Ena Lab Manual - Solved

EE Department Electrical Network Analysis
PRACTICAL WORK BOOK

For The Course
EE-211 Electrical Network Analysis
For
B.E. Electrical Engineering
Complied By: Checked By:

Lab. Engineer Bahzad Zaib Assistant Professor Sobia Hayee
DEPARTMENT OF ELECTRICAL ENGINEERING

College of Electrical & Mechanical Engineering (CEME), NUST-Pakistan
CEME (NUST), Rawalpindi 1

LIST OF EXPERIMENTS
S.NO. TITLE OF EXPERIMENT
01 Introduction to lab equipment
02 Transient Analysis of RC circuit and determination of Time Constant
03 To Study Resonance in RLC Series Circuit
04 To Study the response of Passive RC & RL Low Pass Filters
05 To Study the response of Passive RC & RL High Pass Filters
06 To Study the response of Passive RC based Band Pass Filter
07 Analysis of Active Low Pass Filter using R, C & OP AMP
08 Analysis of Active High Pass Filter using R, C & OP AMP
09 Analysis of Active Band Pass Filter using R, C & OP AMP
10 Study of 1 st Order RC Differentiator & Integrator Circuits
11 Evaluation of Two Port Parameters (Z parameters) for a Resistive Network
12 Evaluation of Two Port Parameters (Y parameters) for a Resistive Network
13 Determination of Apparent Power and Power Factor for AC Circuit
14 Study the Significance of Power Factor Correction in AC circuit

EXPERIMENT NO – 01
INTRODUCTION: BASIC CONCEPTS & LAB EQUIPMENT
OBJECTIVE:
- To know and understand basic function of laboratory equipment.
- To become familiar with the correct ways of operating lab instruments.
THEORY:
A few tools are required for basic electronics work. Most of these tools are inexpensive and
easy to obtain.
Digital multi-meter:
First and foremost in your tool collection is a multi-meter. This is an electrical instrument
designed to measure voltage, current, resistance, and often other variables as well. Multi-
meters are manufactured in both digital and analog form. A digital multi-meter is preferred for
precision work, but analog meters are also useful for gaining an intuitive understanding of
instrument sensitivity and range.
Solder-less bread-board:
Also essential is a solder-less breadboard, sometimes called a prototyping board, or proto-
board. This device allows you to quickly join electronic components to one another without
having to solder component terminals and wires together.
The internal structure / layout of solder less bread-board can be depicted as:

we can think of a breadboard as a board that can be divided in 2 functional areas:

– the power strip(s) (in the drawing above A and D)
– the component grid(s) (in the drawing above B and C)
Most breadboards have at least 2 “component grids” (B and C), separated at exactly the
distance between the two pin sides of a DIP IC package between B and C. The pins of the
component grids (B and C) are connected vertically, per column. The grids B and C are not
connected with each other
Bench Top Power Supply:

Bench Top Power Supplies are used for general design, repair, instructional, or testing
purposes and includes both Fixed and Variable output supplies. It is provided with 3 terminals
for connection purposes: positive, negative and ground. The digital display shows the values
of voltage which is adjusted by coarse adjustment and fine adjustment knobs.
Oscilloscope:
The main purpose of an oscilloscope is to graph an electrical signal as it varies over time.
Most scopes produce a two-dimensional graph with time on the x-axis and voltage on the y-
axis.
Controls surrounding the scope’s screen allow you to adjust the scale of the graph, both
vertically and horizontally – allowing you to zoom in and out on a signal. There are also
controls to set the trigger on the scope, which helps focus and stabilize the display.
In addition to those fundamental features, many scopes have measurement tools, which help
to quickly quantify frequency, amplitude, and other waveform characteristics. In general a
scope can measure both time-based and voltage-based characteristics:
› Timing characteristics:
Frequency and period – Frequency is defined as the number of times per second a waveform
repeats. And the period is the reciprocal of that (number of seconds each repeating waveform
takes). The maximum frequency a scope can measure varies, but it’s often in the 100’s of
MHz (1E6 Hz) range.
Duty cycle – The percentage of a period that a wave is either positive or negative (there are
both positive and negative duty cycles). The duty cycle is a ratio that tells you how long a
signal is “on” versus how long it’s “off” each period.

Rise and fall time – Signals can’t instantaneously go from 0V to 5V, they have to smoothly
rise. The duration of a wave going from a low point to a high point is called the rise time, and
fall time measures the opposite. These characteristics are important when considering how
fast a circuit can respond to signals.
› Voltage characteristics:
Amplitude – Amplitude is a measure of the magnitude of a signal. There are a variety of
amplitude measurements including peak-to-peak amplitude, which measures the absolute
difference between a high and low voltage point of a signal. Peak amplitude, on the other
hand, only measures how high or low a signal is past 0V.
Maximum and minimum voltages – The scope can tell you exactly how high and low the
voltage of your signal gets.
Mean and average voltages – Oscilloscopes can calculate the average or mean of your signal,
and it can also tell you the average of your signal’s minimum and maximum voltage.
Oscilloscope Usage:
Here are some of the important oscilloscope buzzwords you should be familiar with before
turning it on.
Key Oscilloscope Specifications
Some scopes are better than others. These characteristics help define how well you might
expect a scope to perform:
› Bandwidth – Oscilloscopes are most commonly used to measure waveforms which have a
defined frequency. No scope is perfect though: they all have limits as to how fast they can see
a signal change. The bandwidth of a scope specifies the range of frequencies it can reliably
measure.
› Digital vs. Analog – As with most everything electronic, o-scopes can either be analog or
digital. Analog scopes use an electron beam to directly map the input voltage to a display.
Digital scopes incorporate microcontrollers, which sample the input signal with an analog-to-
digital converter and map that reading to the display. Generally analog scopes are older, have
a lower bandwidth, and less features, but they may have a faster response (and look much
cooler).

› Channel Amount – Many scopes can read more than one signal at a time, displaying them all
on the screen simultaneously. Each signal read by a scope is fed into a separate channel. Two
to four channel scopes are very common.
› Sampling Rate – This characteristic is unique to digital scopes, it defines how many times
per second a signal is read. For scopes that have more than one channel, this value may
decrease if multiple channels are in use.
› Rise Time – The specified rise time of a scope defines the fastest rising pulse it can measure.
The rise time of a scope is very closely related to the bandwidth. It can be calculated as Rise
Time = 0.35 / Bandwidth.
› Maximum Input Voltage – Every piece of electronics has its limits when it comes to high
voltage. Scopes should all be rated with a maximum input voltage. If your signal exceeds that
voltage, there’s a good chance the scope will be damaged.
› Resolution – The resolution of a scope represents how precisely it can measure the input
voltage. This value can change as the vertical scale is adjusted.
› Vertical Sensitivity – This value represents the minimum and maximum values of your
vertical, voltage scale. This value is listed in volts per div.
› Time Base – Time base usually indicates the range of sensitivities on the horizontal, time
axis. This value is listed in seconds per div.
› Input Impedance – When signal frequencies get very high, even a small impedance
(resistance, capacitance, or inductance) added to a circuit can affect the signal. Every
oscilloscope will add a certain impedance to a circuit it’s reading, called the input impedance.
Input impedances are generally represented as a large resistive impedance (>1 MΩ) in parallel
(||) with small capacitance (in the pF range). The impact of input impedance is more apparent
when measuring very high frequency signals, and the probe you use may have to help
compensate for it.
Anatomy of An Oscilloscope
While no scopes are created exactly equal, they should all share a few similarities that make
them function similarly. On this page we’ll discuss a few of the more common
systems of an oscilloscope: the display, horizontal, vertical, trigger, and inputs.
The Display
An oscilloscope isn’t any good unless it can display the information you’re trying to test,
which makes the display one of the more important sections on the scope.

