Comprehensive Lab Report: Active Low Pass Filter Design and Simulation

This lab report details the design, implementation, and analysis of an active low pass filter. The experiment involved designing a first-order low pass filter using passive components (resistors and capacitors) and an operational amplifier, targeting a cut-off frequency between 10-80 kHz, with a chosen design frequency of 25 kHz. The report includes calculations for component values, simulation results using Multisim, and experimental results obtained from a breadboard circuit. The student investigated the filter's frequency response by varying the input signal's frequency and measuring the input and output amplitudes to calculate the gain. The results, presented in tables and frequency response curves, demonstrate the filter's attenuation characteristics. The report also includes a discussion of the observed results, a summary of the learning experience, and a comparison between simulated and experimental outcomes, highlighting the impact of the operational amplifier and measurement errors on the filter's performance. The report successfully meets the assignment's objectives.

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

Input and output waveform at 15 kHz
Input and output waveform at 20 kHz

Input and output waveform at 21 kHz
Input and output waveform at 22 kHz

Input and output waveform at 23 kHz
Input and output waveform at 24 kHz

Input and output waveform at 25 kHz
Input and output waveform at 26 kHz

Input and output waveform at 30 kHz
Input and output waveform at 50 kHz

Input and output waveform at 75 kHz
Input and output waveform at 100 kHz

Input and output waveform at 200 kHz
Table 1: table of results(simulated)
Frequency
(kHz)
Vin (p-p)
(V)
Vout (p-p)
(V)
Gain-(Vout/Vin) Gain
(dB)=20log(Vout/Vin)
5 1.0 3.0 3.0 9.54
10 1.0 2.8 2.8 8.94
15 1.0 2.6 2.6 8.30
20 1.0 2.3 2.3 7.23
21 1.0 2.2 2.2 6.85
22 1.0 2.2 2.2 6.85
23 1.0 2.1 2.1 6.44
24 1.0 2.1 2.1 6.44
25 1.0 2.0 2.0 6.02
26 1.0 2.0 2.0 6.02
30 1.0 1.8 1.8 5.1
50 1.0 1.2 1.2 1.58
75 1.0 0.8 0.8 -1.94
100 1.0 0.6 0.8 -1.94
200 1.0 0.34 0.34 -9.37

Frequency response curve from simulated results
Experimental results
Table 2: experimental results
V(in) Frequency V(in) V(out) Gain=V(out)/V(in) Gain dB
= 20log
(Gain)
1v p-p 5kHz 1.10 3.28 2.98 9.484
1v p-p 10kHz 1.10 3.08 2.80 8.94
1v p-p 15kHz 1.10 2.80 2.545 8.11
1v p-p 20kHz 1.12 2.48 2.214 6.90
1v p-p 21kHz 1.10 2.44 2.218 6.91
1v p-p 22kHz 1.10 2.40 2.218 6.91
1v p-p 23kHz 1.12 2.40 2.14 6.608
1v p-p 24kHz 1.12 2.32 2.109 6.48
1v p-p 25kHz 1.10 2.32 2.071 6.32
1v p-p 26kHz 1.10 2.16 1.963 5.85

1v p-p 30kHz 1.12 2.00 1.818 5.191
1v p-p 50kHz 1.12 1.36 1.25 1.938
1v p-p 75kHz 1.10 1.00 0.877 -1.14
1v p-p 100kHz 1.14 0.780 0.684 -3.29
1v p-p 200kHz 1.14 0.416 0.364 -8.77
Input and output waveform
From the results of table 2 frequency response curve was plotted as shown below

Discussion
The combination of resistors, capacitor and operational amplifier in figure 2 makes up the active
low pass filter. The designed filter produces high attenuation above cut-off frequency of 25kHz
and little attenuation below the same frequency. That is any signal with a frequency less than
cut-off frequency gets a pass and a signal with frequency higher than the cut-off frequency is
stopped or attenuated. From the input and output waveforms obtained from the low pass filter, t
was observed that amplitude of the output signal is greater compared to that of input signal for
frequencies between 0 Hz and a region less than the cut-off frequency. The amplitudes are
unaffected since the operating frequency is below the cut-off frequency. The amplitude of the
output signal is also observed to be less than that of input signal at frequencies greater than cut-
off frequency as the signals above the cut-off frequency is attenuated (De Santis & Chen, 2017).
Frequency response of the low pass filter is presented in the curve shown above, with the gain as
a function of frequency. From the curve it can be deduced that, gain of the designed low pass
filter decreases with increase in frequency of the input signal. From the curve it is also observed
that, in the passband region, the gain is nearly constant at 8dB for some range of frequencies. In
the stop-band region, gain of the filter decreases gradually for a range of frequencies.
The frequency response curve drops gradually at cut-off frequency as opposed to ideal case
where the curve suddenly drops at cut-off frequency. Cut off frequency is the point where the
curve drops by -3 dB from the pass band. From the curve obtained from simulation, maximum
amplitude of the pass band region is 9.6dB whereas for the experimental results the pass band
region is at 9.4dB. The cut-off frequency will therefore be at 6.6 dB and 6.4dB for simulated and
practical of the response curves respectively. That translate to a cut-off frequency of 25 and 23
kHz from experimental and simulated results respectively. The two values are equal to the value
calculated during the design process with simulated results being more accurate. Experimental
have slightly higher due reading and offset voltages of operational amplifier (Zhang, Hou, Wen
& Lu, 2018).
It is by the action of the operational amplifier used in design of active low pass filter that the
amplitude of the output signal is increased. The frequency response curve obtained from both
simulated and experimental results didn’t produce exact curve as expected from theory.
According to theoretical knowledge, the maximum gain of the pass band is expected to be
constant from as low values of frequency to nearly the cut-off frequency, then suddenly drops
after the cut-off frequency. For the case, the gain didn’t drop suddenly after the cut-off
frequency. This can be due to errors in taking measurements and the range of operating
frequencies chosen(Ling & Kesong, 2019).
Summary of experience
From my efforts, i was able to learn:
 The difference between passive and active low pass filter.

