Electrical Filters
Lab 9
Introduction to Engineering a nd Design
LAB 9: Electrical Filters
9.1
Objective
The purpose of this lab is to introduce the student to the concept of electrical
filters and explain the importance of the 3dB point. The focus of this lab will be on three
of the most commonly used filters; the high pass, low pass and band pass filters. At the
end of the experiment the student is expected to identify the type of filter produced by
each circuit.
9.2
Introduction
9.2.1
Background Information
An important aspect of engineering is the selective filtering of certain frequencies.
One of the most obvious applications is a radio tuner. By tuning to a specific station, you
are isolating a certain radio frequency.
Of hundreds of different stations that are
broadcasting, the radio filters only the frequency that you specify.
9.2.2
Theory
An understanding of the elements that make electrical filtering possible is
necessary to obtain a better understanding of how filters work. Signals that occur
naturally are composed of many frequencies.
The human voice is composed of
frequencies ranging from 0-4kHz. Electrical signals (see figure below) are used to carry
information. They may also carry noise or unwanted information at different frequencies.
These different frequencies that constitute the sound we hear are called harmonics. A
harmonic is a whole number multiple of a fundamental frequency. Voltage or
electromotive force and frequency are two of the basic building blocks of an electrical
signal. Voltage is a force that propels electrons through a medium and frequency is the
rate at which the signal repeats itself. When a signal is applied to a filter usually the
unwanted bands are filtered out.
A filter is a circuit that shapes and controls the
bandwidth of a signal. A circuit is the physical connection or path through which
electrical signals travel, and bandwidth is the range of frequencies that the filter allows to
pass.
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Fig. 9.1
The elements that make up the filters that we are going to use consist of resistors
and capacitors. A resistor is a circuit element that opposes the flow of electrons and a
capacitor is an element that stores electrons. Different combinations of these elements
allow the formation of different types of filters. These elements can be arranged in three
different formations.
connected end to end.
Series circuit elements are elements whose conductors are
See Fig. 9.2. Parallel circuit elements are elements whose
conductors are connected together at the opposing ends. See Fig. 9.3. Conductors are
elements that allow electrons to flow. The three types of filters that we will consider are
the band-pass, low-pass and high-pass filter.
Fig. 9.2
Fig. 9.3
To get a graphical representation of the characteristic behavior of the circuit that
is being analyzed, it is necessary to graph the gain of the circuit versus the frequency that
the electrical signal will consist of. The voltage gain is a unit defined in decibels. It is
calculated using the following formula 20*log (Vout /Vin). Gain is a measure of the
relative voltage. The 3db drop from the highest point on the gain vs. frequency graph is
the point at which the signal can no longer be heard by the human ear. It is also used to
calculate the cut-off frequency. It is also called the 3 dB point, and it represents the point
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where the output power (Pout) drops to one half the input power (Pin). Power is the rate at
which work is being done.

Band-Pass Filter
This type of filter is called a band-pass filter because it only allows a certain range
of frequencies to pass through, and blocks all other frequencies. The band-pass filter
shown in Fig 9.2 passes frequencies from approximately 30 Hz to 90 Hz; this is the
bandwidth of the filter. To find the bandwidth, the 3dB point is noted and the points that
intersect the graph are used to calculate the two frequencies needed. The following graph
shows the characteristic behavior of a band-pass filter (Fig. 9.4).
0
Gain (dB)
-5
-10
-15
-20
-25
-30
1
10
100
1000
Frequency (Hz)
Fig. 9.4

Low-Pass Filter
In some applications it is beneficial to remove the high frequency components
from a signal because this is where noise usually resides. The filter that does this is the
low-pass filter. Note that its response is such that it passes the low frequencies while
blocking the higher ones. At 40 Hz we can see that the gain drops from –2dB to –5dB,
this is the also the 3db point and it is used to approximate the cut-off frequency. Thus we
can say that the filter has a bandwidth of 40 Hz or that the filter only allows frequencies
that are between 0 Hz and 40 Hz to pass through. The following graph shows the
characteristic behavior of a low-pass filter (Fig. 9.5).
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Introduction to Engineering a nd Design
0
Gain (dB)
-5
-10
-15
-20
-25
-30
1
10
100
1000
Frequency (Hz)
Fig. 9.5
Fig. 9.3

