# What does bandwidth mean in general, and in the context of the following examples?

Some examples :
1.The bandwidth of an operational amplifier
2.The bandwidth of a transmitted amplitude modulated signal
3.The bandwidth of a signal used in coaxial cables / optic fibre cables
4.The bandwidth of a signal used for satellite communication

I was recently reading about the usage of two different frequencies (uplink and downlink) for satellite. The reason that both of these frequencies were in the order of GHZ was because high frequencies mean large energies, so large range, and high frequencies also mean large bandwidths. I'd like to learn what 'bandwidth' generally means, and also how it applies to the examples I've given.

• Do you understand the difference between carrier frequency and modulated signal bandwidth? In general, bandwidth is the difference between the lowest and highest frequencies of a signal. For example, for old analog telephony, the bandwidth of the voice signal was of around 3kHz, from 300 Hz to 3.3kHz (baseband) – Claudio Avi Chami May 9 '17 at 17:52
• Yes, the bandwidth is twice the maximum frequency of the modulating signal, but the carrier frequency is just one frequency. However, I do not know why it is useful.. Like, what is the purpose for introducing this quantity? – John May 9 '17 at 18:04
• Sorry but no, you are a bit confused. I recommend you to go and read a good book on signal theory. Bottom line: the bandwidth of a signal is proportional to the quantity of information it can contain. A video signal is much wider than an audio signal because the quantity of information on a video signal is GENERALLY much bigger than in audio – Claudio Avi Chami May 9 '17 at 18:07
• And I say generally because a black screen doesn't convey much information, but a video signal has the CAPABILITY of transporting a very detailed picture. The BW of a signal or of a device gives us a measurement of how much information it can process. – Claudio Avi Chami May 9 '17 at 18:07
• But how is this related to the frequencies of signals used in satellite communication, or other forms of communication like optic fibre cables? – John May 9 '17 at 18:18

Bandwidth is a term used in describing the analog behavior of a system. Whenever you have a bandwidth, you have a band -- a range of frequencies upon which you are transmitting. The bandwidth is the difference between those frequencies.

Specifically addressing your question from the comments, there are practical reasons why we use slices of bandwidth from high frequencies rather than low frequencies.

Thank you for the answer. In your last paragraph, is there any problem if we assign 0 HZ to 10,000 MHZ to 100 people, each 100 MHZ wide, rather than 20 GHZ to 30 GHZ?

You can do this. It will work. However, there are physics reasons not to. The primary reason you don't allocate low frequency bandwidth this way is that our filters typically operate in terms of relative frequencies. A simple 1st order lowpass filter will provide 20dB of attenuation per decade. That means if you have a lowpass filter with a corner frequency of 100MHz, it will theoretically pass 100MHz through perfectly, 1000MHz through with 20dB of attenuation and 10000MHz through with 40dB of attenuation.

If you only wanted to assign a single band to each person, this wouldn't cause too much of an issue. However, what if those people wanted to share bandwidth? What if you wanted to have a radio that could tune to different radio stations? Radio stations require a bandwidth of about 20kHz. You could assign one of them the band from 20-40kHz, then one to 40-60kHz, the none from 60-80kHz and so on. If you had 10 such channels, you'd need 200kHz of bandwidth, ranging from 20kHz to 220kHz. That's about 3.5 octaves. If, instead you had started the first radio station at 100MHz, then 100.020MHz, 100.040MHz and so on, you would still need 200kHz of bandwidth, but it would range from 100Mhz to 100.220Mhz. That's only 0.003 octaves! It's much easier to design an antenna to resonate well over 0.003 octaves than it is to make an antenna that resonates well over 3.5 octaves.

The other big reason to assign higher frequency bands is uniformity. The effects of the atmosophere and other interactions with the environment are pretty well distributed in a logarithmic space. Why? It's the same reason as above: the effects tend to operate proportional to the frequency just like our simple 1st order lowpass filter did.

