DESIGN AND IMPLEMENT OF ACTIVE LOW - PASS FILTER
- DESIGN AND IMPLEMENT OF ACTIVE LOW - PASS FILTER
- Introduction
- Design Requirements
- Feasibility Study and circuit selection
- Circuit Selection
- CALCULATING PASSBAND GAIN AND CONER FREQUENCIES
- VERIFY TRANSFER FUNCTION USING MATLAB
- Circuit design and component selection
- Frequency response magnitude characteristics of the circuits
- Deviate two values 5% from nominal values - IMPLEMENTATION RESULTS
- DISCUSSION
GROUP MEMBERS
| NAME |
|---|
| S.A.P. Kavinda |
| H.M. Wannigamage |
| M.D. Gunarathna |
| D.L.N. Duminda |
Introduction
This project is centered on the design and implementation of two active low-pass filters using operational amplifiers, based on given requirements. The primary focus is on the design of second-order filters.
We will delve into the mathematics involved in transforming standard filter-table data into the necessary transfer functions for constructing filter circuits. Filter tables, which are designed to simplify circuit design, are based on the concept of cascading lower-order stages to create higher-order filters. These tables include scaling factors (FSF) for the corner frequency (fc) and the required quality factor (Q) for each stage of the filter being designed. This allows designers to directly calculate the required circuit component values.
There are primarily three types of filters: Bessel, Butterworth, and Chebyshev. Additionally, there are two main circuit topologies: Sallen-key and Multiple Feedback. For this project, we used the Multiple-feedback topology in conjunction with the Butterworth type to design two filter circuits.
We used MATLAB, LTSpice, and Proteus to verify the transfer function and design the circuit. The implemented filter circuits utilized 4558D operational amplifiers.
Design Requirements
Problem 1: Low-pass active filter circuit with a roll off attenuates frequency components at 10 kHz by more than 10 dB. Desired passband gain of 20 dB and does not deviate by more than 3 dB. The passband frequency needed is 600 Hz.
Problem 2: Low-pass active filter circuit with a roll off attenuates frequency components at 12 kHz by more than 15 dB. Desired passband gain of 20 dB and does not deviate by more than 3 dB. The passband frequency needed is 800 Hz.
Feasibility Study and circuit selection
Order Selection
Finding the required order of low-pass filter is one of the critical designs when design and filter. Here used bode plot method to finding the required order.
Figure 2‑1: Bode Plot for finding the required order of filters.
As the figure illustrate, -20 dB attenuation was not sufficient to meet the given design requirement and -40 dB/decade is enough. Therefore, 2nd order filter had to use. Figure 1 illustrate the tentative bode plot for 1st problem and similar graph obtained for 2nd problem also.
Circuit Selection
Problem 01
Since design required flat bandpass response (maximum 3 dB allowed), and no concern about the phase, Butterworth filter type is preferred.
Let,
Passband = 600 Hz, Stop band frequency Maximum passband attenuation , Minimum stop band attenuation .