 The difference between high and low pass filter.
 How to calculate values of passive components of a low pass filter.
 Function of an operational amplifier in the circuit
 Working principle of the low pass filter
 How to interpret frequency response of a low pass filter
The experience in the design was fascinating. The design of active low pass filter using passive
components and operational amplifier was a success. The filter met the design specifications as
analyzed using the amplitude of the output signal and the frequency response. Objectives of the
experiment was met.
Discussion topics
1. Calculations showing how component values were determined.
Cut off frequency of the low pass filter is chosen to be 25kHz
The formula for calculating cut-off frequency of a low pass filter is
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 as shown below
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.
Resistors value of R1 was arbitrarily chosen as 2.2kΩ.
2. Schematic of a low pass filter

3. Table of collected results
Table of simulated results
Frequency
(kHz)
Vin (p-p)
(V)
Vout (p-p)
(V)
Gain-(Vout/Vin) Gain
(dB)=20log(Vout/Vin)
5 1.0 3.0 3.0 9.54
10 1.0 2.8 2.8 8.94
15 1.0 2.6 2.6 8.30
20 1.0 2.3 2.3 7.23
21 1.0 2.2 2.2 6.85
22 1.0 2.2 2.2 6.85
23 1.0 2.1 2.1 6.44
24 1.0 2.1 2.1 6.44
25 1.0 2.0 2.0 6.02
26 1.0 2.0 2.0 6.02
30 1.0 1.8 1.8 5.1
50 1.0 1.2 1.2 1.58
75 1.0 0.8 0.8 -1.94
100 1.0 0.6 0.8 -1.94
200 1.0 0.34 0.34 -9.37
Table of experimental results
V(in) Frequency V(in) V(out) Gain=V(out)/V(in) Gain dB
= 20log
(Gain)

1v p-p 5kHz 1.10 3.28 2.98 9.484
1v p-p 10kHz 1.10 3.08 2.80 8.94
1v p-p 15kHz 1.10 2.80 2.545 8.11
1v p-p 20kHz 1.12 2.48 2.214 6.90
1v p-p 21kHz 1.10 2.44 2.218 6.91
1v p-p 22kHz 1.10 2.40 2.218 6.91
1v p-p 23kHz 1.12 2.40 2.14 6.608
1v p-p 24kHz 1.12 2.32 2.109 6.48
1v p-p 25kHz 1.10 2.32 2.071 6.32
1v p-p 26kHz 1.10 2.16 1.963 5.85
1v p-p 30kHz 1.12 2.00 1.818 5.191
1v p-p 50kHz 1.12 1.36 1.25 1.938
1v p-p 75kHz 1.10 1.00 0.877 -1.14
1v p-p 100kHz 1.14 0.780 0.684 -3.29
1v p-p 200kHz 1.14 0.416 0.364 -8.77
4. Simulated response curve
5. Results verification

Frequency response curve from simulation
Response curve from experimental results
6. Comparing the results
The maximum gain obtained from frequency response of simulated and experimental results are
9.6 and 9.4 dB respectively. Furthermore, cut-off frequency from simulation is 23kHz and that
from experiment is 25 kHz. Amplitude of output voltages are higher in simulated results
compared to experimental results. The difference is due to the experimental errors and the type
of operational amplifier used.
7. Time required- 4 hours

BIBLIOGRAPHY
CircuitDigest, 2018, passive low pass filter. Available from
https://circuitdigest.com/tutorial/passive-low-pass-filter Accessed on January 11, 2020
De Santis, D. and Chen, M., 2017. Design of active low pass filters to reduce harmonic current
emission. In IECON 2017-43rd Annual Conference of the IEEE Industrial Electronics
Society (pp. 1059-1065). IEEE.
Electronics Hub, 2019, Active low pass filter. Available from
https://www.electronicshub.org/active-low-pass-filter/ Accessed on January 11, 2020
Electronics Tutorials, n.d, Active low pass filter. Available from https://www.electronics-
tutorials.ws/filter/filter_5.html accessed on January 11.2020
Ling, W. and Kesong, C., 2019. The Performance Analysis of Second Order Band-pass Filter.
In 2019 3rd International Conference on Circuits, System and Simulation (ICCSS) (pp. 41-45).
IEEE.
Moschytz, G.S., 2019. Passive LCR and Active-RC Filters. In Analog Circuit Theory and Filter
Design in the Digital World (pp. 149-166). Springer, Cham.
Upadhyay, A. and Pal, K., 2017. First Order All Pass, Low Pass and High Pass Filters Using
Differential Voltage Current Conveyors. Journal of Active & Passive Electronic Devices, 12.
Yan, G., 2017. Design of Active Low-Pass Filter Based on Multiple Feedback Circuit. In 2017
9th International Conference on Intelligent Human-Machine Systems and Cybernetics
(IHMSC) (Vol. 1, pp. 7-10). IEEE
Zhang, C., Hou, X., Wen, W. and Lu, T., 2018, May. Stability of Active-RC LPF Designed by
Cascade Method. In 2018 3rd International Conference on Information Systems Engineering
(ICISE) (pp. 104-111). IEEE.