İzmir University of Economics
EEE201 Electrical Circuits I Lab
EXPERIMENT 8:
Operational Amplifier (Opamp) II:
Summer, Differentiator and Integrator
Objective:
The students will be able to learn:

How to use of an Opamp to perform linear algebraic and dynamical analog signal
processing tasks.
B. Background
B.1. Basic Signal Waveforms
Although the term DC stands for "direct current", DC often is used to refer "constant" signals.
It is possible to refer a constant voltage as DC voltage, or similarly a constant current as DC
current. The waveform of a 10 volt DC voltage is plotted in Fig.8.1.
10
VCC, volts
t, sec
Figure 8.1. DC Voltage waveform
In electrical circuits, besides DC signals, most commonly used signal types are sinusoidal,
triangular and square waveforms as shown in Fig. 8.2.
xS(t)
Sinusoidal
t, sec
xS(t)
Triangular
t, sec
xS(t)
Square Wave
t, sec
Figure 8.2. (a) Sinusoidal Waveform, (b) Triangular Waveform, (c) Square Waveform
Above waveforms are periodic. Usually the time reference t=0 sec is not reachable. For periodic
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signals, the period must be defined. The period T is measured as shown below in Fig. 8.3.
xS(t)
T
Vp
Vp-p
t, sec
Figure 8.3
It is usually more convenient to measure peak-to-peak voltage instead of peak voltage. The
peak-to-peak voltage Vp-p is defined in Fig. 8.3. If the periodic voltage has zero average value,
then the peak voltage is just the half of peak-to-peak voltage, i.e., Vp = Vp-p/2.
Duty cycle is a property of square waves. A perfectly symmetrical square wave has a 50% duty
cycle. A waveform which is on for 1 ms and off for 9ms has a 10% duty cycle. Though this
waveform is not “square” it is still commonly referred to as a square wave.
B.2. Oscilloscope
Oscilloscope is a device that is used to display periodic waveforms. (If a signal is not periodic,
then sample values are taken and then displayed.) The oscilloscope that is used in the
laboratory is given in Fig. 8.4.
Figure 8.1. Tektronix TDS100 Oscilloscope
An oscilloscope has always a display section (monitor) on the front panel to display the time
waveform. Only voltage waveforms are measured and displayed using an oscilloscope. If current
waveforms are needed to be measured, a voltage that is proportional to the current must be
generated.
The display details of the screen of the oscilloscope used in the laboratory is given on Figure
8.1. The display section has 10 horizontal (time) divisions and 8 vertical (voltage) divisions. It is
possible to measure two signals (Channel 1 – CH1 and Channel 2- CH2) simultaneously using
TDS1000.
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Figure 8.2. Display Section of Tektronix TDS100 Oscilloscope
The voltage value (500mV) on the right to CH1 indicates the voltage scale of each vertical
division for CH1 (yellow waveform). According to this scaling, CH1 has a peak-to-peak voltage
of approximately 3.6x500mV=1.8 V. For Channel 2 (light blue waveform) has peak-to-peak
voltage of approximately 2.6 V since the voltage scale for CH2 is 1.00V as given on the display.
For time measurements, the scale of the each division is given on the right of M parameter. For
the above signals, each time division is 25.0nsec. Then the period of CH1 is 2x25.0nsec=50
nsec. Similarly the period of CH2 is just 25.0 nsec.
The frequency of a signal is determined using T as f=1/T. The unit of the frequency is hertz
(Hz).
For CH1 voltage waveform, f = 1/50 nsec = 20x106 Hz = 20 MHz as displayed on the screen as
20.0002MHz. For CH2 f = 1/25 nsec = 40x106Hz = 40 MHz.
The signs 1 and 2 indicate the zero voltage axis of the voltages at CH1 and CH2
respectively.
B.2. Function Generator
A function generator is a very versatile instrument that is extensively used in electronics,
mechanics, bioengineering, physics and many other fields. It allows you to create a wide variety
of synthesized electrical signals and waveforms for testing and diagnostic applications. Figure
8.3 shows the most common functions such as the sine, square, triangle and ramp functions.
Figure 8.3. Waveforms generated by a function generator
Each of the waveforms can be adjusted through the front panel controls or remotely for
frequency, amplitude, DC offset voltage and duty cycle. As an example, let us look at a sine
function described by the following equation,
v(t)=VA sin(21 f t) + VOFF
in which f is the frequency, VA the amplitude, and VOFF the offset voltage as shown in Figure 2.
Instead of amplitude one often used the RMS (Root Mean Square) value to express the signal
voltage level. For a sine wave the RMS value is the amplitude divided by the square root of 2 or
VRMS = VA/1.41. The RMS is the most useful way to specify AC signal amplitudes.
