Bandwidth VS Power VS Distance

[Foxxz]

My brain is having a hard time wrapping itself around a concept here and people have told me I'm wrong and I can't find equations that say otherwise so maybe you can help me.

You have a 100W transmitter. You transmit a 100Hz wide signal. I feel like the amplitude is 1W/Hz and your signal strength is strong and should go further than say...
You have a 100W transmitter. You transmit a 1,000,000Hz wide signal. I feel like the amplitude is 0.0001W/Hz and your signal strength is weaker overall for the same distance.

Calculating RF path loss doesn't seem to take into account signal bandwidth. It says for a given distance/frequency/power both of those signals will attenuate the same (or thereabouts given the low/high frequency edges).

So is the only difference then on the receiver side where the Nyquist noise floor comes into play based on receiver sensitivity VS bandwidth? To get better receiver sensitivity do I need to narrow my receiver bandwidth? IE - Am I going to better hear that 100Hz signal better if I'm not pulling in 1,000,000Hz? I'm guessing yes since I'm having to deal with the additive or average noise floor of the entire 1,000,000Hz VS just 100Hz of noise floor?

Even given receiver/bandwidth sensitivity I just can't see how the signal attenuates the same no matter if the power is spread over 100Hz or 1,000,000Hz. Help me out here.

[Foxxz]

Is this what I'm looking for? It seems close but im not quite sure

https://broadbandlibrary.com/total-power-and-power-spectral-density/

https://www.itu.int/en/ITU-R/space/WRS16space/WRS-16%20avg%20BW.pdf

[Kim Christensen]

Think of a 25watt CW signal... That's 25 watts power at "one" frequency.
Then think of an 25 watt FM modulated signal where the baseband signal is a 0.1Hz sinewave that shifts the carrier slowly between 100Mhz to 100.1Mhz  (100Khz bandwidth)
Basically you have a CW signal that drifts back and forth between 100Mhz and 100.1Mhz every 10 seconds. Now do it faster.

[tggzzz]

Think of a 25watt CW signal... That's 25 watts power at "one" frequency.
Then think of an 25 watt FM modulated signal where the baseband signal is a 0.1Hz sinewave that shifts the carrier slowly between 100Mhz to 100.1Mhz  (100Khz bandwidth)
Basically you have a CW signal that drifts back and forth between 100Mhz and 100.1Mhz every 10 seconds. Now do it faster.

Now do the same over a much wider bandwidth, so that the CW power at any wavelength is below the receiver noise level.

Provided you can determine what the signal ought to be at any time (i.e. lock onto the signal), you can recover the signal from below the receiver's noise level. Yup, that's called spread spectrum

The OP may care to understand the definition of "signal" in the Shannon and Nyquist equations. It is not related in the slightest to the carrier frequency

[gf]

To get better receiver sensitivity do I need to narrow my receiver bandwidth?

The problem is: If you make the receiver bandwidth narrower than the occupied bandwidth of the useful signal, then you will also lose parts of the useful signal (which you probably don't want). So the only thing that really helps is a narrower bandwidth of the signal (then the receiver bandwidth can be narrower, too), but this means that it can carry less information per unit of time.

[tggzzz]

To get better receiver sensitivity do I need to narrow my receiver bandwidth?

The problem is: If you make the receiver bandwidth narrower than the occupied bandwidth of the useful signal, then you will also lose parts of the useful signal (which you probably don't want). So the only thing that really helps is a narrower bandwidth of the signal (then the receiver bandwidth can be narrower, too), but this means that it can carry less information per unit of time.

Note, however, that in information theoretic terms (i.e. Shannon's Law) the signal bandwidth is not the same as the bandwidth occupied by the transmitter/receiver.

The classic example of that is DSSS where "The direct-sequence modulation makes the transmitted signal wider in bandwidth than the information bandwidth." https://en.wikipedia.org/wiki/Direct-sequence_spread_spectrum

[gf]

To get better receiver sensitivity do I need to narrow my receiver bandwidth?

The problem is: If you make the receiver bandwidth narrower than the occupied bandwidth of the useful signal, then you will also lose parts of the useful signal (which you probably don't want). So the only thing that really helps is a narrower bandwidth of the signal (then the receiver bandwidth can be narrower, too), but this means that it can carry less information per unit of time.

Note, however, that in information theoretic terms (i.e. Shannon's Law) the signal bandwidth is not the same as the bandwidth occupied by the transmitter/receiver.

