Jacobs University Bremen Natural Science Laboratory Electrical Engineering Module II Spring Semester 2014

Jacobs University Bremen
Natural Science Laboratory
Electrical Engineering Module II
Spring Semester 2014
Course 300112
Instructors
- Prof. Werner Bergholz and
- Uwe Pagel
e-mail
- [email protected]
- [email protected]
Website
- http://www.faculty.jacobs-university.de/upagel/GeneralEELab
February 20, 2014
tel.: +49 421 200 3111
tel.: +49 421 200 3114
Contents
I
General remarks on the course
5
1 Grading of the course
1.1 About the Group Quiz . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 About the Final . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 About the Lab reports . . . . . . . . . . . . . . . . . . . . . . . . . .
6
6
6
6
2 Report Writing Guidelines
2.1 Report Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 An advice to save your time . . . . . . . . . . . . . . . . . . . . . . .
2.3 You are not responsible for the report - what to do? . . . . . . . . . .
8
8
9
9
3 Manual Guideline
10
3.1 Circuit Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Values in Circuit Diagrams . . . . . . . . . . . . . . . . . . . . . . . . 12
II
Experiments
13
4 Experiment 1 : Usage of Oscilloscope
4.1 Objective . . . . . . . . . . . . . . . . .
4.2 Theory . . . . . . . . . . . . . . . . . . .
4.3 Preparation . . . . . . . . . . . . . . . .
4.4 Part 1 : Usage of the Vertical Control . .
4.5 Part 2 : Usage of the Horizontal Control
4.6 Part 3 : Trigger Section . . . . . . . . .
4.7 Part 4 : Using the Probe . . . . . . . . .
4.8 Part 5 : Discharging a capacitor . . . . .
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14
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31
5 Experiment 2 : AC Properties and Measurements
5.1 Objective . . . . . . . . . . . . . . . . . . . . . . .
5.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Part 1 : Measure AC-Signal Properties . . . . . . .
5.4 Part 2 : Measure AC Circuit Properties . . . . . . .
5.5 Evaluation . . . . . . . . . . . . . . . . . . . . . . .
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49
50
6 Experiment 3 : Filter
6.1 Objective . . . . .
6.2 Theory . . . . . . .
6.3 Part 1 : Hi-Pass . .
6.4 Part 2 : Notch . . .
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6.5
Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
7 Experiment 4 : The Wheatstone bridge
7.1 Objective . . . . . . . . . . . . . . . . . . .
7.2 Theory . . . . . . . . . . . . . . . . . . . . .
7.3 Part 1 : Balanced DC Wheatstone bridge . .
7.4 Part 2 : Unbalanced DC Wheatstone bridge
7.5 Part 3 : Balanced AC Wheatstone bridge . .
7.6 Evaluation . . . . . . . . . . . . . . . . . . .
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9 Experiment 6 : Solar Cells
9.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2 Theory & General Setup . . . . . . . . . . . . . . . . . . . . . . . . .
9.3 Part 1 : Dark/Illuminated forward/reverse U-I characteristic . . . . .
9.4 Part 2 : I-U characteristic with different illumination and temperature
9.5 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
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III
68
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8 Experiment 5 : JFET
8.1 Objective . . . . . . . . . . . . . . . . . . . .
8.2 Theory . . . . . . . . . . . . . . . . . . . . . .
8.3 Part 1 : Measure IDSS and VP . . . . . . . . .
8.4 Part 2 : 2 Pole Current Source . . . . . . . . .
8.5 Part 3 : Current Source with auxiliary supply
8.6 Evaluation . . . . . . . . . . . . . . . . . . . .
Additional Information
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A Appendix
69
A.1 Hardcopy from oscilloscope screen . . . . . . . . . . . . . . . . . . . . 69
3
4
Part I
General remarks on the course
5
1. Grading of the course
All grades are collected in percent according to the Jacobs grading scheme. The
final grade is calculated as the weighted average of the following components:
Group Quiz for each experiment (written) Team
5%
Exam (written, during finals)
Individual 50%
Lab Report
Individual 45%
Any missing or incomplete component means fail of the course.
1.1
About the Group Quiz
The Group Quiz takes place before EVERY experiment. It will last for about 15
minutes and will ask simple questions about the main topics of the experiment. This
quiz should assure that the group is prepared for the session. All members of the
group will get the same grade.
1.2
About the Final
The final is like a normal final at the end of the semester. It will take place during the
examination week. The topics are about problems around lab work, the instruments,
and the executed experiments.
1.3
About the Lab reports
1. Submission of the requested number of reports is mandatory. A missing report
means fail of the course.
2. Every group (2 or 3 students) has to submit reports for each experiment. The
group is responsible on its own how to distribute the work!
3. Every member of a group has to write 4 reports. The reports for experiment
1 and 2 ( ’Oscilloscope’ and ’AC Properties and Measurement’) are
mandatory!
Since the workload differs on each experiment, define the responsibility for each
report in the first session to balance the workload for each member of the group.
The instructor/TA may give some advice!!
4. Grading of reports is done individually, i.e. each student is given his grade for
the lab reports written by him. The other student(s) of the group has/have to
release the raw data taken during the experiment. Submission of these data
is easily done by Email and should happen directly after the experiment.
5. The deadline for submission of a report is the second weekend after execution,
Sunday evening 24:00! (In other words you should submit after nine or ten
days after the experiment). In general:
6
a. Only those reports are treated as delivered which include a sufficient
amount of gradable content!!!!
Rule of thumb: Reports without Experimental Set-up and Results and -SOLVED- Evaluation section definitely do not have
enough content!
b. Reports submitted after the deadline will be downgraded by one full mark
per day (15.01%). After 7 days the report counts as not submitted!!!!
These strict rules reflect the importance of writing reports to achieve the goal
of the lab course.
6. Return of the handed in report is usually about 2-3 days after delivery. If you
like you can correct and redeliver the report during the next seven days. The
grade will be adjusted dependant on your corrections.
This part of the report procedure is especially important so that you do not
only get feedback on how to improve but that you actually can benefit from
spending that extra amount of time, both in terms of your grade and what
you have learned.
7. In case of cheating or plagiarism (marked citations are allowed but no complete
copies from a source) we will follow ’The Code of Academic Integrity’ and
the report will be counted as not submitted.
Note that there there can be more consequences of a disciplinary
nature depending on the circumstances.
7
2. Report Writing Guidelines
2.1
Report Structure
The main purpose for a lab report is to enable others to duplicate the work in a
straightforward manner and to communicate the results. When preparing the report
you can use word processors, spreadsheets, graphic and CAD tools. In case of computer problems a hand written report is fine too! Submitting is possible on paper
or by Email. Preferred format is PDF. Try to avoid special formats. Convertors to
PDF are available for all programs and systems.
A report should be as short as possible but contain all necessary information. It
should be presented in the following (or a similar!!) format (numbering is mandatory):
1. Cover Sheet
• Title (name of the experiment)
• Location, Date of the experiment, Semester
• Names of the students in the group
• and important - Name of the author of the report
• also important - IRC mailbox number
2. Introduction
Objective of the experiment and a short summary of the theory.
3. Experimental Set-up and Results
This section is the documentation of the conducted experiment:
• Show the experimental set-up
• Show the results of the experiment.
4. Evaluation
Here you should answer all the questions from the Evaluation section(s). Answer as short as possible. For any calculation show the used formulas together
with the numbers and units. The result should have a reasonable number of
digits.
Depending on the experiment item 3 and 4 may have several subsections.
In this case it is sufficient to specify the used instruments only once in the
beginning of the section!
5. Conclusion
This is the final part of the report! Here you should summarize the results
and compare them to theory. Draw your conclusions related to the topic of
the experiment. Address directly what has been learned in lab. Discuss the
possible errors and deviations so far not already done during evaluation.
8
6. References
List -ALL- sources you used to write the report.
You can find a skeleton lab report on the course web page under
http://www.faculty.jacobs-university.de/upagel/GeneralEELab/Extra_Docu/
Sample_Report.pdf
2.2
An advice to save your time
When doing the measurements, have tables prepared before the experiment, plot
the graphs simultaneously either by hand on graph paper or in Excel, using the
”XY (Scatter)” option. In this way you will see odd results straight away. With a
theory already written and preparation in this manner the quiz is no problem and
50% of your lab report is already done when leaving the lab. One hour preparation
will save you 2 - 3 hours later!
2.3
You are not responsible for the report - what
to do?
It is essential that you also work on the experiment. For your own records and
to get a full documentation about the experiment (-you might have similar problems/experiments during the next semesters-) you should at least bring the data into
a ’readable’ form and you should answer the evaluation questions. And by the way,
this is important to survive the exam! It goes without saying that the team
member who writes the report also gives a copy to his fellow team members.
9
3. Manual Guideline
The manual and the course web-site contains all necessary information around the
course. Beside this the manual includes a description of all experiments. Every
experiment is divided in the Objective section and one (or more) sub section(s)
with Preparation,Execution and Evaluation.
The Objective Section should give an introduction to the problem. In some
cases it also contains theory not completely covered in the lecture.
The Preparation Section describes the electrical setup.
The Execution Section is a detailed description on what to do and how and
what to measure.
The Evaluation Section should deepen the understanding of the topic. There
are questions about the experiment. You should solve these with help of the taken
data and compare the results to theory.
Before you start working on a (sub)section read -the whole- section carefully. Try
to understand the problem. If something is not clear read again and/or ask the TA
or instructor. Follow the preparation carefully to have the right setup and not to
destroy any components. Take care that you record -ALL- requested data. You
may have problems to write a report otherwise!!
3.1
Circuit Diagrams
Next is an overview about the symbols in circuit diagrams.
Connections
wire
connected
wires
not connected
wires
Connection are usually made using 1 or 0.5m flexible lab wires to connect the setup
to an instrument or voltage source and short solid copper wires one the breadboard.
In most of our experiments we consider these connections as ideal, i.e. a wire is a
real short with no ’Impedance’. In the following semesters you will see that this is
not true.
10
Instruments
+
+
A
V
ammeter
connected
wires
wire
voltmeter
not connected
wires
Since we have ’Multimeters’ this symbol tells you how to connect and configure the
connected
not connected
instrument. wire
Be careful, in worst
case you blow it!!!
wires
+
wires
+
Voltage/Current
Sources
~
V
+
+
variable
V
real
ideal
voltage source
fixed variable
real
ideal
+ voltage source
real
ideal
current source
fixed
A
ammeter
AC source
~
signal generator
real
ideal
current source
pulse
generator
AC source
signal generator
pulse
generator
+
V
voltmeter
These are the symbols used in the manual. If you check the web and look into
+
+
different books there are also other symbols in use!
A
V
ammeter
voltmeter
Lumped Circuit Elements
+
resistor
variable
resistor
capacitor
+
electrolytic
capacitor
+
+
inductor
variable
electrolytic
There is a resistor
different symbol for
every lumped circuit
element. Depending
which
capacitor
resistor
capacitor
standard is used (DIN or IEC).
Semiconductors
inductor
NPN
PNP
Transistor
N-channel P-channel
JFET
diode
zener diode
Same as with the symbols before you may find different representations for every
component!
