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Op Amps: Electric Circuits Fundamentals - ECEN 2714
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3/2/2025 ECEN 2714 Toolbelt Fundamentals of Electric Circuits ECEN 2714 Spring 2025 Dr. Keith A. Teague, Professor School of Electrical and Computer Engineering Oklahoma State University teague@okstate.edu 1 1 2 Op Amps Chapter 5 – Operational Amplifiers 3 1. Overview 1. Overview 2. Voltage follower circuit 2. Voltage follower circuit 3. Common op amp circuits 3. Common op amp circuits 4 3/2/2025 Operational Amplifiers – Op Amps Operational Amplifiers – Op Amps • Usually called Op Amp for short • An op amp is shown in a circuit diagram as a “functional block” – there are many components inside • An op amp is an “active element”, as opposed to a resistor which is purely passive • Requires an external power source • Acts like a voltage controlled voltage source (a dependent source) • Provided via an integrated circuit (IC) in many different packages and power ratings • Useful for voltage amplification • In combination with other elements it can be made into other dependent sources • Op amps can be used to build many useful circuits 𝑉 • A very common “building block” • Provides much more flexibility than simple passive circuits 𝑉 • Op amps can perform mathematical operations on analog input signals, including addition, subtraction, multiplication, differentiation, and integration some function of 𝑉 and 𝑉 • The simplified symbol above only shows inputs and outputs • In this class we will consider ideal op amps (a more realistic model will be introduced later) 5 5 𝑉 6 6 Standard Terminals on an Op Amp Standard Terminals on an Op Amp • Often in a circuit diagram connections to the power supply terminals for an op amp are obscured (omitted) and simply taken for granted Positive supply voltage (i.e., VCC) 𝑉 • Most op amps require two voltage sources (+ and -) with a ground reference between them Non-inverting input Output • This gives positive and negative supply voltages with respect to the reference (ground) 𝑉 𝑉 𝑉 The supply voltage pins may not be shown in circuits, and they may have different names from what is shown here – every op amp is assumed to have a proper connection to a power supply Inverting input The positive and negative power supply voltages are usually equal (symmetric about ground) Negative supply voltage (i.e., VEE) 7 7 𝑉 8 3/2/2025 Standard Terminals on an Op Amp Op Amp – Output Voltage • This is a typical “pinout” for a common op amp looking down from above • The output voltage of an op amp is proportional to the difference between the noninverting and the inverting inputs • The indention on the package provides a reference for pin 1 𝑣 𝐴𝑣 𝐴 𝑣 𝑣 • Here, A is called the open loop gain • Ideally – open loop gain in infinite • Practically (in real devices) – open loop gain is finite but still large • 105 to 108 volts/volt Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Typical ranges for op amp parameters. Parameter Typical range Open-loop gain, A 10 to 10 ∞ Input resistance,𝑅 10 to 10 Ideal values ∞ Output resistance, 𝑅 10 to 100 0 Supply voltage, 𝑉 5 to 24 V 9 9 10 10 Op Amp – Feedback Op Amp – Voltage Saturation • Op amps take on an expanded functional ability with the use of feedback • As an ideal amplifier the output voltage would be unlimited (could become infinite) 𝐴𝑣 𝐴 𝑣 𝑣 • Practically, the output cannot exceed the power supply voltage • Feedback – the output of the op amp is connected back into the inverting input terminal • An output that would otherwise exceed the positive or negative supply voltage will “saturate” (be limited) at the supply voltage • Depending on other circuit elements this feedback signal passes through, the gain and behavior of the op amp changes • This condition is called “saturation” • Feedback to the negative (inverting) input terminal is called “negative feedback” • The range between positive and negative saturation is called the “linear region” where the op amp operates linearly (the output voltage is a linear function of the input voltage) • Positive feedback (reinforcement) could lead to oscillation or other undesirable behavior • Amplifiers usually operate in the linear region • Circuits for digital usually operate in saturation (on or off) 11 11 𝑣 Linear region 12 12 3/2/2025 Op Amp – Ideal Behavior Op Amp – Practical (Real) Behavior • An ideal op amp has certain perfect characteristics • Open loop gain is large, but not infinite 1. Infinite open loop gain 2. Infinite input resistance (resistance looking into an input terminal) 3. Zero output resistance (resistance looking back into the output) • Open loop gain can be greater than one million with some devices • Input resistance is very high, but not infinite • Input resistance can be 106 to more than 109 ohms • Input current is thus effectively zero (in actuality it’s very very small) • An ideal op amp will not affect any node its inputs are attached to since it draws no current (infinite input resistance) • An ideal op amp is independent of the load attached to its output terminal (Thevenin resistance is zero) • With negative feedback, the output voltage adjusts so that the two input terminals have the same voltage • Real op amps can come close to this behavior 13 13 14 14 Golden Rules for Ideal Op Amps 1. Op-amp draws no current into (or out of) its input terminals: 𝐼 0 and 𝐼 0 2. Op-amp maintains equal voltages at input terminals 𝑉 𝑉 • Op-amp maintains this equality by adjusting the output voltage 𝑉 • Requires connecting output terminal to inverting input terminal (negative feedback) 15 Golden Rules for Ideal Op Amps 