Electronic Filters: An Introduction

Electronic filters are everywhere, shaping signals, reducing noise, and helping circuits operate reliably. Learn how low-pass, high-pass, band-pass, and band-stop filters work, and see why even simple first-order circuits are so useful in real-world electronics.

Editor's note: This is excerpt from the second chapter of the book, Introduction to Electronic Filters: Learn RC and RL Filters with Hands-On Circuits and Simulation (P. Dalmaris, Elektor, 2025).

Introduction to Filters

Filters are essential building blocks in the design and analysis of electronic circuits. They allow engineers and hobbyists to control which signals pass through a system and which signals are attenuated or blocked. At their core, filters shape the flow of electrical energy, enabling the separation, enhancement, or suppression of diff erent parts of a signal.

Filters are used across countless applications. In audio systems, filters can remove unwanted noise or adjust the tonal quality of sound. In communication systems, they are vital for selecting specific frequency bands. In power electronics, filters suppress voltage spikes and reduce electromagnetic interference. Filters are critical components of virtually all non-trivial electronic systems, and this is why a solid understanding of their behaviour is so important.

Filter Applications

To give you a sense of the wide application of filters in all sorts of gadgets, I have constructed the table below.

Example applications of Filters — Example applications of filters.

Classification of Filters

In the broadest sense, filters can be classified into two main categories:

Analog filters operate directly on continuous-time signals using resistors, capacitors, inductors, and active components like operational amplifiers.
Digital filters work on discrete-time signals, manipulating digitized data using algorithms implemented in software or digital circuits.

Further classification is based on frequency behaviour:

Low-pass filters allow low-frequency signals to pass while attenuating high frequency signals.
High-pass filters allow high-frequency signals to pass while attenuating low frequency signals.
Band-pass filters allow a specific range of frequencies to pass while attenuating frequencies outside this range.
Band-stop filters attenuate a specific range of frequencies while allowing others to pass.

Components in First- and Second-Order Filters

The fundamental components used to build analog filters are familiar to you from the "Introduction to Electronics" course:

Components used in first and second order filters — Components used in fi rst and second order filters

First-order filters typically use one reactive component (either a capacitor or an inductor) and one resistor. These simple circuits introduce a frequency-dependent behaviour that creates a gradual transition between passband and stopband.

Second-order filters introduce a second reactive component. This addition allows for steeper transitions and more selective frequency control. For example, a second-order lowpass filter might use two capacitors and two resistors, or one inductor and one capacitor combined with resistors.

Later in the book, you will see examples of how specific combinations of these components create diff erent types of first-order filters.

Knowledge Prerequisites

If you completed my course "Introduction to Electronics", you already have a strong foundation for understanding how filters work:

You know how resistors, capacitors, and inductors behave individually in a circuit.
You are familiar with concepts such as voltage division, time constants, and impedance.
You have seen how capacitors block DC signals and pass AC signals, while inductors do the opposite.
You have used Ohm's Law, Kirchhoff 's Laws, and basic circuit analysis techniques to solve practical problems.

First-order filters naturally extend these ideas. For instance:

A simple RC low-pass filter is just a resistor and a capacitor arranged to favour low-frequency signals.
An RL high-pass fi lter is a resistor and an inductor arranged to favour highfrequency signals.

Second-order filters build upon this even further, requiring you to combine what you know about how capacitors and inductors behave when they interact together in more complex networks.

Throughout this book, you will see how familiar principles are applied in new ways to design and analyse filters, and you will acquire the additional mathematical tools needed to work with more advanced concepts.

Why Focus on First-Order Filters?

This book focuses specifically on first-order analog filters because they are the most accessible and versatile type of filter:

Main attributes of first and second order filters — Main attributes of first- and second-order filters

First-order filters are easy to design, analyse, and implement. They provide a solid entry point into the world of signal filtering without requiring complex mathematics from the start. As you move through this book, you will learn the necessary mathematics and design techniques needed to create your own first-order filters confidently. The step-by-step approach ensures that every new concept builds naturally on what you already know.

First-Order Filters in Real-Life Applications

First-order and second-order filters are far more than academic exercises. They are essential tools in modern electronics, shaping signals, protecting circuits, and enabling communication, control, and precision. By mastering first-order filters, you gain practical skills that are directly useful across a wide range of real-world applications. The concepts you are about to learn will not only help you in designing circuits, but also deepen your understanding of how everyday technologies around you operate.