Every oscilloscope display should be criss-crossed with horizontal and vertical lines
called divisions. The scale of those divisions are modified with the horizontal and vertical
systems. The vertical system is measured in “volts per division” and the horizontal is
“seconds per division”. Generally, scopes will feature around 8-10 vertical (voltage) divisions,
and 10-14 horizontal (seconds) divisions.
Older scopes (especially those of the analog variety) usually feature a simple, monochrome
display, though the intensity of the wave may vary. More modern scopes feature multicolor
LCD screens, which are a great help in showing more than one waveform at a time.
Many scope displays are situated next to a set of about five buttons – either to the side or
below the display. These buttons can be used to navigate menus and control settings of the
scope.
Vertical System
The vertical section of the scope controls the voltage scale on the display. There are
traditionally two knobs in this section, which allow you to individually control the vertical
position and volts/div.
The more critical volts per division knob allow you to set the vertical scale on the screen.
Rotating the knob clockwise will decrease the scale, and counter-clockwise will increase. A
smaller scale – fewer volts per division on the screen – means you’re more “zoomed in” to the
waveform.
The display on the GA1102, for example, has 8 vertical divisions, and the volts/div knob can
select a scale between 2mV/div and 5V/div. So, zoomed all the way in to 2mV/div, the
display can show waveform that is 16mV from top to bottom. Fully “zoomed out”, the scope
can show a waveform ranging over 40V. (The probe, as we’ll discuss below, can further

increase this range.)

The position knob controls the vertical offset of the waveform on the screen. Rotate the knob
clockwise, and the wave will move down, counter-clockwise will move it up the display. You
can use the position knob to offset part of a waveform off the screen.
Using both the position and volts/div knobs in conjunction, you can zoom in on just a tiny part
of the waveform that you care about the most. If you had a 5V square wave, but only cared
about how much it was ringing on the edges, you could zoom in on the rising edge using both
knobs.
Horizontal System
The horizontal section of the scope controls the time scale on the screen. Like the vertical
system, the horizontal control gives you two knobs: position and seconds/div.
The seconds per division (s/div) knob rotates to increase or decrease the horizontal scale. If
you rotate the s/div knob clockwise, the number of seconds each division represents will
decrease – you’ll be “zooming in” on the time scale. Rotate counter-clockwise to increase the
time scale, and show a longer amount of time on the screen.
Using the GA1102 as an example again, the display has 14 horizontal divisions, and
can show anywhere between 2nS and 50s per division. So zoomed all the way in on the
horizontal scale, the scope can show 28nS of a waveform, and zoomed way out it can show a
signal as it changes over 70 seconds.
The position knob can move your waveform to the right or left of the display, adjusting the
horizontal offset.
Using the horizontal system, you can adjust how many periods of a waveform you want to
see. You can zoom out, and show multiple peaks and troughs of a signal:
Or you can zoom way in, and use the position knob to show just a tiny part of a wave:
Trigger System
The trigger section is devoted to stabilizing and focusing the oscilloscope. The trigger tells the
scope what parts of the signal to “trigger” on and start measuring. If your waveform
is periodic, the trigger can be manipulated to keep the display static and unflinching. A poorly
triggered wave will produce seizure-inducing sweeping waves like this:

The trigger section of a scope is usually comprised of a level knob and a set of buttons to
select the source and type of the trigger. The level knob can be twisted to set a trigger to a
specific voltage point.
A series of buttons and screen menus make up the rest of the trigger system. Their main
purpose is to select the trigger source and mode. There are a variety of trigger types, which
manipulate how the trigger is activated:
› An edge trigger is the most basic form of the trigger. It will key the oscilloscope to start
measuring when the signal voltage passes a certain level. An edge trigger can be set to catch
on a rising or falling edge (or both).
› A pulse trigger tells the scope to key in on a specified “pulse” of voltage. You can specify
the duration and direction of the pulse. For example, it can be a tiny blip of 0V -> 5V -> 0V,
or it can be a seconds-long dip from 5V to 0V, back to 5V.
› A slope trigger can be set to trigger the scope on a positive or negative slope over a specified
amount of time.
› More complicated triggers exist to focus on standardized waveforms that carry video data,
like NTSC or PAL. These waves use a unique synchronizing pattern at the beginning of every
frame.
You can also usually select a triggering mode, which, in effect, tells the scope how strongly
you feel about your trigger. In automatic trigger mode, the scope can attempt to draw your
waveform even if it doesn’t trigger. Normal mode will only draw your wave if it sees the
specified trigger. And single mode looks for your specified trigger, when it sees it it will draw
your wave then stop.
The Probes
An oscilloscope is only good if you can actually connect it to a signal, and for that you need
probes. Probes are single-input devices that route a signal from your circuit to the scope. They
have a sharp tip which probes into a point on your circuit. The tip can also be equipped with
hooks, tweezers or clips to make latching onto a circuit easier. Every probe also includes
a ground clip, which should be secured safely to a common ground point on the circuit under
test.

While probes may seem like simple devices that just latch onto your circuit and carry a signal
to the scope, there’s actually a lot that goes into probe design and selection.
Optimally, what a probe needs to be is invisible – it shouldn’t have any effect
on your signal under test. Unfortunately, long wires all have intrinsic inductance, capacitance,
and resistance, so, no matter what, they’ll affect scope readings (especially at high
frequencies).
There are a variety of probe types out there, the most common of which is
the passive probe, included with most scopes. Most of the “stock” passive probes
are attenuated. Attenuating probes have a large resistance intentionally built-in and shunted by
a small capacitor, which helps to minimize the effect that a long cable might have on loading
your circuit. In series with the input impedance of a scope, this attenuated probe will create
a voltage divider between your signal and the scope input.
Most probes have a 9MΩ resistor for attenuating, which, when combined with a standard
1MΩ input impedance on a scope, creates a 1/10 voltage divider. These probes are commonly
called 10X attenuated probes. Many probes include a switch to select between 10X and 1X
(no attenuation).

Attenuated probes are great for improving accuracy at high frequencies, but they will
also reduce the amplitude of your signal. If you’re trying to measure a very low-voltage
signal, you may have to go with a 1X probe. You may also need to select a setting on your
scope to tell it you’re using an attenuated probe, although many scopes can automatically
detect this.
Beyond the passive attenuated probe, there are a variety of other probes out here. Active
probes are powered probes (they require a separate power source), which can amplify your
signal or even pre-process it before it get to your scope. While most probes are designed to
measure voltage, there are probes designed to measure AC or DC current. Current probes are
unique because they often clamp around a wire, never actually making contact with the
circuit.
Using an Oscilloscope
The infinite variety of signals out there means you’ll never operate an oscilloscope the same
way twice. But there are some steps you can count on performing just about every time you
test a circuit. We’ll show an example signal, and the steps required to measure it.
Probe Selection and Setup

First off, you’ll need to select a probe. For most signals, the simple passive probe included
with your scope will work perfectly fine.
Next, before connecting it to your scope, set the attenuation on your probe. 10X – the most
common attenuation factor – is usually the most well-rounded choice. If you are trying to
measure a very low-voltage signal though, you may need to use 1X.
Connect the Probe and Turn the Scope On

Connect your probe to the first channel on your scope, and turn it on. Have some patience
here, some scopes take as long to boot up as an old PC.
When the scope boots up you should see the divisions, scale, and a noisy, flat line of a
waveform.