1. Op-amp draws no current into (or out of) input terminals: 𝑉 𝑉 𝑉 𝐼 𝐼 + − 𝐼 0 and 𝐼 0 2. Op-amp maintains equal voltages at input terminals 𝑉 𝐼 𝑉 𝑉 𝑉 • An Op-amp maintains this equality by adjusting the output voltage 𝑉 • This condition requires connecting the output terminal to the inverting input terminal (negative feedback) 16 𝑉 𝑉 𝑉 𝐼 + − 𝐼 𝑉 𝐼 𝑉 An op-amp can also operate without feedback, but the analysis techniques covered here do not apply. In this configuration it can be a “comparator”. You’ll look at this configuration in a lab assignment. 3/2/2025 Voltage Follower Circuit Op Amps Analyze this circuit using the “golden rules” 1. Overview 2. Voltage follower circuit 𝑉 3. Common op amp circuits 𝑉 − Notice the negative feedback – output connected to the inverting input terminal. 17 18 Op Amps Voltage Follower Circuit Golden Rules Always assume: The voltages on the two input terminals are the same, and there is no current into or out of the input terminals. 𝑉 𝑽𝒊𝒏 𝑉 𝐼 and 𝐼 + − 𝑉 𝑽𝒐𝒖𝒕 + − 𝑉 − 𝑉 𝑉 𝑉 𝑉 0 1. Overview 𝑉 2. Voltage follower circuit A voltage follower is an amplifier with a gain of unity (1) + 𝟎𝐕 𝑉 𝑉 𝑉 + 𝑉 − Most of the remainder of the chapter will be devoted to analyzing a variety of practical op amp circuits. When we finish you should be able to analyze an arbitrary op amp circuit using the properties of ideal op amps and the circuit analysis techniques from Chapter 4. We will use the techniques from Chapter 4 for the rest of the semester. 19 + − 𝑉 + 3. Common op amp circuits It is useful as a buffer between two circuits (it has infinite input resistance and zero output resistance so it isolates whatever is connected to the input from whatever is connected to the output 20 Golden Rules 𝐼 and 𝐼 𝑉 0 𝑉 3/2/2025 Inverting Amplifier Circuit Common Op-Amp Circuit #1 The input signal, Vin, is connected to the inverting input terminal through the “input resistor” R1 Inverting Amplifier 𝑉 Notice the output is connected to the input through the “feedback resistor” R2 𝑅 𝑅 𝑉 𝑉 + − − + Golden Rules + 𝐼 and 𝐼 𝑉 𝑉 0 𝑉 − Analyze this circuit – What do we know? Apply the golden rules 21 22 Inverting Amplifier Circuit Inverting Amplifier Circuit 𝑅 Label what we know – input, output, and ground 𝑅 Golden Rules 𝐼 and 𝐼 𝑽𝒐𝒖𝒕 Next, analyze the circuit 𝑉 𝑅 𝑽𝒊𝒏 𝑉 + − 𝑉 𝑉 0 𝑅 𝑉 𝑽𝒊𝒏 − + + 𝑉 𝑉 + − 𝑉 𝟎𝐕 𝑉 𝑉 − + 0 𝑉 + 𝑉 𝟎𝐕 𝟎𝐕 𝟎𝐕 Golden Rules 𝐼 and 𝐼 𝑽𝒐𝒖𝒕 − − The positive input terminal is connected to 0V (ground). We know the positive and negative input terminals will be equal, so both must be 0V. 23 24 3/2/2025 Inverting Amplifier Circuit Inverting Amplifier Circuit 𝑅 Apply the tools you already know to do the analysis 𝑅 1 𝑽𝒊𝒏 𝐼 𝑉 − + 𝑉 + − 𝑉 𝑉 𝟎𝐕 𝐼 𝑉 𝑅 𝑽𝒊𝒏 0 0 𝑅 𝐼 𝑉 𝑅 𝑉 𝑅 𝑉 − + + 𝑉 𝟎𝐕 𝑉 0 𝑅 25 0 𝐼 𝑉 𝑅 𝑉 𝑅 𝑉 𝑅 𝑉 Solve for the output voltage in terms of the input voltage 𝑅 𝑉 𝑅 26 Inverting Amplifier Circuit 