Lecture 9: Operational AmplifiersI-V RelationshipRails and SaturationExample: Voltage FollowerIdeal Op-Amp AssumptionsIdeal Op-Amp ModelSlide 7Utility of Voltage FollowerOp-Amp CircuitsExample: Inverting AmplifierExample: Inverting Summing AmplifierNon-inverting AmplifierImportant PointsExample: Voltage DividerExampleSlide 16Lecture 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. VO is called the output terminal.* There are actually more connections to the device that are not shown. The device connects to a power supply, which is needed for proper operation, as well as ground.+V+VV0I-V RelationshipThe 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 VO is within a certain range.++V0AV1+V1RiCircuit Model in linear regionRoRails and SaturationThe output VO must lie within a range determined by the supply voltages, which are not shown. It will limit or “clip” if VO attempts to exceed the boundaries. We call the limits of the output the “rails”.In the linear region, the op-ampoutput voltage VO is 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 AV0VVlower railupper railExample: Voltage FollowerFind the output voltage. Assume the rails are not exceeded.V0+ VIN++V0AV1-+V1RiRoVINi1o1oRVRAVVoIN1VVV INoioioVRR)1A(RRAVIdeal Op-Amp AssumptionsWhile we can always use our circuit model for the linear region, it is complicated.Ri is usually very large.RO is usually very small.A is usually very large(like 103 to 106).Thus, we can make the following ideal assumptions for easier, but still pretty accurate, analysis:Assume A = ∞. Assume Ri = ∞. Assume Ro = 0 ++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 Ri is 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+VV0++V0AV1+V1RiRoExample: Voltage FollowerV0+ VINFind the output voltage. Assume the rails are not exceeded.VO = VIN+Utility of Voltage FollowerSuppose 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 the load, the voltage follower replicates the desired voltage, and can also provide current through its power supply.Digital CircuitOp-Amp CircuitsOp-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 Vin and op-amp inputs) Use Rule 1: V+-V- = 0Step 2: Find the current in the feedback path Use Rule 2: No current into/out of op-amp inputsStep 3: KVL around output loop (involves Vo and feedback path) Remember current can flow in/out op-amp outputExample: Inverting Amplifier V0+R1R2VIN Input LoopFeedback PathOutput LoopINV1R2RoV V1V0+V3V2RFR1R2R333F22F11F0VRR VRR VRRV Example: Inverting Summing AmplifierNon-inverting AmplifierINV1R2R1oVR1 R2V INVoImportant PointsThe 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 DividerSuppose I want to use the following circuit to supply a certain fraction of VIN to whatever I attach.What is VO if nothing is attached?What is VO if a 1 kresistor 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 VIN to any attached device?VIN1 k1 k+VO_ExampleDesign a circuit whose output is the sum of two input voltages.ExampleDesign a circuit whose output is the average of two input
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