Lecture 9: Operational AmplifiersToday, we will introduce our first integrated circuit element: the operational amplifier.The operational amplifier,or op-amp, has three terminals*: V+is called the non-inverting input terminal. V-is called the inverting input terminal. VOis called the output terminal.* There are actually more connections to the device that are notshown. The device connects to a power supply, which is needed for proper operation, as well as ground.+−−−−V+V−−−−V0I-V Relationship The I-V relationship for the op-amp is complicated, since it has multiple terminals. The op-amp can be modeled using the following circuit: You can simply replace the op-amp symbol with the above circuit for analysis. However, the above model is only valid when VOis within a certain range.+−−−−+−−−−V0AV1+−−−−V1RiCircuit Model in linear regionRoRails and Saturation The output VOmust lie within a range determined by the supply voltages, which are not shown. It will limit or “clip” if VOattempts to exceed the boundaries. We call the limits of the output the “rails”. In the linear region, the op-ampoutput voltage VOis equal to thegain A times the voltage acrossthe input terminals. You can “blindly” usethe linear region model,and check if the outputexceeds a rail. If so,the output is equal to that rail voltage.Slope is AV0−−+VVlower railupper railExample: Voltage Follower Find the output voltage. Assume the rails are not exceeded.V0+−−−−VIN+−−−−+−−−−V0AV1-+V1RiRoVINIdeal Op-Amp Assumptions While we can always use our circuit model for the linear region, it is complicated. Riis usually very large. ROis usually very small. A is usually very large(like 103to 106). Thus, we can make the following ideal assumptions for easier, but still pretty accurate, analysis: Assume A = ∞. Assume Ri= ∞. Assume Ro= 0 Ω+−−−−+−−−−V0AV1+−−−−V1RiCircuit ModelRoIdeal Op-Amp ModelOur idealized op-amp follows these rules within the linear region: Rule 1: V+-V-= 0. Why? If the output voltage is limited by rails, and the gain A is very large, then V+-V-must be very small. Rule 2: No current goes in/out of the input terminals. Why? V+-V-is very small and Riis very large. Remember current can go into/out the output terminal. Why? There are connections not shown, and the current comes from those connections.+−−−−V+V−−−−V0+−−−−+−−−−V0AV1+−−−−V1RiRoExample: Voltage FollowerV0+−−−−VIN Find the output voltage. Assume the rails are not exceeded.Utility of Voltage Follower Suppose I have a voltage coming out of a digital circuit. I want to apply the voltage to “turn on” some device that requires high power (the device “drains” a substantial amount of current). Digital circuits usually cannot provide much current; they are designed for low power consumption. If we put a voltage follower between the digital circuit and theload, the voltage follower replicates the desired voltage, and can also provide current through its power supply.Digital Circuit+−−−−Op-Amp Circuits Op-Amp circuits usually take some input voltage and perform some “operation” on it, yielding an output voltage. Some tips on how to find the output, given the input:Step 1: KVL around input loop (involves Vinand op-amp inputs)Use Rule 1: Vp-Vn = 0Step 2: Find the current in the feedback pathUse Rule 2: No current into/out of op-amp inputsStep 3: KVL around output loop (involves Voand feedback path)Remember current can flow in/out op-amp outputExample: Inverting AmplifierV0+−−−−R1R2VINInput LoopFeedback PathOutput LoopV1V0+−−−−V3V2RFR1R2R3Example: Inverting Summing AmplifierNon-inverting AmplifierR1R2VINVoImportant Points The amplifier output voltage does not depend on the “load”(what is attached to the output). The “form” of the output voltage (the signs of the scaling factors on the input voltages, for example) depends on the amplifier circuit layout. To change the values (magnitudes) of scaling factors, adjust resistor values. Input voltages which are attached to the + (non-inverting) amplifier terminal get positive scaling factors. Inputs attached to the – (inverting) terminal get negative scaling factors. You can use these principles to design amplifiers which perform a particular function on the input voltages.Example: Voltage Divider Suppose I want to use the following circuit to supply a certain fraction of VINto whatever I attach. What is VOif nothing is attached? What is VOif a 1 kΩresistor is attached? This circuit clearly doesnot supply the same voltage to any attached load.What could I add to the circuit so that it will supply the same fraction of VINto any attached device?VIN1 kΩ1 kΩ+VO_Example Design a circuit whose output is the sum of two input voltages.Example Design a circuit whose output is the average of two input
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