High-Pass Filter
A third type of filter is the high-pass filter. This filter passes the high frequencies
but blocks the low ones. This is the opposite response of a low-pass filter. The break
frequency for the filter is 60 Hz, and it is determined using the same method that was
used for the low-pass filter. Thus we can say that the filter has a bandwidth of 60 Hz to
infinity or that the filter only allows frequencies that are greater than 60 Hz to pass
through. The following graph shows the characteristic behavior of a low-pass filter (Fig.
9.6).
Gain (dB)
0
-5
-10
-15
-20
-25
-30
1
10
100
Frequency (Hz)
Fig. 9.6
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Introduction to Engineering a nd Design
An important consideration in using filters is their non-ideal behavior.
For
example, suppose one wants a low-pass filter that passes all the frequencies less than 40
Hz and blocks all others completely (See Fig 9.7). It is impossible to build a filter with
such a sharp cutoff frequency. The actual filter used is the one shown in (See Fig. 9.5).
Note that this filter passes frequencies less than 40 Hz and reduces the amplitude at high
frequencies to very small values.
At 50 Hz the gain is approximately 1.1 dB,
corresponding to very low output amplitude Vout (To prove this set the gain formula to
1.1 and solve for Vout). Thus a low-pass filter will still pass some high frequencies, but
with almost negligible amplitude. This non-ideal behavior is also true for band-pass and
high-pass filters.
0
Gain (dB)
-5
-10
-15
-20
-25
-30
1
10
100
1000
Frequency (Hz)
Fig. 9.7
9.3
Materials and Equipment:

Virtual Bench Oscilloscope

0.001μF Capacitor

DMM

Coax Cable

1MΩ Resistor

Breadboard

100kΩ Resistor

Function Generator

0.01μF Capacitor

Wires
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Electrical Filters
9.4
Lab 9
Introduction to Engineering a nd Design
Rules of Competition
Not applicable
9.5
Procedure
9.5.1
Circuit 1 - Design
Fig. 9.5

Use the DMM to check the resistance of the resistors.

Connect the 1MΩ resistor and the 0.01μF capacitor in series. Note the order of
the connections, see Fig. 9.5.

Connect the function generator to LabVIEW using pins 1 and 9. Insert the
coaxial cable to the opening labeled “MAIN”.

Connect the red alligator clip to pin 1 on the DAQ board and the black
alligator clip to pin 9.

Open the oscilloscope.vi in LabVIEW.

Adjust the “Timebase” and “Volts/Div” buttons until a continuous,
recognizable sine wave can be seen.

Connect the coaxial cable across the Vin of the circuit and then connect the
Vout to pins 1 and 9 on the DAQ board.
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Introduction to Engineering a nd Design
9.5.1.2 Circuit 1 – Test

Set the function generator to apply a maximum voltage of 2V.

Set the function generator to 1 Hz.

Record the output voltage displayed on the Virtual Bench Oscilloscope.

Increment the input frequency by 10 Hz. Make sure to record the output
voltage after each increment.

Record output voltages for each frequency up to and including 500 Hz.
9.5.1.3 Circuit 1 - Data

Make sure that the TA signs your results.

Using the results that you have recorded set up a table (Table 9.1)

Generate a graph of 20 log (Vout / Vin) vs. Frequency. Make sure that the xaxis on your graph is log scale.
Frequency (Hz)
Vin (Volts) Vout (Volts) 20*log (Vout/Vin) (dB)
1
10
20
30
.
.
.
.
.
.
.
.
.
.
2
2
2
2
.
.
.
.
.
.
.
.
.
2
Table 9.1
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9.5.2.1 Circuit 2 - Design
Fig. 9.6

Use the DMM to check the resistance of the resistors.

