Bandwidth and Channel capacity
Above is a basic analog sine wave that will be used to show the relationship between bandwidth and channel capacity.
A wave as shown above can be altered (modulated) to carry information. The basic unit of information, for the present, is one bit, a single binary digit. Frequency of a wave is measured in Hertz, in honor of Heinrich Hertz whom recognized and generated the first radio waves (electromagnetic waves). Note the wave period above: Simply put, one Hertz = one period/second. For example an AM radio signal could be at 600 kilo Hertz typically abbreviated as 600 kHz.
Say you had a device that could make radio waves from 600 kHz to 2400 kHz. This device has a bandwidth of 1800 kHz. If the device gave you a frequency range of 1000 kHz to 1500kHz you would have a usable bandwidth of 500 kHz.
So bandwidth is the difference between the upper and lower frequency you are allowed to work width.
Channel capacity can be measured in bits/second, but be careful, channel capacity is NOT necessarily the same as the wave frequency as I will demonstrate.
Now I need to introduce the fundamental work of Claude Shannon whom developed the mathematical relationship between channel capacity and bandwidth over a real channel. Here is the formula we will use:
channel capacity = bandwidth X base 2 log (1 + S/N) where S is signal strength in linear power watts and N is signal noise in linear power watts. (decibel is non linear power and needs conversion to watts)
You might not have encountered base 2 log, foe example 10=base 2 log(1024) or 2 exponent 10 =1024. We need these base 2 units to stay binary.
Real life example:
My hearing aids have a range of about 300 Hz to 3000Hz thus a bandwidth of 2700Hz. The devices are micro digital processors. The S/N ratio is 1000/1 so we apply Shannon:
Channel capacity = 2700 X base 2 log (1001) or channel capacity = 2700 X 9.967 which is 29.9 k bits/second.
So my hearing aids have available to process 29.9 kbit/sec. This is a maximum for the bandwidth. The important thing to realize is we can calculate the maximum channel capacity using Shannon's formula and it applies to any transmission medium with, of course, proper measurement units.
The Digital World
Let's consider the terms used for bandwidth as applied to the digital internet where web browsers and email allow us contact to the world wide web. The fundamental description is simply in bits/second. The actual use of the term "bandwidth" has been changed for simplicity. You are actually being provided with the available channel capacity your provider is selling you but it may be referred to as bandwidth. Channel capacity for a specific medium is finite. For example a typical fiber optic cable strand is 100 gigabits/second and you can purchase from a provider, for example, 50 gigabits/second for a specific charge. Clearly the greater this digital bandwidth is the faster your computer should run on the internet. Things are not that simple. Internet providers typically "overbook" their systems because all users are not expected to be online at the same time. A common cyber attack exploits this vulnerability. This is called a DNS or denial of service attack. A miscreant hacker takes over several computers and routers with malware and bombards nonstop some site with information messages.
Users will see the site as very slow or not at all. All bandwidth is gobbled up by the hacker.
For a few more details on common web based information movement check out the column to the right ---->
Routers, Coding and Noise
Do you get all the channel capacity your internet provider sells you? The answer varies and is rarely consistent from a practical use standpoint. Your internet provider can only guarantee this channel capacity to the first router in the network or until the information packet leaves their system. Oops! What is an information packet? You see the http header which stands for hyper text transfer protocol. This is the primary coding protocol that groups a fixed "packet" of information bits with a leading header of bits that tells the router where it is going and a trailing end group with information ABOUT the information packet and to indicate the end. This is a simplification but good enough for this discussion. In other words the information you want to send or receive has overhead to make sure it gets to its destination correctly and if detected in error insures it gets sent again. This overhead uses up some of your channel capacity. Noise is a physical reality and if your packet gets errors due to noise they get resent.
The WWW does not expect every possible user to use the facility at the same time. There isn't sufficient capacity or bandwidth. So if you purchase more channel capacity you may see greater data rate or it may not be what you expect. All this depends on location and provider. Only pay for what works for you. There are web sites that will measure your data rate. Do this before an upgrade and after the upgrade to see if you spent wisely.