The screen should also show previously set values for time and volts per div. Ignoring those
scales for now, make these adjustments to put your scope into a standard setup:
› Turn channel 1 on and channel 2 off.
› Set channel 1 to DC coupling.
› Set the trigger source to channel 1 – no external source or alternate channel triggering.
› Set the trigger type to rising edge, and the trigger mode to auto (as opposed to single).
› Make sure the scope probe attenuation on your scope matches the setting on your probe (e.g.
1X, 10X).
For help making these adjustments you can consult scope’s user’s manual.
Testing the Probe

Let’s connect that channel up to a meaningful signal. Most scopes will have a built-in
frequency generator that emits a reliable, set-frequency wave – on the GA1102CAL there is a
1kHz square wave output at the bottom-right of the front panel. The frequency generator
output has two separate conductors – one for the signal and one for ground. Connect your
probe’s ground clip to the ground, and the probe tip to the signal output.
As soon as you connect both parts of the probe, you should see a signal begin to dance around
your screen. Try fiddling with the horizontal and vertical system knobs to maneuver the
waveform around the screen. Rotating the scale knobs clockwise will “zoom into” your
waveform, and counter-clockwise zooms out. You can also use the position knob to further
locate your waveform.
If your wave is still unstable, try rotating the trigger position knob. Make sure the trigger isn’t
higher than the tallest peak of your waveform. By default, the trigger type should be set to
edge, which is usually a good choice for square waves like this.
Try fiddling with those knobs enough to display a single period of your wave on the screen.
Or try zooming way out on the time scale to show dozens of squares.
Compensating an Attenuated Probe

If your probe is set to 10X, and you don’t have a perfectly square waveform as shown above,
you may need to compensate your probe. Most probes have a recessed screw head, which you
can rotate to adjust the shunt capacitance of the probe.
Try using a small screwdriver to rotate this trimmer, and look at what happens to the
waveform.
Adjust the trimming cap on the probe handle until you have a straight-edged square wave.
Compensation is only necessary if your probe is attenuated (e.g. 10X), in which case it’s
critical.
Probing, Triggering, and Scaling Tips

Once you’ve compensated your probe, it’s time to measure a real signal! Go find a signal
source e.g. frequency generator and start.
The first key to probing a signal is finding a solid, reliable grounding point. Clasp your
ground clip to a known ground, sometimes you may have to use a small wire to intermediate
between the ground clip and your circuit’s ground point. Then connect your probe tip to the
signal under test. Probe tips exist in a variety of form factors – the spring-loaded clip, fine
point, hooks, etc. – try to find one that doesn’t require you to hold it in place all the time.
Once your signal is on the screen, you may want to begin by adjusting the horizontal and
vertical scales into at least the “ballpark” of your signal. If you’re probing a 5V 1kHz square
wave, you’ll probably want the volts/div somewhere around 0.5-1V, and set the seconds/div
to around 100µs (14 divisions would show about one and a half periods).
If part of your wave is rising or falling of the screen, you can adjust
the vertical position to move it up or down. If your signal is purely DC, you may want to
adjust the 0V level near the bottom of your display.
Once you have the scales ball parked, your waveform may need some
triggering. Edge triggering – where the scope tries to begin its scan when it sees voltage rise
(or fall) past a set point – is the easiest type to use. Using an edge trigger, try to set the trigger
level to a point on your waveform that only sees a rising edge once per period.
Now just scale, position, trigger and repeat until you’re looking at exactly what you need.
Measure Twice, Cut Once

With a signal scoped, triggered, and scaled, it comes time to measure transients, periods, and
other waveform properties. Some scopes have more measurement tools than others, but they’ll
all at least have divisions, from which you should be able to at least estimate the amplitude
and frequency.
Many scopes support a variety of automatic measurement tools, they may even constantly
display the most relevant information, like frequency. To get the most out of your scope,
you’ll want to explore all of the measure functions it supports. Most scopes will calculate
frequency, amplitude, duty cycle, mean voltage, and a variety of other wave characteristics for
you automatically.

Using the scope’s measure tools to find VPP, VMax, frequency, period and duty cycle
A third measuring tool many scopes provide is cursors. Cursors are on-
screen, movable markers which can be placed on either the time or voltage axis. Cursors
usually come in pairs, so you can measure the difference between one and the other.
Measuring the ringing of a square wave with cursors.

Once you’ve measured the quantity you were looking for, you can begin to make adjustments
to your circuit and measure some more! Some scopes also
support saving, printing, or storing a waveform, so you can recall it and remember those good
old times when you scoped that signal.
To find out more about what your scope can do, consult its user’s manual!
Voltmeter Usage:
A multi-meter is an electrical instrument capable of measuring voltage, current, and
resistance. Digital multi-meters have numerical displays, like digital clocks, for indicating the
quantity of voltage, current, or resistance. Analog multi-meters indicate these quantities by
means of a moving pointer over a printed scale.
Some digital multi-meters are auto-ranging. An auto-ranging meter has only a
few selector switch (dial) positions. Manual-ranging meters have several different selector
positions for each basic quantity: several for voltage, several for current, and several for
resistance.

In order to measure voltage of a battery set your multi-meter’s selector switch to

the highest-value ‘DC volt’ position available. Auto-ranging multi-meters may only have a
single position for DC voltage, in which case you need to set the switch to that one position.
Touch the red test probe to the positive (+) side of a battery, and the black test probe to the
negative (-) side of the same battery. The meter should now provide you with some sort of
indication. Reverse the test probe connections to the battery if the meter’s indication is
negative (on an analog meter, a negative value is indicated by the pointer deflecting left
instead of right).
If your meter is a manual-range type, and the selector switch has been set to a
high-range position, the indication will be small. Move the selector switch to the next lower
DC voltage range setting and reconnect to the battery. The indication should be stronger now,
as indicated by a greater deflection of the analog meter pointer (needle), or more active digits
on the digital meter display. For the best results, move the selector switch to the lowest-range
setting that does not ‘over-range’ the meter. An over-ranged analog meter is said to be
‘pegged,’ as the needle will be forced all the way to the right-hand side of the scale, past the
full-range scale value. An over-ranged digital meter sometimes displays the letters ‘OL’, or a
series of dashed lines. This indication is manufacturer-specific.
Ohmmeter Usage:
Be sure to never measure the resistance of any electrically ‘live’ object or circuit. In other
words, do not attempt to measure the resistance of a battery or any other source of substantial
voltage using a multi-meter set to the resistance (ohms) function, failing to heed this warning
will likely result in meter damage and even personal injury.
Connect the meter’s test probes across the resistor as such, and note its indication on
the resistance scale:

If the needle points very close to zero, you need to select a lower resistance range on the
Meter. If you are using a digital multi-meter, you should see a numerical figure close to 10
shown on the display, with a small ”k” symbol on the right-hand side denoting the metric
prefix for ”kilo” (thousand). Some digital meters are manually-ranged, and require
appropriate range selection just as the analog meter. If yours is like this, experiment with
different range switch positions and see which one gives you the best indication.
Ammeter Usage:
Current is the measure of the rate of electron ‘flow’ in a circuit. It is measured in the unit of
the Ampere, simply called ‘Amp’, (A).
The most common way to measure current in a circuit is to break the circuit open and insert
an ‘ammeter’ in series (in-line) with the circuit so that all electrons flowing through the circuit
also have to go through the meter. Because measuring current in this manner requires the
meter be made part of the circuit, it is a more difficult type of measurement to make than
either voltage or resistance.
Some digital meters, like the unit shown in the illustration, have a separate jack to insert the
red test lead plug when measuring current. Other meters, like most inexpensive analog meters,
use the same jacks for measuring voltage, resistance, and current.

