This project explores the design and implementation of a second-order universal active (biquad) filter supporting low-pass, high-pass, band-pass, and band-stop responses. The filter is realized across simulation, ASLK PRO kit, and PCB platforms, with performance evaluated through frequency and time-domain analysis. Emphasis is placed on gain, phase, and transient behavior, highlighting the alignment and trade-offs between theoretical and practical results in analog filter design. GitHub Repo
This project aims to design an analog universal biquad filter for a corner frequency of 1 kilohertz and a quality factor of 10. This was implemented from specification to simulation and finally to physical layout. This includes schematic design and simulation, functional modeling, and full PCB design. The utilisation of modern simulation tools and open-source platforms was immense for the developement of this project.
The key feature of this project is to focus on simulation-based design using KICAD for schematic capture and analysis of the circuit and analysing the performance in frequency and time domain. For PCB implementation and layout, the same open-source tool is used and the functional modelling of the circuit is done using Analog System Lab Kit (ASLK) and Red Pitaya. The use of Red Pitaya is mentionable as it provides a cost-effective and adaptable platform for measuring the frequency response of ALSK tool kit circuit. The design workflow also includes documentation and analysis using Quarto, Jupyter Notebooks, and supporting tools such as Python, Numpy, and Matplotlib. All components of this project are managed using Git and documented in reproducible formats.
NOTE: All design files, source code, and documentation are shared publicaly under our GitHub repository.
For many real life applications like audio processing, sensor signal conditioning and instrumentation, the signals can be corrupt due to unwanted noise and interference of the signals. One of the most important solution would be the use of filters especially analog filters with which it can be used to clean and shape signals before they are digitized or processed further.
The use of analog filter are advantageous over digital filters, even though it is way more flexible and programmable, because it has better power consumption, size, or cost constraints. Among analog filters, the biquad filter gets highlighted for its Second-order response which allows a precise control over frequency characteristics, flexibility to configure it as a low-pass, high-pass, band-pass or band-stop filters and its stability when implemented using op-amps and passive components.
This project focuses on designing, simulating, and implementing a biquad filter, using KiCad for schematic design, simulation, and PCB layout and ALSK tool kit for practical filter implementation and behavioral response testing using Red Pitaya. This whole projects motivates to have an understanding of how analog filters are practically implemented using op-amps, learn PCB design basics and fabrication, learn the usage of KICAD tool as well as integrating tools like ALSK and Red Pitaya into the design loop. Finally it gives a complete analog design experience, from concept to functional hardware, reinforcing both theoretical understanding and practical skills in analog electronics and system prototyping.
Filters, as the name suggests, is used to filter out the unwanted signals. Based on different fields, its usage is also different like in analog electronics, they can be used to shape certain signals while attenuating other. Other applications of filters are to remove noise to improve the signals quality in certain fields like audio processing, biomedical instrumentation, communication systems, or sensor signal conditioning.
There are four types of filters which are low pass filter, high pass filter, band pass filter and band stop filter or notch filter. Filters are classified based on allowing or blocking different band of frequencies. They treat different frequencies of the spectrum in various ways [1]. The low pass filter allows the low frequency signals to pass through the filter and attenuates the higher frequency signals. Whereas high pass filter works just the opposite of this by allowing the high frequency signals to pass through the filter and attenuates the low frequency signals. Band pass filter passes a specific range of frequencies and attenuates the rest and the band stop cuts off a specific range of signals and allows the rest to pass through the filter. The frequency response of each filters are Figure 9.1 for a better understanding of the types of filters:
There are some terminologies to keep in mind when taking about filter designing, namely cutoff frequency, order of the circuit and roll off which is defined below.
It is the frequency at which the filter starts to significantly reduce the signal strength. It is also known as corner frequency or break frequency [2] and can be determined by the formula:
\[ f_c = \frac{1}{2 \pi R C} \]
where:
- \(f_c\) is the cutoff frequency (in Hz),
- \(R\) is the resistance (in ohms),
- \(C\) is the capacitance (in farads).
