is also connected to the same op-amp input. v b ~ v a 0V, it's connected to ground i in in But this current can't low into the op amp, so it must low up through (the eedback resistor). ECE 0 Lecture notes Wed, /22/03, p2

3 i in in i v b 0 Again, you can get whatever gain you want just by selecting the right resistor values. O:. The - sign means "inverting". You can tell this at a glance that this is an inverting amp i you see that the input is connected to the inverting (-) input. Usually the noninverting input is hooked to ground through a resistor such that: ~ in This doesn't aect our ideal calculations above, but does make real op amps appear more like ideal ones. We'll revisit this again when we talk about the non-ideal eects and how to deal with them. Summer This is a variation o the inverting amp. v v 2 v 3 3 i v b O:. v. v. 2 v 3 3 Dierentiator Another variation o the inverting amp. i C. C d dt O:.. C d dt Integrator Another variation o the inverting amp. i in i C C. d in dt integrate both sides in. V in dt C. O:.. in C V in dt This is a nice circuit, but impractical in real lie. The slightest DC voltage at will make the output drit to one o the rail voltages. Even i you hooked to ground, imperections in the op amp would cause the same result. A practical variant is the running average or Miller Integrator. allows the capacitor charge to leak o. This and all the previous circuits could also be looked at in terms o steady-state AC analysis: Z i in i O:. Z in Z Z ECE 0 Lecture notes Wed, /22/03, p3 The - sign means a 80 o phase change.

4 Active ilters By using various networks o resistors and capacitors in place o Z and Z you can make all sorts o excellent ilters without using inductors. That's good because real inductors are expensive and not nearly as ideal as real capacitors. In the case o the Miller integrator:.. Z j ω C.. j. ω. C... Z v. in in j. ω. C. in in A single-pole low pass ilter with: ω C A good reerence: Active ilter Cookbook by Don Lancaster, published by Howard W. Sams & Co.. Dierential ampliier v a. v 2 v b. C v b. v The two s are equal in value. They must be equal. 2 v. v 2. 2 v v. o. 2 v 2. 2 v. v. o.. 2 v 2 Or, Calculated by superposition:. 2 v.. v 2 O:. v 2 v The two s are equal in value. v a. v 2 v a 0 What remains is just an inverting ampliier What remains is just a noninverting ampliier 2. v v o2. v a v 2. v 2 Together:. v 2 v Input resistance problem Input resistance or v 2 is: Input resistance or v is: but may change i v 2 changes. What i v a v? Then v b v and then the input resistance or v is! One cure or this variable input resistance is to buer both inputs, and this will indeed make a good dierential ampliier. However, varying the gain o this ampliier would involve changing two resistors at a time. ECE 0 Lecture notes Wed, /22/03, p4

5 Instrumentation ampliier The circuit below is only slightly more complex, but oers a simple way to change the gain. To ind the gain o the let part o the circuit: ~ v 2. I and: v v 2 I. ~ v ~ v 2 so: ~ v 2 2 v v v 2 v 3 I. I v 2 v Uses So where might you use one o these instrumentation ampliiers? Here's an example o where I personally used one. The objective was to add orce sensing to a robot gripper. The sensors were called "load cells" and are based on a ull wheatstone-bridge o strain gages. Lets look at stain and strain gages irst: Stain is the stretch o a material under stress (orces) L L strain L L stress A A cross-sectional area length strain gage: A strain gage is a thin backing material with a wire and two contacts. recall: A. ρ length A So, as the wires in a strain gage are stretched, the resistance goes up 4 strain gages are usually wired into wheatstone bridges, like the one shown below, where each o the resistors is a strain gage attached to a beam. This helps cancel temperature dependencies. Two strain gages on top stretch ( & 4 ) Beam: Two strain gages on bottom compress ( & 3 ) ECE 0 Lecture notes Wed, /22/03, p5

6 A load cell generally contains 4 strain gages in a ull bridge V+ The load cells we used were shaped like washers They react to an axial orce out + out - v a v b wires Two load cells were placed under the gripper "ingers". obot gripper movement V- movement load cell spring I the gripper has a part, the load-cell orce goes down. i the part hits something as it's being inserted, the orce goes up. part I used an instrumentation ampliiers to ampliy the dierential voltage (V ab ) rom each load cell. Nonlinear Circuits You may get the idea rom the previous circuits that v a v b in all cases, but that is not always true-- the op amp is not always in its active region. Not only that, but you can make useul circuits even i the op amp can only switch between the two rail voltages. Comparator Without negative eedback the op amp is simply a comparator. I v a > v b I v a < v b then L+, the positive output limit (+ rail). then L-, the negative output limit (- rail). You now have a digital output that tells you which voltage is greater. one o the two voltages typically comes rom a voltage divider: I v a ~ v b the output will switch at the slightest noise on the inputs. The next circuit will ix that. Schmitt Trigger Now we've got some positive eedback. This causes a "toggle" action or hysteresis in the switching. As soon as the output switches, the switching level changes as well. The switching level is:. + i is +, - i is - There are other ways to make Schmitt triggers, but all have some positive eedback. Other Nonlinear Circuits You'll see more in the Nonlinear Op Amp Circuits lab. eerences or practical circuits IC Op-Amp Cookbook by Walter G Jung, published by Howard W. Sams & Co.. The Art o Electronics by Horowitz and Hill published by Cambridge University Press ECE 0 Lecture notes Wed, /22/03, p6 Next time: Non-ideal eects