California State University, Long Beach

PHYSICS 380: ELECTRONICS Laboratory Manual

Copyright © Mladen Barbie 2008 (version 1)

Yohannes Abate 2013 (version 2)

All rights reserved DEPT/CRS:PHYS 380 AUTHOR: 008 BARBIC AND VENDOR: CCC CAMPUS CO TITLE: PHVS 380 LAB MANUAL. SKU: 12764945

78764941 NEW TEXT

ii

Table of Contents

Introduction

References

Laboratory 1: Introduction to Instruments for Electronic Measurements

Laboratory 2: AC Circuits: Signals, Impedance, Filters

Laboratory 3: Transformers - Principles and Applications

Laboratory 4: Semiconductor Diode Circuits

Laboratory 5: Semiconductor Transistor Circuits

Laboratory 6: Operational Amplifiers - Principles and Applications

Laboratory 7: Digital Logic Circuits

Title Graphic: Worlds first semiconductor transistor - 1947 point contact

transistor made by Walter Brattain and John Bardeen

iii

Introduction

Welcome to the CSULB Physics 380: Electronics Laboratory! The goal of the course

is to train science students, both undergraduate and graduate, to be able to make

electronic measurements and to build small practical circuits. The laboratory is the center

of the learning experience in this course. The lecture prepares the student to be more

competent in the laboratory. The aim of the experiments is to teach a practical skill that

the student can use in the course of his or her own experimental research projects in

physics or other fields in science. A lot of experiments are based on topics that are of

special interest to professional physicists designing electronic circuits for their high

sensitivity and performance experiments. For example, when we discuss in the laboratory

the topics of Thevenin Equivalents, the reason is not only that they are academically

interesting. Rather, the reason is that in many physics experiments the observations of

physical phenomena are performed by physical sensors that can be represented by such

equivalents. The sensors can be for example a coil, a resistor, a crystal, or a photo-

detector, and their output characteristics in terms of Thevenin Equivalents are very

different and should be well understood. By understanding the output characteristics of a

sensor, one can then make an educated and critically important choice of a sensor and

then an amplifier that often has to follow the sensor in the detection chain of the

measurement circuit.

Along with the instructions for the various laboratories, there will be questions that

you have to answer or calculate. These questions are really meant to get you to think and

analyze carefully certain laboratory exercises, and show you that some assumptions about

circuit elements or techniques have to be used with caution. It is assumed throughout this

iv

course that you have taken and passed CSULB Physics 152 Lab or equivalent. Therefore, it is

assumed that you are very familiar with and can use Ohm's Law, Kirchhoff s Laws, the

concepts of resonance, voltage and current dividers, know how to measure phase difference

between two signals on an oscilloscope, add components in series and parallel, etc. In Physics

380 Laboratory you will learn more advanced topics listed in the Table of Contents. You will

maintain a laboratory notebook (5X5 Quad Ruled is preferred), and you are required to make

your recordings in it with pen for a permanent record of your work. Please be aware that

significant departmental resources have been spent to provide for you the advanced electronic

instrumentation in the lab. So please handle it with care and respect so that many future

generations of students after you can benefit from this investment.

One of the main goals of the Physics 380 Laboratory is to first get rid of the fear you might

have when faced with sophisticated instruments, and then train you in the use of sophisticated

measurement methods and techniques in order to prepare you for successful careers in

experimental physics or related fields. So hopefully, by the end of the semester, you will be

comfortable with turning the knobs, trying things out on your own, and perhaps even

developing some novel electronic circuits and techniques for physics and engineering

applications. And most importantly, try to have fun!

v

References

Many examples and sections in these laboratories were motivated by the topics these

books discuss.

L. R. Fortney: "Principles of Electronics: Analog & Digital"

P. Horowitz and W. Hill: "The Art of Electronics "

T. C. Hayes and P. Horowitz: "Student Manual for the Art of Electronics "

H. W. Ott: "Noise Reduction Techniques in Electronic Systems "

R. Morrison: "Grounding and Shielding Techniques "

C. D. Motchenbacher and J. A. Connelly: "Low-Noise Electronic System Design "

E. Fukushima and S. B. W. Roeder: "Experimental Pulse NMR "

C. Bowick: "RF Circuit Design "

R. L. Liboff and G. C. Dalman: "Transmission Lines, Waveguides, and Smith

Charts "

T. H. Wilmshurst: "Signal Recovery from Noise in Electronic Instrumentation "

The lab manual has been revised from its original version. The original manual was

developed with consultation of the electronics laboratory materials from:

■ University of California, San Diego

■ California State University, Long Beach ■ Duke University ■ California Institute of Technology ■ Massachusetts Institute of Technology ■ Harvard University ■ University of Pennsylvania

1

LABORATORY 1

Introduction to Instruments for Electronic Measurements

Physics 380 Laboratory is equipped with state of the art electronic measurements

instrumentation for common inspection and analysis of electronic components and

circuits. In the Laboratory 1 you will learn how to use these instruments, and then you

will utilize some of them to characterize a well-known set-up called a Wheatstone bridge.

The User Manuals for all of the instruments are provided in the laboratory. Please consult

them as much as you need to, as it is redundant to reprint the same instructions for their

use in this manual.

Tektronix TDS2002 Digital Storage Oscilloscope

Digital Oscilloscope you will be operating is a sophisticated instrument used for

the measurements of time varying electric signals. Before studying electronic

components and circuits, it is important to first understand the input stage representation

of an oscilloscope in order to avoid making errors in measurements. Typical scope has

an input resistance of about 1MΩ. with a parallel input capacitance of about 20 pF. In

addition, the cables used to connect the electronic circuit nodes to the oscilloscope also

have a capacitance that one may have to worry about when using the scope. We want to

make sure that we do not unintentionally affect the circuit measured (circuit loading) and

the best way to do this is to use the 10X passive oscilloscope probe. This device is very

convenient, as it can be used on one end to hook up to the nodes of an electronic circuit

while the other end is connected to the scope input. When properly tuned, the probe

serves to increase the input impedance of a scope by a factor of 10.

2

The procedure for introducing you to the operation of the digital oscilloscope follows:

1. First follow the instructions in the Oscilloscope Manual to turn on the scope,

connect properly the oscilloscope 10X probe for tuning, set the channel setting to

a 10X probe, and display the approximately square waveform on the oscilloscope

screen. Make sure you are comfortable with adjusting the knobs for horizontal

(time) and vertical (volts) settings, as well as adjusting the triggering and cursor

settings. Record in your lab notebook the diagrammatic representation of the

experimental set-up.

2. Calibrate the 10X scope probe to display a pure square wave. This procedure will

increase the input impedance of the scope by a factor of 10 for all incoming

frequencies. Show to the lab instructor your compensated probe waveform.

3. Now that you have square waveform displayed, use the cursor functions on the

scope to precisely measure the period of the square wave and the peak-to-peak

magnitude of the square wave. Compare your measurements to the values listed at

the output of the probe compensation ports on the scope.

4. Play some more with the various functions on the scope, turn the knobs, push the

buttons, change the settings, and get very comfortable with the instrument, as you

will use it a lot during the course of the semester and throughout your professional

careers.