11
3.2
Values in Circuit Diagrams
As you will see in the lab, we use resistors with colored rings. These rings represent
numbers or a multiplier. Most of the resistors have five rings. Three digits for the
value, one multiplier for the dimension, and one for the tolerance. In the circuit
diagrams we have a similar scheme. There are three digits and a dimension. The
letter of the dimension also acts as the comma i.e.:
1R00, 10R0, 100R for 1Ω, 10Ω, 100Ω
1K20, 10K0, 100K for 1.2KΩ, 10KΩ, 100KΩ
1M00, 10M0
for 1MΩ, 10MΩ
(= V alue ∗ 100 )
(= V alue ∗ 103 )
(= V alue ∗ 106 )
The numbering for capacitors in the circuit diagram is similar. Only the dimension
differs. Instead R, K, M (Ω, KΩ, MΩ) we have µ, n, or p (µF, nF, pF) (i.e. 1n5
means 1.5nF). The value is printed as number on the component.
12
Part II
Experiments
13
4. Experiment 1 : Usage of Oscilloscope
4.1
Objective
The following experiments should familiarize you with the principles and the handling of an oscilloscope, which is one of the most important tools for an electrical
engineer.
!! Don’t forget!! All members of the group have to write a report for
this experiment!!
This time the report should include only the execution and the evaluation part! Your
report should become a ’How to use’ documentation. So execute and document all
steps of the manual carefully. Record the data and -important- observations! Take
screen copies for the different measurements since you can find most of the ’forgotten’
readings on the screen.
4.2
Theory
Prior to execution of this experiment, it makes sense to read the following documents:
• TDS220 Oscilloscope Manual
Chapter Getting Started, Basic Concepts, Operating Basics
• TDS220 Oscilloscope Operator Training
Chapter 1, 3, 4, 5 and Appendix B
You will find the manuals on the course web page.
4.3
Preparation
Sometimes it is helpful to have screen copies from from the oscilloscope. Use section A.1.2 to section A.1.5 of the manual to enable the hard copy device for your
computer.
14
4.4
4.4.1
Part 1 : Usage of the Vertical Control
Objective
The oscilloscope normally displays voltage as a function of time. The vertical section
controls how the signal at the input channels appears on the screen in vertical
direction.
4.4.2
The elements of the vertical section
• POSITION knob Ch1/Ch2
The POSITION knob is used to position a waveform vertically on the display.
• Ch1/Ch2 Menu
These buttons open the Vertical Control menu for
Ch1 or Ch2 on the right side in the display (description see below). If the menu is already open
this channel is switched off or on, depending on
the former state.
• MATH MENU
Displays waveform math operations menu and can
also be used to toggle the math waveform on and
off. (Not used in the moment)
• VOLTS/DIV knob Ch1/Ch2
The VOLTS/DIV knob is used to modify the calibration of the vertical scale
of the channel. In other words, the VOLTS/DIV knob allows you to increase
or decrease the vertical resolution of a displayed waveform.
• Input BNC-connector Ch1/Ch2
Connectors for the input signal. Keep in mind that the ground of these plugs
is connected together and both are connected to PE of the power plug! That
means you only can measure related to a common ground.
To the right the Vertical Control side screen menu is shown.
It is switched on with the Ch1/2 menu button.
• Coupling - DC, AC, Ground
• BW Limit - Bandwidth Limit On, Off
• Volts/Div - Coarse, Fine
• Probe - 1x, 10x, 100x, 1000x
• Invert - On, Off
The buttons on the right of the screen beside the shown items
scroll or select the different menu items.
15
4.4.3
Measure voltage using the graticule divisions
Objective
We measure the voltage by counting the major and minor graticule divisions between the minimum and maximum values of the waveform. The counted number
of divisions has to be multiplied by the scale factor given in the lower left of the
oscilloscope screen:
Counted Divisions in [cm] * Scale Factor in [V/division] = Value [V]
For all steps of execution record the Sensitivity of the input amplifier (the V/div
setting) and the estimated resolution of your readings!!
Preparation
1. As signal source we use the small black box labeled ’Signal Generator for
Exp.2’. Set one of the power supplies in your workbench to 20V and connect
the signal source to this supply.
2. Turn the oscilloscope on. Connect a probe to the CH1 BNC input connector on
the front panel. For the first parts of the experiment we need the attenuation
set to 1x. So set the switch at the probe to 1x.
3. Connect the CH1 probe tip to pin 2 of the signal source and the ground lead
to the pin 1.
4. Dependent on the last use of the scope you may or may not see a signal on the
screen. To bring the scope into a defined state push the SAVE/RECALL
menu button on the top of the front panel. Push the appropriate side-screen
menu button to select Setups. Then select Recall Factory. This resets the
instrument to a known state.
5. Push the CH 1 MENU button in the VERTICAL section of the front panel.
Since we have set the attenuation at the probe to 1x, we have to set Probe
in the side screen menu also to 1x. Be sure that the attenuation switch on the
probe is set to match the Probe menu selection in the oscilloscope every time
before you use the probe. The Probe menu setting compensates the attenuation
setting at the probe to get a proper reading for the displayed units.
6. As a last step push the AUTOSET button. Now you should see a small sine
wave signal. Maybe it is moving because the oscilloscope is not able to trigger.
Since we are only interested in measuring the amplitude at the moment simply
push the RUN/STOP button to halt it!
Execution
• First take a hardcopy of the screen. Then measure and record the minimum,
the maximum, and the peak-to-peak voltage of the Signal.
Remember: the arrow with the 1 on the left side of the screen shows the 0V position. The parts of the signal below this line are negative and above positive!
16
To make reading of the graticule divisions easier you can shift the signal in the
horizontal direction by use of the POSITION knob in the HORIZONTAL
section of the scope.
• Increase the sensitivity of the input amplifier (VOLTS/DIV knob) to 500
mV/DIV. The waveform displayed will expand and should exceed the upper part of the display. Use the POSITION knob to see the complete signal
again. Don’t forget that the ground level belongs to the signal!! Push the
RUN/STOP button. Now the Oscilloscope shows a stable signal!
Take a hardcopy and measure and record the minimum, the maximum, and
the peak-to-peak voltage of the Signal.
Example for a table:
Range
Vmin
V/[div] counted divs
4.4.4
Vmax
VP P
estimated
resolution
counted divs divisions
V/[div]
Measure Voltage using the cursors
Objective
With older analog scopes counting graticules was the only way to get the values! In
our case we can use cursors to mark and measure points of interest on the screen.
First an introduction to the cursor menu:
This is the side screen menu when pushing the CURSOR
knob:
• Type - Off, Voltage, Time
• Source - CH1, CH2, MATH, REF A, REF B
• Delta
• Cursor 1
• Cursor 2
The Type and Source items are switched with the buttons on
the right of the screen. The other positions are displays for the
values! To move the cursors use the POSITION knobs from the
VERTICAL section. (Cursor 1 with CH1, Cursor 2 with CH2)
In general the cursors measure relative to the ground marker. They only can measure
parts of a signal which are visible on the screen inside the grid!
Preparation
• Do not change the wiring. Push the AUTOSET button.
17
• Push the CURSOR button to change the side screen menu.
• In the cursor menu set Type to Voltage. Two horizontal cursors should
appear on the screen.
• Since we are working with CH1 set Source to CH1.
Hint : If you work with two channels don’t forget to set the right source! The
measured graticule divisions might be multiplied with the wrong range factor!
Execution
Use the table below for the measurements!
• Now repeat the two measurements from 4.4.3. Take hard copies for both cases
with cursors in place!
Do not forget to record the voltage range of the amplifier!!
Both cursors show the voltage relative to the ground marker. Set cursor 1 to
the bottom of the wave and cursor 2 to the top. Read and record the values
from cursor 1, cursor 2 and the delta. Also record the resolution of the cursor.
What is the smallest change you can set?
• For error calculation we need the vertical position of the curve. You can read
this value in the bottom of the screen if you turn the position knob carefully.
The readings from the cursors are not affected. Record the value!
Example table:
Range
Vmin
Vmax
VP P
V/[div]
[V]
[V]
[V]
4.4.5
resolution one
cursor step
[V]
vertical position
divisions
Measure Voltage using the measure function
Objective
With digital oscilloscope there is normally a third way to measure properties of a
signal. The MEASURE function. Similar to the cursor function you define which
channel is the source. But then instead of choosing a cursor mode you select the
wanted property in the side screen menue.
Preparation
• Do not change the wiring. Push the AUTOSET button.
• Push the MEASURE button to change the side screen menu and choose the
following quantities for CH1 : Min, Max, and Pk-Pk.
Execution
Repeat the two measurements from 4.4.3. Take hard copies which shows all values!
18
4.4.6
Switching the Input Coupling
Objective
In our case we have a mixed signal, a DC voltage with a small sine wave (AC voltage)
on top. To take a closer look at the AC component you need to increase only the
resolution of the AC part of the signal. From the step before you already saw that
this is almost impossible because in this case the graph moves outside the screen.
Sometimes you can use the POSITION knob but especially with very small AC
components this -IS- impossible. The solution to this problem is to insert a high
pass filter into the signal path. So the -Coupling- of the signal is selectable. The
Principle is shown in the following circuit:
Coupling Select
BNC-Input
Plug
DC
AC
Gnd
to Input Amplifier
Input Coupling
C
Ri and Ci
Input Impedance
Coupling is the method to connect an electrical signal to the oscilloscope. You can
select AC, DC, or Ground coupling at the oscilloscope. The different settings have
the following effects:
• AC coupling blocks the DC component of a signal and displays only the AC
component of the waveform, centered around zero volts.
But be careful; it also affects the display of small frequencies!
• DC coupling displays the entire signal.
• Ground coupling disconnects the signal from the input and displays a horizontal line at zero volts.
Preparation
• Switch Coupling in the CH1 menu to AC.
• Push the AUTOSET button. You should see a sine curve centered around the
ground marker. If the signal is not stable change the trigger level with the
LEVEL knob in the trigger section.
Execution
Measure and record the voltage parameters of the signal. Use the best suitable
method! Take a hard copy.
19
4.4.7
Verify the measurements with a multimeter
Objective
Until now you got a lot of different values. From the experiment with the multimeter
you already should know that it is quite precise. The ones in our lab are even capable
to measure this mixed signal. In the DC range it takes the mean value of the signal.
The mean value of a sine is zero, so we get the DC part of our signal. In the
AC range it takes the true RMS value if the frequency is below 10kHz. With the
oscilloscope we measured the amplitude in VP P . You can convert the RMS value
from the multimeter into VP P with the following formula:
√
VP P = VRM S ∗ 2 2
Preparation
Remove the oscilloscope probe from the signal generator and connect the Elabo
multimeter in DC-voltage range. GND of the Elabo to pin 1 and Vin to pin 2.
Execution
For all measurements do not forget to record the used ranges of the multimeter!!
• Measure and record the DC part of the voltage. Use the best possible range.
• Switch the Elabo to AC. Measure and record the AC part of the voltage. Again
use the best possible range.
4.4.8
Evaluation Vertical Control
• Calculate all voltages from the counted divisions. (Vmin , Vmax , Vpp , VDC )
• Calculate the remaining component of the signal from the measurements using
the cursors, and the MEASURE function. (Vpp , VDC )
• Produce a table with all measured and calculated values. Include the values
from all methods.
• What is the accuracy of the oscilloscope for the vertical section (3 cases, see
Manual!)? Rate the values from your table!
