# A ω( )= R2A0 ω( ) R1A0 ω( )+ R1 + R2 A0( )

```OPERATIONAL AMPLIFIERS
EXPERIMENT 11:
LINEAR OP-AMP CIRCUITS
(revised 11/24/10)
In this experiment we will examine the properties of operational amplifier circuits with various
feedback networks. Circuits which perform four basic linear mathematical operations - addition,
subtraction, integration, and differentiation - will be studied.
We will use a model &micro;A741, operational amplifier. This is a general purpose, integrated-circuit op-amp
with detailed specifications listed in the appendix to this experiment. The op-amp requires a &plusmn;15 V
power source. We will use a small power supply that provides these voltages plus a zero to &plusmn;5 V
variable DC output. The op-amp will supply a maximum output current of about 25 mA and has typical
offset currents of about 20 nA. This implies that resistors in the range 1 kΩ to 100 kΩ should be used.
All of this information and more, including circuit suggestions, is shown on the component data sheet
included at the end of the lab. Note that as with most integrated circuits, the first two characters “&micro;A”
identify the manufacturer, and “741” is the relevant portion of the part number. The LM741, OP741, or
AD741 would be closely equivalent parts made by other companies. In most cases these can be freely
substituted, but you should check the manufacturers’ data sheets to be sure for parameters critical to
Use a scope for all measurements.
1.
(a)
(b)
Construct the operational feedback amplifier shown below with R1 = 1 kΩ and R2 = 20 kΩ
with vin grounded, adjust the pot on the circuit board for zero output voltage. Using sine
waves from the function generator for vin (with the amplitude set for 0.5 Volts peak-topeak), measure and tabulate the amplitude and phase of vout for 100 Hz ! f ! 1 MHz (take
VEE (–15V) power supplies must be connected to the proper pins and their returns to circuit
ground even though this is not conventionally shown on the schematic diagram.
For a feedback amplifier the gain is given by:
R2 A0 (&quot; )
V
A(&quot; ) = out =
VIN R1A0 (&quot; ) + R1 + R2
where A0(ω) is the open loop gain and A(ω) is the
closed loop gain. Use this formula and your measured
values
! of A(ω) to find A0(ω) at 20 kHz and 200 kHz.
Assuming that A0(ω) varies with frequency according
to:
A0
A0 (&quot; ) =
#
&quot;&amp;
%1+ j (
&quot;C '
\$
where ωC = 10π radians/s, find the DC open-loop gain, A0. Compare your result to
the typical value given in the “Large Signal Differential Voltage Amplification” plot in
the data
! sheet. Note that for frequencies &gt;&gt; ωC, all that matters is the product A0ωC.
This is called the “gain-bandwidth product” of the op-amp, and will be equal to the
closed loop gain &times; 3db closed loop corner frequency of your circuit.
1
OPERATIONAL AMPLIFIERS
2.
3.
Change R2 to 10 kΩ and set f = 1 kHz. Increase the amplitude of vin until vout exhibits
saturation at both positive and negative voltages. Sketch and determine the saturation
voltages.
(a) The slew rate of the amplifier is defined as the maximum rate of change of the output voltage.
Switch the input to square waves and set f = 10 kHz. Adjust the amplitude to obtain a peakto-peak output voltage of 10 Volts. Measure the slew rate by observing dvout/dt and compare
your result to the typical value listed in the appendix.
(b)
Suppose you want to use the amplifier to produce a sine wave output with an amplitude of
10 Volts peak-to-peak. What is the maximum frequency you can use before the output wave
begins to be distorted by the finite slew rate of the amplifier? Switch the input to sine waves
and observe what happens when you exceed that frequency. Sketch the input and output
waveforms.
4.
Set up the summing amp circuit shown below with Ri = Rf = 10 kΩ. Use the Lambda DC power
supply for V1, and the &plusmn;5 V supply for V2. Measure Vout for three or four different values of V1
and V2 (using both positive and negative values of V2) and verify that Vout = (− Rf /Ri)(V1 + V2).
5.
Set up the circuit shown below for amplifying the difference of two voltages. As in the previous
step, use Ri = Rf = 10 kΩ. Measure Vout for three or four different values of V1 and V2, and verify
that Vout = (Rf/Ri) (V2 − V1). If we define VOUT = AD (V2–V1) + AC ((V2+V1)/2), what should the
common mode gain AC of this circuit be? Can you measure it?
differential or “instrumentation” amplifier
2
OPERATIONAL AMPLIFIERS
6.
7.