2 kΩ Golden Rules Plug in some component values as an example 1 kΩ 𝑉 𝐼 1 𝟓𝐕 𝐼 𝑉 𝑉 𝑉 5V + − + 0 Common Op-Amp Circuit #2 𝑉 + 𝑉 − 𝟎𝐕 Non-Inverting Amplifier 10 V − I/O Function: 𝑉 27 𝐼 and 𝐼 𝟏𝟎 𝐕 𝑅 𝑉 𝑅 𝑉 2000 𝑉 1000 𝑉 2𝑉 Ohm’s law: 𝐼 𝐼 𝑉 0 𝑅 𝑉 𝟓 𝐦𝐀 0 𝑅 𝟓 𝐦𝐀 𝟏𝟎 𝐕 28 0 𝑉 The ratio of the two resistors determines the amplification (gain) of the circuit − KCL @ Node 1: 𝐼 We use KCL, not KVL, when analyzing op amp circuits, usually starting at the input terminal(s) 𝑉 𝑅 𝑉 𝟎𝐕 − KCL @ Node 1: 𝐼 1 + − 𝑉 𝑉 𝟎𝐕 𝐼 𝐼 𝑉 𝟎𝐕 Golden Rules 𝐼 and 𝐼 𝑽𝒐𝒖𝒕 0 + 𝟎𝐕 𝑉 𝑅 Golden Rules 𝐼 and 𝐼 𝑽𝒐𝒖𝒕 Negative sign inverting 3/2/2025 Recall – Standard Terminals on an Op Amp Non-Inverting Amplifier Circuit Positive supply voltage (i.e., VCC) 𝑅 𝑉 Non-inverting input Remember the inverting op amp circuit on the right from before – the input is connected to the inverting input Output 𝑉 𝑉 𝑉 Inverting input 𝑅 𝑉 + − Re-design with the input connected to the non-inverting input to produce a non-inverting circuit 𝑉 𝑉 − + + 𝑉 − Negative supply voltage (i.e., VEE) 29 29 30 Non-Inverting Amplifier Circuit Non-Inverting Amplifier Circuit Although the input signal is connected to the non-inverting input terminal, we still have to have negative feedback 𝑅 Golden Rules 𝐼 and 𝐼 𝑉 𝑅 𝑉 𝑉 𝑉 − + 𝑅 0 𝑉 𝑉 𝑅 + 𝑉 𝑉 − + − − + 𝑉 − Label what we know – the input and output terminals 32 + 𝑽𝒊𝒏 𝟎𝐕 The input is on the non-inverting terminal now 31 𝑉 𝟎𝐕 𝑉 + − Golden Rules 𝐼 and 𝐼 𝑽𝒐𝒖𝒕 0 𝑉 3/2/2025 Non-Inverting Amplifier Circuit Non-Inverting Amplifier Circuit 𝑅 Apply the golden rules 𝐼 and 𝐼 𝑽𝒐𝒖𝒕 𝑉 𝑽𝒊𝒏 𝑅 𝑉 𝟎𝐕 𝑉 𝑉 𝑉 1 𝑉 𝑉 − + 𝑉 𝟎𝐕 − KCL @ Node 1: 𝐼 0 𝑉 0 𝑉 + 𝑽𝒊𝒏 + − 𝑉 As always, the ideal op amp has the same voltage on both the inverting and noninverting terminals – this time it is not zero, it is Vin 𝐼 𝑉 𝑅 Apply KCL at the node labeled “1” – remember the inverting and non-inverting terminals are at the same voltage, and there is no current into either terminal! 𝑉 𝑅 34 𝑅 𝐼 and 𝐼 𝑅 𝑉 𝑽𝒊𝒏 1 𝟎𝐕 𝐼 𝑉 − + 𝑉 𝑉 + − + 𝟎𝐕 KCL @ Node 1: 𝐼 0 𝑉 𝑅 𝐼 𝑉 𝑉 𝑅 𝑉 𝑅 𝑉 𝑉 𝑅 𝑉 1 𝑅 𝑅 𝑉 𝐼 Add some component values as an example 𝑉 − + 𝟓𝐕 5V + − 𝑉 36 0 𝑉 + 𝟎𝐕 Once again, the output is a function of the input and the ratio of the feedback to input resistors – but there is no inverting − 𝑉 𝐼 𝟎𝐕 𝑉 Doing the algebra we can write a formula for the output voltage in terms of the input voltage 𝑉 𝑽𝒊𝒏 1 kΩ 0 Golden Rules 𝐼 and 𝐼 𝟏𝟓 𝐕 Golden Rules 𝑽𝒐𝒖𝒕 𝐼 2 kΩ Non-Inverting Amplifier Circuit Non-Inverting Amplifier Circuit 35 𝐼 𝐼 − 𝑉 𝑽𝒊𝒏 𝟎𝐕 33 𝐼 and 𝐼 𝑽𝒐𝒖𝒕 + 𝟎𝐕 Golden Rules 0 𝑅 − + 𝑽𝒊𝒏 + − 𝑉 𝑅 Golden Rules 𝑉 15 V 𝑉 𝑅 𝟓 𝐦𝐀 − I/O Function: 𝑉 1 𝑅 𝑅 𝑉 1 2000 𝑉 1000 𝑉 3𝑉 𝟏𝟓 𝐕 𝑉 Ohm’s law: 𝐼 𝐼 𝑉 𝑉 𝑅 𝟓 𝐦𝐀 3/2/2025 Cascading Op Amp Circuits Common Op-Amp Circuit #3 More interesting circuits can be constructed by cascading (series connection) of op amp circuits 37 Cascade (Series) Connection of Two Inverting