Jacobs University Bremen

Electrical Engineering I

Lab

Fall Semester 2018

Course CH10-300111

Instructors - Uwe Pagel, Res.I Room 37

e-mail - u.pagel@jacobs-university.de tel.: +49 421 200 3114

Website - http://www.faculty.jacobs-university.de/upagel

October 11, 2018

Contents

I General remarks on the course 5

1 Grading of the course 61.1 About the Exam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2 About the Lab reports . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Report Writing Guidelines 82.1 Report Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 An advice to save your time . . . . . . . . . . . . . . . . . . . . . . . 92.3 What to do with the second topic? . . . . . . . . . . . . . . . . . . . 92.4 My data ’disappeared’ or ’I’m lost’ because of the topic– what to do? 9

3 Manual Guideline 103.1 Circuit Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2 Values in Circuit Diagrams . . . . . . . . . . . . . . . . . . . . . . . . 123.3 Before the first Lab Session . . . . . . . . . . . . . . . . . . . . . . . 12

II Experiments 13

4 Experiment 1 : Usage of Multimeter 144.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.3 Part 1A : Voltage Measurement . . . . . . . . . . . . . . . . . . . . . 184.4 Part 1B : Voltage Measurement Pitfall . . . . . . . . . . . . . . . . . 184.5 Part 2 : Current Measurement and Pitfalls . . . . . . . . . . . . . . . 194.6 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5 Experiment 2 : Ohm’s Law 225.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225.3 Part 1 : Resistance of a copper wire . . . . . . . . . . . . . . . . . . . 225.4 Part 2 : Resistance of a metal film resistor . . . . . . . . . . . . . . . 235.5 Part 3 : Resistance of a PTC resistor . . . . . . . . . . . . . . . . . . 245.6 Part 4 : Resistance of a NTC resistor . . . . . . . . . . . . . . . . . . 255.7 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

6 Experiment 3 : Thevenin’s and Norton’s Theorem 286.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296.3 Part 1 : Wheatstone Bridge . . . . . . . . . . . . . . . . . . . . . . . 30

2

6.4 Part 2 : Determine Thevenin’s and Norton’s parameters . . . . . . . 316.5 Part 3 : Determine VAB ≡ V 5 and IAB ≡ I5 using Thevenin’s Circuit 326.6 Part 4 : Determine IAB ≡ I5 using Norton’s Circuit . . . . . . . . . . 336.7 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

7 Experiment 4 : Single PN - Junction 357.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357.3 Part 1 : Determine Anode and Cathode . . . . . . . . . . . . . . . . 357.4 Part 2 : Forward V-I-Curve of a general purpose diode . . . . . . . . 367.5 Part 3 : Reverse and Forward Characteristic of a Z-Diode . . . . . . . 377.6 Part 4 : A Zener Shunt Regulator . . . . . . . . . . . . . . . . . . . . 387.7 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

8 Experiment 5 : Transistor Characteristics 418.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418.3 Part 1 : Input Characteristic . . . . . . . . . . . . . . . . . . . . . . . 418.4 Part 2 : Output Characteristic . . . . . . . . . . . . . . . . . . . . . . 438.5 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3

4

Part I

General remarks on the course

5

1. Grading of the course

1. All grades are collected in percent according to the Jacobs grading scheme.The final grade is calculated as the weighted average of the following compo-nents:

Exam (written, during finals) = 40%Lab Reports (20% each) = 60%

2. Attendance to the course is mandatory. Missing an experiment without validexcuse will subtract 20% from the final grade

1.1 About the Exam

The exam is like a normal final at the end of the semester. It will take placeduring the examination week. The topics are about problems around lab work, theinstruments, and the executed experiments.

1.2 About the Lab reports

1. For the experiment(s) of a week every student has to deliver the data for allexperiments and has to write one report. In total 3 reports for the wholecourse.

2. The reports have to follow the ’Report Writing Guidelines’. Objectiveof the lab is not only to consolidate the EE lecture. You should learn toconduct and to document an experiment and to interpret the results. This isan essential pre-requisite to perform research at a later stage in your studies.

3. Submission of the notes and the requested number of reports is mandatory. Amissing report count 0% for the grade!!! Grading is done individually. Reportsare no group work.

The deadline for submission of the notes and the report is the second weekendafter execution, Sunday evening 24:00! (In other words you should submitafter nine or ten days after the experiment). In general:

a. Only those reports are treated as delivered which include a sufficientamount of gradable content!!!!Rule of thumb: Reports without Experimental Set-up and Re-sults and -SOLVED- Evaluation section definitely do not haveenough content!

b. Reports submitted after the deadline will be downgraded by one full markper day (15.01%). After 7 days the report counts as not submitted!!!!

A broken computer or ’lost’ data is no reason formissing the deadline

6

These strict rules reflect the importance of writing reports to achieve the goalof the lab course.

4. Return of the handed in report is usually about 2-3 days after delivery. If youlike you can correct and redeliver the report during the next seven days. Thegrade will be adjusted dependant on your corrections.This part of the report procedure is especially important so that you do notonly get feedback on how to improve but that you actually can benefit fromspending that extra amount of time, both in terms of your grade and whatyou have learned.

5. In case of cheating or plagiarism (marked citations are allowed but no completecopies from a source) we will follow ’The Code of Academic Integrity’ andthe report will be counted as 0%.Note that there there can be more consequences of a disciplinarynature 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 ina straightforward manner and to communicate the results. When preparing thereport you can use word processors, spreadsheets, graphic and CAD tools. In caseof computer problems a hand written report is fine too! Submitting is possibleon paper or by Email. Preferred format is PDF. Try to avoid special formats.Convertors to PDF are available for all systems.A report should be as short as possible but contain all necessary information. Itshould be presented in the following (or a similar!!) format:

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. IntroductionObjective of the experiment and a short summary of the theory.

3. Experimental Set-up and ResultsThis section is the documentation of the conducted experiment:

• Show the experimental set-up (circuit) and describe the procedure.

• Show the results of the experiment.