• Calculate the relative error for Vpp with the best resolution using the cursor.
Ignore that we didn’t use average mode.
• Calculate the relative error of Vpp measured with the multimeter.
• Enumerate the error sources for the different ways we measured the amplitude.
(systematic and methodical!)
• Why is it important to use a hight resolution.
• What is the disadvantage if you use AC coupling?
• Compare the errors of multimeter and oscilloscope! What is the conclusion
when using an oscilloscope to measure voltages?
20
4.5
4.5.1
Part 2 : Usage of the Horizontal Control
Objective
Next step is to measure time and frequency. Like in the vertical section it is possible
to use the graticule divisions to measure time. This time we start with the cursors
directly.
4.5.2
The elements of the horizontal section
• POSITION knob
Adjusts the horizontal position of all channels and math
waveforms. The resolution of this control varies with the
time base.
• HORIZONTAL MENU button
Displays the horizontal menu
• SEC/DIV knob
Selects the horizontal time/div (scale factor) for the main
or the window time base. When Window Zone is enabled,
it changes the width of the window zone by changing the
window time base.
Preparation
• Connect a probe to the CH1 BNC input connector on the front panel. Set the
attenuator switch at the probe to 1x. Connect the probe tip to pin 4 of the
signal generator and the ground strap to pin 3.
• Set the coupling of CH1 to DC. Push the AUTOSET button. Now adjust
the SEC/DIV and the horizontal and vertical POSITION knob in a way
that you get a similar picture as shown below:
• Switch the side screen menu to the CURSOR functions. Select Time for TYPE
and of course CH1 for Source. You can see two vertical cursors. The POSITION knobs from the vertical menu again are used to move the cursors.
21
Execution basic functions
The signal you see on the screen has three repetitive components. The period of
the rectangle, the period of the sine, and the time between the rectangles. Now we
measure the time and frequency of all components.
1. First make a hardcopy of the signal.
2. Measure and record the time between the rectangular components.
Take the rising edge in the middle of the rectangular signal as reference. Measure the time in both directions between the trigger marker and the next
beginning cycle. The values for cursor 1+2 show the time distance from the
trigger point. The delta value is the time between the cursors. So in our case
the wanted value!
3. Measure and record the frequency of the the rectangular component. As in
the vertical section the accuracy increases if the signal is expanded over the
full size of the display. So adjust it in a way that the trigger marker is still on
the screen and the single rectangle is as big as possible.
Record the scale factor of the time base (setting of the TIME/DIV
knob)!!
4. Measure and record the amplitude of the rectangular part of the signal.
5. Measure and record the frequency of the sine component.
Use a cross point between the signal and the grid as reference points for the
cursors.
6. Measure and record the Vpp value of the sine component and its offset from
ground.
7. Measure and record the time distance of the sine from the beginning of the
signal (the starting rectangle). Do not forget to note which edge you use as
reference!
4.5.3
Delayed and expanded view of signals
You should have noticed that it was not so easy to measure the sine part of the
signal. A way to view parts of the signal far behind the trigger point is the Window
function in the HORIZONTAL MENU. You first mark and then expand a region
of interest to view.
Preparation
• Push the AUTOSET button and adjust the screen as in the previous part.
• Push the HORIZONTAL MENU button. Main should be selected at the
moment.
• Select Window Zone from the side screen menu. You should see two additional
vertical broken lines on the screen.
22
• With the SEC/DIV knob you can vary the distance between these lines. In
the bottom of the screen you can see what the time base in this region is.
Select a bit more than one period of the sine. With the POSITION knob
from the HORIZONTAL section you now can adjust the position of the
window.
• Now select WINDOW from the side screen menu and the selected region
becomes expanded in time.
• Since the signal is quite small to measure the amplitude and to find a reference
for the beginning and end of the period first increase the horizontal and vertical
resolution.
Hint : Change resolution and coupling.
Execution
Measure and record the properties of the sine again. Use the best suitable method!
Take a hard copy.
4.5.4
Evaluation
• Create a table with all measured properties.
• Enumerate the systematic error sources for the different ways we measured
the frequency.
• What is the accuracy of the oscilloscope for the horizontal section?
• What is the error in percent from the time measurement of the rectangle part
of the signal. Take the ’Single-shot, Sample mode’ accuracy from the manual!
• If you compare the results of the sine sine measurement from normal and
window mode, what is the advantage of using the window mode.
• What is the conclusion when using an oscilloscope to measure time or frequency?
23
4.6
4.6.1
Part 3 : Trigger Section
Objective
The trigger circuit examines the incoming voltage signal and starts the acquisition
and display at the same point in the repetitive cycle for each new sweep. This results
in a visually steady display of the input. The trigger can be the signal from any
channel, an external signal, or the power line.
4.6.2
The elements of the trigger section
• LEVEL
This control sets the amplitude level the signal
must cross to cause an acquisition.(i.e. make the
scope start to record the signal)
• TRIGGER MENU
Displays the trigger menu.
• SET LEVEL TO 50%
The trigger level is set to the vertical midpoint
between the peaks of the trigger signal.
• FORCE TRIGGER
Starts an acquisition regardless of an adequate
trigger signal. This button has no effect if the
acquisition is already stopped.
• TRIGGER VIEW
Displays the waveform connected to the trigger circuit when pressed.
• Input EXT TRIGGER
Input for an extra trigger signal.
Following the trigger side screen menu:
• Type
There is a special mode to trigger on video signals implemented. The normal use in our case is always Edge!
• Source
Determines which input is the source for the trigger circuit.
• Slope
Determines if the trigger circuit reacts on a rising or falling
signal slope.
• Mode
Selects type of trigger.
• Coupling
Adds filter circuitry for DC, high, and low frequency to the
input. Similar to the coupling for the vertical section.
24
4.6.3
Using the basic trigger controls
Preparation
The oscilloscope should still be connected to the signal generator pin 3 + 4 via the
probe to channel 1.
• Set the coupling of channel 1 to DC.
• Use the AUTOSET button and the different controls to get the same view
as before.
• Push the TRIGGER MENU button. Verify that Edge, CH1, and Rising
Slope is selected.
Execution
For evaluation follow the different tasks and record your observations as exact as
possible.
• Take a hardcopy to record the trigger position, the trigger level and the slope.
• Shift the trigger level slowly from -1V to +6V. How did the signal behave?
Describe your observations!
• Set the vertical resolution to 500mV/DEV and vary the trigger level slowly
between 2V and 3V. Look especially around 2.5V ! Record your observations!
• Switch SLOPE in the TRIGGER MENU to FALLING. Adjust the trigger
level if necessary. Take a hardcopy. What is the difference to before?
4.6.4
Other important trigger controls
Objective
Source - Every input may be used as trigger source. CH1, CH2, and EXT.
Of course the input has to be connected but has not to be made visible. The EXT
TRIG is an already ’invisible’ channel. There is no range control for that channel.
Except that you can select EXT /5 in Source. This attenuates the signal by a
factor of 5. You can view the signal at the trigger circuit if you press the button
TRIGGER VIEW in the trigger control section.
Coupling - In case of a complicate or noisy signal it might be difficult for the
trigger circuit to stop the sweep. Similar to the coupling in the input channels
Coupling for the trigger switches a filter at the input at the trigger circuit. DC
connects the signal straight through. AC removes the DC part. The other settings
insert a high- or low-pass filter to remove noise or high/ low frequency components.
With TRIGGER VIEW you can check the signal behind the coupling circuit.
Mode - The MODE settings determine how the oscilloscope starts a sweep. Either repetitive and automatically (Auto) even with instable picture, or only when
a proper trigger condition applies (Normal), or manual (Single Shot).
25
Preparation/Execution
• COUPLING
Connect the probe to pin 4 of the signal generator. Switch the COUPLING
menu to every mode and check the output to the trigger circuit with TRIGGER VIEW knob. Record what happens on the screen.
• Mode
- Set COUPLING back to DC. Connect the probe to pin 6 of the signal
generator. Push the AUTOSET button to get a signal. Set the trigger
level to -3V. Now you should see a moving signal!
- Disconnect the probe tip from pin 6!! Set Mode to Normal.
- Connect the probe back to pin 6 of the generator. Do you see a signal?
Record your observation. Use the trigger level to get the signal back!
Single Shot mode will be demonstrated in the last part of the experiment!
4.6.5
Evaluation
• Describe the meaning of trigger position, trigger level and the slope.
• Compile a table from your observations when varying the trigger level. Describe why the signal is sometimes not stable.
• Use one of the hardcopies and mark at which positions you see a rising and at
which positions you get a falling slope.
• What is the difference between Auto and Normal mode? When might it be
useful to use the different modes?
26
4.7
Part 4 : Using the Probe
4.7.1
Load Effects of a Probe - Probe Selection
Objective
Until now we didn’t take care how we connect the signal to the oscilloscope input.
That might be a challenging thing!! The kind of probe, and/or the probe setting
has to be selected dependant on the signal. Even the connection of a suitable probe
might be not easy.
There are different kind of probes available:
• Passive probes with different attenuations
1:1 - it’s a high load for the circuit. Works only for low frequencies/ slow
slew rates.
10:1, 100:1 - medium load for the circuit. Usable for medium and higher
frequencies and fast slew rates. The attenuation is used to extend the frequency range. Disadvantage is that the signal at the oscilloscope becomes
smaller.
1000:1 - that is a probe for high voltage. The attenuation is mainly used
to reduce the voltage!
• Active probes
Active probes carry an amplifier in the tip. This amplifier decouples the signal
from the input of the oscilloscope. That reduces loading effects drastically since
the input of the amplifier has an extreme low impedance. These probes are
the choice for high frequency and high slew rate signals.
• Differential probes
Differential probes are active probes measuring not related to ground.
For general purpose use passive probes with 1:1 and 10:1 attenuation are common
and used in our lab.
The 1:1 probe A principle diagram of a 1:1 probe is shown below:
Schematic of 1:1 Probe
Signal
Tip
Cabel
Resistance
of Koax Line
In
Gnd
Oscilloscope
input
Koax-Line
Ground
strap
Ri
Cabel
Capacitance
of Koax Line
Ci
(~1MOhm/20..50pF)
The resistance and capacitance of the coax line depends on the manufacturer. In
our case R ≈ 300 − 500Ω and C ≈ 50 − 150pF . From the diagram it is obvious that
the probe acts like a low pass filter! For the probes in the lab the cutoff frequency is
27
around 7 − 10M Hz. Since the cutoff frequency is defined for a sine you have to be
careful in case of a signal with low frequency but fast rising slopes (high slew rate!).
The maximum slew rate is the maximum slope of a sine at about 7 − 10M Hz. As
rule of thumb t10%−90& = 0.5/fmax
The 10:1 probe A principle diagram of a 10:1 probe is shown below:
Schematic of 10:1 Probe
Shield
Ckomp
Oscilloscope
input
Koax-Line
Signal
In
Gnd
9MOhm
Probe Tip
Cabel
Resistance
of Koax Line
Inductance of
ground strap
Ri
Cabel
Capacitance
of Koax Line
Ci
(~1MOhm/20..50pF)
The additional components form a frequency dependant voltage divider. If Ccomp
is adjusted well the network reduces the input impedance of the probe-oscilloscope
chain. Typical values are Ri = 10M Ω and Ci = 15pF .