Keithley Model 2000 Digital Multimeter

The second important electronic instrument you will use extensively is the lab is

the digital multimeter. Familiarize yourself with the user manual for this instrument, as it

is again redundant to rewrite the manual here. There is nothing particularly difficult about

this instrument, and you should feel comfortable using its features. You should be aware

3

of the different settings for DC and AC measurement, and of the input impedance when

used in different modes for voltage and current measurements in the lab. You will use the

DC Voltmeter mode of the multimeter for the measurement of the Wheatstone bridge

output voltage.

SC-2075 National Instruments Proto Board

In order to test your work, you will often have to use a breadboard for

construction of various circuits. The manual for this board is available in the lab. This

board is connected to the computer that powers it for certain applications. For example,

the board has some output ports for +/- 15 Volts that will be used for biasing transistors

and operational amplifiers in later labs. In this lab, turn the board on by switching the

switch to the INTERNAL position. The LEDs should light up. Test with the multi-meter

that the three ports for +15V, GND, and -15V are working. We will only use the basic

features of this board, such as the breadboard and the bias voltage ports. We will not use

the computer in this course, except to bias the board.

HP 33120A Function Generator/Arbitrary Waveform Generator

The third sophisticated electronic instrument you will use extensively is the

Function Generator. As with the oscilloscope, it is very important to understand how this

instrument interacts with the circuits it is connected to. In that regard, characterizing its

output waveforms and its output impedance will be the topics studied in this lab. Again,

first familiarize yourself with the user manual for this instrument, as it is redundant to

rewrite the manual here. This function generator has a nominal output impedance of 50

Ohms (although it can be set to have a much higher output impedance). This output

4

impedance is much smaller than the standard input impedance of the oscilloscope, and

therefore, connecting the scope directly to the function generator at low frequencies will

not affect (load) the generator. The procedure for introducing you to the operation of the

function generator follows:

1. Connect the function generator directly to the scope Channel 1 and arrange the

scope settings to display the waveform.

2. Familiarize yourself with the function generator output functions by varying the

waveform type (sine, square, etc.), amplitude, frequency, and DC offset. Make

sure that you can measure on the scope precisely any waveform type the generator

can provide.

3. Measure the output impedance of the function generator. First measure and record

the voltage value of the function generator sine wave connected directly to the

scope. This is the open circuit voltage (Thevenin equivalent VTH)- NOW connect a

decade resistance box to the function generator and measure on the scope the

voltage across the resistor.

Record in your lab notebook the diagrammatic representation of the

experimental set-up.

4. Tune the value of the resistance until the waveform amplitude is exactly half the

value of the open circuit voltage of the function generator you recorded

previously.

Show your circuit and result to the lab instructor.

Disconnect the resistance box from the function generator without modifying

the resistance values on the box, and measure its resistance with a multimeter.

This is the output impedance of the function generator.

Why? Derive and explain.

5

Digital scopes can perform mathematical analysis on the recorded waveforms,

such as the Fast Fourier Transform or the FFT. You will learn how to use this function of

the scope. The Fourier Theorem states that any periodic function can be represented as a

sum of sine functions of different amplitude and frequencies and phases. For example,

the Fourier series representation for a square wave is:

The time and frequency domain representation of a square wave are shown in the figure

below.

5. Change the output waveform types and perform the FFT using the scope for a sine

wave, square wave, and a triangle wave of same frequency.

Record your FFT results (for both frequency and magnitudes of the peaks) and

comment on your observations.

T

t

ν0

-ν0

ν(t)

ω

V

ω0 3ω0 7ω0 5ω0 9ω0

6

Try using the Hanning and Flattop windows and see their effect on the FFT.

6. Play some more with the various functions on the function generator, turn the

knobs, push the buttons, change the settings, and get very comfortable with the

instrument, as you will use it a lot during the course of the semester and

throughout your professional careers.

HP E3631A Triple Output DC Power Supply

The 380 Lab is equipped with a triple output DC power supply. Again, first

familiarize yourself with the user manual for this instrument, as it is redundant to rewrite

the manual instructions here. We will use this power supply in two of its modes to

investigate the properties of a very useful device called a Wheatstone bridge. This power

supply can be operated in the Ideal Voltage Source mode and the Ideal Current Source

mode. An ideal voltage source is a source able to maintain a given voltage difference Vs

across a load RL irrespective of the load value RL. Therefore, an ideal voltage source can

in principle provide a required current Is necessary to keep constant voltage across the

load, as shown in the figure below

An ideal current source is able to deliver a given current Is irrespective of the load RL

attached to it. Therefore, an ideal current source is able to produce the voltage

I V

+

-

Vs

R

I

Vs

V

7

difference across the load needed to keep the current through the load constant, as

shown in the figure below.

Show analytically in your lab notebook that an ideal voltage source is a low

output impedance device, while an ideal current source is a high output impedance

device. We will use both modes of the power supply in the study of a model variable

resistor sensor described below.

Suppose you have a resistive sensor that changes its resistance as a function of an

external parameter and you wish to measure this resistance change. This is a very

common problem. For example, a thermistor is a device that changes its resistance as the

temperature changes. A magneto-resistor is a device that changes its resistance as

different magnetic fields are applied to it. There are also pressure gauges whose

resistance changes as a function of pressure. Often in physics experiments, this resistance

change is very, very small and the challenge to an experimental physicist is to develop a

very sensitive method to measure such a minute resistance change. One choice of

measurement is shown in the textbook in Problem 1.27. As an exercise, solve Problem

1.27 from the textbook in your lab notebook. The good thing about this measurement

method is that the output voltage is linear with the resistance change. The bad thing about

I V R

Is

Is I

Vs

V

8

this method is that the small voltage changes due to small resistance changes have to be

measured in the presence of a large DC voltage. So you might have to measure mV

changes on top of DC voltages on the order of Volts, and that is very inconvenient and

imprecise. The following measurement circuit deals effectively with this problem, but it

needs to be used carefully, as it has some drawbacks you should be aware of.

Wheatstone Bridge

In Chapter 1 on pages 18-21, the textbook discusses the standard Wheatstone

bridge and some of its properties with respect to its output impedance and Thevenin

equivalent voltage (the output voltage of the bridge that you will measure).

We will look here in more detail at this arrangement, as it has some nuances

that are important. The book discusses the output voltage of the bridge (Equation

1.33) when driven by an Ideal Voltage Source:

VAB =VsR3

R1 + R3−

R4R2 + R4

"

#$

%

&' (1.1)

9

From the voltage divider rules it should also be clear that the Wheatstone bridge is

balanced (nulled) when the ratios of resistances are: R3R1=R4R2

=C (1.2)

Lets rewrite Equation 1 in terms of the parameter C in order to find out for what

resistance ratios the output of the bridge is maximized around the balanced (nulled)

region. First lets assume that one of the resistors is the tunable one (your sensor)

say R2 = R2 ± X :

VAB =VSR3 R11+ R3 R1

−R4 R2

1± X R2 + R4 R2

"

#$

%

&'=VS

C1+C

−C

1+C ± X R2

"

#$

%

&' (1.3)

Lets plot the output VAB as a function of C:

The output of the bridge is maximized when C=l, i.e. the resistors on each side of the

bridge are matched! This is a very useful fact to know when constructing Wheatstone

bridge circuits for detecting small changes in the tunable resistor sensor you may have.