4. EvaluationHere you should answer all the questions from the Evaluation section(s). Ans-wer as short as possible. For any calculation show the used formulas togetherwith the numbers and units. The result should have a reasonable number ofdigits.

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 thebeginning of the section!

5. ConclusionThis is the final part of the report! Here you should summarize the resultsand compare them to theory. Draw your conclusions related to the topic ofthe experiment. Address directly what has been learned in lab. Discuss thepossible errors and deviations so far not already done during evaluation.

8

6. ReferencesList -ALL- sources you used to write the report.

7. AppendixThe data of the other experiment of the week.

You can find a skeleton lab report on the course web page under

http: // www. faculty. jacobs-university. de/ upagel/ 01. 0. generaleelab/

01. 3. extra_ docu/ sample_ report. doc

2.2 An advice to save your time

It is a good idea to prepare an experiment the day/ morning before the lab. Atleast read the manual better also a second source. Prepare the needed tables andgraphs! During the experiment plot the graphs simultaneously. In Exel using the”XY (Scatter)” option. In this way you will see odd results straight away. With atheory already written and preparation in this manner ≈ 50% of your lab report isalready done when leaving the lab.

2.3 What to do with the second topic?

It is essential that you also work on the experiment you do not write the reportfor. Since you deliver the notes you have a full set of data. You should answerthe evaluation questions as exercise on your own. This is important to survive theexam! It goes without saying that the team member who writes a report also givesa copy to his fellow team members.

2.4 My data ’disappeared’ or ’I’m lost’ because

of the topic– what to do?

In case of ’lost’ data ask your group mates or someone from other groups. Of courseyou can also get a full set from the instructor. In the last two cases don’t forget tomention it in the report.If you lose track among the evaluation questions ask the instructor! He should bemore or less always available!!! Either personal in his office (9:00 to 16:00 for sure)or by mail. Contact info is on the cover page.

9

3. Manual Guideline

The manual and the course web-site contains all necessary information around thecourse. Beside this the manual includes a description of all experiments. Everyexperiment 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 somecases 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 andwhat to measure.

The Evaluation Section should deepen the understanding of the topic. Thereare questions about the experiment. You should solve these with help of the takendata and compare the results to theory.Before you start working on a (sub)section read -the whole- section carefully. Tryto understand the problem. If something is not clear read again and/or ask the TAor instructor. Follow the preparation carefully to have the right setup and not todestroy any components. Take care that you record -ALL- requested data. Youmay have problems to write a report otherwise!!

3.1 Circuit Diagrams

Next is an overview about the used symbols in circuit diagrams.

Connections

wire connected wires

not connectedwires

Connection are usually made using 1 or 0.5m flexible lab wires to connect the setupto 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 areal short with no ’Impedance’. In the following semesters you will see that this isnot true.

10

Instruments

ammeter voltmeterA+

V+

Since we have ’Multimeters’ this symbol tells you how to connect and configure theinstrument. Take care of the polarity. Be careful, in worst case you blow it!!!

Voltage/Current Sources

real idealcurrent source

AC sourcesignal generator

pulsegenerator

~+

fixed variablereal

voltage sourceideal

+

V

These are the symbols used in the manual. If you check the web and look intodifferent books there are also other symbols in use!

Lumped Circuit Elements

resistorvariableresistor capacitor electrolytic

capacitor inductor

++

There is a different symbol for every lumped circuit element. Depending whichstandard is used (DIN or IEC).

Semiconductors

diode zener diodeNPN PNPTransistor

N-channel P-channelJFET

Same as with the symbols before you may find different representations for everycomponent!

11

3.2 Values in Circuit Diagrams

As you will see in the lab, we use resistors with colored rings. These rings representnumbers or a multiplier. Most of the resistors have five rings. Three digits for thevalue, one multiplier for the dimension, and one for the tolerance. In the circuitdiagrams we have a similar scheme. There are three digits and a dimension. Theletter of the dimension also acts as the comma i.e.:

1R00, 10R0, 100R for 1 Ω, 10 Ω, 100 Ω (= V alue ∗ 100)1K20, 10K0, 100K for 1.2 KΩ, 10 KΩ, 100 KΩ (= V alue ∗ 103)1M00, 10M0 for 1 MΩ, 10 MΩ (= V alue ∗ 106)

The numbering for capacitors in the circuit diagram is similar. Only the dimensiondiffers. Instead R, K, M (Ω, KΩ, MΩ) we have µ, n, or p (µF, nF, pF) (i.e. 1n5means 1.5nF). The value is printed as number on the component.

3.3 Before the first Lab Session

As preparation for the first lab session read the description of the workbench, es-pecially the parts about the power supply and the multimeter. You will find thedocument at:http: // www. faculty. jacobs-university. de/ upagel/ 01. 0. generaleelab/

01. 5. 0. instrument_ manuals/ index. html

12

Part II

Experiments

13

4. Experiment 1 : Usage of Multimeter

4.1 Objective

This experiment is a two days experiment. It includes safety instructions and anoverview about errors and error calculation. A short ’How To start’ to write a reportfollows. Main purpose is to introduce and to demonstrate the usage of multimeters.The multimeter is one of the most important instrument in electrical engineering. Itis used to measure basic electrical properties and a basic tool to troubleshoot circuitproblems. In this experiment you should become familiar with the usage and learnhow to get accurate results from the measurements.

4.2 Theory

To analyze the measurements we need Ohm’s Law and Kirchhoff’s Laws. Bothtopics should have been covered by the lecture. To apply these laws we also needsome basic knowledge about the multimeter and it’s usage.

4.2.1 Measuring Voltage and Current

There are several methods to measure these quantities. For nearly every method itis true that it takes power from the circuit under test.

!! Always keep in mind that a connected volt-, or ammeterchanges the circuit under test !!

You are responsible to keep this influence negligible or at least acceptable.

