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Name ______________
Date ______________
Operational Amplifier (I)
/ Reading:
Text: 5.1- 5.4. (or reference [1]: 4.4; 4.5; 4.6)
Appendix 5
Lecture notes
Questions marked (*) in this lab script.
Inverting Amplifier; Non-inverting Amplifier; Unity-Gain Follower;
Summing Amplifier.
Oscilloscope (Tektronix TDS210, dual channel, 60 MHz)
Function generator (BK Precision 4011A, sine, triangle, square, logic
level; to 5 MHz)
Breadboard (PB-503, powered, with a built-in function generator)
Digital multimeter (DMM, FLUKE 187)
LM741CN op amp (1)
LF411CN op amp (1)
1 M resistor (1)
1 k resistor (1)
10 k resistor (2)
15 k resistor (1 required; or use two resistors, 10k + 5k.)
20 k resistor (1)
100 k resistor (3)
L4: -1
1. The Inverting Operational Amplifier Circuit
Operational Amplifiers (Op-Amps) are almost always used with negative feedback since it
provides many beneficial effects. One of these effects is stabilization of the gain of the amplifier.
The operational amplifier has an intrinsic voltage gain of A, the open loop gain, without feedback.
This gain, while large is temperature dependent, and also varies from device to device even
within the same family.
Negative feedback results when a signal path exists between the amplifier output and its
inverting input. Fig. 4.1 shows this type of feedback provided by the impedance Z f.
Fig. 4.1
In addition, an impedance Z1 has purposely been introduced between the signal source and the
inverting input. The node where the currents add is called the summing junction (S.J.). At the
S.J., we have, by Kirchhoff's current law,
Normally, we choose components so that the currents i1 and if are very much greater
than iin. In effect, this requires that the input impedance, Z i, to the operational amplifier be much
greater than Z1 or Zf. If this condition is satisfied (or if the op-amp is close to an ideal one), then
We can express the currents i1 and if in terms of v1, vd and vo as follows,
Note that vd is the differential input voltage to the Op-Amp, in this case, it is just the voltage at the
inverting input. Hence, in terms of vd, we have vo = - Avd . Now we use this relation to eliminate vd
from Equations 3 and 4. This provides a relationship between vo and v1,
Remember, the open loop gain A is large so we can safely neglect unity (two places) in Equation
5. Hence, we get a very simple and useful expression for the gain of the inverting amplifier with
negative feedback,
L4: -2
Equation 6 shows that the voltage gain of this amplifier is a constant given by the ratio of two
impedances. Notice that the voltage gain no longer depends on the open loop gain A of the
operational amplifier. In practice, we may choose stable precision resistors for Zf and Z1 and
obtain an output voltage which is a precise multiple of the input voltage that will be independent of
frequency. The minus sign in Equation 6 shows that the output voltage is 180 o out of phase with
the input.
Input Impedance of the Inverting Op-Amp Circuit
The input impedance of the inverting operational amplifier circuit is important because it
determines the loading by the amplifier on the signal source. The input impedance may be
calculated as follows:
Referring to Fig 4.1 and using KLV at the input gives
Dividing by i1, we get
The quantity v1/i1 is the input impedance Zin of the inverting amplifier with negative feedback.
Note that the input impedance depends on two terms, namely Z1 and Vd/i1. The latter is the
apparent impedance between the summing junction and ground. This apparent impedance can
be expressed in terms of Zf and A using Equation 4 and vo = - Avd . This gives
Thus, the input impedance is
Typically, Zf is on the order of 1 kΩ and A  105 and therefore the apparent impedance is 10-2 Ω
and is usually negligible compared with Z1.
In summary, we have seen that, if the open loop gain of the amplifier is large, we can
have an amplifier circuit whose gain depends only on the ratio of passive components and whose
input impedance is equal to Z1.
2. The Non-Inverting Op-Amp Circuit
This circuit, also called a follower with gain, is shown in Fig 4.2. The circuit has negative
feedback via resistor Rf.
Fig. 4.2
L4: -3
The voltage gain is easily found by applying Kirchhoff's current law to the currents at the
summing junction, and assuming iin << i1 or if , we have i1 = -if . Since the voltage across Rf is VRf
= vo - (vd + v2), we have
We also have vo = -Avd, where A is the open loop gain of the Op-Amp. If we apply Kirchhoff's
voltage law to the input path, we get
Using Equation (8) to eliminate i1 and substituting vd = - vo/A into (9), we have
Equation (10) may be re-arranged so that the effect of the open loop gain is evident. That is,
Provided A/(1+Rf /R1)>>1, then Equation (11) becomes
Equation 12 shows two features. First, no phase difference exists between input and output;
secondly, the voltage gain depends only on the ratio of passive components. Furthermore, if R f is
zero and if R1 approaches infinity, then the circuit operates as a true voltage follower featuring
high input impedance and low output impedance (not proven here).
