Experiment: Filters

Objectives:
1. To learn how different filters work both ideal and practical.
2. To understand the meaning of cutoff frequency in both ideal and practical
cases.
3. To see the difference between low pass filters and band pass filters.

Introduction:
A filter is an electrical circuit that modifies the characteristics of a signal
based on its frequency. Filters can either allow specific frequencies to pass
through or attenuate certain frequencies while preserving others. Here are
some key points:
1. Types of Filters:
o Low-pass filter (LPF): Allows low-frequency signals to pass while
attenuating high-frequency components.
o High-pass filter (HPF): Permits high-frequency signals and suppresses
low-frequency ones.
o Band-pass filter (BPF): Passes a specific range of frequencies (a band)
and attenuates others.
o Notch filter (or band-reject filter): Suppresses a narrow frequency
band while allowing other frequencies to pass.
2. Passive vs. Active Filters:
o Passive filters use only passive components (resistors, capacitors, and
inductors). They are responsive in the frequency range of
approximately 100 Hz to 300 MHz.
o Active filters incorporate active components (such as op-amps) alongside
resistors and capacitors. They can handle very low frequencies and
provide voltage gain.
o
3. Applications:
o Radio communications: Filters help receivers isolate desired signals from
background noise.
 frequency we only have to determine the moment when the signal’s
amplitude drops to 70.7% of its original value and then we determine the
frequency.

Step (1): we set the voltage to 5 volts and the sweep settings as follows:

Step (2): we run the function generator and we just wait until the signal’s
amplitude drops to 70.7% of its original value.

• As we see from the previous picture that at 1.5 KHz the signal is still almost
at 5 volts level which means that it hasn’t reached the cutoff frequency yet.
• While in the previous picture the amplitude dropped to 3.6 volts which is
approximately 70.7% of its original value, and that indicates that the cutoff
frequency is 2.5KHz.

• This picture shows the signal in the frequency domain ,which has a
frequency of 1KHz and we can obviously see that the signal is not affected
by the filter yet because it is not even close to the cutoff frequency which is
2.5KHz
• But in this picture, we see that the frequency is 3KHz now which means it
exceeded the cutoff frequency, we notice here that the amplitude dropped
by approximately 3 dB which is 70.7% in the voltage scale which is expected
to happen.

Part (B): In this part instead of using the RC LPF, we will use a filter with
an adjustable cutoff frequency called the tunable LPF. our goal here is to
observe how different frequencies behave while countering this filter which
has a preselected cutoff frequency.

Step (1): we set the settings of the function generator as follows:

 Step (2): we set the cutoff frequency to
200 Hz; the following pictures show the
result:
• In time domain:
 • In frequency domain:

• It is obvious that nothing appered in both frequency and time domains

because the cutoff frequency is much smaller than the signal’s frequency

Step (3): We now set the cutoff frequency to 4.5KHz, the following picture shows
the result:
 • We notice here that the signal started to appear gradually because the
cutoff frequency is set near the signal’s frequency.
Step (4): Now we set the cutoff frequency above the signal’s frequency, the results
is shown in the next pictures:
• In time domain:

• In frequency domain:

• We notice here that the signal appeared in its original form without
attenuation because the cutoff frequency now exceeds the signal’s
frequency which means that the filter has no effect on the signal anymore.
Part (C): In this part of the experiment, we will add to signals with different
frequencies and feed them to the filter to see how multiple signals behave while
countering a LPF.

Step (1): The selected frequencies of signals are 2KHz and 5KHz, first we set
the cutoff frequency to 3KHz; the following pictures show the results in
both time and frequency domains:

• We see from these pictures that only the signal with a frequency of
2KHz appeared; which is expected to happen because the cutoff
frequency is between the first and the second signal’s frequencies.
Step (2): Now we increase the cutoff frequency until it exceeds the 5KHz, what we
expect to happen here is that both signals will appear without attenuation, the
following two pictures illustrates the results:

Part (D): What are we are going to do here is very similar to what we did in the
previous part of the experiment, but instead of adding to signals we’ll multiply
them and then feed them to filter:
 Step (1): after multiplying two signals with frequencies of 2KHz of 5KHz
the result of this multiplication is 7KHz and 3KHz , In order for the
two signals to appear without any attenuation the cutoff frequency should
be higher than 7KHz ; the results are shown in the following pictures:

Part (E): In this part instead of using a low pass filter we’ll use a bandpass filter
to see how signals behave while countering this type of filters, our main goal here
is to determine the cutoff frequencies of the bandpass filter by using the option
we used in the first part which is the sweep.
Step (1): by adjusting the settings of the sweep as follows

Step (2): to determine the first cutoff frequency we just need to

determine the moment when the signal’s amplitude decrease for the
first time to 70.7% of its original value, the following pictures show the
moment the signal reaches 70.7% of its original value:

• In time domain
 • In frequency domain

• We notice here that the first cutoff frequency is 92KHz

because at this frequency the observed voltage is 70.7% of
the preselected one.
Step (3): the second cutoff frequency is determined by determining the
second time the voltage drops to 70.7% of the original one, the results
are shown in the next pictures:
• In frequency domain

• In time domain
 • It is clear from the previous pictures that 110KHz is the
cutoff frequency; which makes the bandwidth of the
bandpass filter is 18KHz.

Conclusion:
In this experiment, we explored different types of filters used in
electronics, and we learned what is meant by the cutoff frequency
and how to find it and how determine the bandwidth of any filter,
and here is a brief explanation of what we’ve learned in this
experiment

1. Low-Pass Filters (LPFs):

o LPFs allow low-frequency signals to pass while attenuating

high frequencies.
o At the cutoff frequency the signal’s amplitude drops to

70.7% of its original value

o They are essential for noise reduction, audio systems, and

signal conditioning.
2. Bandpass Filters (BPFs):
o BPFs selectively pass a specific range of frequencies.

o A bandpass filter has to cutoff frequencies and the difference

between them is the bandwidth of the filter.

o They find applications in audio, radio communications, and

astronomy.