In our lab we will use probes that can be switched between 1:1 and 10:1. So it has
to be taken extra care before starting a measurement! First we want to investigate
the effect on a wrong used probe.
Preparation
• The probe should be connected at pin 6. Check if the probe is still set to
attenuation 1x. Also the probe factor in the vertical menu.
• Set the coupling of channel 1 to DC. Get the wave by using the AUTOSET
button of the scope.
• Change the time base so that you see one period. Do not forget to increase
also the vertical resolution to the highest possible range!
Execution
• Use the measure function. Take a hardcopy to record the properties of the
signal with 1x attenuation. (Vpp and f ).
• Now switch the probe to attenuation 10x. Do not forget to set the probe factor
in the vertical menu of CH1!
Use the probe adjustment tool provided with the probe and turn the variable
capacitor in the probe about 90◦ clockwise. (plug the tool into the small slot
either in the probe tip or in the small box at the connecter).
• Adjust horizontal and vertical resolution of the signal on the screen. Again
take a hardcopy showing the properties of the signal.
• Again turn the capacitor about 90◦ deg clockwise. Take another hard copy
with the values.
28
4.7.2
Probe Compensation
Objective
In the section above you should have gotten three different -wrong!- values from
the same signal!! Next step is to setup the probe for a proper measurement.
If you want to use the probe with 10x magnification you need to adjust the frequency
response. When you attach a passive voltage attenuation probe to an oscilloscope,
the capacitances of both the probe cable and the oscilloscope’s input combine. This
combined capacitance must match the capacitance of the input attenuation circuit
of the probe. You must balance these capacitive effects between the probe and
oscilloscope.
Schematic of 10:1 Probe
Shield
Ckomp
Oscilloscope
input
Koax-Line
Signal
In
Gnd
9MOhm
Probe Tip
Cabel
Resistance
of Koax Line
Inductance of
ground strap
Ri
Cabel
Capacitance
of Koax Line
Ci
(~1MOhm/20..50pF)
Probes are designed to match the inputs of specific oscilloscope models. However,
there are slight variations between oscilloscopes and even between different input
channels in an oscilloscope. To minimize these variations, attenuating passive probes
(10X and 100X probes) have built-in compensation networks. You need to adjust
this network to compensate the probe for the oscilloscope channel that you are using.
Note: If you use attenuation (only then!) you must compensate a passive voltage
attenuation probe every time you change a probe/channel connection on your oscilloscope. This ensures that the probe accurately transfers the signal from a signal
source to the oscilloscope.
The following procedure enables you to balance the capacitive and resistive effects
of a probe by compensation.
Preparation
1. Connect the CH1 probe tip to the Probe Comp output at the oscilloscope.
Check for attenuation 10x at the probe and in the probe menu.
2. Push the AUTOSET button.
3. Increase the horizontal and vertical resolution of one period of the signal to
maximum.
29
Now you should observe a wave similar to
one of the waveforms shown below. To the
left you see an over compensated, and to the
right an under compensated probe. Beside
to the right the probe is compensated well.
Execution
• It is most likely that your probe is not compensated. Use the probe adjustment tool to get a waveform with square corners. Take a hardcopy of the
compensated signal.
• Now connect the probe back to the signal generator (pin 5 GND, pin 6 Sig3).
Measure the properties of the signal and take a hardcopy.
4.7.3
Evaluation
• Compile a table with all measurements (4!).
• Calculate the methodical error for the first three values (Att. 1x, Att. 10x
uncompensated). Take the compensated value as reference.
• What are the reasons for the differences?
• What is the bandwidth for the oscilloscope with probe switched to 1x? Calculate using the ≈ values from the Objective section! Compare with the value
from the data sheet.
• What is the conclusion? What are the possible errors you can make?
30
4.8
Part 5 : Discharging a capacitor
The last part of the experiment is a real measurement. Determine the discharge
curve of a capacitor by the use of an oscilloscope.
Preparation
• Build the circuit from below on the breadboard.
CH A CH B
10V
10K0
1%
Ext.
Trig
100n
+/-20%
Gnd
Use the probe with appropriate attenuation!
• Set the trigger of the scope to ’Normal’ mode, falling edge. Choose the appropriate trigger level.
Execution
• Switch the supply on and charge the capacitor. Wait some seconds. Now
the oscilloscope should show 10V . To discharge the capacitor and start the
measurement, pull out one cable from the DC supply. Repeat this several times
to adjust the time base. Now switch the trigger mode to SINGLE. Retake the
signal and adjust the oscilloscope in a way that the curve is spread over the
whole screen.
• Make a hardcopy of the final graph.
• Record the final settings of the oscilloscope.
Evaluation
• Calculate the value of τ .
• Find τ by analyzing the signal shape from the hard copy.
• Show the prove that the discharge is exponential. Plot the vertical axis on a
logarithm scale the and verify that you get a straight line!
• Determine τ from the logarithmic plotted curve.
• Discuss the errors of getting τ with the different methods. Which method is
the best?
31
5. Experiment 2 : AC Properties and Measurements
5.1
Objective
The objective of this experiment is to determine properties of AC-signals and to
measure and display the behavior of simple AC-circuits.
5.2
5.2.1
Theory
Periodic AC-Wave Properties
Annotations - How to write wave form properties
To describe a DC parameter like voltage and current capital letters U and I are
used. Since these values are taken as constant (means no change over time) no
differentiation is necessary. For AC this is a bit different
• Time varying signal properties are usually written in small letters, u, i,. E.g.
u(t) = u
b sin ωt
• u
b is the peak value or amplitude of a voltage
• u¯ is the mean value of a voltage
b6 ϕ = u
b(cos ϕ + j sin ϕ)
• u is a complex voltage. E.g. u = u
In the following section you will find that the RMS values are written in capital
letters. Like described there RMS values are taken as equivalent to DC values. Of
course you have to take care if you work with RMS values and the circuit consists
of energy storing components like capacitors and inductors.
Periodic Signals
A sequence which is repeated in a same time again and again is called periodic
signal. It is described by the equation
u(t) = u(t + nT )
u(t) might be any periodic function e.g. a sin, n any integer number and T is the
time of one period. From T we can determine f the frequency. That is how many
times per second this sequence is repeated.
f=
1
1
= = 1Hz(Hertz)
T
s
Arithmetic Mean Value
f and T are the time properties. u
b is the peak value of the wave, e.g. u(t) =
32
u
b sin ωt. To get information about the effects of a periodic function over time sometimes it is sufficient to use the arithmetic mean value for u(t), i(t), or p(t), e.g.
1
u¯ =
T
Z
t0+T
u(t)dt
t0
For alternating periodic functions (or signals) with no DC component the mean
value over time is zero!
Root Mean Square Value
To make electrical quantities for signals like power comparable to each other a
second value was defined, the root mean square value. All currents and voltages
with the same RMS value put the same energy over time into a load, in other words,
they have the same power (see GEEI lecture!). For DC holds
W = U It = RI 2 t =
U2
t
R
If u and i is time dependent for short time dt
dW = uidt = Ri2 dt =
u2
dt
R
The energy is calculated by integration. The resistor needs to be constant as precondition!
Z t
Z t
Z
1 t 2
2
W =
uidt = R
i dt =
u dt
R 0
0
0
If this should be comparable to the DC case following conditions must hold
Z t
Z t
2
2
u2 dt = U 2 t
i dt = I t
0
0
Since we are dealing with a periodic function we can start integrating at any time t
for one period T
Z t0+T
Z t0+T
2
2
i dt = I T
u2 dt = U 2 T
t0
t0
The integral and the multiplication will calculate the same area under the function.
Dividing the equation by the period T and taking the square root over the whole
function will calculate U or I from the function as root mean square (rms) value
s
s
Z t0+T
Z
1
1 t0+T 2
2
I=
i dt
U=
u dt
T t0
T t0
What happens in case of a periodic function superimposed by a DC value? The
equation for the current may be rearranged in the following way
s
s
Z t0+T
Z
1
1 t0+T 2
2
I=
(I− + i∼ ) dt =
(I− + 2I− i∼ + i2∼ )dt
T t0
T t0
33
Integrating over the components
s
Z t0+T
Z t0+T
Z
1 t0+T 2
2I− i∼ dt +
i2∼ dt
I=
I− dt +
T t0
t0
t0
will give three terms under the root. The first and last one are like the ones for the
pure DC and periodic RMS signal. The second one beside the constant 2I− is the
mean value which becomes zero. So the RMS value of a mixed signal is calculated
q
I = I−2 + I∼2
Measuring AC-Signal Properties
There are several ways to measure mean and RMS values.
• Specially designed instruments for measuring RMS values independent from
frequency and signal shape.
• Using an oscilloscope and determine the signal properties and finally calculate
the values. This method may be limited by the signal shape. In our case it
is much simpler. We can use the ’Measure’ function and get the numerical
values directly. The only care to be taken is that at least one full period of the
signal is visible. The measure function will work with all frequencies below
the bandwidth of the oscilloscope and is also independent of the signal shape.
• Using a multimeter! The requirements are that you use a so called ’True RMS’
multimeter and that the frequency of the signal you want to measure lies inside
the specification of the multimeter. In our case both requirements are fulfilled.
To get a valid RMS value it is necessary to measure voltage or current twice.
First in DC range then in AC range. The DC value is the mean value (or the
DC offset) of the signal. The measured AC values is the RMS value of the
signal without offset. As last step the RMS value has to be calculated using
the formula from above
q
I = I−2 + I∼2
This example calculates a current. RMS voltage calculation is similar.
5.2.2
Calculate AC-Circuit Properties
General Rules
Kirchoff’s rules KCL and KVL are also valid for time variable signals! It still holds
that for any node (junction) in an electrical circuit, the sum of currents flowing into
that node is equal to the sum of currents flowing out of that node.
n
X
ii = 0
i=1
Also the directed sum of the electrical potential differences around any closed circuit
must be zero.
n
X
ui = 0
i=1
34
That means that all calculations are carried out in the same way as known from
DC-circuits. DC voltages, currents, and power are replaced by the corresponding
complex RMS counterpart (again see GEEI lecture!).
How to measure AC-circuit Properties
If an AC-circuit includes only resistive components it is sufficient to take only the
RMS voltage, or current values, since there is no phase shift. If frequencies are low
(≤ 10KHz) the simplest way is to use a multimeter! As soon as there are impedances
with a reactive (=imaginary) component you have to measure magnitude and phase
over each component. It is still possible if the frequency is low enough to use a
multimeter for the magnitude. For phase shift an oscilloscope is needed.
How to proceed?
• Define one reference signal! For this signal the phase is 0◦ . Depending on
the circuit it might be a voltage or the current. Connect this signal to channel
1 of the oscilloscope. The phases of all other signals are measured relatively
to this signal using channel two of the oscilloscope.
• If the frequency is low like in our experiment use the multimeter for magnitude
values of U and I. Take care for later calculations not to mix RMS and Peak
values!!
• Do not forget that the ground of the two oscilloscope channels is connected.
That means that you might not be able (depending on the circuit) to get a
value directly. For all conversions you have to use complex calculation.
• For the phase determination of a current you need a resistive component somewhere in the branch under test.
