Ideal Op Amps. The Two Golden Rules for circuits with ideal op-amps*

Transcription

1 Ideal Op Amps The Two Golden Rules for circuits with ideal op-amps* No voltage difference between op-amp input terminals No current into op-amp inputs * when used in negative feedback amplifiers 1

2 Approach To Solve All Op-amp Circuits First check to make sure the feedback is negative If not stop! Find the output voltage that will make the input difference 0 Assume V - is equal to V + Apply nodal analysis to find V out M. Horowitz E40M Lecture 19 2

3 Non-inverting Amplifier 3

4 Inverting Amplifier 4

5 Lecture 20 Op Amps & Instrumentation Amps Copyright 2017 by Mark Horowitz 5

6 By the End of Lecture, You Should Be Able To: Create a circuit that can amplifier a signal by 10 Or any number you chose Do it with either inverting or non-inverting amplifier Create filters with a gain greater than one Just replace some resistors in op-amp circuit with RC Analyze a differential and instrumentation amplifier The output voltage depends on only on the input difference 6

7 USEFUL OP AMPS CIRCUITS 7

8 Summing Amplifier 8

9 Current-to-Voltage Converter 9

10 OP AMP FILTERS 10

11 Adding Capacitors C1 Vin R1 R2 + 11

12 Adding Capacitors C1 Vin R1 + R2 12

13 Sketching the Bode Plot 20 log 10 V o /V s R 1 = 1 kω, R 2 = 100 kω, C1 = 160 nf f [Hz] 13

14 DIFFERENTIAL AMPLIFIERS 14

15 What Happens If We: Take an inverting amplifier and drive the other input? v1 v2 Not quite what we want. 15

16 Differential Amplifier 1.0 If R1 =R3, and R4=R2 16

17 SAFETY 17

18 Current Through Your Body is Dangerous I assume everyone has been zapped by static electricity before Some probably have touched 110V It doesn t feel good, But generally won t do permanent damage That is because your skin is not a good conductor Generally ~1MW 110V/1M = 110mA It takes mas to be dangerous Water makes your skin more conductive That is why you don t want 110V new the tub! 18

19 ECG Needs to Make Good Skin Contact Otherwise it is too hard to see the signal Use special pads to place on your skin This makes good connection to your body Warning! Warning! Now 100V could be fatal Machines that connect to these pads must follow safety rules Must limit the current through patient even if something fails We are going to use triple isolation Will protect you even if two things fail A TA must check your circuit before you attach it to yourself 19

20 Triple Isolation All leads that attach to the body must have >100K resistors This will limit max current through the person to safe levels The electronics will be run off a battery We will give you an isolated USB connector for your circuit Your ECG Gnd will not be directly connected to your laptop Gnd Even if your computer gets connected to 100V you will be safe Your circuit should be running off your solar charger battery The computer should be running from its battery So nothing will connect to the wall power 20

21 But We Need to Use a Differential Amplifier! Those 100K resistors are going to be a problem Need to use instrumentation amplifier Built for exactly this situation It essentially can be thought of as 3 amplifiers Two non-inverting amplifiers (so there is no input current) One differential amplifiers These parts are built to match very well So it is better than building the circuit yourself This is a common situation for many types of instruments Hence the name, instrumentation amplifier 21

22 Instrumentation Amp (Used in ECG Lab) Kind of looks like two noninverting amplifiers But they are connected together in a funny way Fortunately the IA can be solved using the Golden Rules: Write KCL for - input of the op amp Find the output voltage that satisfies KCL when the voltage at the - input is equal to the voltage on the + input M. Horowitz 22

23 Start with KCL at Inverting Input of Op Amp #1 At node v 1 and assuming no op amp input current, we have i 1 i 2 i 3 v 2 v 2 v 1 R G v 1 v o1 10k v 1 v ref 40k i 1 Since v IN v 1 and v IN v 2 v 1 i 3 i 2 v o1 v IN v IN R G v IN v o1 10k v IN v ref 40k v ref M. Horowitz 23

24 Now Find V o1 -- the Output Voltage of Op Amp #1 v IN v IN R G v IN v o1 10k v IN v ref 40k v 2 i 1 i 2 v o1 10k v IN 10k v IN v ref 40k v IN v IN R G v 1 i 3 v o1 v ref v o1 5v IN 4 v 10kv ref 4 IN v IN R G M. Horowitz 24

25 Next: KCL at Inverting Input of Op Amp #2 At node v 2 and assuming no op amp input i, we have i 4 i 1 i 5 v 2 v o v 2 40k v 2 v 1 v 2 v o1 R G 10k i 1 i 5 i 4 Since v IN v 1 and v IN v 2 v 1 i 2 v o v IN 40k v IN v IN R G v IN v o1 10k i 3 v o1 v ref M. Horowitz 25

26 Solve for V o v o v IN 40k v IN v IN R G v IN v o1 10k v 2 i 1 i 5 i 4 v o 40k v IN 40k v IN v IN R G v IN v o1 10k v 1 i 3 i 2 v o1 v o 5v IN 40kv IN v IN R G 4v o1 v ref M. Horowitz 26

27 The Finale: Combining The Results v o1 5v IN 4 v 10kv ref 4 IN v IN R G i 1 v 2 i5 i 4 v o 5v IN 40kv IN v IN R G 4v o1 i 2 v 1 v o 80k 5 R v IN v v IN ref G i 3 v o1 This confirms the gain expression v ref given in the 1NA126 data sheet! (using v ref = 0). M. Horowitz 27

28 By the End of Lecture, You Should Be Able To: Create a circuit that can amplifier a signal by 10 Or any number you chose Do it with either inverting or non-inverting amplifier Create filters with a gain greater than one Just replace some resistors in op-amp circuit with RC Analyze a differential and instrumentation amplifier The output voltage depends on only on the input difference 28

29 Designing More Complex Filters 29

30 Designing More Complex Filters 30

31 Instrumentation Amplifier 31

32 Instrumentation Amplifier 32

33 Instrumentation Amplifier 33

34 Instrumentation Amplifier And solving for v o2 34