What Is Bandwidth?

This article explores the surprisingly complicated details associated with a word that we frequently use but perhaps don’t fully understand.

The term “bandwidth” arises in a wide variety of engineering discussions. Analog circuits, test and measurement, RF systems, digital communications, computing—the concept of bandwidth is integral to modern electronic technology.

So ... what does it mean?

I sincerely wonder how many of us could immediately produce a coherent definition or explanation of the word “bandwidth.” Much of the difficulty originates from the fact that the word has several meanings. Another source of confusion, or at least uncertainty, is found among subtle details that we can sometimes ignore.

 

The Definition of Bandwidth: The Width of the Band

Whenever possible, I like to start with a definition that is based on a term’s constituent words, or on the etymology when constituent words are not readily recognizable. The term in question is obviously composed of “band” and “width.” This “band” refers to a band, or range, of frequencies, and “width” refers to the appearance of this band when viewed in the frequency domain.

 

A frequency-domain representation of a signal composed of two single-frequency sine waves.

 

Narrowband vs Wideband

This brief analysis has already uncovered a problem. Let’s say we’re taking a stroll in the woods and I point to a stream. “Is that stream wide?” I ask. There is, of course, no answer to this question. Sure, it’s wide for the tadpole that’s trying to swim across it, but it wouldn’t be wide for an elephant.

Likewise, if we describe a bandwidth as wide or narrow, we’re actually comparing the bandwidth to something else. If everyone understands the point of comparison, there shouldn’t be any confusion, but it’s good to remember that “wideband” and “narrowband” might mean very different things to, for example, a researcher working with ultra-wideband systems and an analog designer accustomed to low-noise op-amp circuits that don’t need to process frequencies greater than a few tens of kilohertz.

In many cases, it makes more sense to actually specify the bandwidth. This certainly eliminates the ambiguity of describing a bandwidth as “wide” or “narrow,” but it’s by no means a perfect solution.

How to Choose a Band

If someone hands you an amplifier module and says that it has a bandwidth of 200 kHz, what does that mean? Presumably, some prominent aspect of the amplifier’s frequency response involves frequencies covering a range of 200 kHz. That sort of vague information doesn’t belong anywhere near an engineering project, though, so let’s look more closely.

The bandwidth of an amplifier or filter does not specify the range of frequencies for which the circuit is functional, if “functional” means “able to produce some kind of output signal.” Rather, it specifies the range of frequencies for which the circuit meets some performance criterion. The most common criterion is based on the –3dB frequency. A reduction of 3 dB in magnitude corresponds to 50% reduction in power, and this has been chosen as a convenient way to identify the bandwidth.

 

 

Band-Pass Filter Bandwidths?

For a low-pass filter, then, a 200 kHz bandwidth indicates that 200 kHz is the frequency at which the circuit suppresses half of the signal power, and that all frequencies below 200 kHz have less than 50% power suppression.

It’s important to understand that bandwidth could mean something else in this context. Maybe a device will provide adequate performance even when the input signal is reduced in power by 80%. In this case, it would be feasible to define the bandwidth as extending from 0 Hz to the frequency at which the filter suppresses 80% of the power.

What then, is the bandwidth of a high-pass filter?

If someone tells you that a high-pass filter has a 200 kHz bandwidth, feel free to reply with a blank stare. If we apply the low-pass-filter logic to a high-pass response, the band extends from the –3dB frequency to infinity. I suppose the bandwidth of a high-pass filter could be the width of the band of frequencies that experience more than 50% power suppression, but I don’t think that people use the term this way.

The bottom line here is that bandwidth is a fairly nebulous term, even in the limited context of amplifiers and filters. When in doubt, ask for clarification.

Bandwidth in Radio-Frequency Applications

The design of RF systems involves extensive analysis of how signal frequencies change and interact, and references to bandwidth are by no means uncommon. Unfortunately, “bandwidth” is not a particularly straightforward term in the RF world.

 

The -3dB Bandwidth

First, we have the –3dB version of bandwidth. If a baseband signal is being described, I would assume that bandwidth indicates the range of frequencies from 0 Hz to the frequency at which the frequency-domain representation of the signal has a magnitude that is 3 dB lower than the maximum magnitude.

 

Modulated Signals and Channel Spacing

Next, we have bandwidth in the context of modulated signals and channel spacing. The issue here is the necessary frequency separation for modulated signals that might interfere with one another.

If a certain wireless standard uses channels that have a 1 MHz bandwidth, does this mean that the entire spectrum of one modulated signal is contained within a 1 MHz band? No, because small amounts of energy inevitably extend far beyond a spectrum’s center frequency.

One of my textbooks says that RF engineers commonly use the “99% bandwidth,” i.e., a frequency range that contains 99% of the spectrum power. The point here is that performance will not be significantly degraded if channels are spaced such that only 1% of signal power is interfering with adjacent channels. This diagram conveys the general idea:

 

 

Negative Frequencies

Finally, there’s the issue of negative frequencies. Sometimes, bandwidth includes negative frequencies; other times, it doesn’t.

For example, if we’re talking about a baseband signal, bandwidth might refer to a frequency range extending from 0 Hz to some (positive) frequency related to the baseband spectrum. However, if that baseband signal is shifted to a higher frequency via (for example) amplitude modulation, the negative frequencies are shifted, as well, and now the bandwidth of the modulated signal is wider than the bandwidth discussed in the previous sentence.

 

 

Bandwidth in Other Contexts

If this article has made you more aware of the complications associated with the concept of bandwidth, I hope that it has also helped you to understand these complications and how to deal with them. In the next article, we’ll continue this discussion by exploring bandwidth in the context of digital signals, communication systems, and processors.