35
5.3
Part 1 : Measure AC-Signal Properties
5.3.1
Objective
5.3.2
Preparation
Connect generator, the oscilloscope and a multimeter using a BNC cable, the BNCT-connector, and the BNC-Banana connector with some lab wires. The initial
settings for the generator are as follows:
Function
Symmetry
Frequency
Amplitude
Offset
5.3.3
=
=
=
=
=
Triangle (’Ramp’ for Agilent 33220A generator!)
50% (only for Agilent 33220A generator!)
1kHz
2Vpp (measured at the oscilloscope!!)
0V
Execution
• Before you start check if Vpp -IS- ≈ 2V !!
• Calculate the theoretical values for v, V (Vrms !!). The following formula is
implemented in the generator:
u




-t
−T
T
2
2
t
4ˆ
u
t + uˆ + uof f
T
f (t) =

u

 − 4ˆ
t + uˆ + uof f
T
T
≤t≤0
2
T
0≤t≤
2
: −
:
-u
• Measure and record Vpp , v, V (Vrms !!) with the oscilloscope using the measure
function. Take hardcopies!
• Record the voltage with the multimeter in DC and AC range.
• Change the offset at the generator to 1V .
• Calculate the theoretical values for v, V (Vrms !!)
• Measure all values with oscilloscope and multimeter like above.
• Switch the generator to
Function
Frequency
Amplitude
Offset
=
=
=
=
Arb - select ’Exp Fall’
1kHz
2Vpp (measured at the oscilloscope!!)
0V
Repeat all measurements without and with 1V offset from above.
36
5.4
Part 2 : Measure AC Circuit Properties
5.4.1
Objective
5.4.2
Preparation
• Find the components for the circuit from the diagram below in the experiment
box. Measure the impedance of the inductor and the capacitor at 1kHz with
the RLC-meter in room 54. Use serial representation circuit for the inductor
and parallel representation circuit for the capacitor. Use the Elabo multimeter
to determine the exact value of the resistor.
• Now assemble the following circuit on the breadboard:
Tenma
(100Ohm!!)
+
A
AC − μ A
US
10Vpp
no Offset
Sine
1000Hz
100mH
47nF
U RC
~
Us
2KOhm
UR
• Calculate all ˆi and vˆ values using the nominal (theoretical) input voltage and
the measured impedance values at 1KHz.
5.4.3
Execution
For all measurements uS = 5V 6 0◦ is the reference signal.
Part 1
• Record the phaser current from the Tenma multimeter. Do not forget to switch
to -AC-. Use µA range.
• Measure the phaser voltage v S , v R , and uRC using the Elabo multimeter.
• To get the complete phaser v R , and v RC measure the phases with the oscilloscope. Phase of v S = 0◦ since this is our reference.
Hint: Take a hardcopy of every measurement with the oscilloscope! In case
of problems during evaluation it may be helpful to check the sign of the phase
again!!
37
5.5
Evaluation
5.5.1
Part 1 : Measure AC-Signal Properties
• If not already shown in the execution section, calculate the theoretical v¯ and
V of the triangle wave for offset 0V and 1V .
The following formula is implemented in the generator:
u




-t
−T
T
2
2
4ˆ
u
t + uˆ + uof f
T
f (t) =

u

 − 4ˆ
t + uˆ + uof f
T
t
T
≤t≤0
2
T
0≤t≤
2
: −
:
-u
• Calculate the theoretical v¯ and V of the ExpFall wave for offset 0V and 1V .
The following formula is implemented in the generator:
U = uˆ(2ekt − 1) + uof f
Hint: k is a constant! Determine from the hardcopy!
• If you focus on the multimeter:
- What did you measure in DC an AC range?
- Determine all V values using the multimeter measurements!
• Compile a table for every signal with all measured (multimeter, oscilloscope)
and calculated values. Give reasons for differences compared to the set values,
discuss errors and error sources.
38
5.5.2
Part 2 : Measure AC Circuit Properties
ˆ values using the nominal (theoretical) input voltage and
• Calculate all ˆi and u
the measured impedance values at 1KHz.
• Determine u
ˆ over every component from the measured current and voltage
values.
• Compile a table with all measured and calculated ˆi and u
ˆ values. Compare
and discuss errors!
• Calculate the impedance(resistance and reactance!) of R, L and C from the
measured current and voltages. Determine the element values, use the same
representation circuits as for the measurement with the LCR meter. (L=series,
C=parallel)
• Compile a table with all measured and calculated element values. Compare
and discuss the different errors!
39
6. Experiment 3 : Filter
6.1
Objective
The objective of this experiment is to show the behavior of simple passive RLCNetworks with a sinusoidal signal of different frequencies as an input signal. You
should learn how to measure the properties of these circuits and how to analyze and
represent the result of the measurements.
6.2
6.2.1
Theory
What is a filter?
Definition and technical implementation
A filter is a network used to select a frequency or a range of frequencies of an input
signal, while rejecting all other frequencies. There are several ways to construct these
filters. One way is to use active components like transistors or operational amplifiers
together with networks of resistors, capacitors, and inductors. Another way is to
use digital signal processors together with analog to digital and digital to analog
convertors. The simplest way is to use a passive network of resistors, capacitors, or
inductors. There are four general types filters. High Pass, Low Pass, Band Pass,
and Notch filters.
Filter properties:
• Frequency response - The frequency response is the measure of the filter’s
response at the output to a signal of varying frequency but constant amplitude
at its input. The frequency response is typically characterized by the magnitude of the system’s response, measured in dB, and the phase shift relative to
the input signal, measured in radians, versus frequency.
The so called ’Order’ of a filter describes the general behavior on how good it
damps the unwanted frequencies. Simple filters like the ones from our experiment are of ’1. Order’.
• Cutoff frequency - The cutoff frequency or corner frequency is the frequency
either above which or below which the power output of the filter is half the
power
of the passband, and since voltage is proportional to power P, Vout is
p
1/2 of the Vout in the passband. This happens to be close to -3 decibels, and
the cutoff frequency is referred to as the -3dB point.
• Center frequency - A bandpass circuit and a notch filter has two cutoff
frequencies. Their geometric mean is the center frequency. The geometric
mean of two numbers is:
p
fbw = f1 ∗ f2
40
• Bandwidth - The bandwidth for a bandpass or notch filter is the difference
between the upper and lower cutoff frequencies.
• Time constant - In an RC circuit, the value of the time constant (in seconds)
is equal to the product of the circuit resistance (in ohms) and the circuit
capacitance (in farads), i.e. τ = RC. It is the time required to charge the
capacitor, through the resistor, to 63.2% (∼ 63%) percent of full charge; or to
discharge it to 36.8% (∼ 37%) of its initial voltage. These values are derived
from the mathematical constant e, specifically 1 − e−1 and e−1 respectively. e
is the base of the natural logarithm.
• Angular frequency ω - Is a scalar measure of rotation rate. One revolution
is equal to 2π, hence
ω=
2π
= 2πf
T
The unit of omega is radians, i.e. one full cycle is 2pi, which is about 6.28.
You will also find that it is given in degrees, where one full cycle corresponds
to 360 degrees. So, 2pi correspond to 360 degrees, or one radian is about 57
degrees, a useful number to know by heart.
41
6.2.2
High Pass
R
A High Pass is a circuit which transfers signals
with high frequencies nearly unchanged. With
low frequencies the signal is attenuated and the
phase shift of the output signal is in advance to
the input signal, i.e. the phase shift is positive.
To the right passive RL and RC circuits are
shown. For both types we get the amplitude ratio A(jω) and the phase shift ϕ from the voltage
divider formula. Since we have AC we use the
complex form (to follow the calculations, you
have to apply your knowledge about complex
numbers).
Uin
L
Uout
R
Uout
C
Uin
RL → A(jω) =
U out
jωL
1
=
=
U in
R + jωL
1 − j(R/(ωL))
RC → A(jω) =
U out
1
R
=
=
U in
R + 1/(jωC)
1 + 1/(jωRC)
with ω = 2πf
(6.1)
(6.2)
By using formula (6.1) and (6.2) we get terms for magnitude and phase shift.
1
|A| = p
1 + (R/(ωL))2
and ϕ = arctan
1
|A| = p
1 + 1/(ωRC)2
and ϕ = arctan
R
ωL
1
ωRC
(6.3)
(6.4)
These are the formulas
for magnitude and phase shift. To get the cutoff frequency
√
we set |A| = 1/ 2 or −3dB and the phase to +45◦ . ωRC or R/ωL becomes 1 at
this point.
f−3dB =
1
2πRC
or
f−3dB =
R
2πL
(6.5)
With the formulas for the magnitude and phase you can verify the result of the experiment. Formula (6.5) already gives you an estimation about the general behavior
without any calculations or measurements.
42
6.2.3
Low Pass
A Low Pass is a circuit which transfers signals
with low frequencies nearly unchanged. With
high frequencies the signal is attenuated and
the phase shift of the output signal follows to
the input signal, i.e. the phase shift is negative.
To the right passive RL and RC circuits are
shown. For both types we get the amplitude ratio A(jω) and the phase shift ϕ from the voltage
divider formula. Since we have AC we use the
complex form (the calculations are in complete
analogy to the previous section).
L
Uin
R
Uout
R
Uin
C
Uout
A(jω) =
U out
R
1
=
=
U in
R + jωL
1 + jωL/R
(6.6)
A(jω) =
1
U out
1/(jωC)
=
=
U in
R + 1/(jωC)
1 + jωRC
(6.7)
By using formula (6.6) and (6.7) we get terms for magnitude and phase shift.
1
|A| = p
1 + (ωL/R)2
1
|A| = p
1 + (ωRC)2
and ϕ = − arctan (ωL/R)
and ϕ = − arctan (ωRC)
(6.8)
(6.9)
The formulas for the cutoff
√ frequency are the same as for the High Pass. The magnitude is again A = 1/ 2 or −3dB. Since the phase is negative the shift is −45◦ at
this point, i.e.the voltage of the output lags by 45 degrees behind the input voltage!
With the formulas for the magnitude and phase you can verify the result of the experiment. Formula (6.5) already gives you an estimation about the general behavior
without any calculations or measurements.
43
6.2.4
Band Pass
A band-pass filter is a device that passes frequencies within a certain range and attenuates frequencies outside that range. A RLC
combination may be used to create the circuit. The simplest way to build a band-pass
is to combine a high and a low pass. The
circuit is shown to the left.
To calculate magnitude and frequency response we combine the formulas for high and
low pass.
C1
Uin
R2
R1
C2
Ahi (jω) =
U out hi
U in
(6.10)
Alo (jω) =
U out lo
U out hi
(6.11)
Formula 6.11 inserted in formula 6.10 gives
Ahi (jω) ∗ Alo (jω) =
U out lo
U in
(6.12)
Written in a different way
|A| hi ∗ ejωhi ∗ |A| lo ∗ ejωlo = |A| hi ∗ |A| lo ∗ ej(ωhi+ωlo) =
U outh i
U in
(6.13)
we can see that we can use the already derived formulas to calculate magnitude
and phase shift for the bandpass. The magnitude for high and low pass have to be
multiplied and the phases have to be added. The formula for the cutoff frequency
is also the same as for high and low pass (6.5). The only difference is that we have
to apply it for each stage of the filter!