The cut-off frequency is a key parameter in filter design and determines the point at which the output signal falls to 70.7% of the input or from the frequency response curve or bode plot, it is -3dB (20 log (Vout/Vin)) of the input Figure 9.2.
It is determined to measure the rate at which the filter attenuated the signal after the cut-off frequency [3]. More steeper the roll-off factor more better the filter works. So in order to increase this factor we need to look into other parameter called the order of the filter.
The order of a filter is determined by the number of reactive elements in the circuit like capacitance or inductance [4]. As we add one reactive element more, we increase the maximum roll-off by 20 db/decade. So the key point here is to add more reactive elements in order to increase the order of the filter but this increase affects other parameter like phase shifting, as order increases phase shift increases. So we can’t increase it as much as we can.
It is the range of frequencies that passes through the filter without attenuation [1]. The bandwidth can be calculated by taking the difference of the frequnecies at -3db gain as shown in Figure 9.3 \[ BW = f_2 - f_1 \] The bandwidth of low pass filter can be frequnecy at 3db and for band pass it is as shown above while it is not defined for band stop and high pass filters.
It is used to measure how well a filter isolates a desired frequency band while attenuating other frequency ranges. This factor affects the bandpass and bandstop filters. As the bandwidth becomes narrower the Q-factor increases which denotes a higher selection of frequency to pass or stop. This can be calculated by
\[ Q = \frac {f_0} {BW} \]
where,
\(Q\) is the quality factor
\(f_0\) is the cut-off frequency
\(BW\) is the bandwith
But the increase in quality factor can show undesirable oscillation and bring more instability to the circuit. Also the values of passive components like resistor and capacitors affect the performance. Practically acheiving high Q-factor is difficult due to the limited component quality and manufacturing tolerances.
A biquad filter is a second-order active filter commonly used for building all the four types of filters LPF, HPF, BPF, and BSF. The term “biquad” comes from bi-quadratic, meaning the transfer function contains up to \(s^2\) in both numerator and denominator. It provides better control over gain, Q (quality factor), and center/cutoff frequency than first-order filters. Moreover as we increase the order by one, we increase the maximum roll off by 20 db/decade. The general transfer function can be written as: \[ H(s) = \frac{b_0 + b_1 s + b_2 s^2}{a_0 + a_1 s + a_2 s^2} \]
The structure of the transfer function tells us how the frequency components of the input signal are modified, how poles and zeros determine the frequency response, how component values (R, C) and op-amp behavior affect real-world performance.
There are mainly two types of topologies for designing a second order analog filter, they are Sallen-Key topology and Multiple feedback biquad topology. MFB is generally used to design high Q factor and high gain circuits and in our project we aim to design a biquad filter with quality factor 10. The need for a high quality factor in our design led us to select Multiple Feedback Biquad (MFB) topology developed by Texas Instruments [5].
Let us take transfer function into consideration as it helps to analyse the filter performance based on the component values used in the circuit. Transfer function in general can be defined as: \[ H(s)= \frac{V_{\text{out}} (s)}{V_{\text{in}} (s)} \]
Consider the circuit diagram for second order low pass filter Figure 10.1
In this MFB low pass filter, we use the op-amp in inverting configuration. \(R_1\) and \(R_3\) are input and feedback resistors and \(R_2\) is part of feedback loop. \(C_1\) and \(C_2\) are frequency controlling capacitors [6]. We can use nodal analysis for finding the transfer function. According to Kirchhoff’s Current Law (KCL), we can write the eqaution as :
\[ \frac{V_{in} - 0}{R_1} + s C_2 (V_{in} - 0) + \frac{V_{out} - 0}{R_2} + s C_1 (V_{out}-V_-) = \frac{V_- - 0}{R_3} \approx 0 \]
Or simply:
\[ \frac{V_{in}}{R_1} + s C_2 V_{in} + \frac{V_{out}}{R_2} + s C_1 V_{out} = \frac{0}{R_3} \approx 0 \] In ideal op-amp we assume that \(V_-\) and \(V_+\) are 0. So when solving this equation we come up with the transfer function for MFB low pass filter with a gain \(H_0\),
\[ \frac{V_{out}(s)}{V_{in}(s)} = H_0 \cdot \frac{\omega_0^2}{s^2 + \frac{\omega_0}{Q} s + \omega_0^2} \] So the transfer function of a low pass circuit would be: \[ H(s) = \frac{H_0 \cdot \omega_0^2}{s^2 + \frac{\omega_0}{Q}s + \omega_0^2} \]
Similarly we can derive for high pass, bandpass and band stop which are:
High pass: \[ H(s) = \frac{H_0 \cdot s^2}{s^2 + \frac{\omega_0}{Q}s + \omega_0^2} \]
Band pass: \[ H(s) = \frac{H_0 \cdot \frac{\omega_0}{Q} \cdot s}{s^2 + \frac{\omega_0}{Q}s + \omega_0^2} \]
Band stop: \[ H(s) = H_0 \cdot \frac{s^2 + \omega_0^2}{s^2 + \frac{\omega_0}{Q}s + \omega_0^2} \]
This section models the behavior of a second-order band-pass filter using the transfer function derived from a general second-order circuit. Since the filter was designed with zero gain (i.e., \(H_0 = 1\)), the focus is on the shape of the response rather than amplification.