Transient Analysis of RC circuit and determination of Time Constant
OBJECTIVE:
 To study the response of a series RC circuit.
 To differentiate between steady state and transient response.
 To understand & evaluate time constant concept using step input.
THEORY:
For the RC network of Figure 1, voltage VC(t) across the capacitor is given by
where, V is the applied source voltage to the circuit for t ≥ 0. RC = τ is the time constant. The response
curve is increasing and is shown in Figure 2.
Figure 1: RC Series Network
Figure 2: Capacitor Charging
The discharge voltage for the capacitor is given by
where Vo is the initial voltage stored in capacitor at t = 0, and RC = τ is time constant. The
response curve is a decaying exponentials as shown in Figure 3.

Figure 3: Discharging of Capacitor
APPARATUS:
1. DC Power Supply 2. Jumper Wires 3. Oscilloscope Function

Generator
1
4. Fixed Resistor ___kohm 1
5. Capacitor ___µF 6. Bread board
7. Digital Multimeter
PART - I
PROCEDURE:
Capacitor Charging
1. Compute the theoretical value of time constant using expression Ʈ=RC
1.00 ms
Time Constant (theo) =_________________________________________________________
10 V.
2. Construct the circuit in accordance with figure below and set DC voltage to __
3. Using Oscilloscope across capacitor monitor the voltage build-up across capacitor and let the
capacitor charge to almost 6.26 V(equal to Source Voltage).
4. Draw the corresponding graph as below:

5. Using the above graph evaluate the time at which capacitor is 63% charged i.e. 0.63 x Source
Voltage. The resulting time is Time Constant
1.02 ms
So, Time Constant (measured) =___________________________________________
Also mention the co-ordinates on graph sheet corresponding to Time Constant.
Capacitor Discharging
6. Now, consider the circuit shown in figure below and connect components on breadboard
accordingly.
7. Using oscilloscope obtain the graph of voltage across capacitor. Let the capacitor discharge
completely (approximately to zero voltage)

8. Use graph to extract out the value of time at which capacitor is 63% discharged i.e. voltage equal to
37% of the source voltage (5V in our case).
1.02 ms
So, Time Constant (measured) =________________________________________
Mention co-ordinates corresponding to Time Constant in graph.

9. Compare theoretical value of Time Constant with measured values
__________________________________________________________________________________
The theoretical value was 1.00 ms.
__________________________________________________________________________________
__________________________________________________________________________________
The practical value was 1.20
1.02ms,
ms
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
___________________________
PART – II
1. Replace DC source by a source capable of generating square waves. Use function generator for this
purpose.
The output of a square wave generator alternates between two different voltages separated by a
potential difference V. When the output is at higher potential the capacitor is charging up. When the
output switches to lower potential, the capacitor discharges. The capacitor then alternates between
charging and discharging cycles in accordance with output of a square wave generator.
2. Connect the circuit as shown in figure below.
3. Adjust the frequency to such a value such that the capacitor is sufficiently charged and discharged
alternatively. This can simply be done by reducing the frequency using frequency setting knob of
function generator.
6.68
4. Set peak voltage of input square wave to _____V. Draw this input wave form.
5. Observe the output on oscilloscope and sketch the resulting graph.

6. Using expression below calculate value of voltage across capacitor for t= 1Ƭ
For t = 0, For t = T, For t = 5T, For t = ∞,
7. For the above calculated voltage across capacitor determine time from graph of output (charging
portion).
1.201.02
ms ms
Time Constant = _________________________________
8. Use following expression to calculate voltage across capacitor
For t = 0, For t = T, For t = 5T, For t = ∞,
9. For the above calculated voltage across capacitor determine time from graph of output (discharging
portion).
1.201.02
ms ms
Time Constant = _________________________________

10. Compare theoretical value of Time Constant with those determined in step (7) & (8)
__________________________________________________________________________________
The value of theoretical and calculated experiments is approximately same.
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________

To Study Resonance in RLC Series Circuit
OBJECTIVE:
-To study the resonance in RLC series circuit.
-To calculate the resonant frequency, bandwidth and Q factor
THEORY:
 A circuit containing R, L and C elements is resonant when the circuit power factor is unity, i.e.
the applied voltage and the circuit current are in phase. If such condition occurs in a series
circuit, it is termed as series resonance.
 In an RLC series circuit, when XL = XC, the impedance will be purely resistive in nature. In
polar form impedance can be written as Z 0, R= 0 and the voltage and current are in-phase.
This condition is known as Resonance in R L C series circuit.
When XL = XC, the magnitude of impedance will be only R which is the minimum value
possible for Z. At resonance, i.e., at XL = XC , Z will be minimum and hence current will be
maximum. A curve between current as function of frequency is known as the Resonance
curve. The value of current at resonance is denoted by Io. Since Io is the maximum value of
current, the maximum power in the circuit
Half of this maximum power occurs at a current of
The corresponding frequencies (f2 and f1) are known as half power frequencies. They are also
known as cut off frequencies.

APPARATUS:
1. Function Generator 2. Breadboard 3. Oscilloscope
4. Jumper Wires 5. Capacitor 6. Probes
7. Resistor 8. DMM
FIGURE:
PROCEDURE:
1. Connect the circuit as shown in the circuit diagram after noting down following values.
1 k ohm
10 mH
1 uF
2. Adjust the voltage to 5 V (p-p).

3. Keep the frequency to some minimum value (say 10 Hz) and note the current.
4. Increase the frequency and for each frequency note the corresponding current.
5. Draw the resonant curve by taking (I) along y-axis and log(f) on x-axis.
6. Find the resonant frequency, half power frequencies, bandwidth and Q factor.
7. Compare them with the theoretical values.
OBSERVATIONS:

Resonance Curve

1.59 kHz
3.18 mA
2.24 mA
10 kHz
0.1 kHz
= 9.9 kHz
= 0.16
= 1.6 kHz
= 3.2 mA
= 15928.5
= 0.1
CONCLUSION
Percentage error of I = 0.625 %
When impedance is minimum, the I is maximum.

To Study the response of Passive RC & RL Low Pass Filters
OBJECTIVE:
To study the Gain vs. Frequency response of Passive RC, RL Low Pass Filters
THEORY:
RC Low Pass Filter:
The reactance of a capacitor varies inversely with frequency, while the value of the resistor
remains constant as the frequency changes. At low frequencies the capacitive reactance, (Xc)
of the capacitor will be very large compared to the resistive value of the resistor, R and as a
result the voltage across the capacitor, Vc will also be large while the voltage drop across the
resistor, Vr will be much lower. At high frequencies Vc will be small and Vr will be large.
wс
Transfer function = H(w) = = =
w с
сw
| (w)| =
(w )
From equation
H(0)=1 & H(∞)= 0.
Cut-Off Frequency:
The cut off frequency or half power frequency is obtained by setting
| (w)|=
√
| (w)| = =
(w ) √
wс =
A low pass filter is designed to pass only frequencies from dc up to the cutoff frequency.
RL Low Pass Filter:
The reactance of a INDUCTOR varies directly with frequency, while the value of the
resistor remains constant as the frequency changes. At high frequencies the inductive reactance,
(Xv) of the inductor will be very large compared to the resistive value of the resistor, R and as
a result the voltage across the inductor, Vv will also be large while the voltage drop across the
resistor, Vr will be much lower. At low frequencies Vv will be small and Vr will be large.

