Chapter 30 Operational Amplifiers

2 Introduction Characteristics –High input impedance –Low output impedance –High open-loop gain –Two inputs –One output –Usually + and – dc power supplies

3 Introduction Ideal Characteristics –z in (inverting) ≈ ∞ –z in (non-inverting) ≈ ∞ –z out ≈ 0 –A v ≈ ∞ - + V-V- V+V+ Output Inverting Input Non-Inverting Input

4 Introduction Uses –Comparators –Voltage amplifiers –Oscillators –Active filters –Instrumentation amplifiers - + V-V- V+V+ Output Inverting Input Non-Inverting Input

5 Introduction Single-ended amplifier –One input grounded –Signal at other input Double-ended amplifier/Differential amplifier –Signals at both inputs - + V-V- V+V+ Output Inverting Input Non-Inverting Input

6 Differential Amplifier and Common-Mode Signals Basic differential amplifier –Q 1 identical to Q 2 –R C1 = R C2 – I C1 = I C2 and emitter currents equal –Also, I C ≈ I E for high β –and V BE ≈ 0.7 V Similar calculation of Bias

7 Differential Amplifier and Common-Mode Signals ◦ ◦ RERE –V EE IEIE __ _ - __ _ - R C2 R C1 I C1 I C2 V CC Q1Q1 Q2Q2

8 RERE –V EE IEIE R C2 R C1 I C1 I C2 V CC Q1Q1 Q2Q2 __ _ - ◦ ◦ __ _ - Differential Amplifier and Common- Mode Signals Apply same signal to both Bases V out = V out1 – V out2 ≈ 0 –Eliminates common- mode signals –60 Hz –Noise

9 Differential Amplifier and Common- Mode Signals Apply sinusoids to both bases: –Same amplitude, 180° difference in phase, if V in1 = –V in2 V out = 2V in RERE –V EE IEIE Q1Q1 Q2Q2 __ _ - ◦ R C2 R C1 I C1 I C2 V CC ◦ __ _ -

10 Differential Amplifier and Common- Mode Signals Common-mode signals –Differential voltage gain also called open-loop voltage gain 20,000 ≤ A v ≤ 200,000

11 Differential Amplifier and Common- Mode Signals Common-mode signals – Common-mode voltage gain

12 Differential Amplifier and Common- Mode Signals Common-mode rejection ratio (CMRR) –Equations –Values

13 Differential Amplifier and Common-Mode Signals Noise –Static in audio signal –Increases as signal is amplified –Common mode signal –Significantly reduced by differential amplifier __ _ - __ _ v noise v in

14 Negative Feedback Op-amp –Large differential, open-loop voltage gain A vol ≈ 100,000 –Small input yields saturated output (V CC or V EE )

15 Negative Feedback Negative feedback –Returns a portion of output signal to the input –Open-loop voltage gain decreased

16 Negative Feedback Input impedance still high Output impedance low Circuit voltage gain, A v –Adjustable –Stable - + Negative Feedback __ _ - v in v out

17 Inverting Amplifier Basic circuit

18 Inverting Amplifier Output 180° out of phase with input Significant decrease in gain –Gain now called closed-loop voltage gain Output impedance ≈ 0 v d ≈ 0

19 Inverting Amplifier Inverting input at virtual ground, v in(-) ≈ 0 i in to op-amp ≈ 0 Input current only dependent on v in and R 1 A vcl only dependent on input resistor and feedback resistor

20 Inverting Amplifier - + __ _ - v out(OC) vdvd +-+- R in RFRF -+-+ __ _ - v in R1R Model v d ≈ 0 R in ≈ ∞ i in = i f z in ≈ R 1 i = 0 i in ifif R out A vol v d internal

21 Inverting Amplifier - + __ _ - i out(sc) vdvd R in RFRF -+-+ __ _ - v in R1R i = 0 i in ifif R out i1i1 __ _ - A vol v d internal Low output impedance

22 Non-Inverting Amplifier Circuit

23 The Non-Inverting Amplifier Very high input impedance Voltage gain related to the two resistors Very low output impedance Excellent buffer

24 Non-Inverting Amplifier Differential voltage –v d ≈ 0 Input current to op-amp –i = 0 Closed-loop voltage gain (A vcl ) is a resistor ratio

25 Non-Inverting Amplifier

26 Non-Inverting Amplifier Model Input impedance - + __ _ - v out vdvd R in RFRF -+-+ __ _ - v in R1R1 i in ifif R out A vol v d internal z in

27 Non-Inverting Amplifier Model Output impedance - + __ _ - vdvd R in RFRF -+-+ __ _ - R1R1 i in ifif R out A vol v d internal __ _ - i out(sc) i2i2

28 Non-Inverting Amplifier Very high z in Very low z out Good buffer circuit Also called voltage follower (gain = 1) Or adjustable gain > 1

29 Non-Inverting Amplifier Voltage Follower Buffer Circuit –Gain = 1 –High impedance source drives low impedance load

30 Op-Amp Specifications LM 741 series –Inexpensive –Widely used –Good general specifications –Characteristic of all op-amp specifications Provide Minimum, Typical, and Maximum ratings

31 Op-Amp Specifications Input Offset Voltage, V io –LM741C, V io typical is 2 millivolts –Model is voltage source with value, V io in series with + input

32 Op-Amp Specifications Input Offset Voltage, V io –Without feedback this would saturate output with no input –With negative feedback, output due to V io is closed-loop gain times V io

33 Op-Amp Specifications Input Offset Current, I os I os = Difference between bias currents at + and – inputs of op-amp 741C typical I os is 20 nanoamps Multiplying resistor used to measure I os

34 Op-Amp Specifications Input Resistance –741C: minimum =.3 MΩ, typical = 2 MΩ Open-Loop Voltage gain (A vol ) –741C: A vol = Large Signal Voltage Gain minimum = 20,000, typical = 200,000 –Closely related to Bandwidth, BW

35 Op-Amp Specifications Gain-bandwidth product –741C = 1,000,000 = 10 6 MHz

36 Op-Amp Specifications Gain versus frequency curve for op-amp

37 Op-Amp Specifications Slew rate –Maximum rate of change of output voltage 741C maximum slew rate = 0.5 V/μsec

38 Op-Amp Specifications Fastest time for output to go from 0 to 10 volts is 20 μsec Can distort waveforms that have too fast a rise time

39 Op-Amp Specifications Slew rate required for Sinusoid with frequency f and amplitude A Maximum amplitude of a sine wave with frequency f for a given slew rate

40 Op-Amp Specifications Bias Compensation: use R C = R 1 ||R F

41 Troubleshooting an Op-Amp Circuit Problems occur when circuit is first built Most important –Correct connection of dual power supply Connecting a – supply to a + input (or vice versa) can burn out an op-amp Single earth ground Short connecting wires