The band-pass filter transfer function is given by:
\[ H(s) = \frac{H_0 \cdot \frac{\omega_0}{Q} \cdot s}{s^2 + \frac{\omega_0}{Q}s + \omega_0^2} \]
To normalize and simplify the simulation, we divide numerator and denominator by \(\omega_0^2\):
\[ H(s) = H_0 \cdot \frac{s / Q}{s^2 + s / Q + 1} \]
With \(H_0 = 1\), the final simulation model becomes:
\[ H(s) = \frac{s / Q}{s^2 + s / Q + 1} \]
This normalized second-order band-pass filter exhibits a peak at the resonant frequency \(\omega_0\), with sharpness controlled by \(Q\) Figure 13.1.
The filter has unity gain, as expected from the design. The Bode plot shows a peak at 1000 Hz, confirming the resonant frequency. The accompanying phase response reveals how the phase of the output signal shifts relative to the input across different frequencies. In band-pass filters, this phase shift is steepest near the resonant frequency, indicating a rapid change in the system’s reactive behavior. This characteristic is crucial in applications involving signal timing, modulation, or phase-sensitive detection. The step response Figure 11.2 shows damped oscillations typical of underdamped second-order systems with high Q.
This behavioral model validates the expected frequency and time-domain characteristics of a second-order band-pass filter. It helps verify that the circuit design aligns with theoretical predictions before practical implementation.
A second-order band-pass filter was chosen for its frequency-selective properties, making it ideal for isolating a narrow frequency band around a target center frequency. The topology used was MFB (Multiple Feedback Biquad). It allows simultaneous extraction of LPF, HPF, BPF, and BSF outputs from a single op-amp-based structure.
The filter was designed to achieve a center frequency of 1000 Hz, with a quality factor \(𝑄 = 10\) to emphasize selectivity. A unity gain was selected to focus the design on shaping the frequency response rather than amplification. The resistance and capacitance values were determined using the following equation.
\[ \omega_0 = 2\pi f_0, \quad \omega_0 = \frac{1}{RC} \]
The TL082 dual JFET-input op-amp was selected for its high slew rate and wide bandwidth, making it suitable for audio- and low-frequency analog filtering. Its availability in the ASLK PRO kit further streamlined practical implementation.
The following code can also be used to calculate the required capacitor value given a desired resistance, center frequency, and quality factor.
import numpy as np
def calculate_resistances(f0, Q, C):
"""
Calculate required resistor values (R2 and R3) for the given
center frequency (f0), quality factor (Q), and capacitances C1, C2.
"""
w0 = 2 * np.pi*f0
R = 1/ (w0 * C)
return R
# Example values
f0 = 1000 # Hz
Q = 10 # Quality factor
C = 0.01e-6 # Farads
R = calculate_resistances(f0, Q, C)
print(f"Calculated R: {R:.0f} Ω")Calculated R: 15915 ΩThis utility provides practical flexibility in component selection by enabling capacitance tuning based on resistor availability.