Transfer function = H(w) = =
| (w)| =
(w )
From equation
H(0)=1 & H(∞)= 0.
Cut-Off Frequency:
The cut off frequency or half power frequency is obtained by setting
| (w)|=
√
| (w)| = =
(w ) √
wс =
A low pass filter is designed to pass only frequencies from dc up to the cutoff frequency.
APPARATUS:
(1) Digital multi-meter (DMM).
(2) Function generator
(3) CRO
(4) Resistor ( 1k ), Capacitor ( 0.1 uF) , Inductor (10mH )
(5) Connecting wires
(6) Breadboard.
CIRCUIT DIAGRAM:

RC Low Pass Filter
RL Low Pass Filter
PROCEDURE:
RC Low Pass Filter:

- Connect the circuit elements on the bread board as shown in the above circuit
- Apply the sine wave from the function generator
- Put the terminals of the oscilloscope/ DMM (AC Voltmeter) across the capacitor
- Start by giving a very small frequency on the function generator
- There will be an output displayed on the oscilloscope/ DMM (AC Voltmeter)
- Keep on increasing the frequency
- Note the response on the oscilloscope/ DMM (AC Voltmeter)
- When the magnitude of the voltage across the capacitor becomes 70% of the peak
value, note the frequency
- This is the cut off frequency of the low pass filter
- Keep on increasing the frequency, the magnitude of voltage will decrease
- This shows that the circuit is acting as a RC low pass filter.
- Note down all essential readings
- Draw gain vs. frequency curve and perform error analysis for calculated and measured
values of cut-off frequencies.
RL Low Pass Filter:



- Put the terminals of the oscilloscope/ DMM (AC Voltmeter) across the resistor
- There will be an output displayed on the oscilloscope / DMM (AC Voltmeter)
- Note the response on the oscilloscope / DMM (AC Voltmeter)
- This is the cut off frequency of the RL low pass filter
- Keep on increasing the frequency, the magnitude of voltage will decrease
- This shows that the circuit is acting as a low pass filter
OBSERVATIONS AND CALCULATIONS:
RC Low Pass Filter
160 Hz
Calculated Cut-Off Frequency=________________________________________
Graph (Gain vs. Frequency):

190 Hz
Measured Cut-Off Frequency=________________________________________
18.75 %
Error Analysis=___________________________________________________
RL Low Pass Filter
15.9 kHz

14.9 kHz
0.67 %
Error Analysis=___________________________________________________
CONCLUSION:
In Low Pass Filter the inductor acts as a short-circuit due to its low impedence towards the low
frequencies while the capacitor acts as a open-circuit due to its high impedence towards low
frequencies.
In High Pass Filter it has clearly been shown that the impedence of the capacitor is minimum
for the high pass functions as it allows only the high frequencies to through it and does not
allow the low frequencies to pass through it and capacitor acts as a short-circuit for high
frequencies and open-circuit for low frequencies.

To Study the response of Passive RC & RL High Pass Filters
OBJECTIVE:
To study the Gain vs. Frequency response of Passive RC, RL High Pass Filters
THEORY:
RC High Pass Filter:
In the circuit of Passive RC High Pass Filter, we find the response across the resistor. Since
capacitor acts as an open circuit initially, it blocks the output across resistor for lower
frequencies. The current keeps on increasing and for higher values of frequency, maximum
current flows through the resistor due to low impedance of capacitor at higher frequencies and
we get a High-Pass response.
Similar analysis can be done for RC high pass filter as we did for RC low pass filter to establish
that the set points/ check points for high pass filter only get verified when we take the output
across resistor. The set points are:
H(0)=0 & H(∞)= 1
Cut-Off Frequency:
The cut off frequency or half power frequency is obtained in the same way as it was
done for RC low pass filter.
wс =
A high pass filter is designed to pass only frequencies from above the cutoff frequency.
RL High Pass Filter:
In RL high pass filter we observe the response across the inductor. We get a high-pass
response because at low frequencies, an inductance acts as a short circuit while at higher
frequencies the inductance will act as an open circuit
Similar analysis can be done for RL high pass filter as we did for RL low pass filter to establish
that the set points/ check points for high pass filter can only get verified when we take the output
across resistor. The set points are:
H(0)=0 & H(∞)= 1
Cut-Off Frequency:
The cut off frequency or half power frequency is obtained in the same way as it was
done for RC low pass filter.
wс =
APPARATUS:
(1) Digital multi-meter (DMM).
(2) Function generator
(3) CRO
(4) Resistor ( 1k ), Capacitor ( 0.1 uF) , Inductor (10mH )
(5) Connecting wires
(6) Breadboard.
CIRCUIT DIAGRAM:
RC High Pass Filter
RL High Pass Filter
PROCEDURE:
RC High Pass Filter:

- Put the terminals of the oscilloscope/ DMM (AC Voltmeter) across the resistor
- There will be an output displayed on the oscilloscope/ DMM (AC Voltmeter)
- Note the response on the oscilloscope/ DMM (AC Voltmeter)
- This is the cut off frequency of the high pass filter
- Keep on increasing the frequency, the magnitude of voltage will increase
- This shows that the circuit is acting as a RC high pass filter.
RL High Pass Filter:

- Put the terminals of the oscilloscope/ DMM (AC Voltmeter) across the inductor
- There will be an output displayed on the oscilloscope / DMM (AC Voltmeter)
- Note the response on the oscilloscope / DMM (AC Voltmeter)
- When the magnitude of the voltage across the inductor becomes 70% of the peak
- This is the cut off frequency of the RL high pass filter
- Keep on increasing the frequency, the magnitude of voltage will increase
- This shows that the circuit is acting as a high pass filter
OBSERVATIONS AND CALCULATIONS:
RC High Pass Filter
160 Hz

gain
frequency
155 Hz
3.125 %
Error Analysis=___________________________________________________
RL High Pass Filter
16 kHz


gain
frequeny
15.3 kHz
4.375 %
Error Analysis=___________________________________________________
CONCLUSION:
It has been clearly shown that the reactance of the capacitor is inversely propotional with
the frequency and reactance of inductor is directly propotional to the frequency as
shown.

To Study the response of Passive RC based Band Pass Filter
OBJECTIVE:
To study the response of RC Passive Band Pass Filter
THEORY:
Band pass filter is a combination of both low pass filter and high pass filter. The name of the filter
itself indicates that it allows only a certain band of frequencies and blocks all the remaining
frequencies. In audio applications, sometimes it is necessary to pass only a certain range of
frequencies, this frequency range do not start at 0Hz or end at very high frequency but these
frequencies are within a certain range, either wide or narrow. These bands of frequencies are
commonly termed as Bandwidth.
Band pass filter is obtained by cascading passive high pass and passive low pass
filters. This arrangement will provide a selective filter which passes only certain frequencies. This new
RC filter circuit can able to pass either a narrow range of frequencies or wide range of frequencies.
The upper and lower cut-off frequencies depend on filter design. This band pass filter is simply
appears like a frequency selective filter.
BPF
HPF LPF
So by cascading RC High Pass Filter with RC Low Pass Filter we can have RC Passive Band Pass
Filter.
The cut off frequencies are given as:
Lower Cut-Off Frequency = 1/2πR1C1
Higher Cut-Off Frequency = 1/ 2πR2C2
Band Width = (Higher Cut-Off Frequency) - (Lower Cut-Off Frequency)
FIGURE:
APPARATUS:
(1) Breadboard
(2) Signal Generator
(3) Cathode Ray Oscilloscope
(4) DMM
(5) Resistors

PROCEDURE:
- Set-up the RC circuit in figure with the signal generator as the power source (Input).
- Apply a sinusoidal input from the signal generator; measure the amplitude of the
source with the help of the CRO/ DMM (AC Voltmeter) and note it down in Table
below.
- Now connect CRO/ DMM (AC Voltmeter) across the capacitor C2.
- Starting from zero adjust the frequency from the signal generator so that the output is
equal to 0.707 of the amplitude of the source.
- Note it down as the Lower Cut-off frequency in Table below.
- Compare the experimental value to the theoretical value calculated earlier for
verification (Error Analysis)
- Increase the frequency so that the condition of 0.707 of the amplitude of the source is
again met.
- Note it down as the Higher Cutoff frequency in Table and compare this experimental
value to the theoretical value calculated earlier for verification (Error Analysis)
- Obtain Gain vs. Frequency Curve.
OBSERVATIONS:
130 Hz
Lower Cut-Off Frequency (calculated) = 1/2πR1C1 = _______________
2 kHz
Higher Cut-Off Frequency (calculated) = 1/ 2πR2C2 = ______________
Band Width (calculated) = (Higher Cut-Off Frequency) - (Lower Cut-Off Frequency)
1870 Hz
=____________________________

130.425 Hz
Lower Cut-Off Frequency (measured) = 1/2πR1C1 = _______________
2.006 kHz
Higher Cut-Off Frequency (measured) = 1/ 2πR2C2 = ______________
Band Width (measured) = (Higher Cut-Off Frequency) - (Lower Cut-Off Frequency)
1875.575 Hz
=____________________________
0.29 %
Error Analysis =___________________________________________________________
CONCLUSION:
The percentage error is 0.29 %.