Often, all the resistors are chosen to have the same value, and Equation 3

then becomes:

.025

.020

.015

.010

.005

0 0 1 2 3 4 5 6 7 8 9 10

10

VAB =V±X

4R± 2X (1.4)

This equation has several important features. The great thing about the Wheatstone

bridge is that it is a difference measurement device. This means that for the balanced

bridge and X=0 the voltage output measured is zero. So we are measuring small

changes in X on top of zero Volts base level, which is very nice. However, the

output of the bridge is not linear with X. Equation 4 is plotted here as a function of X.

You will try to reproduce this curve experimentally using the Constant Voltage

output mode of the power supply. Set-up the Wheatstone bridge circuit on the

breadboard, with the resistor values of 50 Ohms. One of the resistors has to be tunable.

The bridge is to be biased at 1 Volt from the DC power supply, and the bridge output

voltage is to be measured by the multimeter. Record in your lab book the

diagrammatic representation of your experimental set-up. Also record the current

output of the Power Supply at the balanced bridge condition and confirm in your

lab notebook that it is of the correct value. Measure the output of the Wheatstone

bridge circuit as a function of tunable resistance as it changes from 0 Ohms to 100 Ohms

(X varies from -50 to +50 Ohms). Plot in your lab notebook the data you took and see

how well it matches the theoretical curve from the figure. Next, analytically

0.2

0

-0.2

-0.4

-50 -40 -30 -20 -10 0 10 20 30 40 50

11

calculate in your lab notebook the voltage output of the Wheatstone bridge when

driven by an Ideal Current Source. Is the output now different from the Ideal Voltage

Source driven bridge as described in Equation 4? Also in your lab notebook, analytically

calculate the Thevenin Equivalent source resistance for this situation. Switch the

output of the Power Supply to the Constant Current mode and balance the bridge.

Bias the bridge with the same current from the Power Supply that was displayed in the

constant voltage measurement. Again measure the voltage output of the bridge as you

tune the resistor. Record in your lab notebook the experimental arrangement and

plot the experimental data points on the same graph and compare. Describe the

difference you observe in the results.

The point of these exercises is to show you that there is a real difference when

choosing between the Ideal Current source and Ideal Voltage source for your

measurements, and the choices can influence the measurement output. In addition, many

different sensors behave usually as either approximately ideal voltage sources or as

approximately ideal current sources. This will influence which type of amplifier you

connect to the sensor. So before doing any physics measurements with a sensor, try to

understand its fundamental electronic properties for optimal results in terms of

sensitivity, precision, and signal-to-noise ratio.

The example of a resistive Wheatstone bridge was the simplest one we could try.

You should be aware that there are many variants of the presented bridge: Kelvin bridge

(for measuring small resistances), Maxwell bridge (AC measurements), Wien Bridge

(complex components), etc. Final suggestion: In sophisticated physics experiments where

you want to detect small changes of a certain parameter (resistance, gravity, pressure,

etc.), always try to set up a difference measurement method if at all possible as it will

usually provide a much better precision and sensitivity, as was exemplified by the simple

12

Wheatstone bridge in this lab.

13

LABORATORY 2 AC Circuits:

Signals, Impedance, Filters

In this laboratory you will build many types of four-terminal networks that

uniquely shape the incoming signals. At low frequencies these passive electronic

structures will behave as various filters, but it is important to understand that these

structures also change the input and output impedance of the driving and receiving

channels connected to these four-terminal networks. You will plot the transfer functions

of these four-terminal networks as Bode plots (log-log scale) and confirm the theoretical

predictions from the lecture part of the Physics 380 Course. You will also construct more

complex structures with unique transmission properties that will teach you how

complicated these apparently simple structures can get. Finally, you will learn that simple

cables as you know them at low frequencies behave quite differently at high frequencies.

In that regime, you cannot assume a cable to be a simple wire, but must view it as a

transmission line with characteristic capacitance, inductance, and impedance. You will

see this demonstrated in a dramatic fashion on a coaxial cable acting as a A/4 transformer.

A Note on the Log-Log Plots in Electronics

Throughout this lab you will be measuring many transfer function curves of

various electronic devices. They are most often (but not always) plotted on a log-log

scale. The question often comes up as to how to sweep the frequency so that the data

points are equally spaced on a log-log plot. The best suggestion is to tune the frequency

in this sequence: 1, 2, 5, 10, 20, 50, 100, 200, 500, ... in Hz, or kHz or whatever the

appropriate unit is. This will space the data points fairly equally in the plot. It is

emphasized, however, that for the case of resonances or corner frequencies, it is highly

14

recommended you take more closely spaced frequency points for more accurate

measurements of the relevant parameters from the log-log plots.

Impedance of a Capacitor

From the lecture part of the course you learned what the impedance of a capacitor

is, its frequency dependence, and how it affects the signals across the capacitor in terms

of voltage versus current and phase relationships. This knowledge can be used in a neat

way to again measure the output impedance of the function generator using a capacitor of

known value. Again connect the output of the generator to the oscilloscope directly and

set the amplitude of the sine wave to be 6 divisions on the scope screen. Now select a

capacitor of a known value and connect it to the function generator. Using a 10X passive

scope probe, measure the voltage across the capacitor. Unlike in the previous decade

resistor method, here tune the frequency of the function generator output and monitor

when the voltage across the capacitor is 0.707 times the output of the generator when

unloaded (this will be when the voltage across the capacitor is at 4.2 scope divisions).

Record this frequency and calculate the magnitude of the impedance of this capacitor at

this frequency. This is the output impedance of the function generator. Derive why this is

the case in your lab notebook and compare you result to the measurement from Lab 1.

This is a nice and quick way to find the output impedance, as you can usually much more

easily and precisely tune the frequency of the source than tuning the impedance of the

resistive load.

Low-Pass RC Filter

Construct a simple low-pass RC filter as shown in Textbook Figure 3.5a. Pick a

15

resistance value of around 1 kΩ and a capacitor of value around 0.1 µF. Calculate

algebraically the corner frequency of this filter.

It is a good practice to connect the input of the network to scope channel 1 and the output

of the network to the scope channel 2. Channel 1 trace should not change much, but you

never know and should take precautions. Draw the schematic diagram of your

experimental arrangement in your lab notebook. Measure the transfer function of this

four-terminal network and plot it on a log-log scale as a Bode plot on the diagram

provided at the end of the Laboratory 2 write-up. When you have completed the graph,

cut and staple (or glue) it in your lab notebook. Keep the corner frequency of the filter in

mind, and try to plot the graph with that frequency at the center of your graph. Take extra

few data points around the corner frequency of the filter for completeness. Verify that the

filter is behaving properly in terms of the corner frequency and slopes of the Bode plot,

and comment in your lab notebook on your findings. Measure the phase transfer

function of this four-terminal network. Plot the phase graph on a linear-log plot.

Now apply the square wave at 10X the corner frequency to the low-pass filter and

I Vout Vin R

C

I

16

comment on the output of the filter. With the generator set to the 10X corner frequency,

take the FFT of the input square waveform and the output waveform with the

oscilloscope, measure them carefully in terms of both magnitudes and frequency

locations, and comment. How does the low pass RC filter affect high frequencies? Next

change the input frequency and find the frequency regime where the RC filter is acting

as an integrator of the input waveform. Prove this by recording in your lab notebook the

trace on channel 1 of the scope (input waveform) and the trace on channel 2 of the scope

(output waveform), and record the value of the frequency range where you feel the filter

is acting as an integrator properly. We will see that we can do much better in later labs

using operational amplifiers.

High-Pass RC Filter

Next, interchange the locations of the resistor and capacitor in your four-terminal

network. This forms a high-pass RC filter with the same corner frequency.

