# How does bandwidth relate to the bitrate?

This might be a really trivial question, but I can't wrap my head around it.

In almost every textbook, we're told that bandwidth (among power and noise), is the factor for both range and bitrate. I've been struggeling to find out why.

I'm aware of the Shannon-Hartlet theorem, but I cannot understand why. With this theorem, the capacity is equal for me transmitting data on a channel from 115-120 MHz and 1150-1155 MHz, since the bandwith is both 5MHz. Why? Am I misunderstanding the term bandwith? Is it because I fx. send my bits on relative 1, 2, 3, 4 and 5 MHz of the bandwith?

And why does the frequency not have any influence? Let's assume I can encode 2 bits into every symbol, wouldn't I be able to transmit 10 times the amount of bits per second on the higher frequency rather than the low frequency, since I have 10 times the oscilations?

I hope somebody can help me understand why bandwidth is so important, and frequency is not.

• so, let me ask the opposite question: Why do you think the frequency should have an influence (long story short, it doesn't)? It's hard to argue against something that is wrong, but not backed by arguments. Imagine this: I say: "The phase of the moon has to be important to the speed of my car. But all mechanical engineering science says it should not matter. Why?" without explaining why I think the phase of the moon would make a difference. – Marcus Müller Aug 31 '17 at 18:32
• and: "bandwidth" is actually "how much change per time is in this signal". So if you modulate a carrier (you don't "send bits on frequencies") ten times as fast, you actually get ten times the bandwidth. So, either you're confused about the definition of bandwidth, or the definition frequency, or the definition of what you mean with "send my bits", but in any case, this is hard to answer without you making clear why you would be able to transport more bits on the higher frequencies – the "I've got more oscillations" part doesn't make sense. – Marcus Müller Aug 31 '17 at 18:36
• I belive I was under the impression, that the carrierwave was limiting at what frequency I could modulate my signal. Though - why does the bandwidth rise when I modulate faster? Let's say my carrier is 1KHz, If I then have a bandwidth of 100 Hz, does that mean I use the frequencyband between 1-1.1 KHz? And when the bandwidth is higher, I can then modulate more bps on to the carrier? – Benjamin Larsen Aug 31 '17 at 18:57
• Math. Do it! :-D If you've heard of the Shannon-Hartley theorem, then you've probably also heard of the Fourier Transformation, right? So, take a fast modulated signal, let's say, a square wave with frequency 1 kHz (imagine you're sending 1,0,1,0,1,…) and transform it to frequency domain. Do the same with a slower square wave (let's say, 100 Hz). Compare results. – Marcus Müller Aug 31 '17 at 19:02
• Oh. Shoot. Now it makes sense... Hahaha. Oh, this is so akward. I haven't done any singal-courses for like two years, and a summer break didn't make it better. Haha! Thank you, Marcus! – Benjamin Larsen Aug 31 '17 at 19:41