4.2.2 Voltmeter

The voltmeter has to be connected in parallel to the circuit under test. It needscurrent to operate and determines the voltage by using Ohm’s Law U = I ∗Ri. Forgeneral purpose instruments like the ones in the lab Ri = 10 MΩ, for single rangeeven Ri = 1 GΩ. The actual resistance of the voltmeter is given in the manual.Under all circumstances the current has to be negligible compared to the currentused by the circuit. If you do not take care the measured value might be accuratebut it is wrong because of the internal resistance. You changed the circuit and thedevice under test doesn’t work properly anymore!!

4.2.3 Ammeter

An ammeter has to be connected in series to the load. It determines the currentalso by using Ohm’s Law I = U/Ri. For general purpose instruments like the onesin the lab the resistance varies dependant of the range between 0.1 Ω and 100 Ω.Again the actual resistances are given in the manual. From the formula you can see

14

that you include two errors into your circuit. First you add an additional load, i.e.the overall current is lowered. Second you get a voltage drop lowering the voltage atthe load. Under all circumstances the voltage drop has to be negligible compared tovoltage at the load. If you do not take care the measured value might be accuratebut it is wrong because of the internal resistance. You changed the circuit and thedevice under test doesn’t work properly anymore!!

4.2.4 Multimeter

A multimeter is a combination of several functions. In almost all cases it is able tomeasure voltage, current, and resistance. Better instruments can test semiconduc-tors, measure capacitance and frequency. Before first use always check the manual.Figure out how to connect the instrument in any mode and find the properties tokeep the influence of the instrument small!

4.2.5 Errors

For a short introduction into errors and the used terms read the chapter 1, 3, and 4of the ’Errorbooklet’ available here:

http: // www. faculty. jacobs-university. de/ upagel/ 01. 0. generaleelab/

01. 3. extra_ docu/ errorbooklet_ physlab_ f2011. pdf

In the Electrical Engineering Lab we only take care about systematical errors! Espe-cially instrument and methodical errors. It is also important to be able to estimatethe error propagation when using measured values in calculations.

Absolute Error

The absolute error is the deviation of the measured value from the true value. Thatis mostly an instrument error. The absolute error of a multimeter is the error/ theaccuracy given as a set of formulas documented in the manual. The accuracy of aninstrument may be defined in different ways and is dependant on the properties ofthe hardware and the used range. The absolute error (Eabs,∆E) of the most DCvoltage ranges of the instruments in lab is:

• Tenma Multimeter ∆E = ±(0.06% rdg + 3 dig) – ∆ E in [V]

• Elabo Multimeter ∆E = ±(0.03% f.Value + 0.01% f.Range) – ∆ E in [V]

For the current and resistor ranges these formulas are different!

Example: You measure with the Tenma and the Elabo. The Tenma is in range1 (4 V) and the Elabo is in the 2 V range! Tenma reading is 1.500 V. Elabo readingis 1.5000 V. Mind the digits after the decimal point!!! More digits meanbetter resolution, so better accuracy.

Calculation for the Tenma, rdg = 1.500 V and 1 dig = 1 mV:

∆E = ±(0.06% rdg + 3 dig) = ±0.06 ∗ 1.500 V

100+ 3 ∗ 1 mV = 0.0039 V

15

E% = ±(

∆E

rdg∗ 100%

)= ±0.26%

Calculation for the Elabo, rdg = 1.5000V and Range = 2V :

∆E = ±(0.03% f.Value + 0.01% f.Range)

= ±0.03 ∗ 1.5000 V

100+

0.01 ∗ 2 V

100= 0.00065 V

E% = ±0.043%

Relative Error

To compare error values the ’Relative Error’ (Erel, Erel%, E%) is used. It is theabsolute error divided by the true value. The general formula is:

Erel =|V almeas − V altrue|

V altrue– or in % – E% =

|V almeas − V altrue|V altrue

∗ 100%

V almeas is a measured value.V altrue is the known true value.

To get the relative error from the measurements with the multimeter we take

V almeas − V altrue ≡ ∆E ≡ Absolute Error from formula

V altrue ≡ reading from multimeter

Erel =Emax

rdg– or in % – E% =

Emax

rdg∗ 100%

Error Propagation

When using measured values in a formula the error of the result will depend onthe individual errors of the values. The general method of getting formulas forpropagating errors involves the total differential of a function.Given is a function x = f(a, b, c, ...) where the variables a, b, c, etc. must beindependent variables! The maximal absolute error is calculated

∆Emax =

∣∣∣∣∣(∂f

∂a

)b,c

∣∣∣∣∣ ∗∆a+

∣∣∣∣∣(∂f

∂b

)a,c

∣∣∣∣∣ ∗∆b+

∣∣∣∣∣(∂f

∂c

)a,b

∣∣∣∣∣ ∗∆c+ ...

∆a, ∆b, and ∆c are the absolute errors in each component.

Simple cases are

• sums and difference.For sums and difference the absolute error ∆E adds up.

• products and ratios.For products and ratios the relative error E% adds up.

16

Example 1: Two resistors with tolerance in series :

R = R1 +R2 with R1 = 100 Ω± 5% and R2 = 100 Ω± 10%

General solution:

∆R =

∣∣∣∣∣(∂R

∂R1

)R2

∗∆R1

∣∣∣∣∣ +

∣∣∣∣∣(∂R

∂R2

)R1

∗∆R2

∣∣∣∣∣Equation solved:

∆R = ∆R1 + ∆R2

So absolute errors add up

∆R = 100 Ω ∗ 5

100+ 100 Ω ∗ 10

100= 5 Ω + 10 Ω = 15 Ω

and the relative error becomes

E% =∆R

R∗ 100% =

15 Ω

200 Ω∗ 100% = 7.5%

Example 2: Ohm’s law:

U = R ∗ I with R = 100 Ω± 5% and I = 1 A± 10%

∆U =

∣∣∣∣(∂U∂R)

I

∗∆R

∣∣∣∣ +

∣∣∣∣(∂U∂I)

R

∗∆I

∣∣∣∣The solution is :

∆U = I ∗∆R +R ∗∆I

If this equation is divided by R ∗ I = U we get the relative error

∆U

U=I ∗∆R

R ∗ I+R ∗∆I

R ∗ I=

∆R

R+

∆I

I

Here the relative errors add up E% = R% + I% = 5% + 10% = 15%

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4.3 Part 1A : Voltage Measurement

4.3.1 Objective

In this part we use the ELABO multimeter as a voltmeter. We measure a singlevalue and determine the change of the value in the different ranges. The goal is toshow the influence of the multimeter range on the accuracy of the result.