Figure 8.4 Sine wave with amplitude VA , frequency f, and offset VOFF
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Figure 8.5 Block diagram of the Agilent 33120A waveform generator.
The heart of the instrument is a random-access-memory (RAM) which stores the function (e.g.
sine) in digital form. This memory is addressed sequentially through an increment register. The
frequency of the voltage waveform is proportional to the speed with which the RAM is
addressed. The output data from the memory is a digital bit stream which is converted in the
actual (analog) wave shape through a Digital-to-Analog Converter (DAC) (see Lab 8) as
illustrated in Figure 3.A low pass filter at the output ensures a smooth waveform. The amplitude
and offset are controlled by changing the signal gain of the amplifier at the output of the DAC.
The front panel of the HP 33120A is shown in Figure 5. There are two outputs on the right hand
side of the front-panel. One is called OUTPUT and is the regular output terminal at which the
specified waveform appears.. The other output terminal is called SYNC and provides a digital
signal (TTL levels) that is "high" when the waveform's output is positive, relative to the zero
level (or the DC offset value). The SYNC signal is "low" when the output is negative. The SYNC
signal is often used as a trigger signal. Both output terminals are of the "BNC" type, which can
be connected to a coaxial cable (i.e. a shielded cable).
Figure 8.6 Front panel of the HP 33120A function generator/Waveform generator
In order to set the amplitude, frequency and offset voltage of a waveform, one needs to enter
numbers. Numbers can be entered in three ways:
(1) Use the circular knob and > and < keys. One of the digits will be blinking on the display.
When you turn the large circular knob you can increase or decrease the number that is blinking.
(2) Use the arrow keys <, >, up or down
(3) Use the "Enter Number" mode to enter the number with the appropriate units shown on the
right side of the panel. First push the "ENTER NUMBER" key, followed by the number (see green
numbers next to the keys on the front panel) and the units. At the end, push the ENTER key to
enter the number (see Figure 6). To cancel the number mode, press SHIFT CANCEL keys.
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Figure 8.7 Entering numbers using the "Enter Number" mode
At power-on the function generator will output a sine wave of 1kHz and amplitude of 100mV
peak-to-peak (for a 50 Ohm load resistance - see above). You can select another function or
change the frequency, amplitude and offset voltage using the MODIFY keys.
B.3. Weighted Summer
Rf
E
R1
I-
R2
VV+ I+
V1
V2
-
Vo
+
-E
Figure 8.8 Weighted Summer
B.4. Differentiator
R
E
C
I-
Vin
VV+ I+ +
Vo
-E
Figure 8.9 Differentiator
B.5. Integrator
C
E
R
Vin
I-
VV+ I+ +
Vo
-E
Figure 8.9 Integrator
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B.6. Differential Amplifier
R2= 47 KΩ
R1=4.7 KΩ
V1
E
IVV+ I+
R3
V2
R4
-
Vo
+
-E
B.7. Schmitt trigger (Hysteresis Phonemenon)
Schmitt trigger have different triggers points for rising edge and falling edge. It can be used to
reduce false triggering. It is positive feedback circuit. Connect 500 Hz, 5 VPP triangle wave. Look
at both the input and the outpu on the scope. Determine the hysteresis, i.e. the difference
between the turn-on and turn-off voltages.
B.8. Logarithm
B.9. Exponentiator
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B.10. Active Rectifier
C. In-Lab Experimental Work
Task C.1.: Construct the summer circuit in Figure 8.9. Then, turn on function generator.
Display both the input and the output on an oscilloscope. Describe what is happening.
Task C.2: Construct the differentiator circuit. Choose R1=47K, C=0.1micro Farad. Input a
square wave to the integrator. Display both the input and the output on an oscilloscope.
Describe what is happening.
Task C.3: Repeat C.3.1 for the integrator circuit with the same parameters R1=47K,
C=0.1micro Farad. Describe what is happening.
Task C.4: Construct the Schmitt trigger circuit. Describe what is happening.
Task C.5: Construct the difference amplifier circuit. Describe what is happening.
Task C.6: Construct the logarithm circuit. Describe what is happening.
Task C.7: Construct the exponentiator circuit. Describe what is happening.
Task C.8: Construct the active rectifier circuit. Describe what is happening.
D. Post-Lab Tasks: Lab Report
The lab report should have the information contained in the pre-lab assignment and also the
answers of the following questions. The lab report should be submitted at the beginning of the
succeeding lab session.


Explain
o What you have done in this lab.
o How do you measure the quantities related to the the experiment.
Reply the questions in the Tasks C.1, C.2 and C.3.
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