Connect the 100kΩ resistor and the 0.01μF capacitor in series. Note the order
of the connections, see Fig. 9.6.

Connect the function generator to LabVIEW using pins 1 and 9. Insert the
coaxial cable to the opening labeled “MAIN”.

Connect the red alligator clip to pin 1 on the DAQ board and the black
alligator clip to pin 9.

Open the oscilloscope.vi in LabVIEW.

Adjust the “Timebase” and “Volts/Div” buttons until a continuous,
recognizable sine wave can be seen.

Connect the coaxial cable across the Vin of the circuit and then connect the
Vout to pins 1 and 9 on the DAQ board.
9.5.2.2 Circuit 2 - Test

Set the function generator to apply a maximum voltage of 2V.

Set the function generator to 1 Hz.

Record the output voltage displayed on the Virtual Bench Oscilloscope.
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Electrical Filters

Lab 9
Introduction to Engineering a nd Design
Increment the input frequency by 10 Hz. Make sure to record the output
voltage after each increment.

Record output voltages for each frequency up to and including 500 Hz.
9.5.2.3 Circuit 2 - Data

Make sure that the TA signs your results.

Using the results that you have recorded set up a table (Table 9.1)

Generate a graph of 20 log (Vout / Vin) vs. Frequency. Make sure that the xaxis on your graph is log scale.
9.5.3.1 Circuit 3 - Design
Fig. 9.7

Use the DMM to check the resistance of the resistors.

Connect the 100kΩ resistor and the 0.01μF (C1) capacitor in series. Note the
order of the connections, see Fig. 9.7.

Connect the 0.001μF capacitor (C2) in series with the first 100kΩ resistor, see
Fig. 9.7.

Connect the second 100kΩ resistor in series with the 0.001μF capacitor (C2).
Make sure that the second 100kΩ resistor is also connected in parallel with the
0.01μF capacitor (C1) (See Fig. 9.7).

Connect the function generator to LabVIEW using pins 1 and 9. Insert the
coaxial cable to the opening labeled “MAIN”.
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Electrical Filters

Lab 9
Introduction to Engineering a nd Design
Connect the red alligator clip to pin 1 on the DAQ board and the black
alligator clip to pin 9.

Open the oscilloscope.vi in LabVIEW.

Adjust the “Timebase” and “Volts/Div” buttons until a continuous,
recognizable sine wave can be seen.

Connect the coaxial cable across the Vin of the circuit and then connect the
Vout to pins 1 and 9 on the DAQ board.
9.5.3.2 Circuit 3 - Test

Set the function generator to apply a maximum voltage of 2V.

Set the function generator to 1 Hz.

Record the output voltage displayed on the Virtual Bench Oscilloscope.

Increment the input frequency by 10 Hz. Make sure to record the output
voltage after each increment.

Record output voltages for each frequency up to and including 2000 Hz.
9.5.3.3 Circuit 3 - Data

Make sure that the TA signs your results.

Using the results that you have recorded set up a table (SeeTable 9.1)

Generate a graph of 20 log (Vout / Vin) vs. Frequency. Make sure that the xaxis on your graph is log scale.
9.5.4 Analysis

Observe the graphs generated from each circuit.

Determine what type of filter each circuit produced.

Locate the 3dB point on each graph and determine the bandwidth of each
filter.
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9.6
Lab 9
Introduction to Engineering a nd Design
Discussion Topics
Independent Report (One report per student)

What type of filter does each circuit produce?

What is the 3db point used for?

What is the bandwidth of each filter?

Name 3 objects that use filters.

Why is the power ratio used in the decibel formula instead of the amplitude
ratio?

9.7
Discuss any problems encountered.
Closing
Make sure to clean up your workstation at the end of the experiment. Before you
leave the lab ensure that your TA has signed all of your data sheets.
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