When designing an RF system, we typically want to find a window where the attenuation is acceptable for our application. If we need a fixed amount of bandwidth (say 200kHz), its easier to find a window of 200kHz with the same properties in high frequencies than it is to find such a simple window at low frequencies.

One final issue to consider: size. Lower frequencies means larger wavelengths. Larger wavelengths means you need larger antennas to efficiently transmit and receive.

One example of low frequency use is submarines. Submarines are known to have transmitted in the ELF region -- Extreme Low Frequency. The US Navy ran a transmitter, Seafarer, which operated at 76Hz! I couldn't find anything on the bandwidth for that particular system, but the transmitting antennas had to be 56km long! The subs can't even send replies because the transmitting antennas are too big and to power-hungry for the sub!

• Thank you for the answer. Could you explain how frequency division multiplexing works? I know that it's rather vaguely related, but I'm finding it difficult thinking about the bandwidth of the signal, the radio stations, and the users at the same time. – John May 9 '17 at 23:36
• The key to FDM is assigning different bands to each user. Each band has a specified bandwidth chosen to suit the signal. Typically these bands are all chosen close together and at a high enough frequency that one piece of hardware can use any band (example: FM radio is 20kHz bands spread out in the 88Mhz to 108Mhz range). As long as the bands do not overlap, everyone can use their band simultaneously without worrying about whether someone in another band is transmitting. – Cort Ammon May 10 '17 at 0:03
• The real trick is how you convert your signal into the desired band. There are many ways to do this, some for digital signals and some for analog. The analog example of heterodyning may be a good one example to look at. It is a very old and well understood physical process for manipulating analog signals and boosting them into higher frequency bands. It can be used as part of your implementation of AM or FM or other modulation approaches. – Cort Ammon May 10 '17 at 0:05
• In your first comment, are you referring to the bandwidth of users of radios, or that of the transmitters? At this point, I've understood the method behind it, but I can't differentiate between the bandwidth of the audio signal, the bandwidth of the final modulated wave, the bandwidth of the users, and the bandwidths of the radio stations. – John May 10 '17 at 8:23
• To answer that question, I'll point out that there are two major "groups" of bandwidths in that answer: the bands which the hardware is capable of working with and the bands to which the hardware is tuned. The former is far larger. With that in mind, the bandwidths would be: The audio signal is roughly 15kHz wide (30Hz-15kHz), and there's two channels of that, Left and Right. For quality reasons, we'll send that as a sum channel (Left+Right) and a difference channel (Left-Right). We modulate the difference channel up so that it is centered on 38kHz, but is still 15kHz wide. – Cort Ammon May 10 '17 at 14:35

"bandwidth" in general is the width of the band, that is the difference between the highest and lowest frequency.

When talking about a signal we mean the range of frequencies used to encode information. When talking about an amplifier, cable, antenna etc we mean the range of frquencies over which the performance is acceptable.

Exactly what is meant by acceptable varies, but a common convention is to use the "-3dB" bandwidth. That is the points at which the signal power is reduced by a factor of two (signal voltage reduced by a factor of $\sqrt{2}$) from it's maximum value.

2.The bandwidth of a transmitted amplitude modulated signal

Assuming simple amplitude modulation the bandwidth of the AM signal is twice the highest frequency in the modulating signal.

This is because when two signals are multiplied you get components at the sum and difference of the two frequencies. So the lowest frequency in the modulated signal is the carrier frequency minus the highest frequency in the modulating signal and the highest frequency in the modulated signal is the carrier frequency plus the modulating frequency.

This is an inefficient modulation scheme as the information in the original signal is essentially duplicated. There are variants of amplitude modulation that try to reduce this inefficiency either by suppressing one of the side-bands of the modulated signal (SSB/VSB) or by encoding two seperate signals on different phases of the same carrier (QAM).

3.The bandwidth of a signal used in coaxial cables / optic fibre cables

As above the range of frequencies used to carry the information. Depending on the context it may also include gaurd bands added to allow for imperfect filtering.

Also for fiber note that we can talk about the electrical bandwidth (the bandwidth of the signal used to modulate the light source) or the optical bandwidth (the range of frequencies in the optical system). If the laser is being amplitude modulated then the optical bandwidth will be twice the electrical bandwidth.