Then the required order of Butterworth filter can be calculated as follows,
Problem 02
CALCULATING PASSBAND GAIN AND CONER FREQUENCIES
Problem 01
Since this design used 2nd order filter, FSF = 1, and Q = 0.7071. Also, from design requirements, = 600 Hz, and K = 20 dB = 10
Problem 02
Since this design used 2nd order filter, FSF = 1, and Q = 0.7071. Also, from design requirements, = 800 Hz, and K = 20 dB = 10
VERIFY TRANSFER FUNCTION USING MATLAB
Problem 1
clc; clear; clf;
num = [10*(1200*pi)^2]
den = [1 1200*pi/0.7071 (1200*pi)^2]
w = logspace(-1,5,10000);
%plotting tf
h = freqs(num,den,w);
mag = (abs(h))
phase = angle(h);
phasedeg = phase*180/pi;
loglog(w,mag)
grid on
xlabel('Frequency (rad/s)')
ylabel('Magnitude')
%checking mag at cutoff
k1 = max(find(w < 600*2*pi));
diff = w(k1+1) - 600*2*pi
k2 = max(find(w < 2*pi*10*10^3))
diff = w(k2) - 10*10^3*2*pi
hold on
loglog(w(k1+1),mag(k1+1),'ro',w(k2),mag(k2),'ro')
Problem 2
clc; clear; clf;
num = [10*(1600*pi)^2]
den = [1 1600*pi/0.7071 (1600*pi)^2]
w = logspace(-1,5,10000);
%plotting tf
h = freqs(num,den,w);
mag = (abs(h))
phase = angle(h);
phasedeg = phase*180/pi;
loglog(w,mag)
grid on
xlabel('Frequency (rad/s)')
ylabel('Magnitude')
%checking mag at cutoff
k1 = max(find(w < 800*2*pi));
diff = w(k1+1) - 800*2*pi
k2 = max(find(w < 2*pi*12*10^3))
diff = w(k2) - 12*10^3*2*pi
hold on
loglog(w(k1+1),mag(k1+1),'ro',w(k2),mag(k2),'ro')
Circuit design and component selection
Frequency response magnitude characteristics of the circuits
At -3db (600 Hz)
At 10 kHz
Deviate two values 5% from nominal values
C2 from 22.6 nF to 23.73 nF
R2 from 16.5K to 17.33 k
Blue Line: With Original Values
Green Line: With Deviated Values
Red Line: Deviation in dB scale
IMPLEMENTATION RESULTS
Circuit:
Results:
Observations and Results
Problem 1
| Frequecy | In(mV) | output(mv) | Gain | Gain(dB) |
|---|---|---|---|---|
| 100 | 10 | 100 | 10 | 20.00 |
| 200 | 10 | 100 | 10 | 20.00 |
| 300 | 10 | 100 | 10 | 20.00 |
| 400 | 10 | 90 | 9 | 19.08 |
| 500 | 10 | 80 | 8 | 18.06 |
| 600 | 10 | 70 | 7 | 16.90 |
| 700 | 10 | 50 | 5 | 13.98 |
| 800 | 10 | 40 | 4 | 12.04 |
| 900 | 10 | 20 | 2 | 6.02 |
| 1000 | 10 | 5 | 0.5 | -6.02 |
Problem 2
| Frequecy | In(mV) | output(mv) | Gain | Gain(dB) |
|---|---|---|---|---|
| 100 | 10 | 100 | 10 | 20.00 |
| 200 | 10 | 100 | 10 | 20.00 |
| 300 | 10 | 100 | 10 | 20.00 |
| 400 | 10 | 100 | 10 | 20.00 |
| 500 | 10 | 100 | 10 | 20.00 |
| 600 | 10 | 90 | 9 | 19.08 |
| 700 | 10 | 80 | 8 | 18.06 |
| 800 | 10 | 70 | 7 | 16.90 |
| 900 | 10 | 55 | 5.5 | 14.81 |
| 1000 | 10 | 45 | 4.5 | 13.06 |
DISCUSSION
During this group project, we designed two second-order low-pass active filter circuits that met the given requirements. Initially, we conducted a feasibility study to identify viable solutions to the problems at hand, and we explored various filter types, commonly used filter circuit topologies, and their differences. We also performed a Bode plot analysis to determine the required filter order.
We selected the Butterworth filter type and the multiple-feedback circuit topology based on our requirements. After choosing the filter type, order, and topology, we calculated the transfer function and the circuit components. We verified the obtained transfer function using MATLAB and simulated the frequency analysis of the circuit designs using LTSpice and Proteus.
After designing the two circuits, we had to adjust the component values due to their unavailability in the market. We recalculated the new component values, implemented the design in the laboratory, and observed the gain at different frequencies. We used a signal generator and an oscilloscope to provide the input signal and measure the output signal. After collecting the necessary observations, we calculated the gain and plotted the graph. The results were as expected, showing a sharp cutoff at 600 Hz and 800 Hz in the first and second circuits, respectively.
We deviated two values by 5% from their nominal values (one resistor and one capacitor in this case). This showed that the deviation is high near the cut-off frequency.
In conclusion, our group successfully designed and implemented two second-order low-pass active filter circuits. Despite challenges related to component availability, we achieved the desired performance. The results of our experiments aligned with our expectations, and we observed the effects of component deviations near the cutoff frequency. Overall, this project provided valuable insights into filter design and practical considerations in real-world implementations.