Amplifier Circuits 38 Cascaded Inverting Amplifier Circuits Cascaded Inverting Amplifier Circuits 𝑅 𝑅 𝑅 − + 𝑉 + − 𝑅 𝑅 𝟎𝐕 − + 𝑅 𝑉 − + + − 𝑅 𝟎𝐕 𝑅 𝟎𝐕 − + 𝟎𝐕 𝟎𝐕 The non-inverting input on each op amp is connected to ground Remember – the inputs on each op amp are at the same potential, which is going to be 0V since one input terminal on each op amp is connected to ground Consider two inverting op amp circuits connected in cascade (series) 39 40 3/2/2025 Cascaded Inverting Amplifier Circuits 𝑅 𝑅 𝑅 𝟎𝐕 𝑅 + − 𝑉 𝑉 𝟎𝐕 𝟎𝐕 , + 𝑉 𝟎𝐕 1 + − 𝑉 , 𝐼 𝟎𝐕 2 𝑉 𝟎𝐕 𝐼 , 𝑽𝒐𝒖𝒕,𝟐 − + + 𝟎𝐕 + 𝑉 𝟎𝐕 , − − − − KCL @ Node 1: 𝐼 𝑉 Label the two outputs – give then different names since they are at different nodes in the circuit. How each op amp operates will depend on the ratio of the feedback and input resistors for that particular op amp circuit. 41 0 0 𝑉 𝑅 𝑉 𝐼 𝑉 𝑅 𝑅 The output of the first op amp circuit is the input to the second op amp circuit. 𝑉 , Apply KCL at node 1 , 𝑅 𝑅 𝑉 𝑅 , 42 Cascaded Inverting Amplifier Circuits Cascaded Inverting Amplifier Circuits 𝑅 𝑅 𝐼 1 𝐼 𝑅 𝑽𝒐𝒖𝒕,𝟏 2 𝑉 𝟎𝐕 𝐼 , 𝟎𝐕 𝑉 0 𝑅 𝑉 𝑅 𝑉 , 0 𝑉 𝑅 𝑉 , KCL @ Node 2: 𝐼 𝑉 0 , 𝑅 , 1 𝑉 , 𝑅 𝑅 𝑅 𝑉 𝑅 𝑉 + 0 𝑉 𝑉 0 𝑅 , 𝑉 𝑅 Apply KCL at node 2 , 𝑅 𝑉 𝑅 𝑉 , 𝐼 , 𝟎𝐕 + 𝑉 , − − KCL @ Node 1: 𝐼 𝑅 , 𝑉 𝟎𝐕 𝑽𝒐𝒖𝒕,𝟐 − + , 𝐼 𝑉 𝑅 𝟎𝐕 2 + 𝟎𝐕 𝑉 𝐼 𝑅 𝑽𝒐𝒖𝒕,𝟏 − + 𝐼 + − 𝑉 − − 𝐼 𝑽𝒐𝒖𝒕,𝟐 − + 𝑅 𝟎𝐕 𝐼 𝑅 𝟎𝐕 + 𝟎𝐕 KCL @ Node 1: 𝐼 𝑅 𝑽𝒊𝒏 − + 𝐼 + − 𝑉 𝑅 𝟎𝐕 𝑽𝒊𝒏 43 𝐼 𝑅 𝑽𝒐𝒖𝒕,𝟏 − + 𝑽𝒊𝒏 𝑽𝒐𝒖𝒕,𝟐 − + 𝟎𝐕 𝐼 𝑅 + 𝑅 Analyze the first stage 𝟎𝐕 𝑅 𝑽𝒐𝒖𝒕,𝟏 − + 𝑽𝒊𝒏 Cascaded Inverting Amplifier Circuits 𝑅 𝑅 𝑉 𝑅 𝑅 44 , 0 𝐼 𝑉 𝑅 𝑉 , KCL @ Node 2: 𝐼 𝑉 0 , 𝑅 , 𝑉 , 𝑅 𝑅 𝑅 𝑉 𝑅 𝑉 0 𝐼 𝑉 𝑅 𝑉 , , 𝑅 , 𝑅 𝑉 𝑅 , 𝑅 𝑅 The output from the first op 𝑉 amp circuit is the input to 𝑅 𝑅 the second op amp circuit 3/2/2025 Cascaded Inverting Amplifier Circuits 𝑅 𝐼 𝑅 1 𝐼 + − 𝐼 𝑅 𝑽𝒐𝒖𝒕,𝟏 − + 𝑽𝒊𝒏 𝑉 𝑅 𝟎𝐕 2 𝑉 𝟎𝐕 𝐼 , 𝟎𝐕 • It is common to use multiple op-amp stages chained together • This head to tail configuration is called “cascading” 𝑽𝒐𝒖𝒕,𝟐 − + + 𝟎𝐕 Cascaded Op Amps 𝟎𝐕 + 𝑉 , • Each amplifier is then called a “stage” − − • The output of one stage is the input of the next stage KCL @ Node 1: 𝐼 𝑉 0 𝑅 𝑉 𝑅 𝑉 , 0 𝐼 𝑉 𝑅 𝑉 KCL @ Node 2: 𝐼 𝑉 , 0 , 𝑅 𝑉 , , 𝑅 𝑅 𝑅 𝑉 𝑅 𝑉 0 𝐼 𝑉 𝑅 𝑉 The total output for the two op amps in series is thus found below , , It’s the product of the two! 𝑅 , 𝑅 𝑉 𝑅 , 𝑅 𝑅 𝑉𝑉, 𝑅 𝑅 𝑅 𝑅 𝑉 𝑅 𝑅 45 46 Cascaded Op Amps • Due to the ideal op-amps’s input and output resistances (infinite and zero, respectively), stages can be chained together without impacting the performance of any one stage Common Op-Amp Circuit #4 • One reason to cascade amplifier stages is to increase the overall gain • The gain of a cascaded connection of amplifiers is the product of the individual gains: 𝐴 Summing Amplifier 𝐴 𝐴 𝐴 • For example, two stages each having a gain of 100, have a combined gain of 10,000 • A very small input voltage can control a much larger output voltage 47 48 3/2/2025 Summing Amplifier Circuit Summing Amplifier Circuit Golden Rules 𝑅 𝐼 and 𝐼 𝑉 − + 𝑅 𝑉 , + − This summing amplifier will add these two input voltages 𝑉 , 𝑉 Perform the same analysis as before. There is only one node where we use KCL – at the inverting input. 