Repeat the measurements by measuring the transfer function of this four-terminal

network and plot it on a new log-log scale as a Bode plot. When finished, cut and staple

I Vout Vin R C

I

17

(or glue) the graph in your lab notebook. Verify that the filter is behaving properly in

terms of the corner frequency and slopes of the Bode plot, and comment in your lab

notebook on your findings. Also measure the phase transfer function of this four-

terminal network and plot it on a linear-log plot.

Now apply the square wave at the frequency of 1/10 of the corner frequency to

the low-pass filter and comment on the output of the filter. With the generator set to the

1/10 of corner frequency, take the FFT of the output waveform with the oscilloscope,

measure it carefully in terms of both magnitudes and frequency locations, and comment.

How does the high-pass RC filter affect low frequencies?

Apply a triangle wave, sweep the frequency and find the frequency regime where

this RC filter is acting as a differentiator of the input waveform. Prove this by

recording in your lab notebook the trace on channel 1 of the scope (input waveform) and

the trace on channel 2 of the scope (output waveform), and record the value of the

frequency range where you feel the filter is acting as a differentiator properly.

Two-Pole High-Pass RC Filter Network

Add another high-pass RC filter section to the original one. Select the values of

the resistor and the capacitor in the second section so that the second section has much

higher input impedance, while at the same time having the same corner frequency as the

first section. A nice trick that accomplishes this is to pick a resistor of 10 times higher

resistance and a capacitor of 10 times less capacitance than the values of the first RC

filter section.

18

Repeat the measurements by measuring the transfer function of this more

complex network and plot it on a new log-log scale as a Bode plot. When finished, cut

and staple (or glue) the graph in your lab notebook. Verify that the filter is behaving

properly in terms of the corner frequency and slopes of the Bode plot, and comment in

your lab notebook on your findings. Now apply the square wave at the corner frequency

to this new high-pass filter and comment on the output of the filter. How does this two-

pole high-pass RC filter affect different frequencies?

RC Band-Rejection Filter

Passive filter designs can get very complex, and you may hear of Butterwoith,

Bessel, Chebyshev, Elliptic, and other types. They all have very unique properties in

terms of sharpness of roll-off, flatness of the pass band, phase response, etc. In many of

these filters you have to use multiple capacitors, inductors, and resistors. Inductors are

problematic as they are not cheap, and are relatively large. There are tricks of using just

resistors and capacitors for desired performance, and this is helpful in terms of cost and

size. Twin-T band-rejection filter shown in Textbook Figure 3.20 is a good example. It is

I Vin R1 C1

I

I Vout R2 C2

I

19

a notch filter with a center frequency of 1/RC, and it is redrawn in the figure below. Pick

the R and C values so that the center frequency is around 10 kHz.

Measure the transfer function of this more complex four-terminal network

and plot it on a new linear-log scale. When finished, cut and staple (or glue) the graph in

your lab notebook. Measure the band of the filter, i.e. two 3dB frequency points next to

the center dip. We will see that we can do much better in later labs using operational

amplifiers. Question:

Describe briefly the significance of equations 2.4 and 2.5, what makes these two

equations important, describe briefly in your own words. Do the experiment

below for 5 extra points!!

Coaxial Quarter Wave Transformer Cable

In most physics experiments that involve electronics, one or more electrical wires

are used to transmit a signal that carries information from one physical location to

another. It is often taken for granted that the signal on one end of the wire will be the

same and simultaneous as on the other end of the wire. This is a simplification, of course,

but it works very well at low frequencies. Signals cannot propagate along a

Output Input 0.5 R

C

R R

2C

C

20

communication channel faster than a speed of light, and it turns out that at high

frequencies, this can have a dramatic effect on signal transmission even over relatively

short laboratory distances. In such cases, one needs to think of conductors and cables as

transmission lines.

One common laboratory cable is the coaxial cable, often called a BNC cable.

At low frequencies a current flows down a center conductor and returns via outer

conductor and inductance is considered negligible. One may have to worry about a

small cable resistance, and worry a little bit more about a cable capacitance (50-150

pF/m). This was one of the reasons to use the 10X passive oscilloscope probe in the

first place, remember. At high frequencies inductance, capacitance, and propagation

speed cannot be ignored anymore, and care has to be taken especially in terms of

impedance matching. Figure below shows a cross section of a coaxial cable (solid

tube semi-rigid) along with the electric and magnetic fields present when a signal is

propagating along the cable.

For a coaxial cable, the capacitance and inductance of the cable are:

C = 2πεln b a( )

F m( ) (2.1)

L =ln b a( )2π

µH m( ) (2.2)

.

.

. . . .

.

.

.

.

.

. . . .

.

.

.

.

.

.

.

.

. . . .

.

.

.

.

.

.

.

.

. . . .

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.

.

.

.

. . . .

.

.

.

.

.

.

.

.

.

.

.

. . . .

.

.

.

E B

Propagation direction 2a 2b

21

where ε is relative permeability of the dielectric, b is the inner diameter of the

outer conductor and a is the diameter of the inner conductor.

The transmission line has an important property called Characteristic Impedance ZC:

ZC =LC

(2.3)

So, if voltage V is known at some point along a transmission line of characteristic

impedance ZC, one can get the current I at that same point along a transmission line.

Most common coaxial cable has a characteristic impedance of value 50 Ohms. An

extremely important situation, shown in the figure below, arises at higher frequencies

when a transmission line of characteristic impedance ZC is used to connect a generator

of (complex) source impedance Z0 to a load of (complex) impedance ZL.

One typically would like to transfer as much energy (information) as possible to the

load from the source via a transmission line, and minimize losses (reflections). One

then encounters a concept of reflection coefficient ρ usually expressed in terms of

characteristic and load impedances:

ρ =ZL − ZCZL + ZC

(2.4)

A very significant point in transmission line theory is evident when ZC = ZL. Then ρ = 0

and there is no reflected voltage and current, and therefore power. All the power

l

Z0 ZL

22

flows into the load, and the transmission line is matched to the load.

A very interesting condition in transmission line theory happens at a single

frequency. It results in a device called a quarter-wave or λ/4 transformer. A quarter-

wave cable acts as a transformer at a specific frequency with a property that:

ZiZo = ZC2

(2.5)

where Zi and Zo are the input and output impedances at the ends of a cable with

characteristic impedance ZC. It turns out that this happens for the cable length that is, at the

given operating frequency, equal to a quarter wavelength λ/4 of the wave propagating down the

transmission line, hence the name. When we use a cable with a characteristic impedance of

50 Ohms, the most common value, it will transform 50 Ohms impedance into 50 Ohms

impedance, i.e. it will be a 1:1 transformer. Nothing exciting, you may say. But suppose a

10 Ohm resistor is connected to the input. The output impedance is now 250 Ohms!

What if the input is shorted (Ri = 0 Ohms)? The output impedance is then Ro = ∞. This

means that hooking up a shorted quarter wave line is like hooking up absolutely

nothing! Similarly, an open-ended quarter wave line (Ri = ∞ Ohms), at the right

frequency, looks like a short (Ro = 0 Ohms)!

