EE 305 Electronic Devices and Design Lab

Syllabus, Theory & Assignments Manual Khalid H. Tantawi Electrical and Computer Engineering Department University of Alabama in Huntsville Huntsville, AL 35899 Table of Contents Syllabus and Lab Instructions…………………………………………………………………………………………………..……page 2 Introduction: Important Notes & Common Operator Errors……………………………………………………..….page 5 Experiment # 1…………………………………………………………………………………………………………………………..…page 6 Experiment # 2…………………………………………………………………………………………………………………………..…page 7 Experiment # 3…………………………………………………………………………………………………………………………..…page 10 Experiment # 4…………………………………………………………………………………………………………………………..…page 12 Experiment # 5…………………………………………………………………………………………………………………………..…page 13 Experiment # 6…………………………………………………………………………………………………………………………..…page 15 Experiment # 7…………………………………………………………………………………………………………………………..…page 16 Experiment # 8…………………………………………………………………………………………………………………………..…page 19 Experiment # 9…………………………………………………………………………………………………………………………..…page 22 Experiment # 11……………………………………………………………………………………………………………………………page 23 Experiment # 12……………………………………………………………………………………………………………………………page 25 Supplementary Exam Questions……………………………………………………………………………………………………page 26 References……………………………………………………………………………………………………………………………………page 27

2012

Course Syllabus & Lab Instructions EE 305 Electronic Devices and Design Lab- Spring 2012 Sections 01, 02, and 03 Course instructor: Khalid Tantawi

Email: [email protected] Twitter: @KhalidTantawi Phone: (256) 824-6469 Office: 410 Optics Building

Office Hours: Monday 11:00 AM - 12:00 AM, Tuesday 2:00 PM- 4:00 PM Meeting Time: Section 01: Thursday

5:30 PM - 8:30 PM Section 02: Wednesday 8:00 AM - 11:00 AM Section 03: Tuesday 5:30 PM - 8:30 PM

Location: Engineering Building 225 Prerequisite: Electronic Measurement Lab Pre/Co requisite: EE 315 Introduction to Electronic Analysis and Design Required Textbook: K.C. Smith, Laboratory Explorations for Microelectronic Circuits, 4th edition, Oxford University Press, 1998 [1].

References: A. S. Sedra and K. C. Smith, Microelectronic Circuits, fifth edition, Oxford University Press, 2004 [2] J. Millman and A. Grabel, Microelectronics, second edition, McGraw Hill, 1987 [3]

Course Objectives: There are three main goals for this course: 1) To introduce the student to some microelectronic devices such as op-amps, diodes, BJTs, and MOSFETs, and to be able to work and design basic circuits using these devices. 2) To use analytical techniques to mathematically derive and predict outputs of electronic circuits. 3) To use computer software to simulate and design microelectronic circuits.

Grading Policy: Attendance & Lab Performance: Pre-lab Assignments: Lab Reports: Mid Term Exam: Final Exam: Letter Grade ranges: 98-100: A+ 80-84.99: B+ 65-69.99: C+ 50-54.99: D

40% 10% 30% 5% (closed book and closed notes) 15% (closed book and closed notes) 90-97.99: A 75-79.99: B 60-64.99: C less than 50: F

85-89.99: A70-74.99: B55-59.99: C-

EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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Topics covered: Class Experiment Number and Topic Lab Explorations 1 Experiment 1 Operational Amplifier Basics E1.1, E1.3, E2.1 2 Experiment 2 Operational Amplifier Applications E2.1, E2.2 3 Experiment 3 Junction-Diode Basics E1.1, E1.2 4 Experiment 4 BJT Basics E1.1 5 Experiment 5 MOSFET Measurement and Applications E2.1 6 Mid term Exam 7 Experiment 6 Differential Amplifiers E1.2 8 Experiment 7 (part 1) Single-BJT Amplifiers E1.1, E3.1 9 Experiment 7 (part 2) E4.1, E5.1 10 Experiment 8 Feedback Principles using op-amps E1.1, E2.1, E2.2 11 Experiment 9 Basic O/P-Stage Topologies E1.2, E2.2, E3.2 12 Experiment 11 Op-Amp-RC Filter Topologies E1.1, E1.2 13 Experiment 12 Waveform Generators E1.1, E2.1 14 Final Exam Note: It is your responsibility to conform to all announcements and changes made in the schedule.