4.3.2 Preparation

Before you start using the ELABO multimeter set the measure mode and the range.In our case ’V’ and ’DC’, and since we always start in the highest range set theturn-wheel to the 2000 V. Assemble the following circuit on the breadboard:

0.9V

R1820R

R2180R ElaboV

+

4.3.3 Execution

Set the voltage supply to 0.9 V. Measure and record the voltage value for the range2000 V, 200 V, 20 V, 2 V, 0.2 V. Take care that you record all digits from the display!Hint: Use tabular form for the recordings. First row is the variable parameter, herethe range. The other rows show the readings.

4.4 Part 1B : Voltage Measurement Pitfall

4.4.1 Objective

In the experiment before we can neglect methodical errors. We only have the in-strument error. But is this true for any circuit?

4.4.2 Preparation

Turn off the power when changing the setup!! We don’t have to change the mode ofthe multimeter. Only set the range turn-wheel back to 2000 V.

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In general you can reduce every resistive DC circuit to an ideal voltage source anda resistor to a so called Thevenin circuit.

Uth1.8V

Rth

Elabo

Thevenin Circuit

Uout

Resistor Decade0R to 10M0

V+

UoutUs3.6V

R1

R2

Voltage divider

V+

The voltage divider converts to ⇒ Uth = USR2

R1 +R2

and Rth =R1 +R2

R1R2

The task is to measure the voltage Uout = Uth. The value should be independentfrom the resistors in the circuit and the connected voltmeter.Assemble the Thevenin circuit from the schematic above.

4.4.3 Execution

Switch on the power and adjust the supply to 1.8 V. Select 0 R at the resistor decade.Set the range of the voltmeter to the best resolution and record the used range. Nowrecord the values at the voltmeter for 0 R, 10 R, 100 R, 1 K00, 10 K0, 100 K, 1 M00, 10 M0.Hint: Use tabular form for the recordings. The first column is the independentparameter, that is varied, here the resistance. The other rows show the readings.

4.5 Part 2 : Current Measurement and Pitfalls

4.5.1 Objective

Like for the voltmeter there are similar instrumental and methodical errors. Thefollowing experiment will demonstrate this.

4.5.2 Preparation

Disconnect all wires from the DC supply. Set the voltage to 1.8V . Now wire up thefollowing circuit:

1.8V R1390R

TENMA

ELABO

MP1 MP2A+

V+

19

Connect the voltmeter in a way that ’MP1’ and ’MP2’ are the plugs at the ammeter!.This is to reduce/eliminate the influence of the connecting wires to the ammeter.Initially use the ’A’ plug of the ammeter. Put the turning knob to ’mA/A’. Beforeyou connect the circuit set the voltmeter to the highest range.

4.5.3 Execution

• Connect the circuit to the power supply and choose the best range for thevoltmeter. Record the range of the voltmeter. The ammeter is already set tohighest range.

• Record the current and the voltages at MP1 and MP2.

• Change the input terminal at the ammeter from ’A’ to ’µA−mA’. Here youchange to a medium range!

• Record the current and the voltages.

• Switch the turning knob of the ammeter to ’µA’. This is the best range (rangewith highest resolution) of the ammeter.

• Record the current and the voltages.

Hint: Use tabular form for the recordings. The first columns show the variableparameters, here ’Plug’ and current range. The other rows show the readings.Example:

Plug Switch Vmp1/[V] Vmp2/[V]A mA/A A

uA - mA mA/A mAuA - mA uA uA

Current

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4.6 Evaluation

4.6.1 Part 1A : Voltage Measurement

1. Calculate all absolute and relative errors of the multimeter values from Part1A. You can find the necessary formulas in the data sheet of the ELABOmultimeter!

2. What is your conclusion regarding the usage of the voltmeter ranges? Whatis the influence of the range to the accuracy?

3. Draw a diagram of the relative error E% = f(U) for the 20 V range.

4.6.2 Part 1B : Voltage Measurement Pitfall

1. Calculate the relative instrument error of the Uth value for all Rth settings.

2. It should be clearly visible that the accuracy of the displayed values is verygood. But some of them are far away from the real values (the Rth = 0 Ωcase). Here we can see a methodical error. What is the course of this error?Calculate the relative methodical error for all cases.

3. What is the internal resistance of the used voltmeter (data sheet!!). Whatshould it be to reduce the methodical error to zero?

4.6.3 Part 2 : Current Measurement and Pitfalls

1. Calculate the relative error of the measured current for all settings.

2. Calculate the relative methodical error for all settings.Hint: To get a ’true value’ use the measured voltage VMP1 and the nominalresistor value R1 = 390 Ω!

3. In the first problem we can see the instrument error. E.g. the accuracy ofthe ammeter. If you look at this and the calculated values for the methodicalerror, what is the best range to measure the current in our case? What is yourconclusion on using an ammeter?

4. Calculate the resistance of the ammeter in all three ranges. There are twoways to calculate the resistance:

Ri =VMP1 − VMP2

I(1) and Ri =

VMP1

I−R1 (2)

Calculate the resistance using both formulas and compile a table with thecalculated values. Compare to the values from data sheet.

5. Why are the previous results are so different? Determine the error propagationof Ri for both formulas when measuring the current in µA range.Why is it not advisable to calculate the error for the other cases? What isyour conclusion in general when using measured values in calculations?

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5. Experiment 2 : Ohm’s Law

5.1 Objective

This experiment should demonstrate Ohm’s Law and show the behavior of differentresistive components.

5.2 Theory

Ohm’s law states that the current through a conductor between two points is directlyproportional to the potential difference across the two points. The constant ofproportionality is called resistance. With this definition this relation is described bythe following formula :

I =V

R

For a strict fulfillment of the rule the temperature need to be constant and theresistance R must be constant, i.e. independent from V and I. Only in this strictcase the behavior is called ’ohmic’. In general the formula yields the instantaneouscurrent.