This section discusses the signal behavior of second-order filters in both the time and frequency domains. The analysis is essential to understanding how filters affect different frequency components of an input signal, as well as how their internal characteristics—such as pole and zero placement—impact signal shaping.
In the frequency domain, filters modify both the amplitude and phase of signals.
A general second-order filter can be described by the transfer function:
\[ H(s) = \frac{a_2 s^2 + a_1 s + a_0}{s^2 + \frac{\omega_0}{Q}s + \omega_0^2} \]
Where:
These responses are typically visualized using a Bode plot, which shows:
These characteristics help identify the filter’s behavior around its cutoff frequency (or resonant frequency in the case of BPF/BSF), and how sharply it attenuates beyond that point (roll-off).
Every transfer function \(H(s)\) has poles and zeros:
The placement of poles and zeros determines:
Higher-order filters (more poles) exhibit steeper roll-offs but may introduce more phase distortion.
Transient Response is how the filter initially reacts to an input signal like a step or pulse. It’s important for understanding startup behavior and stability.
Steady-State Response is the long-term behavior once transients have settled. This represents the filter’s typical operating condition.
The time-domain behavior is often evaluated using:
These help validate how energy is stored and released in reactive components (capacitors and inductors).
Both gain and phase responses are vital in system design, especially in:
Below is a sample image used to visualize gain and phase responses for different filter types based on their transfer functions.
This analysis connects theoretical filter modeling to practical signal behavior, reinforcing both design accuracy and signal integrity across platforms.
Op-amp or operational amplifiers are voltage amplifying devices designed to be used with external feedback components like resistors, capacitors based on its need. These are three terminal devices with an output and two inputs, one inverting (marked with a negative sign) and one non-inverting (marked with a positive sign)[4].
RULE 1: No current flows in or out of the op-amp. Whatever input we give through the inverting or non-inverting terminals, it doesnot go inside of the op-amp for it to work. But works with the other voltage input we give into it.
RULE 2: The output of the op-amp always tries to make the voltage difference between the two input pin to 0V.
We usually won’t use op-amp alone without any elements connected because by nature its amplification property is so high that we need some other elements to reduce it. It can amplify both analog and digital signals making it usable for multiple applications.
There are multiple configurations for op-amp. Here we are only listing two of them as we only use these configurations in the biquad circuit we design.
We give input to the inverting input terminal of the op-amp, thus the name inverting op-amp configuration. We also give feedback from the output to this same input terminal as given in Figure 14.1
According to rule 2, output volatge always tries ot make the two inputs the same or the difefernce between them as 0V. That means \(V_2\) here would can be called as virtual ground since \(V_1\) is connected to the ground.
Lets see how this gives us an amplification with an example. Say, \(R_{\text{in}}\) is 1V as its values is \(1\,\text{k}\Omega\) and \(R_F\) is 10V as this has a value of \(10\,\text{k}\Omega\). Now we give an input of 1V, so 1A current flows across \(R_{\text{in}}\). Now based on rule 1, current does not flow inside the op-amp so it has to flow to \(R_F\). Thus the voltage drop across it would be 10V. With repsct to the groung it enters with a +10V and so we get -10V in the other terminal, resulting in a -10V output.
When deriving this with equations: \[ I_{{R_{\text{in}}}}= I_{{R_F}} \] \[ \frac{V_{\text{in}} - V_2}{R_{\text{in}}} = \frac{V_2 - V_{\text{out}}}{R_F} \]
\[ \frac{V_{\text{in}} - 0}{R_{\text{in}}} = \frac{0 - V_{\text{out}}}{R_F} \] Since x is virtual ground, we can give 0V to it.