44
Uout
6.2.5
Notch Filter
A notch filter (or band-stop filter or bandrejection filter) is a filter that passes most frequencies unaltered, but attenuates those in a
specific range to very low levels. It is the opposite of a band-pass filter. A RLC combination
is used to create the circuit.It is shown to the
left.
We get the magnitude A(jω) and the phase shift
ϕ from the voltage divider formula. Since the
design (in this particular example is different
from the band pass filter, we have to do new
calculations. It is also possible do design a band
pass filter from this circuit. All you have to do
is to use the voltage drop over the resistor as
the output.
U out
U in
A(jω) =
R
C
Uin
Uout
L
1
j ωL −
1
(ωC)
=
=
1
R
R + j ωL −
1−j
ωC
ωL −
(6.14)
1
ωC
From this formula a term for the magnitude and a term for the phase shift can be
derived.
1
|A| = s
1+
R
ωL −
2
and ϕ = arctan
R
ωL −
1
ωC
(6.15)
1
ωC
The center frequency of the band stop filter is at the point where |A| is close to 0.
1
This is the case if ωL −
= 0. Solved for f we get
ωC
1
fcf = √
(6.16)
2π LC
√
The cutoff frequency is defined when the magnitude |A| = 1/ 2 and the phase shift
is ±45◦ . Formula 6.15 is solved for ω at these points. There are four solutions!
ωcut low =
−RC ±
p
(RC)2 + 4LC
2LC
(6.17)
p
(RC)2 + 4LC
ωcut high =
(6.18)
2LC
Of course only two of the 4 solutions are practically relevant. f can be found from
the relation ω = 2πf .
RC ±
45
6.2.6
How to determine the output characteristic of a filter
There are several ways to describe the properties of these kind of networks like time
response or frequency response. The time response will be topic of the following
semester. In our experiments we analyze the frequency response, means what happens at the output when the frequency at the input changes. At several frequencies
over a range of several decades we record the amplitude of the input and output signal. From these amplitudes we calculate the ratio. The unit of the result is decibels,
or dB. dB is a logarithmic value often used for such kind of ratios. It is defined as
A = 20 ∗ log
Uout
Uin
(6.19)
The second quantity measured is the phase shift ϕ between input and output signal.
It is taken relatively to the input signal. If the output signal is ahead the input
signal ϕ is positive else it is negative.
Uout
phi positiv
Uin
Uout pos
Uout neg
Uout
phi negativ
This information is usually used in conjunction with the magnitude, to evaluate how
much an output signal is phase-shifted against an input signal. Like the magnitude
the phase shift ϕ is generally a function of frequency.
Important: In your tables a positive phase shift is written as a positive
value and a negative phase shift as negative value.
N ote: To mix up the signs of the phase shifts is the most frequent source of error
in lab reports and in the final exams, so be especially careful to get the sign of the
phase right. Not to mention the disastrous consequences it may have if you mix up
the phase signs in research or industrial work!
A very common second error source is misuse of the calculator! Take care to use
the right mode if you have calculations in degree or radians (Angular Frequency!)
The usual way to present the result is the Bode Plot. The Bode plot describes the
output response of a frequency-dependent system for a normalized input. It is often
used in signal processing to show the transfer function of a system. It consists of
two graphs. The magnitude and the phase plot.
46
6.2.7
Bode Plot
A Bode magnitude plot is a graph of
magnitude in dB (this is a log scale,
see above!) against frequency on a
logarithmic scale.
Magnitude (dB)
Transfer Function - Magnitude
A Bode phase plot is a graph of
phase against frequency on a logarithmic scale.
Phase (deg)
Transfer Function - Phase
Frequency (f)
Transfer Function - Magnitude
Asymptotic
Slope
20dB
decade
f − 3 dB
Transfer Function - Phase
Phase (deg)
The magnitude-frequency plot can
often be approximated to straight
lines in a Bode plot (Asymptotic
Bode Plot).
Magnitude (dB)
-3dB
Asymptotic
Slope
45°
45
decade
f − 3 dB
Frequency (f)
47
6.2.8
Nyquist Plot
A Nyquist plot is a parametric plot of a frequency response. In Cartesian coordinates, the real part of the transfer function is plotted on the X axis. The imaginary
part is plotted on the Y axis. The frequency is swept as a parameter, resulting in a
plot per frequency.
Given is the following circuit:
R1
50R
L1
80uH
C1
5nF
C2
12.5nF
How is the change of the the complex conductance and the impedance when ω
changes?
ZS = R1 + j(ωL1 −
1
) is the RLC series circuit.
ωC2
Added the parallel capacitor Yall = ωC1 +
1
ZS
With ω varied the left Nyquist plot is generated. The right plot is 1/Yall .
Complex Conductance
Impedance
15
50
5
0
-5
ω
Y
jX/[Ohm]
jB/[mS]
0
ω
10
-50
Z
-100
-150
0
5
10
G/[mS]
15
-200
20
48
0
50
100 150
R/[Ohm]
200
250
6.3
6.3.1
Part 1 : Hi-Pass
Objective
The task is to determine the properties of a High-Pass filter and the characteristics
over a frequency range. The result should be displayed as Bode plot.
6.3.2
Preparation
Build a high pass using the following circuit:
Ch1
Ch2
Oscilloscope
C1
Vin sine
Vpp = 5Vpp
Voff = 0 V
R1
CH 1
CH 2
GND
Ext.
Trig
Probe1 + 2 Gnd
C1 = 100nF and R1 = 1KΩ
Connect the generator via the BNC-to-Kleps cable. Use Ch1 of the oscilloscope
for the input signal and Ch2 for the output signal. Use voltage probes for both
channels. Select an appropriate setting for the attenuation!
6.3.3
Excecution
Vary the frequency of the generator from 50 Hz to 100KHz. Use 1, 2, 5 steps (e.g.
50Hz, 100Hz, 200Hz, 500Hz, 1kHz...) Measure and record the input and output
amplitude and the phase shift between the signals.
Hint: Be careful!!! Phase shift may be positive or negative.
49
6.4
6.4.1
Part 2 : Notch
Objective
The task is to determine the properties of a Notch filter and the characteristics over
a frequency range. The result should be displayed as Bode and Nyquist plot.
6.4.2
Preparation
Build a notch filter using a 2.7kΩ resistor, a 2.2nF capacitor and an 10mH inductor.
Connect the signal generator via the BNC-to-Kleps cable to the input. Use the
oscilloscope to measure input, output signal and the phase shift.
6.4.3
Execution
Use a sine signal with 5V amplitude, no offset.
• Calculate the center-frequency for this setup. Check if your circuit behaves
like a notch filter!
• Determine the center-frequency experimentally. Is it close to the calculated
value (around ±5%)?
Hint: At the center frequency the phase shift between input and
output voltage is 0◦ ! This is a much more accurate way to determine
the center frequency than to find the minimum of the amplitude.
• Now calculate the two cutoff frequencies.
• Create a table for Vin , Vout , and ϕ! Vary the frequency from 10KHz to 100KHz.
Include the cutoff values and the center frequency. Insert five extra values
between each off the two cutoffs (calculated) and the center frequency (experimentally). Prepare also a diagram to see if you have enough values.
• Measure and record the input and output voltages.
• As second step measure and record the phase shift between input and output
voltage for all frequencies from before.
Hint: Be careful, mind the sign of the phase shift. Moreover it will
change!!
50
6.5
6.5.1
Evaluation
Part 1 : Hi-Pass
• Draw the Bode magnitude and phase plot from the values you measured.
• Draw the Bode magnitude and phase plot from the formulas given in the
theory section together with the measured graphs. As variable use the same
frequencies you set in the experiment. Compare!
• Calculate the −3dB frequency from the components given. Read it from the
diagram with the measured values and compare!
• Calculate the phase shift at ω−3dB . Read it from the diagram with the measured values and compare!
• Find the gradient of |A| per decade (unit = dB/decade).
• What is the amplitude ratio in dB and the phase of the High Pass when:
a) f f−3dB
b) f f−3dB
c) f = f−3dB
6.5.2
Part 2 : Notch
• Draw the Bode magnitude and phase plot from the values you measured.
• Read the measured center-, and cutoff frequencies and the bandwidth from
the Bode plot.
• Draw the theoretical Bode magnitude and phase plot given from the nominal
values of the elements together with the measured values. As variable use the
same frequencies you set in the experiment.
• Calculate center-frequency, cutoff frequencies and bandwidth from the components given.
• Compile a table with all calculated and measured key parameters. Compare
the values and discuss the differences.
• Draw the Nyquist plot ULC = f (f ) using the measured voltage and phase shift
values.
51
7. Experiment 4 : The Wheatstone bridge
7.1
Objective
The experiment should demonstrate the general use of a simple circuit to measure
resistance or impedance. The main focus beside the function is to point out systematical and methodical errors.
7.2
Theory
Shown below is a Wheatstone bridge circuit. It consists of four impedances and a
voltage source. The output is between point A and B. The Wheatstone bridge is
widely used to measure impedances. It can be used in two conditions, either balanced or unbalanced.
The balanced bridge is used to measure
Z1
Zx
impedances with high precision. ZX is unknown. One, two or all other Z will be
Vs
A
Vout
B
adjusted in a way that VOut becomes zero.
Z3
Z4
After adjusting VOut the values of these
impedances(s) are known and the unknown
value can be calculated.
The second case is the unbalanced bridge. In most cases it is used in conjunction
with transducers1 to measure physical quantities such as strain, temperature, humidity or pressure. VOut is zero at a know reference point of the transducer (here
ZX ). The change of impedance in the transducer will give a defined change in VOut .
So VOut has a direct known relation to the physical parameter.
7.2.1
DC Bridge
The DC Wheatstone bridge is the simple variant.
impedances are pure resistive. If
VS is a DC source and all
RX
R1
=
⇐⇒ R1 ∗ R4 = R3 ∗ RX
R3
R4
the bridge is balanced and Uout = 0V . This condition is used for the so called
’Balanced bridge’. One Resistor under test is unknown and the others are changed
until Uout = 0V . Using precise known resistors for R1,3,4 and the formula above it is
possible to calculate RX .
The second case is the ’Unbalanced Bridge’. It includes one or more changing
resistive elements like temperature sensors. At one reference point e.g. at 0◦ C
Uout = 0V . The value of the resistance is not important anymore. The change in
Uout is now a direct measure for temperature.
1
a device which converts a physical quantity into a voltage or current
52
7.2.2
AC Bridge
Here VS is an AC source. One or more of the precisely known elements are impedances.
Again Uout should become zero. Like before following condition holds
Z1 ∗ Z4 = Z3 ∗ ZX
The difficulty with the AC circuit is that we have magnitude and phase. So we have
to adjust two properties to make Uout = 0V . To make this visible the formula with
components written in complex notation may be expressed in the following way:
(|Z1 | ∗ |Z4 |) ∗ ej(ϕ1 +ϕ4 ) = (|Z3 | ∗ |ZX |) ∗ ej(ϕ3 +ϕX )
From this formula for absolute value and phase the following applies:
|Z1 | ∗ |Z4 | = |Z3 | ∗ |ZX | and ϕ1 + ϕ4 = ϕ3 + ϕX
To adjust Vout to zero it is now necessary to vary at least two components, one
component for the amplitude and one component for the phase. From the phase
component of this equation it is also recognizable, if it is possible at all to balance
the bridge. Taken the circuit from the experiment section we apply:
(ϕ1 < 0) + (ϕ4 = 0) = (ϕadj < 0) + (ϕ3 = 0)
The left and the right side of the equation are both negative. So it is possible to
balance the bridge.