(a)
Set up the differentiator circuit shown below with C = 100 nF and R = 2 kΩ. For the input
use a 2 Volt peak-to-peak, f = 1 kHz triangle wave. Sketch the input and output waves and
measure the magnitude of vout. Compare your measured value with the expected
result, vout = − RC x dvin/dt. Also, measure and tabulate the values of vout (no sketches
required) for f = 2 kHz with C = 100 nF, and for f =2 kHz with C= 50 nF.
(b)
Switch the input waveform to square wave and sketch vin and vout. Explain why vout looks
the way it does. (Consider the square wave as a Fourier series sum of sine waves.)
(a)
Set up the integrator circuit shown below, with C = 100 nF, RF = 200 kΩ, and R = 10 kΩ.
Use a 2 Volt peak-to-peak, f = 1 kHz square wave for vin. Sketch the input and output wave
forms and determine the magnitude of vout. Compare your measurement with the expected
result v out = !(1/ RC) &quot; # vin dt .
(b)
Observe what happens to the output voltage as you make RF larger and smaller. What
happens when RF is removed (=∞)? Explain why we need to have a feedback resistor in any
integrating circuit.
(c)
Switch the input waveform to triangle wave and sketch the resulting input and output
waveforms. In this case vout looks quite similar to a sine wave. See if you can understand
this result by writing down the integral of a triangle wave.
differentiator
integrator
3
LM741
Operational Amplifier
General Description
The LM741 series are general purpose operational amplifiers which feature improved performance over industry standards like the LM709. They are direct, plug-in replacements
for the 709C, LM201, MC1439 and 748 in most applications.
The amplifiers offer many features which make their application nearly foolproof: overload protection on the input and
output, no latch-up when the common mode range is exceeded, as well as freedom from oscillations.
The LM741C/LM741E are identical to the LM741/LM741A
except that the LM741C/LM741E have their performance
guaranteed over a 0˚C to +70˚C temperature range, instead
of −55˚C to +125˚C.
Schematic Diagram
DS009341-1
Offset Nulling Circuit
DS009341-7
&copy; 1999 National Semiconductor Corporation
DS009341
www.national.com
LM741 Operational Amplifier
May 1998
Absolute Maximum Ratings (Note 1)
Distributors for availability and specifications.
(Note 6)
LM741A
LM741E
LM741
LM741C
&plusmn; 22V
&plusmn; 22V
&plusmn; 22V
&plusmn; 18V
Supply Voltage
Power Dissipation (Note 2)
500 mW
500 mW
500 mW
500 mW
&plusmn; 30V
&plusmn; 30V
&plusmn; 30V
&plusmn; 30V
Differential Input Voltage
&plusmn; 15V
&plusmn; 15V
&plusmn; 15V
&plusmn; 15V
Input Voltage (Note 3)
Output Short Circuit Duration
Continuous
Continuous
Continuous
Continuous
Operating Temperature Range
−55˚C to +125˚C
0˚C to +70˚C
−55˚C to +125˚C
0˚C to +70˚C
Storage Temperature Range
−65˚C to +150˚C
−65˚C to +150˚C
−65˚C to +150˚C
−65˚C to +150˚C
Junction Temperature
150˚C
100˚C
150˚C
100˚C
Soldering Information
N-Package (10 seconds)
260˚C
260˚C
260˚C
260˚C
J- or H-Package (10 seconds)
300˚C
300˚C
300˚C
300˚C
M-Package
Vapor Phase (60 seconds)
215˚C
215˚C
215˚C
215˚C
Infrared (15 seconds)
215˚C
215˚C
215˚C
215˚C
See AN-450 “Surface Mounting Methods and Their Effect on Product Reliability” for other methods of soldering
surface mount devices.