𝑉 𝑽𝒐𝒖𝒕 + − − 1 − + 𝑅 𝐼 + − 𝑉 𝑉 − 𝐼 𝐼 𝑉 , 𝑅 0 0 𝑉 , 𝑅 𝑉 , 𝑅 0 𝑉 + 𝟎𝐕 KCL @ Node 1: 𝐼 𝑉 49 𝐼 𝟎𝐕 An op amp can sum inputs, effectively performing mathematical addition on multiple input voltages 0 The output is the (negative) sum of the two input voltages, each scaled (weighted) by the resistor ratio for that source. 𝑉 𝑅 𝑉 , 𝑉 𝑅 𝑅 𝑅 𝑅 𝑉 , 𝑉 , 𝑅 𝑅 Vout AVin ,1 BVin ,2 A R3 R1 B R3 R2 50 Summing Amplifier Circuit 𝑉 , Golden Rules 𝑅 𝐼 𝑅 𝑉 𝟎𝐕 𝑽𝒊𝒏,𝟐 + − 𝑉 , 𝐼 1 − + 𝑅 𝐼 + − 𝟎𝐕 • This generalizes to multiple inputs – vp 0 What do we do to make this a straight sum of the two inputs? 𝑉 𝐼 𝐼 𝑉 , 𝑅 0 0 0 Special Case: 𝑅 𝑉 𝑅 𝑉 , 𝑉 𝑅 𝑅 𝑅 𝑅 𝑉 , 𝑉 , 𝑅 𝑅 𝑉 𝑉 𝑅 𝑅 𝑉 , 𝑅 𝑅 𝑉 , 𝑅 vn 0 0 va 0 vb 0 vc 0 vo KCL at vn : 0 Ra Rb Rc Rf − KCL @ Node 1: 𝐼 𝑉 , 𝑅 𝑉 , 𝑅 Summing Amplifier Circuit 0 𝑉 + 𝟎𝐕 𝑉 𝐼 and 𝐼 𝑽𝒐𝒖𝒕 𝑽𝒊𝒏,𝟏 51 𝑽𝒊𝒏,𝟐 𝑉 , + + − 𝑉 , 0 𝐼 and 𝐼 𝟎𝐕 𝑽𝒊𝒏,𝟏 𝑅 Golden Rules 𝑅 𝐼 𝑅 𝑅 vo Rf Ra va Rf Rb vb If Ra Rb Rc Rs 𝑅 𝑉 , 𝑅 If Ra Rb Rc Rs R f 𝑉 , Rf Rc VCC vo VCC vc for vo Rf ( va vb vc ) Rs vo ( va vb vc ) • Simply set all the resistors to be equal 52 52 3/2/2025 Difference Amplifier Circuit Consider applying two inputs, one to each input terminal (inverting and non-inverting) Common Op-Amp Circuit #5 Golden Rules 𝐼 and 𝐼 𝑅 𝑉 0 𝑉 𝑅 Difference Amplifier − + 𝑉 , + − 𝑉 , + 𝑉 + − − When we applied multiple inputs to a single input terminal (summing amplifier) the output was the (negative) weighted sum of the inputs. If we apply inputs to each input terminal it makes sense to guess we are going to get a weighted difference. 53 54 Difference Amplifier Circuit 𝐼 and 𝐼 𝑽𝒐𝒖𝒕 𝑽𝒊𝒏,𝟐 𝑅 1 − + 𝑽𝒊𝒏,𝟏 𝐼 𝑉 , + − 𝑉 , 𝟎𝐕 𝑉 , 55 𝐼 𝑉 , 𝑅 𝑉 , 𝑅 𝑉 𝑅 𝑉 , 𝑅 + − 𝑉 Difference Amplifier Circuit – More General 0 𝑉 • Consider the circuit on the left below compared to the first difference amplifier circuit shown on the right below + 𝑽𝒊𝒏,𝟐 Perform the same analysis as before. There is only one node where we use KCL. 𝑉 Both input terminals are Vin,2 − KCL @ Node 1: 𝐼 𝑉 , Golden Rules 𝑅 𝐼 𝑉 , 𝑅 𝑉 𝑅 𝑉 𝑅 𝑉 , 𝑅 𝑉 𝑅 𝑉 , 𝑅 𝑉 𝑅 𝑅 𝑉 , 𝑉 , 𝑅 𝑉 , 𝑅 𝑅 𝑉 , 𝑅 𝑉 , 𝑉 𝑉 , 𝑉 , 𝑅 𝑅 𝑉 , 𝑉 , 𝑉 , Difference + offset • What is the input-output relationship for the new circuit on the left? 56 56 3/2/2025 Difference Amplifier Circuit – More General Difference Amplifier Circuit – More General • Here is an example of a difference amplifier that uses the simplified expression on the previous slide since the resistor ratios are equal Rd Voltage division : v p vb Rc Rd Lots of algebra here, which we will not deal with! KCL at vn : vn va vn vo 0 Ra Rb vn ( Ra Rb ) Rb va Ra vo vo vn If Ra Rc Rb Rd Rb (vn va ) Ra (vn vo ) 0 Ra Rb ( Ra Rb ) R R ( R Rb ) R vb va b va b d a Ra Ra Ra ( Rc Rd ) Ra R R Rb Rd R vo a d vb va b Ra Rc Ra Rd Ra vo R Rb Rc Rb Rd R vb va b b (vb va ) Ra Rc Ra Rd Ra Ra vo If the resistors are picked properly then this circuit produces the true difference between the input voltages (no offset like the first circuit) Rb vb va Ra • Both resistor ratios are 1:5 so the simplified formula applies 57 57 58 58 Operation in the Linear Region Operation in the Linear Region • These example applications all depend on the op amps operating in the linear region • Consider this inverting amplifier circuit with +10V and -15V supply voltages Vout R2 80 Vs Vs 5Vs R1 16 • Consider operation with different input voltages • The output voltage of the op amp must always lie between the positive and negative supply voltages – otherwise saturation occurs 59 59 60 60 3/2/2025 Operation in the Linear Region Operation in the Linear Region • Consider operation with various input voltages • Is the op amp in the linear region? • Find the range of input voltage for which the op amp operates in its linear region Vout 5Vs At what input voltages will the output voltage exceed the allowable range of [+10, -15] volts? Vout 5Vs vs 2 V vo 5vs 15 vs 3 V 2 V vs 3 V 62 62 Design Example Design Example • Design an inverting amplifier with a gain of 10. Use +/-12V power supplies. Find the limits on the input to maintain linear operation. • Multiple possibilities for the resistors – one combination is shown Note: We usually choose resistors in the k-ohm to 10’s of k-ohm (or more) range to keep the currents and powers low • We know the design equation – vo Rf Ri vs only if VCC vo VCC • Choose the two resistors so that the ratio of the feedback resistors to the input resistor is 10, the desired gain. vo 10vs 12 vs 1.2 V vo 10vs 12 vs 1.2 V 63 63 61 61 vo 5vs 10 vo 10vs for 1.2 V vs 1.2 V With an op amp gain of 10, the maximum input voltage must be no more than +/- 1.2V to keep the output to no more than +/- 12V 64 64 3/2/2025 What do you need to know about op amps? • Recognize and know the names of all 5 primary terminals • Be able to reproduce the voltage transfer plot for an op amp and label the three regions of op amp operation • Know the feature of op amp circuits that tends to keep the op amp in the linear region – negative feedback • Know the ideal assumptions (golden rules) of the op amp and the simplifications in analysis these assumptions allow • Recognize and be able to analyze and design the four different basic op amp circuits: inverting amplifier, non-inverting amplifier, summing amplifier, difference amplifier • In general, be able to analyze arbitrary circuits containing one or more op amps by applying the circuit analysis and simplification methods from Chapter 4 65 65
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