53
7.3
7.3.1
Part 1 : Balanced DC Wheatstone bridge
Preparation
• The following circuit should be used:
R1
22K0
1%
U=15V
+
A
R3
2k20
1%
Tenma
R2
R-Decade
1%
V
B
mV
R4
8k20
1%
• Find the resistors R1 , R3 and R4 in the experiment box and measure the
values with the Elabo Multimeter. Use the best range available (Do not forget
to record the used ranges at the multimeter!! )
• Assemble the circuit on the breadboard.
7.3.2
Execution
• Switch on and change the resistance of the R-decade in a way that UAB becomes zero. Record the final UAB . Use the Tenma Multimeter in the mV (!)
range!
• Read and record the resistance from the decade-box.
• Measure the resistance of the R-decade with the Elabo Multimeter.
54
7.4
Part 2 : Unbalanced DC Wheatstone bridge
7.4.1
Objective
The circuit for the next experiment is shown to the left. R1 , R3 , and R4 are high precision resistors. R2 is a PT1000 temR2
perature sensor. The effect of changR1
PT1000
1K00
ing resistance of metal over temperaTemp.
Temna
0.1%
Elabo +
Sensor
Us=1V
ture is used in this case. ’PT’ stands
V
V +
for Platinum, 1000 means that the
R3
R4
Uout
1k00
1k00
resistance of the element is 1000Ω at
mV-Range
0.1%
0.1%
0◦ Deg.
The function of the resistance over temperature is described by:
RT = R0 ∗ (1 + AT + BT 2 − 100T 3 + CT 4 )
The range for T in this formula is (−200 to +800◦ C). Since the used sensor only
can withstand −50 to +150◦ C and we are dealing with a much smaller temperature
range we can simplify the formula in the following way:
RT = R0 ∗ (1 + AT )
RT
R0
T
A
=
=
=
=
Resistance (Ω) at temperature T (◦ C)
Resistance at 0◦ C = 1000Ω
Temperature in ◦ C
temperature coefficient 3.850 ∗ 10−3 ◦ C −1
7.4.2
Preparation
Because of the small sensor and to keep a good accuracy the circuit is already
assembled on a printed circuit board which you can find in the experiment box.
Add the supply and the two voltmeters.
Take care of the polarity of the multimeters!! After assembling everything do not
touch the circuit anymore! This is necessary that the temperature can stabilize at
the PT1000. Wait about 5 minutes to continue!
7.4.3
Execution
• For the evaluation it is important to know the exact input voltage. Measure
and record US with the Elabo multimeter. For accuracy use the optimum
range!
• Record the voltage at UOU T . Use the mV range of the Tenma multimeter!!
• Set US to 10V. Wait about 10 minutes then record US and UOU T again.
55
7.5
7.5.1
Part 3 : Balanced AC Wheatstone bridge
Preparation
• Use the following circuit:
Y1
1uF
R1p
C1p
Rpadj
Cpadj
Yadj
use R- and C-Decade
for Rpadj and Cpadj
replacement circuit
of a capacitor
Generator
R1
1k00
U = 5Vpp
1 kHz sine
no offset
V
A
R3
1k00
Elabo
AC Range
B
R4
1k00
• Pick out R1, R3, and R4 from the experiment box. Measure and record the
values. Use the Elabo multimeter.
• Find Y1 ≡ C1 . Measure the impedance with the RLC-Meter. Use the parallel
equivalent circuit mode like shown in the circuit diagram.
• Assemble the circuit on the breadboard.
• Use the oscilloscope as indicator for the phase shift. Connect CH1 at point A
and CH2 at point B.
• To make the balancing easier, calculate the theoretical values for Rpadj and
Cpadj . Use the measured values for R1 ,R3 , and R4 , take the nominal value for
C1p ! Ignore R1 p for now.
7.5.2
Execution
• Switch on and try to set VAB as close as possible to zero by changing Rpadj
and Cpadj . A value below 5mV is good enough in our case!
Use the oscilloscope for coarse adjustment (phase) and the Elabo multimeter
for the fine-tuning. Watch amplitude and phase change during switching Rpadj
and Cpadj . The difference in amplitude and phase between both channels
should become zero.
• If VAB is sufficiently low record the voltage.
• Record the final values of Rpadj and Cpadj twice. Once as reading from the
decade boxes and then as measured value from the Agilent RLC-Meter (in
room 54).
56
7.6
Evaluation
7.6.1
Part 1 : Balanced DC Wheatstone bridge
• Derive a formula for R2 . Use KVL.
• Calculate R2 twice, first with the nominal resistor values and second with the
measured values from R1 , R3 , and R4 .
• Calculate the maximum relative error of the found R2 values for the following
cases:
- value read from the resistor decade box
- directly measured with the Elabo multimeter
- calculated from the nominal resistor values
- calculated from the measured resistor values
Use the tolerances of the resistors (±1%) and/or the tolerance of the multimeter (see Manual). For the last two cases use partial differentiation to derive a
formula for the maximum relative error. Show the complete way how you got
it!
• Make a table and show all measured and calculated values for R2 together
with its errors. Which value is the best one? What are the error sources for
the different methods?
• As you can see from the values our bridge has not the best accuracy in this
’contest’ !! What should be improved to make it the best way to measure the
resistance?
7.6.2
Part 2 : Unbalanced DC Wheatstone bridge
• Calculate RP T 1000 for the two cases. Use the given component values and the
measured supply voltages!
• Convert the values to temperature.
• What are the error sources for the calculated temperature value?
• With higher supply voltage the sensor is heated because of power dissipation.
What is the additional temperature at the sensor for the used supply voltages?
The maximum self-heating coefficient in air for the sensor is E = 0.2◦ C/mW .
If you look at the calculated temperatures from the question before, what is
the conclusion?
• Until now we completely neglected the influence of the voltmeter which measures UOU T (also for Part 1)!
a) What was the internal resistance of the voltmeter measuring UOU T in the
experiment?
b) What happens with UOU T if you use a voltmeter with only 10kΩ internal resistance? Derive a formula for UOU T = f (Rmulti ). (Rmulti is the
57
internal resistance of the voltmeter). Use 1V for US and a RP t which
corresponds to 20◦ C. What is the maximum relative error with the low
input impedance voltmeter?
(Hint : use the Thevenin equivalent circuit!)
c) Was the accuracy good enough in our experiment? What is the conclusion
for measuring the output voltage of a bridge?
7.6.3
Part 3 : Balanced AC Wheatstone bridge
• Why do we need two components to balance the bridge? Explain!
• If not already done show the complete calculations how you get the values for
Rpadj and Cpadj in the preparation.
• Calculate the complex conductance Y1 ! Extract the values for RP and CP .
Use the measured values from R1 , R3 , R4 , and Yadj .
• Compare the calculation with the measured conductance value of C1 from the
RLC-Meter. Discuss the errors (no calculation)!
• Calculate the bridge voltage uAB for the balanced bridge. Use the measured
component values from the experiment! Is the result comparable to the experiment value?
• What is the influence of the voltmeter and the oscilloscope to our circuit?
58
8. Experiment 5 : JFET
8.1
Objective
One topic of the last semester was the BJT transistor. Now we take a look at
the FET. There are different types of FET. The simple self conduction JFET, the
depletion, and the enhancement MOSFET. In the experiment we use a n-channel
JFET. This is the simplest transistor available. It is self conducting, means there is
a current flow between Drain and Source without any control voltage at the Gate.
Like the other FETs it is a voltage controlled current source.
8.2
Theory
For the classification of the FET’s and the theory look into the lecture script and
use other available literature (e.g. the book recommended for the lecture).
As reminder you can see the Transfer, and Output characteristic of the N-channel
JFET below.
25
Transfer Characteristic
Output Characteristic
Ohmic
region
Id/[mA]
Active region
(Pinch off region)
Ugs=0V
Idss
20
Uk = Ugs - Up
15
Ugs=-1V
10
Ugs=-2V
5
Ugs=-3V
Ugs=-4V
0
-10
Ugs/[V]
-5
0
5
Up
10
15
Uds/[V]
20
It is visible that ID is voltage controlled and that the JFET is self conducting without
input at the Gate UGS = 0. If the Pinch Off voltage UP and the maximum drain
current UDSS is known the following formula calculates ID = f (UGS )
2
VGS
ID = IDSS ∗ 1 −
(8.1)
VP
This is the basic formula to bias a JFET circuit. A second important relation is
VK = VGS − VP
(8.2)
UK is the border between the ohmic and the active region (pinch off region). Like
for a BJT the ohmic region is used for switching and the active region is used in
amplifier applications.
59
8.3
8.3.1
Part 1 : Measure IDSS and VP
Objective
This part prepares the following experiments. Here we want to measure IDSS and
VP . As described before we need these values to bias all circuits from the following experiment. Both properties are also given in
the data sheet, but every single silicon component has it’s individual characteristic with
wide ranges. To make comparison between
theory and measurements easier we use the
measured values for the individual used JFET
not the data sheet values! Below on the left
is the pin out and the bottom view of the
BF245C footprint. Check the setup on your
breadboard twice. If the JFET is inserted the wrong way gate and drain is swapped.
!!! Then you may see smoke !!! Anyway, the transistor is broken in this case.
8.3.2
Measure IDSS - Preparation
BF245C
Generator setup
f = 1660 Hz
square burst
Vpp = 5V
Uoff= 2.5V
8.3.3
27R0
1%
Assemble the shown circuit on the
breadboard.
Take care of the generator settings.
Do not forget to use ’Burst’ mode!!
Measure IDSS - Execution
For the given generator setup the current through the JFET is switched on with
300µs pulses to avoid heating effects. Use the oscilloscope to measure and record
IDSS .
8.3.4
Measure VP - Preparation
+
A
BF245C
To measure UP assemble the shown
circuit on the breadboard. Take care
of the the polarity of the voltmeter!
You measure UGS that means that
the positive terminal of the voltmeter is at the gate (UG+S− !!).
I_D
+
8.3.5
V
Vp
V = 10V
Rs
10M0
R-Decade!
Measure VP - Execution
Measure and record VP .
60
8.4
8.4.1
Part 2 : 2 Pole Current Source
Objective
Because of the self-conductance of the JFET it is possible to develop a 2-pole 1-port
circuit, which behaves like a constant current source (see GEEII lecture). Only one
additional resistor is necessary controlling the current in a feedback loop.
+
A
R_L = 0Ohm
(use a wire)
I_D=2mA
BF245C
Elabo Supply
U = 10V
+
V
Ugs
Rs = ?
use R-Decade
The JFET/resistor combination is also called FET-Diode and it is available as an
integrated component for several currents between 0.1 to 5 mA. This circuit can
replace a resistor directly.
8.4.2
Preparation
• Use the same setup as for the VP measurement.
• Determine VGS and RS to get ID = 2mA. Use formula (8.1)!
• Adjust the supply voltage to accurate 10V, set RS to the calculated value.
Switch on and verify that ID is in a ±10% range around 2mA. If not check
the setup and your calculation for errors!!!