First-order filters, despite their simplicity, are used everywhere because of their efficiency, low cost, and reliability. In many cases, a first-order filter is the best solution: it performs the needed function with minimum components, low power consumption, and minimal design complexity.

Here are some key reasons why learning first-order filters is well worth your effort:

Real-world relevance: Many practical circuits use first-order filters as-is, without modification.
Foundational knowledge: Understanding first-order behaviour is essential even when designing more complex, higher-order systems.
Efficient solutions: When size, power, and cost matter (which they almost always do), first-order filters are often preferred.

Second-order filters certainly have important applications, particularly when more precise or steeper filtering is needed. However, they build on the same ideas you are about to master in studying first-order filters.

Real-World Applications of First- and Second-Order Filters

Here's some everyday applications for these filters:

Audio applications:
When you adjust the bass or treble controls on a music player, simple first-order filters are shaping the sound. Capacitors and resistors modify the balance of low and high frequencies to match your preference.

Sensor inputs:
An Arduino reading a temperature sensor can receive noisy signals due to environmental interference. A small RC low-pass fi lter, using just a resistor and a capacitor, can signifi cantly improve the quality of the sensor reading.

Motor control:
When controlling a motor's speed with PWM (Pulse Width Modulation), a first-order lowpass filter can smooth the voltage and prevent the motor from producing audible whining noises.

Wireless systems:
Before transmitting or receiving wireless signals, circuits often include filters to ensure that only the desired frequencies are used. First-order filters can remove simple spurious signals, while second-order filters are sometimes used for tighter frequency control.

What About Second-Order Filters?

While first-order filters are suffi cient for many tasks, second-order filters are valuable when:

A sharper transition between passed and blocked frequencies is required.
Higher selectivity is needed, such as isolating a very narrow frequency band in communication systems.
Improved stability and control over gain and phase are critical, such as in feedback control systems.

Learning second-order filters becomes natural and much easier once you are confident with the concepts and behaviours of first-order filters.

The Four Filters: Low-Pass, High-Pass, Band-Pass, Band-Stop

In the study of electronic filters, four fundamental types of filters are commonly encountered. Each type plays a specific role in controlling how signals of diff erent frequencies are treated by a circuit. Understanding these filters will give you the ability to design circuits that emphasise or suppress signals based on their frequency content. In this chapter, we will look closely at each of these four filter types, explain what they do, and discuss how they can be realised using first-order or second-order circuits.

Low-Pass Filters

A low-pass filter allows signals with frequencies below a certain cutoff frequency to pass through with little attenuation, while it attenuates signals with frequencies above the cutoff. In other words, low-pass filters "pass the lows" and "block the highs."

Everyday Example:
In an audio system, a low-pass filter can be used to send only low-frequency signals to a subwoofer, removing unwanted higher-frequency sounds.

First-Order Implementation:
A first-order low-pass filter can be built using a resistor and a capacitor (RC circuit) or a resistor and an inductor (RL circuit). The roll-off beyond the cutoff frequency is gentle, at a rate of 20 dB per decade.

Second-Order Implementation:
A second-order low-pass filter uses two reactive components (e.g., two capacitors, or one capacitor and one inductor). The roll-off is steeper, at 40 dB per decade, providing better separation between passed and blocked frequencies.

High-Pass Filters

A high-pass filter does the opposite of a low-pass filter. It allows signals with frequencies above a certain cutoff frequency to pass through, while it attenuates signals with frequencies below the cutoff .

Everyday Example:
In audio systems, a high-pass filter can be used to remove deep, low-frequency rumble from a recording, preserving only the midrange and treble sounds.

First-Order Implementation:
A first-order high-pass filter can be constructed using a capacitor and a resistor (RC circuit) or an inductor and a resistor (RL circuit), but arranged differently from the low-pass configuration. The filter begins attenuating signals below the cutoff frequency at a rate of 20 dB per decade.

Second-Order Implementation:
A second-order high-pass filter uses two reactive components and achieves a steeper attenuation of 40 dB per decade.