\[ \frac{V_{\text{out}}}{V_{\text{in}}} = \frac{-R_F}{R_{\text{in}}} \] \[ A = \frac{-R_F}{R_{\text{in}}} \]
This op-amp gives us an integrated value of the input as output for the circuit. For acheiving this we just replaced the \(R_F\) resistor with a capacitor as given in Figure 14.2
Here also we can give a 1V input and the current flowing across the \(R_{\text{in}}\) is 1A as its value is \(1\,\text{k}\Omega\). Because of rule 1, current flows in through the capacitor and it tries to charge. As we give a positive input capacitor charges negatively and vise versa. Meaning when we give a square wave in the input we get a triangular wave which is the integrated output for a square wave. When calculated using the equations, we get:
\[ I_{{R_{\text{in}}}}= I_{C} \]
\[ \frac{V_{\text{in}} - 0}{R} = C{\frac{d(0-V_{\text{out}})}{dt}} \] \[ \frac{V_{\text{in}}}{R} = -C{\frac{d(V_{\text{out}})}{dt}} \] \[ V_{\text{out}}= -\frac{1}{{R}{C}} \int V_{\text{in}} \, dt \]
In the simulation we are using TL082 op-amp for designing the biquad. The TL082 is a widely used JFET-input operational amplifier known for its low input bias current and wide bandwidth. However, when designing analog filters, we need to think about its specifications:
Slew Rate: It detemines the fastness of change in output voltage which can affect the performance of high frequency signals.The TL082 has a typical slew rate of 13 V/µs.
Gain Bandwidth Product (GBW): The product of gain and frequency is a constant. For example, if the op-amp is used in a configuration with gain = 10, the bandwidth drops to 300 kHz.
Input Offset Voltage: It can slightly shift DC operating points in precision circuits. It is around 3 mV.
Input Bias Current: It is lower than typical BJT-input op-amps because of the JFET inputs. Its value is 65 nA.
Output Voltage Swing: The output doesn’t swing fully to the rails. Usually, it can swing from about ±12V when powered with ±15V.
Power Supply Range:It operates from ±3V to ±18V, or a single supply from 6V to 36V [7].
In this project, the design of a biquad filter requires the use of an operational amplifier (op-amp) as a fundamental component. Passive components alone (resistors and capacitors) cannot achieve the desired performance when sharp frequency selectivity and amplification are involved. The op-amp provides the necessary gain and feedback to construct second-order filter behavior, enabling sharper transitions and resonance at the target frequency. Without an op-amp, it would be difficult to achieve a stable, high-Q response, especially with the narrow bandwidth required in this design. For the implementation we are using TL082 beacuse of its balance in performance, availability, and compatibility with analog filter requirements.
Overall, the TL082 offers a great performance and moreover easiness to use. It meets all the necessary design constraints for designing an analog active filter biquad on PCB while remaining simple to work with in both simulation (KiCAD) and practical experiments (Red Pitaya, ASLK Pro).
This section illustrates the hardware implementation of the biquad filter using KiCad and includes schematic capture, PCB layout (top and bottom), and relevant design constraints.
Below is the schematic created in KiCad for the implementation of the biquad filter circuit.
The following images Figure 15.2, Figure 15.3, Figure 15.4 show the PCB layout used in the design, including the top and bottom routing diagrams. We used surface mount resistors and capacitors(SMD) while for other components, through hole technology(THT) was selected for integration.
The PCB design follows the following specifications:
- Minimum trace width: 0.635 mm
- Placement of decoupling capacitors close to op-amps
To validate the circuit’s performance, we tested the same design using the ASLK Pro kit and Red Pitaya as signal source and oscilloscope. The following picture Figure 15.5 shows the portion of the ASLK Pro board used to construct the biquad filter circuit.
Red Pitaya was used to inject signals and monitor the filter output. The board acted as both a function generator and an oscilloscope. A basic block setup is given in the illustraion Figure 15.6 below for better understanding.
We tested the circuit using:
- Input waveforms: sine waves at frequncies ranging from 500 to 2000Hz.