Analysis of Active Low Pass Filter using R, C & OP AMP
OBJECTIVE:
To Analyze response Active Low Pass Filter Using R,C and OP-AMP
THEORY:
Difference between the passive low pass filter and active low pass filter is that the former uses
only passive devices such as capacitor, inductor and resistors while the latter uses at last one active
device such as op-amp. There are few disadvantages of the passive low pass filter, so we rely on active
low pass filters. One of the disadvantages of the passive low pass filter is that the amplitude of the
output signal is always less than that of the input signal, which means that the gain is unity. For that
purpose, we use active low pass filter which amplifies the signal. The main difference between a
“passive filter” and an “active filter” is amplification.
Design Parameters:
Cut off frequency: fc= 4kHz
Pass band gain: Av= 2
Formulae To Be Utilized:
Cut off frequency: =

Pass band gain: Av= 1 +
FIGURE:
APPARATUS:
(1) Function Generator
(2) Digital Multimeter
(3) Resistors
(4) Capacitor
(5) Op-amp (LM741)
(6) Breadboard
(7) Connecting Wires

PROCEDURE:
- Determine the component values and construct the circuit bread board as shown in the
figure above
- Apply DC voltage of +10V to +Vcc / A+ and -10V to -Vcc/ A-
- Apply the sinosoidal input voltage from function generator.
- Alter the frequency and measure corresponding gain.
- Obtain Gain vs Frequency curve
- Perform Error Analysis
VALUES:
R1 = 40 ohms C = 1 uF
R2 = 2 k ohms Fc = 4 kHz
R3 = 2 k ohms Av = 2
OBSERVATIONS:


gain
frequency
4 kHz
Cut-Off Frequency (measured) = ______________________________________________________
0%
Error Analysis = ___________________________________________________________________
CONCLUSION:
Cut off frequency at gain of 1.4 is 4 kHz.
There is no difference in theoretical and parctical value. Percentage error is

zero

Analysis of Active High Pass Filter using R, C & OP AMP
OBJECTIVE:
To Analyze response Active High Pass Filter Using R,C and OP-AMP
THEORY:
Difference between the passive high pass filter and active high pass filter is that the former uses
only passive devices such as capacitor, inductor and resistors while the latter uses at last one
active device such as OP-AMP. There are few disadvantages of the passive high pass filter, so
we rely on active high pass filters. One of the disadvantages of the passive high pass filter is
that the amplitude of the output signal is always less than that of the input signal, which means
that the gain is unity. For that purpose we use active high pass filter which amplifies the signal.
The main difference between a “passive filter” and an “active filter” is amplification.
Design Parameters:
Cut off frequency: fc= 4kHz
Pass band gain: Av= 2
Cut off frequency: =

Pass band gain: Av= 1 +
FIGURE:
APPARATUS:
(3) Resistors
(4) Capacitor
(5) Op-amp (LM741)
(6) Breadboard

PROCEDURE:
figure above
VALUES:
R1 = 40 ohms C = 1 uF
R2 = 2 k ohms Fc = 4 kHz
R3 = 2 k ohms Av = 2
OBSERVATIONS:


gain
4 kHz frequency
Cut-Off Frequency (measured) = ______________________________________________________
0%
Error Analysis = ___________________________________________________________________
CONCLUSION:
Cut off frequency at gain of 1.4 is 4 kHz.
There is no difference in theoretical and parctical value. Percentage error is

zero
Analysis of Active Band Pass Filter using R, C & OP AMP
OBJECTIVE:
To study the response of Active RC Band Pass Filter
THEORY:
Band pass filter is a combination of both low pass filter and high pass filter. The name of the filter
itself indicates that it allows only a certain band of frequencies and blocks all the remaining
frequencies
Active Band pass filter is obtained by cascading active high pass and active low pass filters.
This arrangement will provide a selective filter which passes only certain frequencies.
Active Active
HPF LPF
Active Band Pass Filter
So by cascading Active RC High Pass Filter with active RC Low Pass Filter we can have RC Active
Band Pass Filter.
Design Parametrs:
Band Width = 1 KHz
fL= 4000 Hz
fH= 5000 Hz
Pass band gain High Pass Filter Av1= 2
Pass band gain Low Pass Filter Av2 = 2
=
Av1= +
Av2= +
APPARATUS:
(3) Resistors
(4) Capacitor
(5) Op-amp (LM353 or LM 741)
(6) Breadboard

FIGURE:
PROCEDURE:
figure above
OBSERVATIONS:


Lower Cut Frequency:
Higher Cut Frequency:
3.45 kHz
Lower Cut-Off Frequency (measured) = __________________________________________________
15.30 kHz
Higher Cut-Off Frequency (measured) = __________________________________________________
18 %
Error Analysis = _____________________________________________________________________
CONCLUSION:
The calculated bandwidth is 10 kHz and the measured bandwidth is 11.81 kHz. Likewise the
calculated lower cut off frequency is 4 kHz and measured is 3.45 kHz. Also the calculated higher cut
off frequency is 14 kHz and measured is 15.29 kHz.
The difference is due to taking rounded off values for calculations.

Study of 1 st Order RC Differentiator & Integrator Circuits
OBJECTIVE:
To analyze response of 1st order RC differentiator and integrator network for different inputs and
at different frequencies.
THEORY:
Differentiator: The voltage (Vc) and current (Ic) relationship for capacitor is by
Ic(t)=C.dVC/dt
This relationship is helpful in implementing a passive differentiator circuit. For an RC series
network to work as an integrator R << XC i.e. voltage drop across resistor is very small and
VIN≈ VC. The tentative output of RC network at ω << 1/RC is shown in Figure. Here ω is the
frequency of input waveform. The said condition on frequency assures that capacitor has time
to charge up until its voltage is almost equal to input voltage.
RC Diffrentiator
KVL equation for the network will be,
VIN=VR+ VC
VR = RI = RC . dVC/dt
Since VIN≈ VC ,Therefore VR≈ RC . dVIN/dt
Thus the output voltage is somehow derivative of input voltage
Integrator: The voltage (Vc) and current (Ic) relationship for capacitor is by
Vc(t)=1/C. ∫ Ic dt
This relationship is helpful in implementing a passive integrator circuit. For an RC series
network to work as an integrator R >> XC i.e. voltage drop across capacitor is very small and
VIN≈ VR. The tentative output of RC network at ω >> 1/RC is shown in Figure. Here ω is the
frequency of input waveform. The said condition on the frequency of input waveform assures
that capacitor does not have sufficient time to charge up, therefore its voltage is very small and
resistor voltage is almost equal to input voltage.