Lab Instructions:  Refer to this manual (Assignments Manual) for details of the required pre-lab assignments and questions to be answered in the post-lab reports, and a background theory.  No makeup sessions will be given for absence without an acceptable and reasonable excuse.  Attendance is very important. Missing four classes or more will result in an “F” grade.  Please put back all lab equipment used during your lab session. Points will be taken off for uncleaned benches.  Pay full attention to the lectures given at the beginning and during the lab session. This is important for you to be able to answer the experiment questions, and do well in exams.  In the case you were not able to finish an experiment during the lab session, complete your report with the data you obtained, and analytically calculated values, as well as simulations.  You are encouraged to ask questions any time.  Please check your university email address regularly for any announcements and changes.

Notes about Pre-Lab Assignments  The Pre-Lab assignments are given in the Instructions and Assignments Manual.  The Pre-Lab Report should contain the simulated results in tabular form (If the results are not tabulated and clearly presented, points will be deducted, I will not search for your answers) and Simulation Plots/Graphs (if simulation is required), and Answers to the given questions.  If a computer simulation is required. You may use any computer software such as Multisim.  The Pre-Lab assignment is due at the beginning of the class of that experiment.

Lab Reports  The Lab Report should include the following parts: 1. Cover page: Should include your name, date report is submitted, course number, section number, experiment number, title, and the date it was performed. 2. Objectives: one or two sentences about the purpose of the experiment. 3. Procedure: a brief description (one paragraph) of what you have done in the lab, explain as if you are explaining to another student how to do the experiment. EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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4. Sketches of the Circuit diagrams 5. Tabulated Lab Data and Results: I will not search for your results if they are not tabulated and clearly presented. 6. Plots and Graphs: should be neatly plotted and captioned. 7. Answers to questions: the questions are given in this manual. I will explain the answers to the questions in my lectures at the beginning and during the lab session. 8. Conclusion: Write what you learned, the conclusion should be related to the core purpose of the experiment, you should show what theory do you conclude from the practical measurements. Please avoid conclusions like “the experiment was interesting”..etc. 9. The signed data sheet attached at the end of the report. 10. Overall neatness  All the parts must be present. Answers like “refer to data sheet” are not accepted.  Each Lab Report is due at the beginning of the following class from which the experiment was performed.

Important Notes:  Late Reports and assignments are not accepted, except in the case of special circumstances.  Neatness counts. Points will be taken off if the report or assignment is not neat.  Please do your own work. Any evidence of plagiarism will result in a grade of zero.

EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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Introduction: Important Notes and Common Operator Errors 1. Voltage and current measurements:

IMPORTANT: when measuring the current, it is absolutely important to double check the connection and make sure that the Ammeter is connected in SERIES in the circuit, to avoid any risk of a short circuit. 2. The following figure shows the electronic devices which you will be seeing in this lab :

You will also study the operational- amplifier (op-amp) and some BJT- based amplifiers. 3. You are expected to be able to read the resistance values of 4-band and 5-band resistors: Resistance Color code Example Black 0 Broun 1 Red 2 Orange 3 Yello 4 Gold ± 5%

Green Blue Violet Grey White Silver

5 6 7 8 9 ± 10%

This resistor has a reading of 10×102 ± 5% = 1 KΩ ± 5%

4. Impedance in the S-domain: Some equations in this manual are derived in the s-domain for ease. To understand the derivations, you need to refresh your memory about how to express the different impedances in the s-domain as is shown in the table below: Element Resistor (R) Capacitor (C)

Impedance R

Inductor (L) 5. Use the following pin diagram for the LM741CN op-amp:

EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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Experiment # 1: Operational- Amplifier Basics Date performed:

.

Lab Explorations: E1.1, E1.3, E2.1 Note: Use the LM741CN chip, refer to its pin diagram on the previous page (do not use the pin diagram in the text, it is not for this chip). Answer the following questions.

Questions and Review: 1.

In the figure below, what is the voltage at node b:

2.

If the output of the signal generater is a pure sine wave with a value of 2 Vpp: a) What is the value of the average voltage (vavg)? b) What is the value of the root-mean-square voltage (vrms)? Answer the analysis questions in the text for parts E1.1, E1.3, and E2.1 What is the value of the output (Vout) in the circuit below (you do not have to build the circuit):

3. 4.

10KΩ

2KΩ

+12V +12V

0.2V

1KΩ

Vout

2KΩ

+

+

-12V

-12V

Theory : Ideal op-amp characteristics: a) Very high input resistance b) Very low output resistance c) The positive and negative terminals are virtually short circuited. 1. Inverting amplifier:

Equation 1.1 (

2. Non-inverting Amplifier :

)

Equation 1.2

R2

R2 +12V

+12V

Vout

Vs

Vout

R1

R1

+ Vs

+

-12V

-12V

Figure 1. (Left) an inverting amplifier configuration. (Right) the non-inverting amplifier configuration

EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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Experiment #2: Operational Amplifier Applications-the Integrator Date performed:

.