5.3 Part 1 : Resistance of a copper wire

5.3.1 Objective

The resistance of a copper wire is described by the following formula:

R = ρl

A

The resistance is dependant on a material constant called resistivity (ρ = Greekletter Rho). It is proportional to the length (l) and inversely proportional to thecross sectional area (A).ρ is different for every material. For copper you will find a lot of different values.This is due to the different purity of the used copper. For the wires we use in ourexperiment the value is given in the data sheet from the manufacturer:

ρ = 0.0195Ω mm2

m

The task is to measure the resistance of a 1 m long wire with 0.25 mm2 cross sectionalarea. Since the resistance is very low we use the so called Kelvin (4-wire) resistancemeasurement method. Using this method the influence of connecting wires/contactsis eliminated. The only important thing is that the voltmeter (see diagram!) isconnected to ends of the piece of wire to be measured. In our case the limitingpoints are the solder spots, i.e. the resistance between the solder spots is measured.

22

5.3.2 Preparation

Before you connect the power select one of the variable supplies from the workbench.Set the voltage to 10 V. In this experiment we use the supply as a constant currentsource. Use a lab wire to shorten the output terminals. Switch the internal instru-ment to current. Set the current to 1 A. Now wire up the following circuit. As testitem use the prepared wire at your workbench :

CU-Wire 1m, 0.25mm2

R = ?? Ohm

Elabo Voltmeter

mV Range

Tenma, A Range

I = 1A

solderspotsthe lenght is determined

between these spots

A+

V+

5.3.3 Execution

• Switch on and record voltage and current.

• Remove the wire from the circuit and measure and record the resistance of thewire with the multimeter.

5.4 Part 2 : Resistance of a metal film resistor

5.4.1 Objective

Metal film resistors are frequently used components in electronic circuits. In thisexperiment it is used as an example for an ohmic resistance. In fact it is not reallytrue, but in the narrow limits of our experiment (and mostly in any circuit design)we can take it as constant. To see the behavior of a metal film resistor we measurethe resistance at different voltage values.

23

5.4.2 Preparation

Wire up the following circuit:

Elabo Voltmeter

Tenma

V R11K00

A+

V+

5.4.3 Execution

Vary the voltage at the supply from 0 V to 15 V in 1 V Steps. Record voltageand current. Record the values directly into a spreadsheet program and draw thediagram.

5.5 Part 3 : Resistance of a PTC resistor

5.5.1 Objective

In the experiment before you should have seen a linear (real ohmic) resistance.The following component is different. The PTC (Positive Temperature Coefficient)resistor changes the resistance dependant on temperature. With higher temperaturethe resistance increases. Most of the used conductors show this behavior! So onehas to take care if components has to operate in harsh environments.For lower temperature ranges (up to ≈ 150 C) following formula applies:

RT = RT0(1 + α∆T )) with ∆T = T − T0RT is the resistance at temperature T . T0 is the reference temperature (in ourcase 0C). ∆T is the difference between T and T0. α is the (linear) temperaturecoefficient. It has the dimension of an inverse temperature (1/K or K−1). Forhigher temperatures quadratic and cubic components are added!We use a PT1000 as PTC resistor. PT means it is made from Platinum, and 1000means that the resistance at 0|unC is RT0 = 1000 Ω. The temperature coefficientis α = 3.85 ∗ 10−3 C−1.The component is heated by the supplied power, so by self heating.

24

5.5.2 Preparation

Wire up the following circuit:

Elabo Voltmeter

Tenma

VR1

1K00PTC

A+

V+

5.5.3 Execution

During measurement do not touch the component. Vary the voltage at the supplyfrom 0V to 15V in 2V Steps. After you set the voltage wait about 5 minutes (inthe lab report, do not forget to mention why!!) until you record voltage and current.Draw the diagram while collecting the data!

5.6 Part 4 : Resistance of a NTC resistor

5.6.1 Objective

The NTC (Negative Temperature Coefficient) resistor also changes the resistancedependant on temperature. For the NTC the resistance decreases with rising tempe-rature. The behavior is dependant by the material and is described by the followingformula:

RT = R0 ∗ eB

(1

T− 1

T0

)It is important that all temperatures in this formula are in K (Kelvin)! RT is theresistance at temperature T . T0 is the reference temperature (here 273.15 + 25 =298.15 K). T is the actual temperature. R0 is the resistance at the referencetemperature. B is a constant dependant on the material. In our case the constantsare R0 = 1000 Ω and B = 3480 K.Again the change of temperature is done by the supplied power.

25

5.6.2 Preparation

Wire up the following circuit:

Elabo Voltmeter

Tenma

VR2

1K00NTC

R1100R

A+

V+

Before you connect the power supply take care that the voltage is set to 0 V!!!

5.6.3 Execution

During measurement do not touch the component. Vary the voltage at the supplyfrom 0 V to 8 V in 1 V Steps. After you set the voltage wait about 5 minutes afteryou record voltage and current. Draw the diagram while collecting the data!

Take care not to exceed the voltage over 8 V!!

26

5.7 Evaluation

5.7.1 Part 1 : Resistance of a wire

• Calculate the theoretical resistance of the wire (l = 1 m−A = 0.25 mm2). Usethe ρ given in the experiment section.

• Calculate the resistance of the wire using the values from the 4-wire measure-ment.

• Calculate the relative error of R using the values from the 4-wire measurement.

• The experimental taken R value should be very accurate. Why there aredifferences to the theoretical value?

• Compare the calculated R value from U and I to the value gotten with themultimeter in resistance range. Using the ohm range of the multimeter includesmethodical error. Name these errors. How they are avoided using the 4-wiremethod?

5.7.2 Part 2, 3, 4 : Resistance of different components

• For all resistors draw the graph R = f(I). Put all three graphs in one diagram.

• Do the graphs show the expected behavior?

• Draw the temperature at the PTC as a function of the resistance of the PTCresistor.