We will demonstrate this dramatic BNC cable impedance transformation

demonstration in the lab. The set-up is very simple. Connect the signal generator output

to the scope through a T adapter, and connect the assigned cable to be measured to the T

on one end and leave it unconnected on the other end. A quarter-wave line length in

meters is approximately 45/Freq in (MHz). So for 45 MHz, the length is about 1 meter,

for 15 MHz is about 3 meters, and so on. First, vary the frequency of the generator and

look for the minimum signal at the lowest frequency (there are other minimums at higher

23

frequencies). When you find it, measure the transfer function of the coaxial cable

transmission line around the minimum, and plot it on a new linear-log scale. When

finished, cut and staple (or glue) the graph in your lab notebook. It should be quite

amazing to you that hooking up a plain cable with nothing else on it attenuates the signal

so spectacularly. Measure the length of the coaxial cable, calculate the expected quarter-

wave length, and compare it to the theoretical value given.

Now short the end of the BNC cable with a short terminator and measure the

transfer function of the shorted coaxial cable transmission line, and plot it on the

very same linear-log plot. What do you observe and why? Finally, terminate the coaxial

transmission line with a 50 Ohm terminator and measure the transfer function of the 50

Ohm terminated coaxial cable transmission line, and plot it on the very same linear-

log plot. Impedance matching of this sort is extremely important in RF applications

24

25

26

LABORATORY 3

Transformers - Principles and Applications

This laboratory is designed to show you the main principles and characteristics of

transformers in their use in electronics applications. Transformers are widely used in

power electronics and RF electronics, as well as in physics experiments where unique

isolation, impedance matching, and small signal detection and processing are required.

As you will learn in the lecture part of the course, transformers can provide voltage and

current transformations from one end of the circuit to another. A more important property

of the transformers occasionally is that they can transform impedances, which is valuable

for proper coupling from sources to loads, as well as from sensors to amplifiers in unique

situations.

The Audio Transformer

In this laboratory we will use a medium scale audio transformer XICON 42TM-

013-RC (pictured below) for our studies. These transformers are used in the audio

frequency band (~300Hz-3kHz). These are well-designed transformers, which means that

they are made to be highly efficient in the designated frequency band, as well as have a

flat frequency response over the same band. Nevertheless, they are not perfect, and have

losses, magnetic leakage, and inter-winding capacitance that modify their behavior from

the ideal.

27

These transformers are designed so that they have a center tap, which can be

very useful in giving you more choices on the number voltage, current, and impedance

ratios you can obtain with the same transformer. Additionally, the center tap can be

very useful in establishing the ground potential on the secondary circuit, since that

circuit is DC isolated from the primary circuit typically driven by a signal generator

with a well defined ground terminal. The audio transformers provided for you have a

clearly labeled primary (P). This assumes, however, that you will use this transformer

for a specific task of driving an audio speaker. But that does not mean that you cannot

use this transformer for other purposes, and both sides of this transformer can be part

of the primary or secondary side of the circuit.

First measure the resistance of various sections of the transformer windings. Be

careful to measure all possible combinations, 1-2, 2-3, 1-3, and so on. Verify that there

is no DC connection between the primary and secondary side of the transformer.

Give a crude estimate of the possible transformer turns-ratios based purely on the

resistance measurements of the windings.

Next build a complete transformer circuit that includes a load resistor, shown below,

and measure the values of the resistors you are actually using in your circuit.

28

Circuit Parameter Transformations using Transformers

You will apply a 5V RMS sine wave at 1kHz from the signal generator to the

circuit. First connect the generator output only to the scope to calibrate the RMS voltage

output of the generator. You will next do the following measurements on the nine

possible configurations, using the primary label side of the transformer (P) as the

primary. The possible configurations are (1-2 input, 5-6 output), (1-2 input, 4-5 output),

(1-2 input, 4-6 output), (2-3 input, 5-6 output), and so on. Note that by reversing the

transformer so that P labeled side is the secondary would result in additional 9

configurations, but we will not do this in the interest of time. It is best to record the

following measurements in a table.

1. Observe the voltages over the primary Vi and secondary transformer V2

connections on the scope. Using the DMM, measure and record in your lab

notebook the RMS voltages Vi and V2. Calculate and record in your notebook the

experimentally determined voltage ratio, and therefore the inverse turns-ratio 1/n,

as well as n.

2. Using the DMM, measure and record the RMS voltage across the 1 kΩ resistor,

from which you can determine and record the current Ii thorough the primary

circuit. Calculate and record in your lab notebook the current ratio, and therefore

the turns-ratio n, as well as 1/n. Why do your observe a difference? Following the

discussion in the book on the current and voltage ratios for perfect and ideal

transformers, use the different results for the voltage and current ratios you

obtained to find the self-inductance of the secondary L2.

3. Using the measured Vj and Ii, calculate and record the input impedance ZIN as

seen at the input of the transformer at the primary.

29

4. Use the measured values of RMS voltages V and RMS currents I to calculate the

power Pi delivered by the generator and the power P2 absorbed by the load

resistor at the secondary for each measured configuration.

Comment on all of your measurements in terms of what was expected and what was

measured, and explain any discrepancies you may have observed.

Ideal vs. Perfect Transformers

There is a subtle difference between an ideal and perfect transformer that is

extensively discussed in the book. By using perfect transformer model, one can predict

with more accuracy the behavior of circuits that involve transformers, while still utilizing

the basic properties of ideal transformers. Perfect transformer model does not assume that

the inductive impedances of the primary or secondary coils are much larger than the

impedance of the load (something the ideal transformer model does assume). This is a

much more appropriate description of the transformer. Just think of what happens at low

frequency with the impedance of an inductor!

To demonstrate the point, you will first measure various inductances associated

with the transformer. First disconnect any load on the secondary of the transformer. In

this case the input impedance of the transformer is n2 L2 = L1 Measure this impedance the

similar way you measured the impedance of a capacitor in Lab 2. Connect the function

generator with the 1 kΩ source resistance to the transformer primary. Sweep the

frequency of the function generator and observe with the scope the voltage across the

primary. Make sure you include the resistance of the primary in your considerations.

Devise a frequency sweep method to measure the primary coil impedance. Calculate and

record in your notebook the inductance of the primary coil of transformer Li, and from

30

your voltage ratio measurement (i.e. turns ratio measurement) calculate the inductance of

the secondary coil of the transformer L2, and finally the mutual inductance between the

two coils of the transformer, M2=L1L2.

Next follow closely the discussion in the textbook with respect to Figure 4.6

and Example 4.1. Connect the capacitor at the secondary of the transformer, as shown in

the figure below. Pick a capacitor value so that the resonant frequency is around 1kHz.

Measure the transfer function of the circuit in the standard Bode plot form by observing

both the input signal to the transformer and the output signal from the transformer on two

channels of the scope. Plot your measurements on the provided graph, and when finished

cut and paste it into your lab notebook. On the same graph plot the expected transfer

function for an ideal transformer model derived for you in Example 4.1 in the textbook.

Of course, assume the same n, R, and C values as in the perfect transformer model.

Comment on your observations and measurements.

Complete Transformer Frequency Response

The audio transformer should have a constant voltage ratio over its specified

frequency range. However, at very high frequencies there are effects due to the inter-

winding capacitance, magnetic losses in the transformer cores, stray inductances, etc.

These limit the operating frequency range of the transformer, although sometimes they

can be uses as an advantage. You will measure the complete transformer frequency

31

response in the Bode plot form on a graph provided for you. Connect the function

generator directly to the primary and measure the secondary open circuit voltage. Sweep

the frequency of the function generator from 100Hz all the way to 10MHz and measure

the frequency transfer function of the pure transformer. For this measurement use the IX

scope probe. Comment on your measurements and observations.