Pre-lab work: Do exploration E2.2 analytically, by filling out the right half of table 2.1 below, Use equations 2.4, 2.5 and 2.6 on the following page to calculate the values analytically. Show a sample calculation of the values of any row of your choice.

Lab Explorations: E2.1, E2.2 Note: Use the LM741CN op-amp. Use the pin diagram that is posted on page 5 of this manual (and on the wall in the lab). Do not use the pin diagram in the text, it is not for this chip. Answer the following questions, and include the answers in your report. Refer to the theory section on the following pages for explanations.

Questions: 1. Fill out the following table with values from your lab measurements and those calculated using equations 2.4, 2.5 and 2.6 (see next page). Table 2.1: Experimental and analytical results

VA

(b) 1Vpp

Vc

Measured experimentally Gain (Vc/VA) frequency 1KHz

phase

Calculated using equations 2.4 and 2.5 Gain (Vc/VA) frequency Phase Vc 1KHz

(c) 1Vpp

1

1

(d1) 1Vpp

0.1

0.1

(d2) 1Vpp

10

10

2. You must have noticed that the output Vc decreases and approaches zero as the frequency increases, the phase also approaches 90o as frequency increases. This is expected by inspection without doing any calculations. Explain how? 3. Using the same argument above, by inspection what value do you expect the output Vc will take if the input was a pure dc signal of 0.2 V? what is the phase angle in this case? Familiarization with the Bode Diagram: 4. An easier way to predict the values in the table above is to use the Bode Diagram. This diagram consists of two plots: the magnitude diagram and the phase diagram. a) Convert the following gain values from decibles to absolute gain in V/V: i) Vc/VA = 3 dB ii) Vc/VA = 0 dB iii) Vc/VA = -20 dB b) Convert the following gain values to decibles: i) Vc/VA = 0.5 V/V ii) Vc/VA = 2 V/V

iii) Vc/VA = -10 V/V

5. Use equation 2.2 to plot the Bode diagram of the system. If you are not familiar with the Bode Diagram, you may use this Matlab code. (Note: the frequencies will be displayed in rad/s, to read them in Hz, you need to divide them by 2π): s=tf(‘s’); G = -1000/(s+10); Bode(G) EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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c) At the frequency of the pole of this system, the magnitude starts dropping, it is called the Cutoff Frequency (also called the Half-Power Frequency) what is the cutoff frequency of the system? 6. Using ideal op-amps, design a circuit that outputs the solution of the differential equation given by: ( ) ( )

Theory: Now we will solve for the analytical values, the circuit diagram in figure 2.3 in the text may be redrawn as follows: R2

C +12V

-

VA

Vc

R1 +

+10 V

R3

-12V

-10 V

Figure 2.1: redrawing of the circuit in figure 2.3 in the text (left). The simplified circuit (right)

As seen, this circuit has two inputs. The input that is composed of the adjustable voltage divider provides an offset compensation, so we will ignore it in the derivation. The gain Vc/VA may be derived in the s-domain for ease, we know that the transfer function is given by:

Equation 2.1 It might be better looking to factor out the coefficient of s, to get an easier expression of the pole: (

)( (

)(

)

Equation 2.2 )

The expression above is called the transfer function. And the values of s that make the denominator equal to zero are called the poles of the system. In the expression above we see that there is only one pole in the system at s = -10. Therefore the pole lies at 10 rad/s = 1.59 Hz. The minus sign indicates that the pole is on the left hand side of the s-plane, and hence the system is stable. ⇒ ⇒| | ⇒

Equation 2.3 Equation 2.4

√

[( ( )

)

]

Equation 2.5 Equation 2.6

The Bode Diagram: The equations above may be calculated or plotted directly using a graphing utility. However an easier way to find the values of the gain and angle vs. frequency, is to use the Bode Diagram. The strength of EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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this tool lies in the fact that it linearizes the system by plotting the logarithm of the transfer function vs. frequency. The magnitude is plotted in units of decibles (dB). To convert from absolute to dB:

|

Example 1: If the absolute gain is 100, then: Example 2: If the gain in decibels is -40 dB, then: |

|

|

Application: Analog Computers and System Realization Example 3: Use ideal op-amps to design a circuit that outputs the solution of the differential equation ( ) ( ) given by: Solution: First put the highest order derivative (in this case it is equation on the other side to get:

) on one side, and all other parts of the

From the equation above, is a summation f three variables, thus we need an op-amp in the summing configuration to get . Then we simply integrate twice to get x. The solution is shown in the figure below. The output of the first op-amp from left is . is then integrated twice to get x, and therefore two integrators are needed as shown. Finally, to account for the initial conditions, the nodes at x and are connected to the virtual ground prior to the time t = 0, at t=0 the the connection to ground is opened. For further reading, you may refer to Engineering Circuit Analysis, 4th ed. by Hayt and Kemmerly [4] and Signal Processing and Linear Systems by Lathi [5].

EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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Experiment # 3: Junction-Diode Basics Date performed:

.

Pre-lab work: simulate explorations E1.1 and E1.2 Lab Explorations: E1.1, E1.2 Important Note !! When performing exploration E1.2, the capacitor must be polarized, and you must make sure that the polarized capacitor is properly connected to the right polarity, if the incorrect polarity is used, the capacitor may short circuit. Answer the following questions, and include them in your report.

Questions: 1. Compare the values of the RC time constant and the period of the input signals in E1.2 2. Refer to the figure below to answer the following questions: a) Draw the output voltage waveforms for the two circuits in the figure superimposed on the input waveform. Assume ideal diodes. b) What is the name of each of the two rectifiers shown in the figure? c) Sketch the waveform of the source current (i) for each circuit. Which one has a non zero average value? d) You are asked to design a rectifier to run a small dc motor (i.e. a load that draws a large current) from a transformer. Based on your answers to part c, why should the half-wave rectifier be avoided as possible?

Figure 3.1: Two types of rectifiers

Introduction to Power Electronics: 3. A thyristor is an electronic device that you will not see in this course (nor in EE 315), it is only used in power applications. Draw the symbol of the thyristor with the names of its terminals. 4. Most loads that demand large amounts of power are inductive in nature (such as electric machinery). The figure below shows two circuits supplying a highly capacitive load (left) and a highly inductive load (right), compare the two cases by answering the questions that follow:

+ 10Vpp

R

C

Vout

-

R Vin

+ Vout

i

←

L

-

Figure 3.2: (Left) with a capacitive load, (Right) with an inductive load.

EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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a) What three ways would you do to reduce the ripple voltage in the waveform of Vout in figure 3.2 (Left figure)? b) What happens to the conduction angle of the diode as the capacitance (C) increases? c) Assuming a very large capacitance, sketch the output voltage waveform superimposed on the input voltage waveform. d) With a highly inductive load in the circuit in figure 3.2-(Right Figure), sketch the current waveform of the circuit superimposed on the input voltage waveform. e) What happens to the conduction angle of the diode as the inductance (L) increases?

Theory: Diodes have many applications such as in power converters and in protecting other electronic components. Probably the simplest power converter is the rectifier, other power converters are shown in the figure below [6]:

Figure 3.3: Power Converters

Rectifiers may be half-wave or full-wave. Half-wave rectifiers suffer from two disadvantages when compared to full-wave rectifiers: 1. The output of the Half-wave rectifier suffers from a higher ripple-voltage. 2. There is a non-zero average current that passes in the AC source, this non-zero average current causes magnetic saturation in the secondary coils of the input transformer if the current is large enough. Therefore, half-wave rectifiers should generally be avoided.

EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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Experiment #4: Bipolar- Transistor Basics Date performed:

.

Pre-lab work: simulate exploration E1.1. Show your results of VB, VC, VE, VBE, IB, IC, IE, in the table below. Then calculate the values of α and β from the equations given below.

Lab Explorations: 1. Do exercise 1 in the book, then use the potentiometer to tell the pins and type of the BJTs that you are handed. 2. do exploration E1.1 Note: the value of the current gain β may vary considerably from one device to another. Answer the following questions, and include them in your report.

Questions: Fill out the table below with your simulated and experimental values. VB

VC

VE

VBE

IB

IC

IE

α

β

Simulated Experimental

1. 2. 3. 4.

5.

What does BJT stand for? Draw by hand the symbols of a pnp and an npn BJT transistor, and show all terminal names. Draw by hand the Ebers-Moll models of the npn- BJT and the pnp-BJT. You were given a BJT with pins x,y, and z. After examining the BJT, you had the following measurements using an ohmmeter: Positive lead negative lead reading x y open circuit x z 350 ohm y x open circuit y z 450 ohm z x open circuit z y open circuit a) What type is this BJT, npn or pnp? b) What are the pins that correspond to the Base, Emitter and Collector of the BJT? Calculate the common-base current gain (α) using two methods, once using the direct measurements of Ic and IE , and once using β.