L4: -4
Note: ------------------------------------------------------------------------------------------------------------Before you build your first op amp circuit, we need to mention the following points:
1) The integrated circuit (IC) package should go to the breadboard as Fig. 4.3 shown.
The package style is “DIP”, which means “dual in-line package”.
2) The op amp always needs power, applied at two pins (see pin identifications in
Fig.4.4). Usually circuit diagrams omit the power connections. Also, op amp circuits
usually do not have direct connection between the IC chip and ground, though a
circuit always includes a ground (common reference called zero volts).
Fig. 4.3
Fig. 4.4
Lab 4-1: Inverting Amplifier and the input impedance --- To examine the properties
(voltage gain and input impedance) of the amplifier.
Connect the inverting op-amp circuit (the part in the dotted box in Fig. 4.5) in series with a
100 k resister (R). Apply a sine wave to the input as Vi’ from the function generator with amplitude
of 1 Vrms, set the signal frequency to about 100 Hz.
Use the scope to observe both input and output signals. We select Vi’ as a sine wave,
what should be the appearance of the voltage waveforms of Vi and Vo? (Be certain that as you do
the experiment your voltage waveforms do not deviate from the expected.)
Fig. 4.5
L4: -5
2. Measure Vi’, Vi and Vo using the DMM (set to AC), and record them into the table below.
Ri (ohm) ]
V i’ (
) |
Vi (
) | Vo (
|] Gv= Vo / Vi |
--------------- ] ------------------ |------------------- |------------------- |]------------------ |------------1M
100 k ]
10 k
1k @ 20 kHz ]
3. Use the scope to measure the voltages for one set of data (i.e., one Ri), compare the results
with those measured using DMM. What is the relationship between the two sets of data?
4. (1) Use your data to calculate the voltage gain Gv for each Ri, and record/list them in the
previous table.
* (2) Compare the voltage gains you obtained from your data with those predicted by assuming
an ideal inverting op-amp circuit. How do you account for discrepancies? (If you care to, you may
make accurate measurements of Rf and Ri using the DMM.)
L4: -6
5. (1) For each Ri, calculate the magnitude of the input impedance |Zin| of the inverting op-amp
circuit (the circuit part in the dotted box in Fig. 4.5), and put results in the previous table.
(2) If you look up the input impedance of the op-amp 741, you find that it is about 2 M (ohm). In
your measurements, do you see any evidence of the 2 M impedance? If not, why not?
Lab 4-2: Non-Inverting Amplifier
* 1. Construct an non-inverting amplifier as shown in Fig. 4.6 (Note that it is another way to draw
the circuit previously shown in Fig. 4.2). Calculate the voltage gain Gv by assuming an ideal noninverting op-amp circuit.
Gv (calculated) = _______
Fig. 4.6
2. Apply an input voltage of 1Vrms sine wave with frequency of 10 kHz. Use the DMM to measure
the input and output voltages.
Vin (measured)
= ____________
Vout (measured) = ____________
Calculate the voltage gain with your data. Compare the gain with the ideal value calculated
previously in step 1.
L4: -7
* 3. What is the input impedance of the circuit? Can you find it experimentally? You need to put a
resistor in series with the input for the measurement. Describe what you do for the measurement
and your results.
Lab 4-3 Unity-Gain Follower
1. Construct the circuit of Fig 4.7. Apply an input signal of 2 Vrms sine wave with frequency of 10
kHz. Use a DMM, and measure the input and output voltages.
Vin (measured) = ____________
Fig. 4.7
Vout (measured) = ____________
2. Compare the circuit voltage gain based on your data, with the theoretical unity gain.
3. (Optional) Measure Zin and Zout experimentally. Describe your approach clearly, and discuss
your results.
L4: -8
Lab 4-4 Summing Amplifier
1. Construct the circuit shown in Fig. 4.8, using 411 (which has the same pin identifications as
741 does). The 10 k adjustable resistor is provided on the PB-503, labelled as “10 k POT” or
“R1”. The circuit sums a DC level with the input signal, thus it lets you add a DC offset to a signal.
Fig. 4.8
2. Verify the gain Gv = -1.
Look at the input and output signal with the two channels of the scope, apply 1Vp sine
wave at 10 kHz from the functional generator. Sketch the waveforms you observed on the scope
screen, and record the vertical and horizontal sensitivities you used.
(Be sure to preset the 0 V line at the middle of the scope’s screen. For the purpose of this part, you should
adjust the “10 k POT” to make the offset level is 0 V, make sense?)
Vertical sensitivity = ______
Horizontal sensitivity = ______
Can you conclude the gain as you expect?
L4: -9
*3. What is the expected offset range, and why?
4. Confirm the offset range experimentally. Describe the method and conditions you used to
determine the offset range.
L4: -10