32

33

34

LABORATORY 4

Semiconductor Diode Circuits

In this laboratory you will investigate the properties of a unique and important

non-linear circuit element. A semiconductor diode is one of the fundamental

semiconductor devices utilizing a p-n junction. You will first study the fundamental

circuit properties of a semiconductor diode by building a dynamic curve tracer, and

then you will build several types of circuits that commonly utilize diodes for

particular applications. You will be able to measure the basic properties of a

semiconductor diode and confirm the theoretical predictions from the lecture part of

the Physics 380 Course.

Diode Characteristics using a Dynamic Curve Tracer

First construct the circuit shown in the figure below. It is called a Dynamic

Curve Tracer, and its purpose is to allow quick measurements of the transport

properties of a semiconductor diode, i.e. the I-V curve. Use the transformer from the

previous lab, and invert the primary and secondary inputs, so that the primary faces

the diode circuit in the diagram below. Explain in your lab book the reason for using

the transformer. In this set up you will have to use the x-y mode of the oscilloscope

display. In this mode the horizontal voltage will be voltage across the diode, while

the vertical scale will be the voltage across the resistor. Explain in your lab notebook

why this results in the I-V trace on the oscilloscope.

Scope channel 1

Scope channel 2

35

Make sure both channels on the scope are set on DC coupled settings. Adjust

the settings on the scope so that you get the expected I-V trace on the screen, and record

your observation precisely in your lab notebook. By adjusting the controls on the

scope, zoom in on the middle-right exponential range of the I-V curve and carefully

measure the I vs. V properties. Take at least 10 data points, and plot them on a semi-

log plot, provided for you at the end of the lab instructions, on which the horizontal

scale is linear while the vertical scale is logarithmic. You should get a straight line.

Carefully measure the slope of this line. The exponential part of the curve should show

the I-V dependence:

I V( ) = I0 e−qVηkBT −1

"

#$$

%

&'' (4.1)

where lo is the reverse saturation current, kB = 1.38xl0-23(J/K) is the Boltzmann constant,

T is the absolute temperature, q = -1.6xl0-19 C the electron charge, and η is a

dimensionless parameter which depends on the diode type. Determine this factor for

your diode.

36

Half-Wave Rectifier

Next construct a half-wave rectifier circuit shown in the figure. Load resistance

should be on the order of 1kΩ. On the oscilloscope display on channel 1 the input signal

(sine wave) and on channel two display the output signal from the half-wave rectifier. It

is helpful to use the same vertical scales for both channels and position the traces so that

both have the ground potential at the same vertical level. Measure carefully the output of

the half-wave rectifier, and explain the output of the measurement.

Next, perform the FFT of the output channel trace using your scope math

function. Record the observed result in your lab notebook and comment on your

observation.

Filtered Half-Wave Rectifier

Next construct a slightly more sophisticated circuit by adding a capacitor C in

parallel with the load resistor. This results in the low pass filtering of the half-wave

rectifier. Select a capacitor C so that the voltage output doesn't drop more than 90% from

the maximum at 100kHz. Record in your lab notebook the resulting waveform and

comment on your results. As with the half-wave rectifier, again perform the FFT of the

output waveform and record your observation in your lab notebook. Comment on your

observation.

37

Full-Wave Rectifier

In the next step, construct a full wave rectifier circuit shown below with the

transformer from the previous lab again with the primary facing the diode bridge circuit.

This circuit is more efficient in rectifying an AC current. Explain the reason for the

transformer coupling. Load resistance should again be on the order of lk£L Measure

separately the input signal to the bridge on A-B terminal and then with the same scope

settings and probes the output signal on terminals C-D. Compare carefully the output of

the full-wave rectifier to the input, and explain the results.

Next, perform the FFT of the output channel trace using your scope math function.

Record the observed result in your lab notebook and comment on your observation

38

Filtered Full-Wave Rectifier

Next construct a filtered circuit by again adding the same capacitor C in parallel

with the load resistor as you did with the half-wave rectifier circuit. This again results in

the low pass filtering of the full-wave rectifier. Observe what happens at the same

frequency of 100kHz. Record in your lab notebook the resulting waveform and comment

on your results. As with the filtered half-wave rectifier, again perform the FFT of the

output waveform and record your observation in your lab notebook and comment.

Voltage Limiter (Diode Clamp)

A very useful circuit is shown in the figure below, and it is often used to protect

sensitive devices such as amplifiers from unexpected surges in voltage. The diodes serve

to limit the voltage applied to an input, and the resistor serves to limit the current flowing

through the diodes. In your simple experiment, Vmax and Vmin will both be at ground, and the

resistor can be 1kΩ. Your device to protect as well as to observe the effect will be the

scope. Apply from your generator a sine wave input with increasing magnitudes from zero

to 1 V in steps of l00 mV. Record your observations and comment on the output that you

see on the scope.

39

40

LABORATORY 5

Transistor Circuits

In this laboratory you will investigate the properties of a famous electronic

element, a semiconductor transistor. This is a device that allowed a fantastic

miniaturization of electronics over the last half-century, and the inventors of this device

were awarded a Nobel Prize for their work. You will first study

the fundamental properties of an NPN transistor by building again

a dynamic curve tracer, and then you will build several types

of single transistor circuits and characterize their properties.

Transistor Characteristics using a Dynamic Curve Tracer

First construct the circuit shown in the figure below. It is again a Dynamic Curve

Tracer from last lab, and its purpose now is to provide quick measurements of the

transport properties of a transistor with the addition of a protection diode. In this set up

you will again have to use the x-y mode of the oscilloscope display. In this mode the

horizontal voltage will be VCE, while the vertical scale will proportional to the IC.

Measure carefully the trace on the scope and plot on your lab notebook page with the

units clearly indicated on the plot.

2N3904

TO-92

2N3904

Scope Channel 1

Scope Channel 2 R = 1 kΩ

Protection diode

41

Common Emitter Amplifier

First you will build the simplest common emitter (CE) amplifier configuration

that produces both current and voltage gain. Construct the circuit shown in the figure

below. You will use a power supply voltage of +15 Volts. Your function generator will

be driving this circuit. Add a 10kΩ source resistor in series with the 50 Ω output

impedance of the function generator, and make sure that you use small input signals. This

will ensure that you can reliably use small signal transistor analysis. Your output signals

from the amplifier should not have amplitudes larger than 1 Volt. Turn off the power

supply during circuit construction!

First you have to design the DC bias for the transistor circuit amplifier. Make the

assumption that HFE =2 50. Determine the resistance values RB and RC that will establish a

DC operating point of VC = 10V and IC = 1mA. The capacitor value in the diagram

should be 0.1 µF, and this will ensure that the DC operating point is not influenced by the

driving signal source. After building the circuit, record the actual DC operating points VC

and IC, as well as measure and record VB. From these results determine the actual hFE of

your transistor and compare to the value found in the spec sheet shown above.

42

Next you will measure the AC parameters of your amplifier. Monitor the input

signal on Channel 1, and the output of the amplifier on Channel 2 of the scope, while

making sure that you satisfy the small signal transistor model requirements.

1. Apply 1kHz signal to the amplifier and measure the AC voltage gain of the

amplifier. Make sure that the input is extremely small so that no saturation at the

output occurs.