Theory: Refer to the diagram of the BJT transistor in the Introduction of this manual if needed. The common-base Current gain: The common-emitter current gain:

EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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Experiment # 5: MOSFET Measurement and Applications Date performed:

.

No Pre-lab work Lab Explorations: E2.1 -Device Transconductance NOTE 1: Connect pin 14 of the 4007 MOS array to the highest positive volt supply, and connect pin 7 to the most negative supply. NOTE 2: maintain the condition

continuously, to avoid failure of the transistors.

Answer the following questions, and include them in your report.

Questions: 1. 2. 3. 4. 5. 6. 7. 8. 9.

10.

What does MOSFET stand for? Draw by hand an n-type and a p-type MOSFET, show names of all terminals. What are the three regions of operation of the MOSFET? In which region should we operate the MOSFET as an amplifier? In the circuit that you built in the lab, consider the biasing circuit alone, and without doing calculations, what is the voltage drop across RG? why? Without doing calculations, what is the value of the gate-to–source voltage VGS ? What is the minimum value of Vc for the transistor to stay operational as an amplifier? Find the value of the drain current ID (remember that Vc = 5V) Use the value of the transconductance gm which you estimated from gm = Av/RD and the drain current ID which you found in question 5 to estimate the threshold voltage Vt. Use equation 5.4 (see next page) Use equation 5.2 to find the k parameter.

Theory: When the MOSFET is used as an amplifier, it operates in the saturation region, therefore: Formula 1 Neglecting the body effect, the drain current in the saturation region is given by:

(

)

Equation 5.1

Device transconductance: For a MOSFET, the transconductance is a function of several paprameters: the drain current, the overdrive voltage, and even the geometry. (Note that for a BJT, the transconductance gm is only a function of the current as we will see later in experiment 7). The unit for the transconductance is 1/Ω = A/V. For a MOSFET, the transconductance may be given in three ways: EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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( √

)

Equation 5.2 Equation 5.3 Equation 5.4

EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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Experiment # 6: The BJT Differential Pair and Applications Date performed:

.

No prelab assignments. Lab Explorations: E1.2 Note 1: Use the CA3046 chip Note 2: Remember to connect pin 13 to the most negative voltage in the circuit, which is -10.7 volts. If pin 13 is not connected, your circuit will not work properly. Note 3: Do not measure the currents for this experiment, only measure the voltages and calculate the currents using Ohm’s Law.

Questions: Answer the analysis questions in the text.

EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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Experiment # 7: Single-BJT Amplifiers at Low and High Frequencies Date performed:

.

Pre-lab work: simulate explorations E1.1 and E3.1 Lab Explorations: E1.1, E3.1, E 4.1, E5.1 Note: To avoid a very common error that results in a big time delay, when connecting the circuit for E3.1, make sure that you connect the circuit on page 65 (not the one on page 63), and make sure that there is no capacitor connected to the collector, but to the node joining Rc to +15V. Answer the following questions, and include them in your report.

Questions: Do the Analysis questions on page 65 of the lab manual. Use equations 7.1 to 7.7 given here (see next page ) to solve them. For part d) of the analysis questions, use the two cutoff frequencies that you measured in the lab to get two values of Cin1 and Cin2, use these two values to solve for Cµ and Cπ . (i.e. two equations with two unknowns.)

Theory: In this experiment you will see three amplifier configurations using single BJTs. 1. The Common-Emitter Amplifier: in this configuration, the emitter of the BJT is connected to an ac ground, i.e. only the ac signal is grounded, but the dc signal is not grounded obviously. This is achieved by placing a large capacitor between emitter and ground. This capacitor, called CE, will act as short circuit for ac signals but as an open circuit for dc signals. Normally this configuration provides high voltage and current gains (advantage), but low input resistance, and high output resistance(disadvantage) ( remember that for an ideal amplifier, the input resistance should be high, and output resistance should be low). 2. The Common-Base Amplifier: here the base is grounded. This amplifier also gives a high voltage gain that is positive in sign, a low input resistance and a high output resistance as well. 3. The Common-Collector Amplifier: also called an Emitter-Follower. Here the value of the input resistance depends on the load resistance. In Explorations 1.1 and 3.1, From an AC point of view, the dc sources are short circuits, the capacitors are chosen such that they act as short circuits for the frequencies at which the circuit will be operated, therefore, the ac signal sees the circuit as follows:

10 KΩ C

10 KΩ 10KΩ

B E

0.1KΩ

Figure 7.1: The circuit as seen by the ac signal EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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The small signal model of a BJT is used to analyze the applied ac signal. This model is called the hybridpi model.