ESD Tolerance (Note 7)
400V
400V
400V
400V
Electrical Characteristics (Note 4)
Parameter
Conditions
LM741A/LM741E
Min
Input Offset Voltage
Typ
Max
0.8
3.0
LM741
Min
LM741C
Typ
Max
1.0
5.0
Min
Units
Typ
Max
2.0
6.0
TA = 25˚C
RS ≤ 10 kΩ
RS ≤ 50Ω
mV
mV
TAMIN ≤ TA ≤ TAMAX
RS ≤ 50Ω
4.0
mV
RS ≤ 10 kΩ
6.0
Average Input Offset
7.5
15
mV
&micro;V/˚C
Voltage Drift
Input Offset Voltage
TA = 25˚C, VS = &plusmn; 20V
&plusmn; 10
&plusmn; 15
&plusmn; 15
mV
Input Offset Current
TA = 25˚C
3.0
TAMIN ≤ TA ≤ TAMAX
Average Input Offset
30
20
200
70
85
500
20
200
nA
300
nA
0.5
nA/˚C
Current Drift
Input Bias Current
TA = 25˚C
Input Resistance
TAMIN ≤ TA ≤ TAMAX
TA = 25˚C, VS = &plusmn; 20V
TAMIN ≤ TA ≤ TAMAX,
VS = &plusmn; 20V
Input Voltage Range
30
1.0
80
6.0
500
80
1.5
0.3
2.0
0.3
2.0
0.5
500
nA
0.8
&micro;A
MΩ
MΩ
&plusmn; 12
TA = 25˚C
TAMIN ≤ TA ≤ TAMAX
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80
0.210
&plusmn; 12
2
&plusmn; 13
&plusmn; 13
V
V
Electrical Characteristics (Note 4)
Parameter
(Continued)
Conditions
LM741A/LM741E
Min
Large Signal Voltage Gain
TA = 25˚C, RL ≥ 2 kΩ
VS = &plusmn; 20V, VO = &plusmn; 15V
VS = &plusmn; 15V, VO = &plusmn; 10V
Typ
Max
LM741
Min
Typ
50
200
LM741C
Max
Min
Typ
20
200
Units
Max
50
V/mV
V/mV
TAMIN ≤ TA ≤ TAMAX,
RL ≥ 2 kΩ,
VS = &plusmn; 20V, VO = &plusmn; 15V
VS = &plusmn; 15V, VO = &plusmn; 10V
VS = &plusmn; 5V, VO = &plusmn; 2V
Output Voltage Swing
32
V/mV
25
RL ≥ 10 kΩ
10
V/mV
&plusmn; 16
&plusmn; 15
V
V
RL ≥ 10 kΩ
&plusmn; 12
&plusmn; 10
RL ≥ 2 kΩ
TA = 25˚C
10
Current
TAMIN ≤ TA ≤ TAMAX
10
Common-Mode
TAMIN ≤ TA ≤ TAMAX
RS ≤ 10 kΩ, VCM = &plusmn; 12V
Rejection Ratio
RS ≤ 50Ω, VCM = &plusmn; 12V
Supply Voltage Rejection
Ratio
25
35
&plusmn; 14
&plusmn; 13
&plusmn; 12
&plusmn; 10
25
&plusmn; 14
&plusmn; 13
V
25
mA
40
mA
70
80
95
86
96
90
70
90
dB
RS ≤ 10 kΩ
TA = 25˚C, Unity Gain
77
96
77
96
dB
&micro;s
0.25
0.8
0.3
0.3
Overshoot
6.0
20
5
5
Slew Rate
Supply Current
Power Consumption
LM741A
dB
dB
Rise Time
Bandwidth (Note 5)
V
TAMIN ≤ TA ≤ TAMAX,
VS = &plusmn; 20V to VS = &plusmn; 5V
RS ≤ 50Ω
Transient Response
V/mV
VS = &plusmn; 20V
RL ≥ 2 kΩ
VS = &plusmn; 15V
Output Short Circuit
15
TA = 25˚C
TA = 25˚C, Unity Gain
TA = 25˚C
0.437
1.5
0.3
0.7
TA = 25˚C
VS = &plusmn; 20V
VS = &plusmn; 15V
80
VS = &plusmn; 20V
TA = TAMIN
%
MHz
0.5
0.5
V/&micro;s
1.7
2.8
1.7
2.8
50
85
50
85
150
mA
mW
mW
165
mW
135
mW
LM741E
TA = TAMAX
VS = &plusmn; 20V
TA = TAMIN
150
mW
150
mW
LM741
TA = TAMAX
VS = &plusmn; 15V
TA = TAMIN
TA = TAMAX
60
100
mW
45
75
mW
Note 1: “Absolute Maximum Ratings” indicate limits beyond which damage to the device may occur. Operating Ratings indicate conditions for which the device is
functional, but do not guarantee specific performance limits.
3
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Electrical Characteristics (Note 4)
(Continued)
Note 2: For operation at elevated temperatures, these devices must be derated based on thermal resistance, and Tj max. (listed under “Absolute Maximum Ratings”). Tj = TA + (θjA PD).
Thermal Resistance
θjA (Junction to Ambient)
θjC (Junction to Case)
Cerdip (J)
DIP (N)
HO8 (H)
SO-8 (M)
100˚C/W
100˚C/W
170˚C/W
195˚C/W
N/A
N/A
25˚C/W
N/A
Note 3: For supply voltages less than &plusmn; 15V, the absolute maximum input voltage is equal to the supply voltage.
