Design of Active Low Pass Filter.

DESIGN OF ACTIVE LOW PASS FILTER
Lab overview
The objective of the experiment is to design and implement first order low pass filter using
passive components (resistor and capacitor) and an operational amplifier. The active low pass
filter is designed to have a cut-off frequency of between 10-80 kHz. To achieve this resistor and
a capacitor values for input impedances are computed using the selected cut-off frequency. For
this experiment, a cut-off frequency of 25kHz was used to compute resistor and capacitor values
of the passive low pass filter. From the design calculations, a resistor and capacitor values of
6.8kΩ and 1 nF was found for the feedback path of inverting filter, these values produce a cut-
off frequency of 23.4kHz. The input impedance resistor of inverting operational amplifier was
also determined as 2.2kΩ.
Function generator was used to generate input signal as it allows us to adjust the frequency. An
oscilloscope was also used to monitor and measure the amplitude of the input and output
waveforms as shown in the results section. To verify the operations of the active low pass filter,
frequency of the input signal was adjusted in a range of frequencies. Amplitude of an input and
output waveforms at different frequencies were recorded as shown in table 1. From the measured
values of input and output voltages, the gain of a low pass filter at a different frequency were
calculated. Frequency response of the designed low pass filter was then drawn from the results
obtained.

Design and results
Low pass filter
A low pass filter is a circuit designed to allow a passage of signals with lower frequencies and
blocks or filter out signal with frequencies higher that the cut-off frequency (Moschytz, 2019).
Low pass filters are categorized into passive and active filters. Passive filters are constructed out
of passive components namely, the resistors and capacitors. Active filters on the other hand, have
an extra amplifying component (operational amplifier) that strengthen the signal, therefore
amplitude or the level of its output is higher compared to one at the input (ElectronicsTutorial,
n.d).
Inverting low pass filter is constructed with a capacitor and a resistor in a feedback path of an
inverter as shown in figure 2. The filter is dubbed first – order since it has one reactive
component (capacitor) in the circuit. The designed filter is made up of basic passive low pass
filter connected to inverting amplifier (ElectronicsHub, 2019).
Design
Cut off frequency of the low pass filter is chosen to be 25kHz as the design specification requires
cut-off frequency between 10kHz and 80kHz.
The formula for calculating cut-off frequency of a low pass filter is given by the equation below
(Yan, 2017)
fc= 1
2∗π∗R2∗C ...........................1
The value of C is arbitrarily chosen to be 1nF, thus the resistor value of R2 can be calculated
using selected cutoff frequency and the formula of equation 1.
fc = 25 kHz,
C = 1 nF
25∗103= 1
2∗π∗R 2∗1∗10−9 ..................2
Making R1 the subject of the formula of equation 2 we get
R 2= 1
2∗π∗1∗10−9∗25∗103 .
= 6.366 kΩ
6.366 kΩ resistor does not exist thus the next available resistor is 6.8 kΩ.
Cut off frequency of the designed circuit is

fc= 1
2∗π∗R2∗C ,
fc= 1
2∗π∗6.8∗103∗1∗10−9 ,
= 23.4 kHz
Procedure
To investigate the operation of active low-pass filter the circuit of figure 2 was simulated using
Multisim software. The function generator and oscilloscope are used to set input signal and
monitor output signal respectively. The function generator is set to produce sinusoidal waveform
with an amplitude of 1 volt. The input signal from signal generator is fed into the low pass filter
circuit. The output signal from the low pass filter is connected to channel A of the oscilloscope
for measurement purposes. Channel B of the oscilloscope is connected to the input or function
generator. The oscilloscope is used to observe the peak to peak value of input and output signal.
Frequency of input voltage is altered by adjusting frequency settings of the function generator.
Corresponding peak to peak value of output voltage is measured and recorded in table 1. A range
of frequencies is used to check the attenuation of the low pass filter. From the measurements
taken (input and output voltages) gain or attenuation of the filter is calculated and fed into table
1.

Figure 2: Active low pass filter circuit
Results
Simulated results
The images below are screenshots of input and output waveforms at different frequencies
obtained from Multisim software.

Input and output waveform at 5kHz
Input and output waveform at 10kHz