Cu

10 KΩ 10KΩ

B

rx rπ

0.1KΩ

Cπ

Collector gmvπ

+ Vout Rc -

Emitter Device transconductance: Equation 7.1 (

The output voltage

)

Rx is the base spreading resistance, it is usually much smaller than rπ ( rx << rπ) therefore, it may be neglected, rx is usually in the range 40-400 ohms. (

the voltage at the base :

)

thus, the CE Voltage gain is: (

)

Equation 7.2

the base spreading resistance rx may be estimated as : Equation 7.3 The cutoff frequency fh is given by : Equation 7.4 Where : (

)|| (

Equation 7.5 )

Equation 7.6

To calculate the collector- to- base and emitter-to-base capacitances, use the two cutoff frequency measurements. (

CB voltage gain: CC voltage gain:

||

)

|| ||

EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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Experiment # 8: Feedback Principles Using an Op-Amp Building Block Date performed:

.

Pre-lab work: Do Exploration 2.1 of the experiment analytically, use equations 8.2 and 8.3 to fill out table 8.1 below:

Lab Explorations: E1.1, E2.1, E2.2 It is recommended that you build the amplifier block circuit (the circuit of figure 8.2 on page 73 of the textbook) on one side of the prototyping board with only three wires connecting Vi1, Vi2, and Vo to the other side of the board. This will make it easier to troubleshoot the circuit if needed in later stages. Answer the following questions, and include them in your report.

Questions: 1. Compare your measurements with the theoretically calculated values for exploration E2.1 in the table below: Table 8.1:

Calculated values R1 (KΩ) R2 (KΩ) a) b) c) d)

1 1 1 1||1

100 10||100 0 100

vin

vc

vb

vc /vin Closed loop gain

Measured values

vc (Vpp)

vb (Vpp)

vc /vin Closed loop gain

0.1 Vpp 0.1 Vpp 0.1 Vpp 0.1 Vpp

Introduction to Control Systems Theory: 2. Is the system that you built a negative or positive feedback system? 3. What is the effect of feedback on the bandwidth of the system? 4. If the open-loop gain of a system is given by:

where k is some positive constant, and the

feedback factor is 1. a) Draw the block diagram of the system b) What are the values of the pole(s) and zero(s) of the open-loop system? c) Sketch the S-plane and show on it the locations of all the pole(s) and zero(s) of the open-loop system. Mark the poles with a (X) mark and the zeros with a (O) mark. d) Is the open-loop system stable, unstable, or marginally stable? e) What is the closed- loop transfer function of the system? let Vin be the input, and Vo be the output. Notice that now the locations of the closed-loop pole(s) will depend on the value of k. f) (Extra credit) For the case in this question, to determine the stability of the closed-loop system, an easy way is to use the Root Locus method. In this method, the locations of the pole(s) of the closed loop system are determined for all values of the gain k from zero to infinity: - Plot the root locus of the system. If you are not familiar with the root locus, use this matlab code: s = tf('s'); G = (s+1)/(s+9); rlocus(G) - From the plot, what is the range of values of k for which the closed-loop system is stable? EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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Theory: This experiment is composed of two stages: Stage 1 The amplifier block (The Open-Loop Gain): In the first stage (in E1.1 of this experiment), you will be building a semi- ideal amplifier block with an amplification gain of 100 v/v. Ideality requires that input resistance be very high, and a very low output resistance so that the gain remains constant regardless of the load at the output. The textbook calls this block µ.

Vi1

e +

-

100

Vo

Vi2 Figure 8.1: In stage one of the experiment, we build a semi-ideal amplifier (Left), which is equivalent to a basic amplifying block which will be called µ that has a gain of 100 V/V (Middle). It may also be represented in block diagram as: Vo = 100(Vi1 - Vi2).

Stage 2 The feedback amplifier (The Closed-Loop Gain): The structure of the feedback amplifier is shown below:

Figure 8.2: Block diagram of a feedback control system.