• Draw the temperature at the NTC as a function of the resistance of the NTCresistor.

• Why is it dangerous to connect a NTC resistor to higher voltages?

• What kind of ’resistor’ is the copper wire? What are the consequences whenusing it with high currents or with hight temperatures.

27

6. Experiment 3 : Thevenin’s and Nor-ton’s Theorem

6.1 Objective

There are a lot of ways to analyze simple linear electrical networks. E.g.

• Ohm’s Law as a basic tool

• Kirchhoff’s laws

• Superposition theorem

• Mesh-current - Node analysis

Depending on the complexity of a circuit it is sometime hard to use the namedtechniques. Especially if you only want to know a single or a few parameters. Inthis case it is possible to simplify and convert a circuit into an equivalent one.Methods are

• Star-Delta and delta-star transformation

• Thevenin’s theorem

• Norton’s theorem

Today’s experiment should introduce Thevenin’s and Norton’s theorem.

28

6.2 Theory

6.2.1 Thevenin’s Theorem

Thevenin’s theorem states that any linear electrical network with voltage and currentsources and resistances can be replaced at terminals A−B by an equivalent voltagesource Vth in series connection with an equivalent resistance Rth.

A

B

A

B

Black Box Equivalent Circuit

thR+

thV+

V

+

A

• The equivalent voltage Vth is the voltage obtained at terminals A − B of thenetwork with terminals A−B open circuited.

• The equivalent resistance Rth is the resistance obtained at terminals A−B ofthe network with all its independent current sources open circuited and all itsindependent voltage sources short circuited.

For AC systems, the theorem can be applied to reactive impedances as well asresistances.

6.2.2 Norton’s Theorem

Norton’s theorem states that any linear electrical network with voltage and currentsources and only resistances can be replaced at terminals A − B by an equivalentcurrent source INo in parallel connection with an equivalent resistance RNo.

A

B

A

B

Black Box Equivalent Circuit

NoR

+

NoI+

V

+

A

• This equivalent current INo is the current obtained at terminals A−B of thenetwork with terminals A−B short circuited.

• This equivalent resistance RNo is the resistance obtained at terminals A − Bof the network with all its voltage sources short circuited and all its currentsources open circuited.

For AC systems the theorem can be applied to reactive impedances as well as resis-tances.

29

6.3 Part 1 : Wheatstone Bridge

6.3.1 Objective

Setup a Wheatstone bridge and determine the current between the terminals A−B.

6.3.2 Preparation

A Wheatstone bridge is special circuit which is used to measure resistance or resis-tance change. This circuit will be a topic in the next semester. Today we use it todemonstrate Thevenin’s and Norton’s theorem. Wire up the following circuit:

R1220R

R2100R

R3100R

R4220R

R5330RVs

15V A B

TENMA

ELABO

ABV

ABIA+

V+

Use one of the multimeters to set the power supply as exact as possible to 15 V.Record the used value.

6.3.3 Execution

Record the voltage VAB and the current IAB.

30

6.4 Part 2 : Determine Thevenin’s and Norton’s

parameters

6.4.1 Preparation

To get the parameter for the two equivalent circuits you can vary the circuit fromabove.

6.4.2 Execution

• Determine VthLike described in the theory section you get Vth when you remove the loadbetween point A−B. Record the voltage at the ELABO voltmeter.

• Determine INo

To get INo you have to replace the load resistor by a short. Record the currentat the TENMA ammeter.

• Determine Rth and RNo

If you read the theory section for Thevenin and Norton you can see that bothresistors are determined the same way!Replace the power supply by a short and remove the load. Now use the ELABOmultimeter and measure/ record the resistance at the terminals A−B.

31

6.5 Part 3 : Determine VAB ≡ V 5 and IAB ≡ I5

using Thevenin’s Circuit

6.5.1 Objective

Here we check the parameters for the Thevenin’s equivalent circuit found in the stepabove.

6.5.2 Preparation

Wire up the following circuit without R5! Use the R-decade for Rth.

thV

thR

R5330R ELABO

TENMAA

B

V+

A+

Set Vth as accurate as possible at the ELABO voltmeter. TAKE CARE OF THEPOLARITY!!!. As last step insert R5.

6.5.3 Execution

Record the current I5 and the voltage V 5. Compare to to Wheatstone experimentvalues. Are they similar? If not check for errors!

32

6.6 Part 4 : Determine IAB ≡ I5 using Norton’s

Circuit

6.6.1 Objective

Here we check the parameters for the Norton’s equivalent circuit found in the stepabove.

6.6.2 Preparation

For this experiment we use the power supply in constant current mode. To get therequired current the voltage in voltage mode needs to be higher than the voltagedrop over R5. Set the voltage of the supply to about V = 10 V. Shorten theoutput terminals now and set the short circuit current to about the needed current(≈ 45 mA). Wire up the following circuit. Use the R-decade for RNo. Take careof the polarity of the power supply!!!)Note : Set the ELABO ammeter to the highest A range -BEFORE- youswitch on, then reduce the range carefully

NoI NoR R5330R

ELABO TENMAA

B

A+ A+

After switching on adjust the supply to the found INo as accurate as possible at theELABO ammeter.

6.6.3 Execution

Record the current at the ELABO and the TENMA voltmeter.

33

6.7 Evaluation

6.7.1 Part 1

Calculate VAB and IAB for the given Wheatstone bridge using either Kirchhoff’slaws or mesh-current and nodal analysis.

6.7.2 Part 2, 3, 4

• Calculate the components for Thevenin’s and Norton’s equivalent circuit ofthe given Wheatstone bridge.

• Calculate V5 and I5 for Thevenin’s and Norton’s circuit.

• Create a table with all measured and calculated values.

• Discuss the errors! Name the methodical and systematical errors and theinfluence on the result.