2. At the same frequency, devise a method to measure the AC current gain of the

amplifier.

3. From the first two measurements, determine the power gain of the amplifier.

4. Measure the frequency transfer function of the amplifier from 10Hz to

200kHz and plot the results in Bode plot form on the paper provided.

5. Devise a method to measure the input impedance of the amplifier.

6. Using the capacitor output impedance measurement method you learned in Lab

2, measure the output impedance of the common emitter transistor amplifier. The

measurement capacitor at the output terminals should be around 0.0 1µF.

7. From your measurements, find out the transistor parameter values of hie and hfe

and compare to the specs below.

43

Common Emitter Amplifier with Emitter Resistor

CE amplifier can be used with an emitter resistor to stabilize both the DC bias and

AC voltage gain of the circuit, as well as increase the input impedance of the amplifier.

You will next construct such a circuit and study its properties. Construct the CE amplifier

with the emitter resistor shown below.

Assuming hFE = 300, choose the resistors RB, RB2 and RE so that the operating point

will be as shown in the figure. Turn off supply power during the circuit construction!

Keep the 10 kΩ. source resistor in series with the 50 Ω output impedance of the function

generator, as well as the 0.1 µF bypass capacitor at the input and make sure that you use

small input signals. After building the circuit, record the actual DC operating points VE

and IC, as well as measure and record VC and VB. From these results determine the actual

hFE of your CE transistor amplifier with emitter resistor. Adjust the resistors to get to

correct target DC operating point for VC and IC.

Next you will measure the AC parameters of this amplifier version. Monitor the

input signal on Channel 1, and the output of the amplifier on Channel 2 of the scope,

while making sure that you satisfy the small signal transistor model requirements.

1. Apply 1kHz signal to the amplifier and measure the AC voltage gain of the

amplifier.

44

2. At the same frequency, devise a method to measure the AC current gain of

the amplifier.

3. From the first two measurements, determine the power gain of the amplifier.

4. Measure the frequency transfer function of this amplifier from 10Hz to

200kHz and plot the results in Bode plot form on the paper provided.

5. Devise a method to measure the input impedance of the amplifier.

6. Measure the output impedance of this common collector transistor amplifier

configuration.

7. From your measurements find again the values of hie and hfe for the transistor.

One advantage of this version of the CE amplifier is that the DC bias settings

should be independent of hFE.

Common Collector Amplifier

As a final task, you will construct the common collector (CC) amplifier

shown below. This circuit produces no voltage gain, and is therefore often called

the Emitter Follower amplifier. It still, however, produces a current gain and

45

therefore a power gain.

Assuming hFE = 300, choose the resistors RB and RE so that the operating point

will be at VE = 5V and Ic = 10mA. Turn off power supply during the circuit

construction! Keep the 10 kΩ source resistor in series with the 50 Ω. output

impedance of the function generator, and make sure that you use small input signals.

After building the circuit, record the actual DC operating points VE and Ic, as well as

measure and record IB and VB. From this result determine the actual hFE of your

transistor. Is there anything different about this CC amplifier hFE than in the CE amplifier

hFE? Why? Adjust the resistors to get to correct target DC operating point for VE and

IC.

Finally, you will measure the AC parameters of this CC amplifier version.

Monitor the input signal on Channel 1, and the output of the amplifier on Channel 2

of the scope, while making sure that you satisfy the small signal transistor model

requirements.

1. Apply 1kHz signal to the amplifier and measure the AC voltage gain of the

amplifier.

2. At the same frequency, devise a method to measure the AC current gain of

the amplifier.

3. From the first two measurements, determine the power gain of the amplifier.

4. Devise a method to measure the input impedance of the amplifier.

5. With the 0.1 µF load capacitor and input at 1kHz, measure the output impedance

of this common collector transistor amplifier.

6. Estimate the AC parameters hfe and hie of your amplifier from your

measurements. Show your equations and work.

46

47

48

LABORATORY 6

Operational Amplifiers

In this laboratory you will investigate the properties of an extremely useful analog

integrated circuit called Operational Amplifier. These devices are very popular, as they

reasonably well approximate the ideal behavior as characterized by the Golden Rules that

the potential difference between the two inputs is maintained at zero and that the current

into the device at both inputs is also zero. This simplicity of the operating rules is

provided by the significant internal complexity of the device, as you can examine in the

schematic diagram of the device in the spec sheets. Because of their simple

operating rules, this device finds wide use in many different applications, some of

which you will demonstrate in this lab. The simple device is shown in the figure

below, along with the pin designations. Note that you have to provide the power to

this device, which is recommended at +15 and -15 Volts from the laboratory power

supply.

Typical differential open loop gain of an operational amplifier is shown in the

figure below. The transfer function with no feedback is best described by a single

pole low pass filter function. For this amplifier, the DC gain is specified at 2x105,

and the unity gain frequency is listed at 1 MHz. This curve limits the range of operation

of the device, and you should always be aware of it, especially when working at

high frequencies.

49

50

Voltage Follower (Unity Gain "Buffer")

We will start with the simplest circuit shown in the figure below. The output

follows the input voltage with unitary gain. As simple as this device is, it is very useful

as an isolation stage (buffer) between two different circuit sections or stages. This is

because of the high input impedance of the device, and its low output impedance.

Construct this simple circuit and apply a sine wave signal at the input, and confirm that

the output signal is as expected. Then measure the transfer function of this circuit from

10Hz to 15MHz, and plot it on the Bode plot graph provided for you at the end of the

lab. This should be a simple task, but pay particular attention to the high frequency

region above 1MHz and take more points in that region as appropriate.

51

Non-Inverting Amplifier

Next construct a non-inverting configuration of the Op-Amp shown in the figure

below. Design the circuit (i.e. pick resistor values), so that the amplifier gain is +10.

Show your work in the lab notebook. Note that the input signal is to the positive Op-Amp

terminal.

Apply a sine wave signal to the input so that the output signal is approximately IV in

amplitude, and confirm that the circuit is working as a non-inverting amplifier with the

designed gain. Then measure the transfer function of this circuit from 10Hz to 15MHz,

and plot it on the same Bode plot graph as you did for the unity gain amplifier in the

previous section. Again, pay particular attention to the high frequency region where the

theoretical amplifier gain should roll off at -6dB.

Inverting Amplifier

Next, construct the inverting amplifier as shown in the figure below. Design the

inverting amplifier circuit so that the gain is -100. Show your work in the lab notebook.

Note that the input signal is now to the negative Op-Amp terminal.

52

Apply a sine wave signal to the input, and confirm that the circuit is working as

an inverting amplifier with the designed gain. Make sure that the input signal is small

enough so that the output signal, for this gain value, is still in the non-saturating amplifier

regime. Then measure the transfer function of this circuit from 10Hz to 15MHz, and plot

it on the same Bode plot graph as you did for the unity gain amplifier and the non-

inverting amplifier in the previous two sections. Again, pay particular attention to the

high frequency region where the theoretical amplifier gain should roll off at -6dB, and

take data points as appropriate to properly plot this transfer function region.

Operational Amplifier Integrator

The next circuit you will build integrates input signals, and is therefore called an

Integrator. The principle of integration of this device is similar to the RC low-pass filter

network analysis, except that this device does it much better over a wide frequency range

and with gain larger than 1, something that was not possible with the passive RC low-

pass filter of Lab 2.

