1	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 ≈ ∞
4	Introduction Uses Comparators Voltage amplifiers Oscillators Active filters Instrumentation amplifiers
5	Introduction Single-ended amplifier One input grounded Signal at other input Double-ended amplifier/Differential amplifier Signals at both inputs
6	Differential Amplifier and Common-Mode Signals Basic differential amplifier Q₁ identical to Q₂ 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
8	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
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
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
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 R₁ A_vcl only dependent on input resistor and feedback resistor
20	Inverting Amplifier
21	Inverting Amplifier
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
27	Non-Inverting Amplifier Model Output impedance
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 = 10⁶ 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 = R₁\|\|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