Band-Pass Filters

A band-pass filter allows signals within a specific range of frequencies (a "band") to pass through while attenuating signals at frequencies lower or higher than this band. Band-pass filters are crucial when only a specific range of frequencies is needed.

Everyday Example:
In radio receivers, a band-pass filter selects the desired broadcast frequency while rejecting others.

First-Order Implementation:
A first-order band-pass filter can be made by cascading a first-order low-pass filter with a first-order high-pass filter. However, the frequency selection is not very sharp. The filter's bandwidth is relatively wide, and its ability to isolate a narrow frequency band is limited.

Second-Order Implementation:
A second-order band-pass filter offers much sharper selection, isolating a narrow band of frequencies with a steeper roll-off on both sides of the band. This is necessary when precise frequency targeting is required, such as in communication systems.

Band-Stop Filters

A band-stop filter (also called a notch filter) does the reverse of a band-pass filter. It attenuates signals within a certain range of frequencies while allowing signals outside this range to pass through.

Everyday Example:
In audio systems, a band-stop filter can be used to eliminate a specific unwanted frequency, such as the 50 Hz or 60 Hz hum from electrical mains interference.

First-Order Implementation:
A first-order band-stop filter can be made by combining a low-pass filter and a high-pass filter in parallel. Like the first-order band-pass filter, it offers only gentle attenuation and a wide transition band.

Second-Order Implementation:
A second-order band-stop filter provides a much sharper notch, attenuating a narrow range of frequencies much more eff ectively. This is ideal when targeting a specific, problematic frequency for removal.

Which Filters Can Be First-Order?

These plots depict the frequency response for the four types of filters:

And, this table summarises which of these filters can be implemented with a first or second order circuit:

Low-pass and high-pass filters are very eff ective even as first-order filters, especially when gentle fi ltering is acceptable or desired.
Band-pass and band-stop filters can be implemented using first-order techniques but perform much better when built as second-order circuits, especially when narrow frequency control is important.

Python Script for the Plots

If you'd like to experiment with the plots, feel free to play with this Python script:

Example: Compare a Filtered and Unfiltered Signal

To better understand the purpose of filters, it is very helpful to visualise the difference between an unfiltered signal and its filtered counterpart. In this chapter, we will look at a simple example using a low-pass filter. We will see, in a qualitative way, how a filter can clean up a signal by removing unwanted high-frequency noise.

We will not dive into the mathematical details yet. The goal here is to build an intuitive understanding of the effect that a filter has on a signal. You will learn the technical reasons behind this behaviour later in the book.

Example: Low-pass filter

Suppose we have a signal that consists of two components:

A slow, low-frequency component (for example, a temperature sensor reading).
A fast, high-frequency noise component (for example, electrical interference from nearby equipment).

In real circuits, this kind of situation is very common. Sensors often pick up unwanted noise from their environment. We can use a low-pass filter to allow the slow signal to pass through while reducing or removing the fast noise. Here is the basic structure of the first-order RC low-pass filter we are using:

Circuit of a first-order RC low-pass filter.

Below is a simple Python script that generates an unfiltered signal and its filtered version using a basic low-pass filter model:

This script generates a signal that combines a low-frequency sine wave with high-frequency noise. It then applies a simple first-order low-pass filter with a cutoff frequency of 20 Hz. Finally, it plots both the original and the filtered signal for easy comparison.

Here is the plot:

An unfi ltered signal (blue) passes through a fi lter and emerges as a filtered signal (orange) — An unfiltered signal (blue) passes through a filter and emerges as a filtered signal (orange).

What Do We See in the Plot?

When you run this simulation, you will notice the following:

The unfiltered signal (blue) looks very noisy and messy. It is difficult to clearly see the underlying slow movement of the signal.
The filtered signal (orange) appears much smoother. The unwanted fast variations are greatly reduced, making it easier to see the true behaviour of the original low-frequency signal.

This is the essence of what a filter does: it improves the quality of a signal by removing unwanted parts without disturbing the useful information too much.

Later in the book, you will learn how the resistor and capacitor work together to create the filtering effect. You will also learn how to calculate the cutoff frequency and how different filters affect different types of signals. For now, it is enough to see that even a very simple circuit can have a big impact on the quality of the information that a system processes.