- Amplitude: 1 V peak-to-peak (OUT1)
- Visualization: Red Pitaya’s web scope and exported .csv data
In this section, we describe the methods used for testing the biquad filter across different platforms:
Simulation:
.ac dec directive.ASLK Pro Kit:
From the csv file we can get - Center frequency (f₀): 1000 Hz - Peak amplitude: 20.1755 dB
For calculating the bandwidth, we need to find the frequencies where the response is 3dB below the peak. Upper -3dB point would be 1056.6 Hz and lower -3dB point would be 954.8 Hz. So bandwidth is the difference between them. It is: \[ BW = |f_{upper} - f_{lower}| \] BW= 1056.6-954.8 = 101.80 Hz
Now to find the quality factor (Q)
\[ Q = \frac {f_0} {BW} \] \[ Q = \frac {1000}{101.80} \] Q = 9.8
From the csv file we can get - Center frequency (f₀): 977.01 Hz - Peak amplitude: 19.17 dB
For calculating the bandwidth, we need to find the frequencies where the response is 3dB below the peak. Upper -3dB point would be 1076.837 Hz and lower -3dB point would be 921.75 Hz. So bandwidth is the difference between them. It is: \[ BW = |f_{upper} - f_{lower}| \] BW= 1076.837-921.75 = 154.96 Hz
Now to find the quality factor (Q)
\[ Q = \frac {f_0} {BW} \] \[ Q = \frac {977.01}{154.96} \] Q = 6.30
The possible causes would be: - KiCad uses ideal components, while real resistors/capacitors have tolerances (e.g., ±5%–10%). - PCB traces add stray capacitance (1–5 pF) and inductance, altering filter response. - KiCad assumes perfect power; real supplies have ripple.
The frequency response of the biquad filter across simulation and ASLK Pro implementation shows expected filter behaviors for all configurations (LPF, HPF, BPF, BSF). In practice, both the LPF and HPF exhibited steeper slopes compared to simulation, likely due to parasitic effects and non-ideal op-amp behavior. The BPF and BSF responses confirmed correct center and notch frequencies around 1 kHz, with minor deviations in amplitude and phase caused by component tolerances and real-world limitations.
Transient analysis for each filter type demonstrated good alignment between simulation and physical implementation. LPF and HPF showed clean responses with minor differences in rise time and settling due to hardware constraints. The BPF displayed underdamped oscillations as expected, while the BSF combined characteristics of LPF and HPF with slightly altered phase behavior in the practical setup. Overall, the filters behaved as intended with predictable real-world variations.
During our course of the project work, we have faced a few issues while implementing the biquad filter in ALSK as well as in KiCAD while designing the schematic diagram and the PCB. Some of them are listed below.
Initially, while implementing the circuit in ALSK pro kit, the output we could get in using the red pitaya was just some noises for all the filter types. When observed closely we found out the need to connect a wire physically in the board from non-inverting terminal of the op-amp to the ground for the two op-amps in op-amp type II full section of the ALSK pro board. Whereas the other two op-amp were internally connected to ground.
Both the PCBs that have designed didn’t give us any output as the we try to measure it using the red pitaya.
On observation it was found that the PIN no 5 and PIN 6 got interchanged in KiCAD as shown in Figure 17.1 even after importing the netlist from the schematic which was working.
Another mistake that occured was while designing the schematic diagram in PCB, the op-amp imported had the inverting terminal connected to the ground. Even after connecting the whole circuit with that configuration, the schematic diagram in KiCAD gave the output and so didn’t cross checked for any mistakes. Thus ending up downloading the same netlist and designed a PCB with changed pins. Even then tried to obtain the output by giving externals connection vai a bread board, still no results were obtained.
The design and implementation of the second-order universal biquad filter provided critical insights into analog signal processing, specifically in how component selection and topology influence filter behavior. Through both simulation and hardware implementation, it became clear how closely the theoretical transfer functions—derived using Laplace and frequency-domain analysis—align with real-world performance. However, discrepancies due to parasitic effects, op-amp limitations, and component tolerances were evident in the practical responses, highlighting the importance of accounting for non-idealities in real-world systems.
During the project, several mistakes were made, particularly in calculating component values to achieve the target quality factor (Q = 10). Early designs also neglected phase behavior, which became apparent during Red Pitaya measurements. These issues required redesign and additional simulation runs. These challenges, while initially frustrating, were ultimately educational—they deepened our understanding of pole-zero placement, transient response, and filter sensitivity. The iterative process reinforced the importance of simulation-validation cycles and careful documentation throughout the design workflow.