53

A capacitor value of Cf = 0.1µF and input resistor of R = 10kΩ should be used.

One problem is that any small (unwanted) DC input signal will get integrated. One

way to resolve that problem is to place a resistor Rf in the feedback loop. A value of

500kΩ should be OK. Another way to deal with the problem is to short the capacitor

feedback loop before the desired integration is started. Now show that the integrator

works as advertised. Apply a sine wave at the input and show that the signal is

transforming a sine into a cosine. Then apply a square wave to the input. What output

do you observe? Compare those outputs to the ones you would expect an integrator to

provide. Carefully note your observations in your lab notebook and discuss your results.

Operational Amplifier Differentiator

The next circuit you will build differentiates input signals, and is therefore

called a Differentiator. The principle of differentiation of this device is similar to the

RC high-pass filter network analysis of Lab 2, except that this device does it much

better over a wide frequency range and with gain larger than 1, something that was not

possible with the passive RC high-pass filter in Lab 2.

54

A capacitor value of C=0.01µF and input resistor of Rf = 100kΩ should be used.

A typical problem with the differentiation circuits is their susceptibility to noise and

spurious oscillations. One way to deal with the problem is to add a feedback capacitor

Cf to the circuit. A value of 50pF should do. Another good practice is to add an

input resistor (not shown in the Figure!) before the input capacitor. A 1kΩ should be

OK. Now show that the differentiator works as advertised by applying a triangle wave at

the input. What output do you observe? Compare that output to the one you would

expect a differentiator to provide. Finally, measure the transfer function of the

differentiator circuit from 10Hz to 15MHz, by applying a sine wave input. Plot it on

the separate Bode plot graph provided for you at the end of the lab. What do you

observe, and how is your result related to the open loop gain curve of the operational

amplifier shown earlier?

The Summing Stage

Operational amplifiers have a wide range of further applications that are truly

diverse. You will build two more just to demonstrate their versatility and the reason

55

why they are called Operational Amplifiers (they can perform mathematical

operations!). You already demonstrated the follower, inverter, amplification,

integration, and differentiation. Figure below shows the typical configuration of an

inverting summing stage that can perform addition. The output signal is proportional to

the sum of the input signals.

You will add just two signals, a sine wave from the output channel of the

function generator and a square wave from the Sync output channel of the function

generator. Pick all input resistors and feedback resistor values to be the same, say

1kΩ, and make sure the sine wave is of appropriate amplitude not to saturate the output

signal. Describe what you observe as the output signal and compare it to what you

expect to observe from the summing device shown in the figure. Try adding a ramp

wave and a triangle wave from the function generator to the Sync output and you will

observe some fun waveforms.

Logarithmic and Anti-Logarithmic Amplifier

Op-amps can also be used to perform logarithmic and exponential (anti-

logarithmic) functions. By combining logarithmic and anti-logarithmic (exponential

56

performing) circuits with the summing junction circuits, one can then implement

analog

multipliers and dividers. With such a large array of available mathematical operations

that Op-amps can perform, one can truly build amazing analog computing machines,

although due to inexpensive digital computers, this is increasingly obsolete. Figure

below on the left shows a logarithmic amplifier whose output is proportional to the

logarithm of the input, while figure on the right shows an anti-logarithmic amplifier

whose output is proportional to the inverse logarithm of the input.

Build these two circuits, and send a triangle wave to the input, and plot in your

lab notebook the output signals and comment on whether you observe the expected

outputs. For completeness, the diagram below show how you can make an analog

multiplier using the basic units described above. Analog divider is very similar in

57

design to the multiplier.

58

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60

LABORATORY 7

Digital Circuits

In this laboratory you will study digital logic gates and circuits. These devices

have revolutionized our technologically developed society in so many ways: in

communication, computation, information storage and exchange, etc. The devices you

will study form the very basis of this technology. First you will investigate individual

logic gates and confirm their truth tables. Then you will build more complicated circuits

from individual logic gates. Finally, you will construct a Divide-by-N counters using a

memory based digital logic J-K Hip-flop device. In order to operate digital logic gates, it

is necessary to have digital logic signals. In this lab they will be provided by the square

wave output of the function generator, the SYNC square wave output of the generator,

and by the square wave signal from the Scope calibration port.

Basic Logic Gates

There are several fundamental logic gates listed below. They are useful for

performing Boolean algebraic operations developed by George Boole in the 1800's.

The logic gates are defined by their Truth tables listed below

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In order to perform complicated logic operations, it is extremely useful to minimize

the complexity of logic circuits as much as possible. For that purpose, several

Boolean identities can be extremely useful for simplifying Boolean algebra

expressions:

The two Boolean identities in the lowest line of the table are known as the DeMorgan's

Theorem. They are extremely useful for simplifying Boolean algebra. An important

consequence of the DeMorgan's Theorem is that any logic function may be

implemented by using only OR and NOT gates or only AND and NOT gates.

The additional two logic gates that are very useful are the XOR or XNOR gates

characterized by the following truth tables.

Boolean Identities A + 0 =A A ! 1 = A

A + B = B + A AB = BA A + (B + C) = (A + B) + C A(BC) = (AB)C A + BC = (A + B)(A + C) A(B + C) = AB + AC

A + A = A A ! A = 0 A + 1 = 1 A ! A = A A + Ā = 1 A ! 0 = 0

A + AB = A A(A + B) = A A + AB = A + B (A + B)(A + C) = A + BC A !BA = B A + B = A !B

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You are given electronic chips with the multiple AND and XOR gates. Connect

the SYNC square wave output of the function generator and the calibration port square

wave of the scope as the two inputs to the individual AND and XOR gates. Observe both

input signals on the scope and adjust the frequency of the function generator to be

slightly different so that you can have all possible inputs for A and B signals. Confirm by

observing the traces on the scope that you have all four possible input signal

combinations available. First predict the outputs of each gate and then observe the

outputs of the two gates on the scope screen. Draw carefully in your Lab notebook your

observation and describe your confirmation of the truth tables for the logic gates you

used.

Sequential Logic Gates without Memory

Simple digital circuits consist of several logic gates connected to perform a more

complicated Boolean algebra operation. In class we learned about the 2-Bit adder circuit.

In this lab you will construct a sequential XOR circuit that produces a second bit sum.

You will need three logic inputs. Two are provided by the function generator and one by

the scope calibration port. Connect the circuit as shown in the figure and confirm the 9-

term truth table of this device.

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Sequential Logic Gates with Memory

So far we have discussed the gates where the output depends on the present state

of the inputs. In the memory based logic devices, the outputs may also depend on the

past state of the inputs. Although there are several memory based devices and logic

familes that are available, we will use only one, the J-K flip-flop. This device is very

useful and avoids some of the potential problems of the less sophisticated flip-flops such

as the S-R flip-flop. The schematic and symbol of the J-K flip-flop are shown below.

The truth table for this device is shown in the table below. Again, using the three

square-wave source that you have available, connect the J-K flip-flop so that you can

experimentally confirm the truth table shown below. Make sure that you record the

output of both Q and Q-NOT ports of the J-K flip-flop in your laboratory notebook and

describe in detail your set-up and observations.

Now construct a simple circuit shown below. It is a divide-by-two device. In your

laboratory notebook derive and describe why the output of the device is as shown.

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Finally construct a more complicated J-K Flip-flop circuit shown in the figure and draw

on the time diagram each output that you observe. Explain your observations.