In some cases people also use "bandwidth" to mean data rate. The achiveable data rate of a communication link is highly dependent on the bandwidth.

4.The bandwidth of a signal used for satellite communication

Much the same answer as above.

Why does a high carrier frequency mean a large bandwidth?

When talking about Radio systems a high carrier frequency doesn't nessacerally mean a high bandwidth but a low carrier frequency almost certainly means a low bandwidth. There are a couple of reasons for this.

One is antenna design. Generally antenna design gets harder as the ratio of highest and lowest frequencies increases. It would be virtually impossible to make an antenna that would work acceptablly over the range of 0Hz to 100MHz but it is relatively easy to make one that will work acceptablly over the range of 1 GHz to 1.1 GHz.

The other reason is that radio spectrum is a shared resource. Sure if you were a dictator you could assign one service 0Hz to 100MHz but what about everyone else? OTOH between 20GHz and 30GHz there would be room for 100 channels each 100 MHz wide.

• Thank you for the answer. In your last paragraph, is there any problem if we assign 0 HZ to 10,000 MHZ to 100 people, each 100 MHZ wide, rather than 20 GHZ to 30 GHZ? – John May 9 '17 at 20:44

With respect to the first two:

1) If an op-amp datasheet refers to bandwidth then it is referring to the maximum frequency with which it can be used, without consideration of the constraints imposed by other components that may be used in conjunction with the op-amp.

2) The bandwidth of an AM signal is the highest frequency that results when the center frequency is modulated with information (mixed with a voice, for instance) minus the lowest frequency that results when the center frequency is modulated. It can vary depending on the context, but it generally reflects how large a chunk of the radio spectrum is occupied by the AM signal. A single pure radio (carrier) signal with no modulation will theoretically occupy only 1 frequency. But when a modulating signal is piggy-backed onto it, a range of frequencies above and below the carrier are produced. The magnitude of that range between the highest and lowest produced frequencies is the bandwidth.

As an example, in AM broadcast radio there were only so many public radio frequencies to transmit on, you could visualize an old radio dial being limited, ranging from 540 to 1600 (representing kHz). Each station is assigned a frequency at least 10 (kHz) away from it's nearest neighbor on the dial. As long as the assigned center frequency (a carrier), when mixed with the modulating information (voice or music maybe) doesn't produce any frequencies outside of that allotted bandwidth of 10 kHz then they won't interfere with their neighbors on the dial. When two frequencies are mixed they produce other frequencies. In this example the other frequencies will be clustered very close to the carrier frequency, above it and below. The bandwidth is the highest frequency in the cluster minus the lowest frequency in the cluster, or how much room they take up on the radio dial. Keep in mind that the frequencies which are present are dynamic and change and shift around rapidly as the type of modulating information (music or whatever) changes. In this example the allotted bandwidth allowed to the station and the measured instantaneous bandwidth may be different. If there is a moment of silence then the instantaneous bandwidth may be 500 Hz, but the sound of a piccolo playing might increase the instantaneous bandwidth to 6 kHz.

• Could you elaborate on the ' it represents how large a chunk of the radio spectrum is occupied 'part? – John May 9 '17 at 18:17
• @Entrepreneur - While your comment is OK for some cases, and specifically is right for comercial AM it is not taking into account many modulation types like SSB and VSB... Not to speak of many other modulation schemes (like FM) where the modulated signal BW is much bigger than the baseband signal BW – Claudio Avi Chami May 9 '17 at 18:18
• @Entrepreneur I can't understand your example. Could you use a particular bandwidth (50 kHz ) as an example to illustrate how more people can 'fit' in the radio band if the bandwidth is lower? – John May 9 '17 at 20:48
• What I meant to convey is that if each transmitter utilized a narrower bandwidth (a smaller slice of the spectrum) then they could be tuned closer together in frequency without overlapping and interfering with each other. – Entrepreneur May 10 '17 at 3:29