Where: Vin is called the input signal Vf is the feedback signal e is the error signal, notice that e = Vin-Vf The block G is called the open-loop gain The block H is called the feedback factor It can be shown that: Equation 8.1 Where: is the closed-loop gain, or the closed-loop transfer function of the system. EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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is the amount of feedback The circuit in figure 8.4 in the text may be redrawn here below and compared to the block diagram above:

Vi

+

µ

B

Vc

R1/(R1 +R2)

Figure 8.3: the circuit of Explorations 2.1 and 2.2 and its Block diagram. By comparison to the block diagram, it can be shown that: Equation 8.2

The voltage at node B is obtained from the voltage divider in the feedback block as: Equation 8.3 Note: The transfer function (Vc/VI) of the system above does not depend on time, this is the simplest type of controllers and is called a Proportional (P) controller. More complex controllers are the PI (Proportional-Integral), and the Proportional-Derivative (PD) controller and the PID controller. Example: If the transfer function of a system is given by

(

)

4) where are the zeros and the poles of the system located? 5) Is this system stable? 6) Show the poles and zeros on the S-plane. Solution: the zeros are the values of s that make the nominator equal to zero, and the poles are the values of s that make the denominator of the function equal to zero. Thus the system G has a zero at s= -4, and two poles at s= -8 and s = 0. A system is stable if all of its poles are located on the left half of the splane, therefore this system is not stable, but is marginally stable because it has a pole at the origin. If the system has any pole on the right half of the s-plane, then it is unstable.

EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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Experiment # 9: Basic Output Stage Topologies Date performed:

.

Pre-lab work: No prelab assignments. Explorations: E1.2, E2.2, E3.2 Answer the following questions, and include them in your report. Questions: Answer the analysis questions in the text

EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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Experiment # 11: Op-Amp RC filters Date performed:

.

Pre-lab work: You may either: 1. simulate explorations E1.1 and E1.2 (a,b,c) and fill out the right half of the table below 2. Or plot a Bode Diagram of equation 11.6. Then fill out the right half of the table below. For parts g)1, and g)2 you need to substitute the new value of C1 in equation 11.5 to get a new expression of the transfer function, then plot the Bode Diagram of the new expression (thus in total you will have 2 plots). Show a sample calculation for converting from decibles to absolute value of the gain.

Lab Explorations: E1.1 and parts a to c of E1.2 Answer the following questions, and include them in your report.

Questions: 1. Compare your experimentally measured values with your simulated/analytical values by filling out the table below: E1.1 Measured experimentally Analytical/ Simulated values C1 Vs Vc Vc/VA f (Hz) f (Hz) ω (rad/s) Vc Gain (Vc/VA) ω (rad/s) a) 100 nf 0.2 Vpp 1000 6283 1000 6283 b)

100 nf 0.2 Vpp

f1 =

f1 =

c)1

100 nf 0.2 Vpp

f1/2 =

f1/2=

c)2

100 nf 0.2 Vpp

f1/4=

f1/4=

d)

100 nf 0.2 Vpp

f2 =

f2 =

e)

100 nf 0.2 Vpp

f2/4=

f2/4=

f)

100 nf 0.2 Vpp

f3 =

f3 =

g)1

200 nf 0.2 Vpp

f4 =

f4 =

g)2

200 nf 0.2 Vpp

f5 =

f5 =

E1.2

C1

Vs

Vc

Vc/VA

f (Hz)

ω (rad/s)

Vc

Gain (Vc/VA)

f (Hz)

a)

100 nf 0.2 Vpp

f6 =

f6 =

b)1

100 nf 0.2 Vpp

2f6 =

2f6 =

b)2

100 nf 0.2 Vpp

4f6 =

4f6 =

b)3

100 nf 0.2 Vpp

20f6 =

20f6 =

c)

100 nf 0.2 Vpp

f7 =

f7 =

ω (rad/s)

2. Draw the S-plane and show on it the analytically-obtained poles and zeros of the system from equation 11.6. 3. At what frequencies in Hz are the poles and zeros of the system located at? Which of the frequencies that you obtained experimentally (f1, f2, f3, f4, f5,f6, f7) is a pole or a zero?

EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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4. By inspection, without doing any calculations, if the input was a pure dc signal of 1 V, what would you expect to see at the output? Why? 5. By inspection, and assuming an ideal op-amp, if the input signal is 1 Vpp at a very high frequency, but lower than the op-amp’s bandwidth, what value would you expect to see at the output? Why? 6. Use equation 11.6 to plot the Bode diagram of the system, then mark the magnitude plot with your experimentally-measured values of Vc/Vs and frequencies. Note: remember that in Bode diagram, the frequencies are in rad/s (not in Hz) by default, and the magnitudes in dB (Gain in dB = 20log|G| ). 7. Using the Bode diagram, what is the range of frequencies at which this filter amplifies the input signal?

Theory: Refer to the circuit in figure 11.2 in the textbook on page 103, the circuit is redrawn here below, the derivation of the transfer function (i.e. the relationship between the output voltage Vc and the input voltage Vs) will need from us to find the equivalent feedback impedance Z f and the input impedance Zin as shown in the figure below, these impedances will be derived in the s-domain for ease.