34

7. Experiment 4 : Single PN - Junction

7.1 Objective

This experiment should demonstrate the behavior of a single pn-junction of twosemiconductors, also called diode. Topics covered in this experiment are:

• the forward bias and V-I-Diagram of a general purpose silicon diode

• the Characteristic of a Zener-Diode

• a simple application

7.2 Theory

As preparation to this experiment read the relevant chapters (semiconductor, singlepn-Junction, Diode) of the lecture or/and read the relevant chapter from Sarma orFloyd. You need the additional information related to the Zener-Diode from here:

http: // www. faculty. jacobs-university. de/ upagel/ 01. 0. generaleelab/

01. 1. generaleelab1/ zener_ book. pdf

7.3 Part 1 : Determine Anode and Cathode

7.3.1 Objective

First task is to determine anode (p type silicon) and cathode (n type silicon) of thediode.

7.3.2 Preparation

Wire up the following circuit. Ignore the polarity of the diode for now.

12V 1N4001

Tenma

ElaboMultimeter

560R

?

A

V

7.3.3 Execution

• Record the voltage drop over and the current through the diode. Record theorientation of the diode in the circuit. Use the ring as reference.

35

• Reverse the diode in the circuit and record the orientation. Measure and recordvoltage drop and current again.

• There is a second easier way to determine the polarity of a diode. You can usethe Tenma multimeter. Connect lab wires with crocodile clips to the ’COM’and the ’V Ω ..’ plug. The ’V Ω ..’ has positive polarity relative to the’COM’. Clamp the diode in both directions to the multimeter. Record thevalues at the multimeter for the two orientations of the diode. Use ’COM’ ofthe multimeter and the ring of the diode as reference.

7.4 Part 2 : Forward V-I-Curve of a general pur-

pose diode

7.4.1 Preparation

Wire the following circuit:

0..25V 1N4001

Tenma

ElaboMultimeter

560RA

V

7.4.2 Execution

Record the forward V-I-curve of the 1N4001 diode from 0− 40 mA. Execute in thefollowing way:

- Set the current at the Tenma ammeter by adjusting the power supply voltage.Use the following approximate current values:

0µA, 30µA, 70µA, 100µA, µA, 500µA, 700µA

1mA, 2mA, 3mA, 4mA, 5mA, 10mA, 20mA, 40mA

- Use the lowest possible range with the Tenma multimeter. Set the values asclose as possible.

- Record the set IF from the ammeter and the resulting UF from the voltmeter!(F denotes forward bias)

Hint : Generate the diagram IF = f(UF ) together with the table! Youcan check your data for errors and you may see if you need more datapoints in regions where the current changes rapidly. Anyway it is neededfor the evaluation.

36

7.5 Part 3 : Reverse and Forward Characteristic

of a Z-Diode

7.5.1 Preparation

Wire up the following circuit on the breadboard:

0..30V BZX85C5V6

Tenma

ElaboMultimeter

470RA

V

7.5.2 Execution

• Record the reverse V-I-curve of the BZX85C5V6 from 0-45mA.

- Take the voltage for the maximum impedance point ZZK (also called theknee voltage, see data sheet) at 1 mA. Record current and voltage at thispoint.

- Find the reverse breakdown voltage (Z-voltage). In the data sheet thisvalue is defined at 45 mA (VZ@IZT ). Record current and voltage at thispoint.

- With these two characteristic points choose appropriate values for recor-ding the rest of the curve. Do not forget to take extra values close to 1mAand 45mA to find the differential resistance dU

dIof the diode (ZZTandZZK)

(for the evaluation!!). Sometimes the differential resistance is also called’dynamic resistance’.Simultaneously with the recording of the data draw the diagram to get a’smooth’ curve!!

• Reverse the polarity of the diode. Record the forward V-I-curve of the BZX85C5V6from 0− 30 mA. Proceed like in 7.4!

37

7.6 Part 4 : A Zener Shunt Regulator

7.6.1 Objective

Unlike the normal diode a Zener-Diode is used in reverse direction. It can be usedto limit or stabilize voltages. Here we want to take a closer look at Zener ShuntRegulator:

RLBZX85C5V6

RV

Zener Shunt Regulator Load

UB

IZ

ILI

V+

The Zener-Diode supplies a nearly constant voltage to a load. For a detailed des-cription of the theory use a book of your choice or have a look at:

http: // www. faculty. jacobs-university. de/ upagel/ 01. 0. generaleelab/

01. 1. generaleelab1/ zener_ book. pdf

In general the circuit behaves like a current divider. The current through RV is sup-plied to RL and the diode. In the experiment we try to understand how the Z-Diodestabilizes the load voltage. We assume/set the input voltage constant. Based on theschematic above the task is to design a circuit which supplies an output voltage of5.6 V and a load current of 10 mA.

7.6.2 Preparation

• The load should be 10 mA at 5.6 V. Calculate RV for two cases. IZ = 1 mAand IZ = 10 mA

• Assemble the following circuit:

RLBZX85C5V6

RV

UB

15V

IZ

ILI

Tenma

Elabo

I

ULV+

A+

Use the R-Decade-Box from the shelf for RL. For the first part insert the RV

you found for IZ = 1 mA.

38

7.6.3 Execution

• Record I and UL for load resistors 56R, 560R, 5K60, and without RL (meansopen circuit!).

• Insert RV for IZ = 10 mA.

• Repeat the measurements from before.

39

7.7 Evaluation

7.7.1 Exp Part 1 : Determine Anode and Cathode

• Use the measurements to explain which terminal of the diode is the anode,and which one is the cathode? In general the lead with the ring has the samepolarity for every diode!

7.7.2 Exp Part 2 : Forward I-V-Curve of a general purposediode

• Plot the diagram IF = f(UF ).

7.7.3 Exp Part 3 : Reverse and Forward Characteristic of aZ-Diode

• Plot I = f(U) for both directions.

• Determine the differential resistance of the diode at ZZT@IZT = 45 mA andZZK@IZK = 1 mA in reverse direction from your experimental data? Com-pare with the data sheet. What information do you get from the differentialresistance?

7.7.4 Exp Part 4 : A Zener Shunt Regulator

• Show the full calculation for RV .

• Compile a table with the measured values.

• Describe the function of the circuit.

• Why is it not advisable to use loads with a too low resistance?