RC Integrator
KVL equation for the network will be,

VIN=VR+ VC
Since VIN≈ VR , therefore, I=VR/R = VIN/R
As Vc(t)=1/C. ∫ I dt , Vc(t)=1/RC. ∫ VIN dt
Thus the output voltage across capacitor is somehow integration of the input voltage.
APPARATUS:
(1) Oscilloscope
(2) Resistor
(3) Capacitor
(5) Bread Board
PROCEDURE:
RC Differentiator:
1. Connect the components as shown in Figure.
2. Apply a square waveform of 6 V peak to peak from function generator.
3. Observe the input waveform and response simultaneously on oscilloscope when T<<RC
where T is the period of input waveform.
4. Observe the input waveform and response simultaneously on oscilloscope when T=RC
5. Observe the input waveform and response simultaneously on oscilloscope when T>>RC
6. Repeat the same steps for a triangular waveform.
7. Repeat same steps for sinusoidal waveform.
RC Integrator:
1. Connect the components as shown in Figure.
2. Apply a square waveform of 6 V peak to peak from function.
3. Observe the input waveform and response simultaneously on oscilloscope when T>>RC
4. Observe the input waveform and response simultaneously on oscilloscope when T=RC
5. Observe the input waveform and response simultaneously on oscilloscope when T<<RC
6. Repeat the same steps for a triangular waveform.
7. Repeat same steps for sinusoidal waveform.
OBSERVATIONS

Differentiator
S.No. INPUT T<RC T=RC T>RC
Sine wave
Square wave
Triangular
Integrator
Sine wave

Square wave
Triangular
CONCLUSION:

Evaluation of Two Port Parameters (Z parameters) for a Resistive Network
OBJECTIVE:
To determine impedance parameters (Z parameters) for a resistive network
THEORY:
A pair of terminals through which a current may enter or leave a network is known as port. A two port
network is an electrical network with two separate ports for input and output. A general two port network
is shown in Figure 1. Each port consists of two terminals. The Z parameters are also known as open circuit
impedance parameters. The Z parameters of a two port network are Z11, Z12, Z21 and Z22 and these are given
by
Z11 = V1/I1 when I2 = 0 i.e. secondary is open circuited.
Z12 = V1/I2 when 11 = 0 i.e. primary is open circuited.
Z21 = V2/I1 when I2 = 0 i.e. secondary is open circuited.
Z22 = V2/I2 when I1 =0 i.e. primary is open circuited.
Figure 1: A Two Port Network

FIGURE:
Figure 2: For Z11 and Z21 where I2=0

FIGURE A:
FIGURE B:
CEME (NUST), Rawalpindi

Figure 3: For Z12 and Z22 where I1=0
APPARATUS:
(2) Resistors
(3) Breadboard
PROCEDURE:
- Connect the components on bread board according the circuit diagram of Figure 2.
- Observe and note values of V1, V2 and I1 by using oscilloscope or multimeter.
- Find Z11 and Z21.
- Now connect the components on bread board according the circuit diagram of Figure 3.
- Observe and note values of V1, V2 and I2 by using oscilloscope or multimeter.
- Find Z12 and Z22.
- Also determine the parametric values using simple circuit analysis techniques.
- Compare theoretical and practical values.
OBSERVATIONS:
CONCLUSIONS:
A two port network is an electrical network with two terminals for connecting external circuits.
The circuit above shows that in order to measure the impedences of resistances in two port circuits
we find the primary and secondary voltages and currents.
The values calculated from the above graph are as under:

V1 = 5 V, I1 = 0.7 mA, V2 = 189.38 V, I2 = 1.6 mA

Evaluation of Two Port Parameters (Y parameters) for a Resistive Network
OBJECTIVE:
To determine admittance parameters (Y parameters) for a resistive network
THEORY:
A pair of terminals through which a current may enter or leave a network is known as port. A two port
network is an electrical network with two separate ports for input and output. A general two port network
is shown in Figure 1. Each port consists of two terminals.
The Y parameters are also known as short circuit admittance parameters. The Y parameters of a two port
network are Y11, Y12, Y21 and Y22 and these are given by
Y11 = I1/V1 when V2 = 0 i.e. secondary is short circuited.
Y12 = I1 /V2 when V1 = 0 i.e. primary is short circuited.
Y21 = I2/V1 when V2 = 0 i.e. secondary is short circuited.
Y22 = I2/V2 when V1 =0 i.e. primary is short circuited.
Figure 1: A Two Port Network

FIGURE:
Figure 2: For Y11 and Y21 where V2=0

FIGURE A:
From the circuit, V1 = 5 V, V2 = 0 V, I1 = 0.8 mA, I2 = 0.4 mA
FIGURE B:
From the circuit, V1 = 0 V, V2 = 5 V, I1 = 0.38 mA, I2 = 1.38 mA

Figure 3: For Y12 and Y22 where I1=0
PROCEDURE:
- Connect the components on bread board according the circuit diagram of Figure 4.
- Observe and note values of V1, I2 and I1 by using multimeter.
- Find Y11 and Y21.
- Now connect the components on bread board according the circuit diagram of Figure 5.
- Observe and note values of I1, V2 and I2 by using multimeter.
- Find Y12 and Y22.
- Determine the theoretical values using circuit analysis techniques.
OBSERVATIONS:
CONCLUSIONS:
A two port network is an electrical network with two terminals for connecting external circuits.
After comparing the theoretical and measured values we see that the percentage error is minimal.
And thus it can be concluded that the results are current and verified.

Determination of Apparent Power and Power Factor for AC Circuit
OBJECTIVE:
To determine apparent power and power factor for AC circuit
THEORY:
This lab assignment emphasizes the use of apparent power and power factor to quantify the AC
power deliveredto a load and the power dissipated by the process of transmitting this power. The apparent
power, average power, and power factor associated with the circuit will be measured and related to
expectations based on analysis of the circuit. It will be seen that the difference between the apparent power
and the average power, as quantified by the power factor, influences the amount of power which is
dissipated during power delivery relative to the power provided tothe load.
The power factor of an AC electric power system is defined as the ratio of the real power flowing
to the load to the apparent power, and is a number between 0 and 1 (frequently expressed as a percentage,
e.g. 0.5 pf = 50% pf). Real power is the capacity of the circuit for performing work in a particular time.
Apparent power is the product of the current and voltage of the circuit. Due to energy stored in the load and
returned to the source, or due to a non-linear load that distorts the wave shape of the current drawn from
the source, the apparent power can be greater than the real power.
In an electric power system, a load with low power factor draws more current than a load with a
high power factor for the same amount of useful power transferred. The higher currents increase the energy
lost in the distribution system, and require larger wires and other equipment. Because of the costs of larger
equipment and wasted energy, electrical utilities will usually charge a higher cost to industrial or
commercial customers where there is a low power factor.
Linear loads with low power factor (such as induction motors) can be corrected with a passive
network of capacitors or inductors. The devices for correction of power factor may be at a central substation,
or spread out over a distribution system, or built into power-consuming equipment.
Circuits containing purely resistive heating elements (filament lamps, strip heaters, cooking stoves,
etc.) have a power factor of 1.0. Circuits containing inductive or capacitive elements (electric motors,
solenoid valves, lamp ballasts, and others ) often have a power factor below 1.0.
AC power flow has the three components: real power (P), measured in watts (W); apparent power (S),
measured in volt-amperes (VA); and reactive power (Q), measured in reactive volt-amperes (var).
The power factor is defined as:
In the case of a perfectly sinusoidal waveform, P, Q and S can be expressed as vectors that form a vector
triangle such that:

If φ is the phase angle between the current and voltage, then the power factor is equal to , and:
Since the units are consistent, the power factor is by definition a dimensionless number between 0 and 1.
When power factor is equal to 0, the energy flow is entirely reactive, and stored energy in the load returns
to the source on each cycle. When the power factor is 1, all the energy supplied by the source is consumed
by the load. Power factors are usually stated as "leading" or "lagging" to show the sign of the phase angle.
FIGURE:
APPARATUS:
1. Function Generator
2. Oscilloscope
4. Inductor
5. Resistor
6. Breadboard
7. Connecting Wires
PROCEDURE:
- Connect the circuit as shown in circuit Fig (a), Use R=____1k Ohm, L=____mH100 and apply a
sinusoidal voltage signal with peak voltage Vm=1V and frequency f=1kHz.
- Measure the RMS voltage of the input voltage signal.
- Measure the RMS voltage across the resistor and divide it by the resistor value to find the RMS
current.
- Use channel 1 (CH1) of oscilloscope to measure the input voltage and channel 2 (CH2)
- of oscilloscope to measure the voltage across the resistor. Measure the phase difference
between the load voltage and the load current.
- Repeat step 2-4 for f=2kHz.
CIRCUITS:
Frequency = 1 kHz
Frequency = 2 kHz

OBSERVATIONS:
Vrms Irms Φ=θv- θi P=VrmsIrmsCos

Sr. S=Vrms*Irms
Frequency (leading or pf=cosΦ Φ
No. (Volts) (A) (VA)
lagging) (W)
1 1KHz 0.707 0.0006 33.5 0.8337 0.000424 0.000353
2 2KHz 0.706 0.0004 52.7 0.6339 0.000312 0.000197
CONCLUSION:
As evident from the above table and the values calculated, power factor and frequency have
inverse releation.

Study the Significance of Power Factor Correction in AC circuit
OBJECTIVE:
THEORY:
The power factor of an AC electric power system is defined as the ratio of the real power flowing to the
load to the apparent power, and is a number between 0 and 1 (frequently expressed as a percentage, e.g. 0.5
pf = 50% pf). Real power is the capacity of the circuit for performing work in a particular time. Apparent
power is the product of the current and voltage of the circuit. Due to energy stored in the load and returned
to the source, or due to a non-linear load that distorts the wave shape of the current drawn from the source,
the apparent power can be greater than the real power.
In an electric power system, a load with low power factor draws more current than a load with a high power
factor for the same amount of useful power transferred. The higher currents increase the energy lost in the
distribution system, and require larger wires and other equipment. Because of the costs of larger equipment
and wasted energy, electrical utilities will usually charge a higher cost to industrial or commercial
customers where there is a low power factor.
Linear loads with low power factor (such as induction motors) can be corrected with a passive network of
capacitors or inductors. The devices for correction of power factor may be at a central substation, or spread
out over a distribution system, or built into power-consuming equipment.
Circuits containing purely resistive heating elements (filament lamps, strip heaters, cooking stoves, etc.)
have a power factor of 1.0. Circuits containing inductive or capacitive elements (electric motors, solenoid
valves, lamp ballasts, and others ) often have a power factor below 1.0.
AC power flow has the three components: real power (P), measured in watts (W); apparent power (S),
measured in volt-amperes (VA); and reactive power (Q), measured in reactive volt-amperes (var).
The power factor is defined as:
In the case of a perfectly sinusoidal waveform, P, Q and S can be expressed as vectors that form a vector
triangle such that:
If φ is the phase angle between the current and voltage, then the power factor is equal to , and:
Since the units are consistent, the power factor is by definition a dimensionless number between 0 and 1.
When power factor is equal to 0, the energy flow is entirely reactive, and stored energy in the load returns
to the source on each cycle. When the power factor is 1, all the energy supplied by the source is consumed
by the load. Power factors are usually stated as "leading" or "lagging" to show the sign of the phase angle.
Power factor correction: It is often desirable to adjust the power factor of a system to near 1.0. This power
factor correction (PFC) is achieved by switching in or out banks of inductors or capacitors. For example
the inductive effect of motor loads may be offset by locally connected capacitors. When reactive elements
supply or absorb reactive power near the load, the apparent power is reduced.
Power factor correction may be applied by an electrical power transmission utility to improve the stability
and efficiency of the transmission network. Correction equipment may be installed by individual electrical
customers to reduce the costs charged to them by their electricity supplier. A high power factor is generally
desirable in a transmission system to reduce transmission losses and improve voltage regulation at the load.
Power factor correction brings the power factor of an AC power circuit closer to 1 by supplying reactive
power of opposite sign, adding capacitors or inductors which act to cancel the inductive or capacitive effects
of the load, respectively. For example, the inductive effect of motor loads may be offset by locally
connected capacitors. If a load had a capacitive value, inductors (also known as reactors) are connected to
correct the power factor. In the electricity industry, inductors are said to consume reactive power and
capacitors are said to supply it, even though the reactive power is actually just moving back and forth on
each AC cycle.
FIGURE:

CIRCUIT:
Frequency = 1 kHz
Frequency = 2 kHz

APPARATUS:
1. Function Generator
2. Oscilloscope
4. Inductor
5. Resistor
6. Capacitor
7. Breadboard
8. Connecting Wires
PROCEDURE:
1k
- Connect the circuit as shown in circuit Fig (a), Use R=_____Ohm, 0.1
L=______mH and apply
a sinusoidal voltage signal with peak voltage Vm=1V and frequency f=1kHz.
- Measure the RMS voltage of the input voltage signal.
- Measure the RMS voltage across the resistor and divide it by the resistor value to find the
RMS current.
- Use channel 1 (CH1) of oscilloscope to measure the input voltage and channel 2 (CH2)
- of oscilloscope to measure the voltage across the resistor. Measure the phase difference
between the load voltage and the load current.
100
- Repeat step 2-4 for circuit in Fig.(b). Use C=_____uF.
OBSERVATIONS:
Vrms Irms P=VrmsIrmsCos

S=Vrms*Irms
Sr. No. Φ=θv- θi pf=cosΦ Φ
(Volts) (A) (VA)
(W)
1 Without
0.707 0.0006 31.3 0.854 0.000424 0.00036
Capacitor
2 With
0.707 0.0005 15.4 0.964 0.000376 0.00036
capacitor
CONCLUSION:
It is observed that after the addition of the capacitor with the voltage source
the power factor increased.

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EE Department Electrical Network Analysis

PRACTICAL WORK BOOK

Complied By: Checked By:

DEPARTMENT OF ELECTRICAL ENGINEERING

CEME (NUST), Rawalpindi 1

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we can think of a breadboard as a board that can be divided in 2 functional areas:

Bench Top Power Supply:

signal is “on” versus how long it’s “off” each period.

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increase this range.)

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Probe Selection and Setup

Connect the Probe and Turn the Scope On

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Testing the Probe

Compensating an Attenuated Probe

Probing, Triggering, and Scaling Tips

Measure Twice, Cut Once

CEME (NUST), Rawalpindi 15

Measuring the ringing of a square wave with cursors.

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In order to measure voltage of a battery set your multi-meter’s selector switch to

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Figure 1: RC Series Network

Figure 2: Capacitor Charging

The discharge voltage for the capacitor is given by

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Figure 3: Discharging of Capacitor

1. DC Power Supply 2. Jumper Wires 3. Oscilloscope Function

1. Compute the theoretical value of time constant using expression Ʈ=RC

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Also mention the co-ordinates on graph sheet corresponding to Time Constant.

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Mention co-ordinates corresponding to Time Constant in graph.

2. Connect the circuit as shown in figure below.

5. Observe the output on oscilloscope and sketch the resulting graph.

For t = 0, For t = T, For t = 5T, For t = ∞,

8. Use following expression to calculate voltage across capacitor

For t = 0, For t = T, For t = 5T, For t = ∞,

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Half of this maximum power occurs at a current of

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2. Adjust the voltage to 5 V (p-p).

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Percentage error of I = 0.625 %

When impedance is minimum, the I is maximum.

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The cut off frequency or half power frequency is obtained by setting

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Transfer function = H(w) = =