Note 4: Unless otherwise specified, these specifications apply for VS = &plusmn; 15V, −55˚C ≤ TA ≤ +125˚C (LM741/LM741A). For the LM741C/LM741E, these specifications are limited to 0˚C ≤ TA ≤ +70˚C.
Note 5: Calculated value from: BW (MHz) = 0.35/Rise Time(&micro;s).
Note 6: For military specifications see RETS741X for LM741 and RETS741AX for LM741A.
Note 7: Human body model, 1.5 kΩ in series with 100 pF.
Connection Diagram
Metal Can Package
Ceramic Dual-In-Line Package
DS009341-2
Note 8: LM741H is available per JM38510/10101
DS009341-5
Order Number LM741H, LM741H/883 (Note 8),
LM741AH/883 or LM741CH
See NS Package Number H08C
Note 9: also available per JM38510/10101
Note 10: also available per JM38510/10102
Order Number LM741J-14/883 (Note 9),
LM741AJ-14/883 (Note 10)
See NS Package Number J14A
Dual-In-Line or S.O. Package
Ceramic Flatpak
DS009341-6
DS009341-3
Order Number LM741W/883
See NS Package Number W10A
Order Number LM741J, LM741J/883,
LM741CM, LM741CN or LM741EN
See NS Package Number J08A, M08A or N08E
www.national.com
4
&micro;A741, &micro;A741Y
GENERAL-PURPOSE OPERATIONAL AMPLIFIERS
SLOS094B – NOVEMBER 1970 – REVISED SEPTEMBER 2000
TYPICAL CHARACTERISTICS
OPEN-LOOP SIGNAL DIFFERENTIAL
VOLTAGE AMPLIFICATION
vs
SUPPLY VOLTAGE
MAXIMUM PEAK OUTPUT VOLTAGE
vs
FREQUENCY
&plusmn; 16
AVD – Open-Loop Signal Differential
Voltage Amplification – V/mV
&plusmn; 18
400
VCC+ = 15 V
VCC – = –15 V
RL = 10 kΩ
TA = 25&deg;C
&plusmn; 14
&plusmn; 12
&plusmn; 10
&plusmn;8
&plusmn;6
&plusmn;4
VO = &plusmn;10 V
RL = 2 kΩ
TA = 25&deg;C
200
100
40
20
&plusmn;2
0
100
10
1k
10k
100k
1M
0
2
4
6
8
10
12
14
16
18
20
VCC &plusmn; – Supply Voltage – V
f – Frequency – Hz
Figure 6
Figure 7
OPEN-LOOP LARGE-SIGNAL DIFFERENTIAL
VOLTAGE AMPLIFICATION
vs
FREQUENCY
110
VCC+ = 15 V
VCC – = –15 V
VO = &plusmn;10 V
RL = 2 kΩ
TA = 25&deg;C
100
AVD – Open-Loop Signal Differential
Voltage Amplification – dB
VOM – Maximum Peak Output Voltage – V
&plusmn; 20
90
80
70
60
50
40
30
20
10
0
–10
1
10
100
1k
10k
100k
1M
10M
f – Frequency – Hz
POST OFFICE BOX 655303
• DALLAS, TEXAS 75265
9
&micro;A741, &micro;A741Y
GENERAL-PURPOSE OPERATIONAL AMPLIFIERS
SLOS094B – NOVEMBER 1970 – REVISED SEPTEMBER 2000
TYPICAL CHARACTERISTICS
COMMON-MODE REJECTION RATIO
vs
FREQUENCY
OUTPUT VOLTAGE
vs
ELAPSED TIME
28
VCC+ = 15 V
VCC– = –15 V
BS = 10 kΩ
TA = 25&deg;C
90
80
24
VO – Output Voltage – mV
CMRR – Common-Mode Rejection Ratio – dB
100
70
60
50
40
30
20
&Iuml;&Iuml;
20
90%
16
12
8
10%
0
10
tr
0
–4
1
100
10k
1M
100M
0
0.5
Figure 9
Figure 8
VOLTAGE-FOLLOWER
LARGE-SIGNAL PULSE RESPONSE
8
VCC+ = 15 V
VCC– = –15 V
RL = 2 kΩ
CL = 100 pF
TA = 25&deg;C
6
Input and Output Voltage – V
1
t – Time − &micro;s
f – Frequency – Hz
4
VO
2
0
VI
–2
–4
–6
–8
0
10
20
30
40
50
60
70
t – Time – &micro;s
Figure 10
10
VCC+ = 15 V
VCC– = –15 V
RL = 2 kΩ
CL = 100 pF
TA = 25&deg;C
4
POST OFFICE BOX 655303
• DALLAS, TEXAS 75265
80
90
1.5
2
2.5
```