40

8. Experiment 5 : Transistor Characteris-tics

8.1 Objective

A bipolar transistor is an active 3 terminal semiconductor device. The three termi-nals are Emitter, Base, and Collector.A transistor is build of consists of 2 junctions forming diodes ’back to back’, i.e.NPN or PNP.

C

B

E

n

p

n

pnp - Transistornpn - Transistor

C

E

B

C

B

E

p

n

p

C

E

B

In this experiment you will explore the transistor parameters, i.e. how the two diodeswork together to perform the transistor action like e.g. current amplification.

8.2 Theory

As preparation to this experiment read the relevant chapters of the lecture or/andread the relevant chapter from Sarma or Floyd.

8.3 Part 1 : Input Characteristic

8.3.1 Objective

The input characteristic shows the behavior of the base emitter diode. We willrecord both, the forward and the reverse characteristic.

41

8.3.2 Preparation

Below is the circuit symbol for an 2N2222 NPN-Transistor together with its pin out.

1997 May 29 2

Philips Semiconductors Product specification

NPN switching transistors 2N2222; 2N2222A

FEATURES

• High current (max. 800 mA)

• Low voltage (max. 40 V).

APPLICATIONS

• Linear amplification and switching.

DESCRIPTION

NPN switching transistor in a TO-18 metal package.PNP complement: 2N2907A.

PINNING

PIN DESCRIPTION

1 emitter

2 base

3 collector, connected to case

Fig.1 Simplified outline (TO-18) and symbol.

handbook, halfpage

MAM2641

3

2

3

12

QUICK REFERENCE DATA

SYMBOL PARAMETER CONDITIONS MIN. MAX. UNIT

VCBO collector-base voltage open emitter

2N2222 − 60 V

2N2222A − 75 V

VCEO collector-emitter voltage open base

2N2222 − 30 V

2N2222A − 40 V

IC collector current (DC) − 800 mA

Ptot total power dissipation Tamb ≤ 25 °C − 500 mW

hFE DC current gain IC = 10 mA; VCE = 10 V 75 −fT transition frequency IC = 20 mA; VCE = 20 V; f = 100 MHz

2N2222 250 − MHz

2N2222A 300 − MHz

toff turn-off time ICon = 150 mA; IBon = 15 mA; IBoff = −15 mA − 250 ns

Pin Description1 emitter2 base3 collector

Wire the following circuit on the breadboard:

Tenma

10k0

UbeElabo

Ib 2N2222A

Ube Supply 0 to 12V

Uce Supply 0.4V

A

V

8.3.3 Execution

• Record the forward characteristic of the base-emitter diode. The procedure issimilar to the normal diode.

- Set the UCE supply to 0.4 V.

- Set the current at the Tenma ammeter. Use the following current va-lues:

0µA, 5µA, 10µA, 20µA, 40µA, 60µA, 80µA, 100µA

200µA, 400µA, 600µA, 800µA, 1000µA

Use the lowest possible range with the Tenma multimeter. Set the valuesas close as possible to the given ones.

- Record the set IBE from the ammeter and the resulting UBE from thevoltmeter!Important : Take the values as quickly as possible, becausethe transistor becomes hot and the characteristics change withtemperature.

• As second step we evaluate the reverse characteristic of the base-emitter diode.Disconnect UCE and reverse the UBE supply. Record the reverse current IBr

as a function of UBE. Use 1V steps for UBE until IBr becomes about 1− 5µA.Then change IBr in similar steps as before. Make sure that you record thevalues with values close enough to each other to get enough points for thegraph when the current starts to change rapidly with increasing reverse biasvoltage.Record UBE and IBr

For both problems immediately create a graph beside the table!

42

8.4 Part 2 : Output Characteristic

8.4.1 Objective

The output characteristic is a series of curves. It shows the the function IC = f(UCE)for various IB. IB is a parameter which represents the input to the transistor fromwhich the current amplification of the transistor can be evaluated.

8.4.2 Preparation

Wire the following circuit on the breadboard.

1K00 IcTenma

2N2222A

UceElabo

Collector Supply 0..25V

100R

IbCurrent Source 10 - 1000uA

+

A

V

The constant current source is the small black box in the shelf of the workbenchlabeled ”Current µA” . Plug it into one of the outputs of the DC-supply. Set thevoltage to 20V. The output of the source is the BNC-plug at the bottom. Use theBNC to Cleps cable to connect it to the circuit. The red wire of the BNC-cable isthe positive terminal and the black wire is the ground.

8.4.3 Execution

• Set IB to 20µA. Vary the collector supply in a way that UCE (read at theElabo) changes from 0V to 20V. Use the following steps:

- from 0V to 1V every 0.2V

- then 2.5V, 5V, 10V, 15V, 20V

Use a spread sheet to record the values of UCE and ICE. Take the valuesquickly because the transistor heats up and changes characteristic. Also itmight be destroyed! Check the power dissipated between the collector and theemitter. Do not exceed PCE = UCE ∗ ICE = 700 mW. Calculate the power forevery step and if you exceeded it or will exceed skip the remaining steps.

• Repeat the first step for IB = 40µA, 60µA, 80µA, and 100µA.

• Record ICE for IB = 100µA, 200µA, 300µA, 400µA, and 500µA with UCE setto 1V. Be careful, adjust UCE every time after you have changed IB!

43

8.5 Evaluation

8.5.1 Part 1 : Input Characteristic

• Draw the diagrams of the input characteristic IB = f(UBE) with UCE =const. = 0.4 V

• Draw the diagram of the reversed base-emitter-diode IBr = f(UBE).

• Compare to the diode curves from the diode experiment.

8.5.2 Part 2 : Output Characteristic

• Plot the output characteristic ICE = f(UCE) for every IB into one diagram.

• The max. power dissipation for the 2N2222 is 700mW. Insert the curve for Ptot

into the ICE = f(UCE) plot. Did you exceed the limit during the measurement?

• Plot the current amplification IC = f(IB) with UCEconst. = 1 V and determinethe current amplification β by fitting a straight line through the data points.

• Indicate in your diagram the area in which linear operation is possible (i.e.the linear region).

44