8.4.3
Execution
Measure and record VGS , and ID .
61
8.5
8.5.1
Part 3 : Current Source with auxiliary supply
Preparation
• Assemble the following circuit
+
A
I_D=2mA
R_L=0Ohm
(use a wire)
R1
10K0
1%
BF245C
U=10V
Ugs
R2
2k20
1%
U_G
U_S
Rs=?
use R-Decade
• Calculate the value for RS to get a current of ID = 2mA !
• Adjust the supply voltage to accurate 10V, set RS to the calculated value.
Switch on and verify that ID is in a ±10% range around 2mA. If not check
the setup and your calculation for errors!!!
8.5.2
Execution
• Measure and record the supply voltage!
• Measure and record ID , VG , VS and VGS .
62
8.6
8.6.1
Evaluation
Part 1 : Measure IDSS and VP
• Compare the found values of IDSS and UP to the values in the data sheet of
the BF245C (IDSS and VGSof f in the data sheet).
• Describe the different systematic and methodical errors while taking IDSS and
VP .
• Calculate the rough estimated relative error for IDSS and VP .
8.6.2
Part 2 : 2 Pole Current Source
• If not already done show the complete calculation for RS .
• What is the maximum relative error of ID when using the measured values
from IDSS and UP .
(Hint : Use Partial Differentiation to determine the error propagation!! Use
the estimated errors for IDSS and UP )
• What is the relative error of the measured ID . Take the wanted value as the
true value. What are the error sources. Is your value in the calculated range
from the problem before?
• In the experiment we used a load resistance (RL ) of 0 Ohm. The current will
be stable over a wide range if we increase RL . Determine the approximate
dimension of RL where ID will start to decrease significantly. Explain from
the output characteristic in the data sheet!
8.6.3
Part 3 : Current Source with auxiliary supply
• If not already done show the complete calculation for RS .
• What is the maximum RL in this case. Calculate!
• What is the difference between the two circuits? What might the advantage
be for each circuit?
63
9. Experiment 6 : Solar Cells
9.1
Objective
Solar cells are one possible way to produce electric energy. Since in the beginning
(≈ 1960s) cost were very high this technology was only used in special cases like
supplying instruments in space with electricity. With progressive development costs
are now in a range that it is also available for general power generation. This
experiment should give a general overview on how a solar cell works and what the
main characteristics are.
9.2
Theory & General Setup
For theory about solar cells refer to the lecture and the different text books.
To measure the characteristics of a solar cell in order to get absolute values for the
energy conversion a quite complicated setup is necessary. We need a solar cell, a
calibrated light source, and a well defined mechanical setup inside a dark room. In
our case the setup is reduced to a small black box which includes all components.
We will not get calibrated values but relative values which gives an overview about
the general behavior of a solar cell. All important properties can be shown and
explained! The setup looks like this:
+10V
I-Forward/Reverse
-10V
I-Lamp
R-Load
Intens. lo 1
Intens. lo 2
+5V
Ucell
Intens. med
Intens. hi
Lamp
+12V
Solar
Cell
Heater
GND
GND
I-Lamp is a switchable constant current source. The Lamp is a high efficiency LED
and the solar cell is a photodiode made of mono crystalline silicon with a size of
1cm2 . The data sheet for both components are supplied on the course web page.
64
9.3
Part 1 : Dark/Illuminated forward/reverse
U-I characteristic
9.3.1
Objective
The first part of the experiment should show how a dark or illuminated solar cell
behaves if a current is supplied in forward or reverse direction to the PN junction.
9.3.2
Preparation
Wire up the the experiment box in the following way:
+10V
I-Forward/Reverse
-10V
I-Lamp
A Icell
R-Load
Intens. lo 1
Intens. lo 2
+5V
Intens. med
Intens. hi
Lamp
+12V
Solar
Cell
V Ucell
Heater
GND
GND
In this experiment we need 3 voltage sources. Use the two variable supplies for
±10V and also the third fixed 5V supply!
Use the Tenma multimeter as ammeter, switch it to the best range.
9.3.3
Execution
• At first we want to record the dark characteristic. So do not connect the 5V
supply.
• Vary the forward/reverse current potentiometer between the maximum values.
Select enough reasonable values especially in critical regions of the curve to
record the graph over the given range.
• Connect the 5V supply and set the current selector to ’Intens. lo 1’.
• Repeat the measurements from before.
65
9.4
Part 2 : I-U characteristic with different illumination and temperature
9.4.1
Objective
In this part we analyze the behavior of the illuminated solar cell. (So the normal
operation when generating power!)
9.4.2
Preparation
Change the wiring at the box in the following way.
In the beginning do -NOT- connect the heater!!
+10V
I-Forward/Reverse
-10V
I-Lamp
R-Load
Intens. lo 1
Icell
Intens. lo 2
+5V
Intens. med
A
Intens. hi
Ucell
Lamp
+12V
Solar
Cell
V
Heater
GND
GND
Use the Tenma multimeter as ammeter again. But this time be careful when selecting the range. We want to measure the short circuit current over the solar cell. This
means that we should have a low load resistance and still a reasonable resolution at
the ammeter. (around 1Ω is fine)
9.4.3
Execution
• Set the current selector to ’Intens. lo 1’.
• Record the I-U load characteristic of the cell. Start from open circuit voltage.
(disconnect the ammeter!) Then vary the load resistor from max. to min.
value and take about 15 values from high load resistance to short circuit (take
care of the ammeter range!!).
• Repeat the measurements from before with ’Intens. lo 2’,’Intens. med’, and
’Intens. hi’.
• Connect the heater to 12V. This will heat up the solar cell to about 40 − 50◦ C.
Wait for about 10 minutes until the temperature at the cell settles. Now repeat
the measurements with ’Intens. hi’.
66
9.5
Evaluation
• Draw the characteristic I=f(U) for the dark and illuminated case in the first
part of the experiment when you supplied current to the cell. Show both
graphs in the same diagram.
• What is the general behavior of the cell? Explain (if you didn’t do it in the
theory section)! Draw the equivalent circuit of a solar cell? (schematic!)
• Draw the characteristic I=f(U) for all 5 measurements. Put all graphs into
one diagram.
• Calculate and draw P=f(U) for the different intensities.
• Compile a table with the following properties for the different intensities:
Short Circuit Current ISC
Open Circuit Voltage UOC
Maximum Power Point values(MPP - determined from P = f (U ) graph)
UM P P IM P P PM P P
• Calculate the Fill Factor for all intensities.
• Calculate the approximate efficiency for the solar cell at ’intens. hi’ and ’intens.
hi; hi temp’. Assume that the light power is 15mW.
• Which physical effects are responsible for reducing the efficiency in general?
What is the special reason of reduction when the cell was heated?
• What is the effect of the parallel (RP ) and serial (RS ) resistance in the equivalent circuit? Explain how the ’intens hi’ graph would change if RS increases
and RP decreases.
67
Part III
Additional Information
68
A. Appendix
A.1
Hardcopy from oscilloscope screen
Sometimes it is useful or mandatory during evaluation of a report to have a copy
of the pictures of the oscilloscope screen. Getting hardcopies from the Textronix
oscilloscope is possible by using either a printer, a computer, or a special interface
connected to the oscilloscope. In our case we use an interface which connects the
serial port of the oscilloscope to the network. A Java applet controls the oscilloscope
and downloads the bitmap. The necessary prerequisites and the procedure how to
do this is described in the following paragraphs.
A.1.1
Oscilloscope Settings
The oscilloscope is configured by the interface before requesting a hardcopy. The
users only have to take care about the RS232 settings. In general we use the defaults.
Only the baudrate is set to 19200.
Use following sequence to configure the RS232 interface of the oscilloscope:
Button UTILITY
Button
Options
Button
RS232 Set-Up
Button
Set to defaults
Menu
Baud
set to 19200
A.1.2
Computer Preparations
You need a Web-Browser which is enabled to execute Java applets. You have to
assure that executing Java (!! not Java Script !!) is allowed to run in your preferred
browser. Second you need the Java Runtime Environment from Oracle. Dependent
on your browser you have to download and install it manually (Windows IE) or the
browser will find the necessary plug in and guide you through the installation when
you use the convertor the first time (Mozilla, Firefox). In both cases the installation
has to be done as ’Administrator’.
A.1.3
Ethernet to Serial Convertor Settings
The convertor is switched on when the workbench is powered with the key switch.
There is nothing to configure! In case there is a problem using the convertor try
resetting it with the reset switch in the front panel! Then wait a few seconds and
restart the applet in the browser.
69
A.1.4
Make a Hardcopy
1. Connect the Oscilloscope to the Ethernet to serial convertor. Use the provided
RS232 cables in the lab.
2. The main power switch of the workbench and the oscilloscope needs to be
switched on.
3. Open the web browser. Start the applet in the convertor by using the following
link:
http://xxx.xxx.xxx.xxx/osci.html
Instead of xxx.xxx.xxx.xxx insert the IP number of your workbench. (That
is the number on the label you find at the power insert of the bench).
4. The applet will start. If you work the first time at this bench a warning
about the certificate will pop up. Confirm that you trust the supplier of this
certificate. (If you check you will find that ’Uwe Pagel’ is the supplier!)
5. The applet shows up. You will see a status message in the upper part of the
screen. It includes the status of the TCP/IP connection and the ID string of
the oscilloscope.
6. The whole setup is now ready for usage. To get an image of the oscilloscope
screen push the ’Start Hardcopy’ button in the applet window. In the status
screen you will see the progress of the operation. If all data is transferred the
image becomes visible. To store the bitmap use the button ’Save Image’.
7. If it is necessary to get the raw data from the screen, then use the ’Capture
Data from ->’ button. But first select the data source in the window beside
the knob. Also here you will see the progress of the operation. When the data
is transferred it is shown in the data window. To save the data use the ’Save
Data’ button.
70
A.1.5
In case of problems!
Here it is assumed that everything is connected and powered and that the right link
is used!!!
• The applet didn’t show up. There is only a curious message somewhere on the
screen!
– The browser isn’t able to execute an applet. Get and install the ’Java
Runtime Environment’ from Oracle (see above).
• The applet window is visible but you get an TCP/IP error.
– Somebody else is already talking to the interface box! It is not possible
to call the applet several times. Only one client is allowed.
– There is a problem with the interface. Use the reset button at the front,
wait about 10 seconds and use the reload button of the browser.
• The applet window is visible, also the TCP/IP status is o.k. but instead of
the oscilloscopes ID there is an error message or you see funny symbols.
– Check if the oscilloscope is on and connected!
– If it is on and connected check if the baudrate of the oscilloscope is set to
19200. If the baudrate is wrong correct it to 19200 and reload the applet.
– Sometimes the controller in the oscilloscope fails! So switch the oscilloscope off and on and try to connect again.
• You pushed the ’Start Hardcopy’ button, the applet started but getting
data is slow (even stops after a while ).
– The serial port of the oscilloscope -is- slow if the ’Measure’ function is in
use! Press the ’RUN/STOP’ button at the oscilloscope and the download
becomes faster.
– If the download is slow and even interrupted after a while you might
be connected to the network via a wireless link. If too much people
are connected the bandwidth is to small. Use the network plug in the
workbench instead.
• Failures during operation.
– Use the reset button right at the front, wait about 10 seconds and use
the reload button of the browser.
71