The transfer function of the circuit is given by: Equation 11.1 Where: Zin = R1 + R3//C1

Equation 11.2

Zf = R4 + R2 //C2

Equation 11.3

Therefore: ( (

)(

) )

)(

⇒

( )

⇒

( (

(

)(

(

)

)( )( )(

Equation 11.4

) ) )

Equation 11.5

Equation 11.5

EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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Experiment # 12: Waveform Generators- The Schmitt Trigger Date performed:

.

NO pre-lab assignments Lab Explorations: E1.1, E1.2 Questions: 1. Fill out the table below for Exploration 1.1: Use equations 12.1, 12.2, and 12.3 (see the following pages) to do Exploration 1.1 analytically. This is done by calculating the values of VAt+ , VAt- and vBpp for the given resistor values in the table below.

R1

R2

vApp

vCpp

5Vpp

20 Vpp

100

5Vpp

20 Vpp

10

50

5Vpp

20 Vpp

5

50

5Vpp

20 Vpp

(KΩ) 10

(KΩ) 100

5

(V)

Calculated Values VAt+ VAtvBpp

Experimentally Measured values VAt+ VAtvBpp tr tf

2. Sketch the transfer characteristic of the non-inverting and inverting Schmitt trigger configurations. 3. Match each of the following circuits to the name most suitable for it

Non-inverting Schmitt Trigger:

Non-inverting Amplifier:

Inverting Schmitt Trigger:

Inverting Amplifier:

EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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Theory and Explanations: For a non-inverting Schmitt trigger, it can be shown that:

( )

Equation 12.1

( ) (

Equation 12.2

)

(

)

Equation 12.3

Where: is the input threshold voltage that causes the circuit to switch to the positive state. is that voltage needed to cause the circuit to switch to the negative state.

EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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Supplementary Exam Questions: 1. If your signal generator is outputting a pure sinusoidal signal that is 4V peak-to-peak. What reading do you expect to see on the digital multimeter (DMM) when your DMM unit is in the AC mode? a) 5.6 V b) 2 V c) 1.41V d) 4 V e) 0V 2. For the signal in the previous question, what would be the reading of your DMM unit if it was in the DC mode? a)5.6V b) 2V c) 1.41V d) 4V e) 0V 3. The BJT is modeled as: a) a voltage-controlled current source. c) a battery in series with a capacitor.

b) a current-controlled current source. d) a voltage-controlled voltage source.

4. If your signal generator is outputting a 10v peak-to-peak (10Vpp) signal, and you press the attenuation button “-20 dB” what will be the new value of the signal? a) -30Vpp b) 1 Vpp c) 0.5 Vpp d) 8 Vpp e) stays the same 5. What is the value of Vout of the circuit in the figure: a. Vout = -4 V b. Vout = 4 V c. Vout = -6 V d. Vout = 6 V

2KΩ +12V

Vout

1KΩ + 2V

-12V

Figure P5

6. The circuit in the figure below may be modeled by the block diagram shown. If the gain block µ is an ideal gain block with a value: µ = 10 v/v and H = 1 v/v what is the closed-loop gain Vc/Vi ? a) 10/11

b) 11/10

c) 10/9

Vi

+

d) -10/9

µ

B

e) -9/11

Vc

R1/(RH1 +R2)

H 7. Redraw the circuit in the figure with an Ammeter connected properly to measure the collector current. 8. Redraw the circuit in the figure with a voltmeter connected properly to measure the Base-to-Emitter voltage. 9. What value of the Base-to-Emitter voltage do you expect to measure in part b above If the Emitter Base Junction is forward biased?

EE 305 Theory & Assignments Manual by Khalid Tantawi, Electrical Engineering Dept. UAHuntsville, 2012

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References: [1] K. C. Smith, Laboratory Explorations for Microelectronic Circuits, Fourth ed., Oxford University Press, 1998. [2] A. S. Sedra and K. C. Smith, Microelectronic Circuits, Fifth ed., Oxford University Press, 2004. [3] J. Millman and A. Grabel, Microelectronics, Second ed., McGraw Hill, 1987. [4] W. Hayt and J. Kemmerly, Engineering Circuit Analysis, Fourth ed., McGraw Hill, 1986. [5] B. Lathi, Signal Processing and Linear Systems, Berkeley Cambridge Press, 1998. [6] M. Rashid, Power Electronics: Circuits, Devices and Applications, 3rd ed., Pearson, 2003. [7] N. Nise, Control Systems Engineering, 5th ed., Wiley, 2008.

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