The classic example of that is DSSS where "The direct-sequence modulation makes the transmitted signal wider in bandwidth than the information bandwidth." https://en.wikipedia.org/wiki/Direct-sequence_spread_spectrum

Yes, of course. I did not want to go that far, as even the "simple case" was obviously not completely understood.

[A.Z.]

a question; how is the signal radiated, I'm asking it, since the transducer plays a role

just to make an example, let's say we are using a frequency of 666MHz and our antenna has a radiation solid showing that it mostly radiates at near vertical angles...

[tggzzz]

To get better receiver sensitivity do I need to narrow my receiver bandwidth?

The problem is: If you make the receiver bandwidth narrower than the occupied bandwidth of the useful signal, then you will also lose parts of the useful signal (which you probably don't want). So the only thing that really helps is a narrower bandwidth of the signal (then the receiver bandwidth can be narrower, too), but this means that it can carry less information per unit of time.

Note, however, that in information theoretic terms (i.e. Shannon's Law) the signal bandwidth is not the same as the bandwidth occupied by the transmitter/receiver.

The classic example of that is DSSS where "The direct-sequence modulation makes the transmitted signal wider in bandwidth than the information bandwidth." https://en.wikipedia.org/wiki/Direct-sequence_spread_spectrum

Yes, of course. I did not want to go that far, as even the "simple case" was obviously not completely understood.

Accepted.

However the OP's picture included UWB, GPS, 802.11n, 802.11ac
Good luck trying to understand UWB with it's enormous bandwidth and miniscule peak power
GPS's DSSS isn't much easier for a beginner to understand, and even if you know what is happening, seeing bits dug out of noise is viscerally enthralling.

[A.Z.]

well in such a case (digital signaling) the error recovery may help, but won't play miracles

[rhb]

FWIW 

If you're coming to FDIM I've organized a SIG meeting on CCW/QRSS/DSSS.

I'll start the meeting with a 10 minute review of Fourier theory in graphical form to make certain everyone is using the same terminology.  No equations more complex than vector addition and multiplication.  The messy stuff will simply be sketches of the time and frequency domain results.

There are 3 relevant parameters, signal BW, data rate and ERP.  I usually state this as time, BW and ERP.  To avoid having 2 BWs, data and signal, I substitute the inverse of the data rate in the form of symbol duration time.

I'm working on algorithms to implement antipodal transfer of a 2 kB message transfer at << 1 W ERP overnight.  However, primary SIG focus will be CCW/QRSS.

I'm presenting pieces of this in the qex@groups.io list.  Please join if you're interested.

Have Fun!
Reg

[radiolistener]

You have a 100W transmitter. You transmit a 100Hz wide signal. I feel like the amplitude is 1W/Hz and your signal strength is strong and should go further than say...
You have a 100W transmitter. You transmit a 1,000,000Hz wide signal. I feel like the amplitude is 0.0001W/Hz and your signal strength is weaker overall for the same distance.

yes, the signal power is spread across signal bandwidth.
If you want to keep the same power for all frequencies within more wide bandwidth, you're needs to increase power.

Calculating RF path loss doesn't seem to take into account signal bandwidth. It says for a given distance/frequency/power both of those signals will attenuate the same (or thereabouts given the low/high frequency edges).

The RF path calculation just estimates how power from isotropic radiator is reduced with distance. It is reduced because radiated power is spread across entire sphere surface all around isotropic radiator. For real antenna with some radiation pattern it just add some gain in the direction of the main lobe. Longer distance means more large sphere and as result the power received with fixed area receiver antenna will be less.

If you build receiver antenna as a sphere all around transmitter, the power loss on the receiver will be zero, because it will receive all radiated power independently on the distance between transmitter in the center and receiver sphere around it. 

As you can see, the signal bandwidth is not needed for RF path loss calculation.

To get better receiver sensitivity do I need to narrow my receiver bandwidth?

Yes, the receiver sensitivity is limited with environment noise floor and noise figure of receiver RF frontend, but you can improve sensitivity by reducing bandwidth. This is possible, because noise power is spread across entire spectrum. So, if you reduce bandwidth, you're cutting part of noise power outside bandwidth of your interest. Since noise power is reduced, you're get better sensitivity. More narrow bandwidth means that you remove more noise power and get more high sensitivity. This is how processing gain works.

But there is a con of more narrow bandwidth - it means that you're needs more time to transmit the same amount of information, so it leads to smaller transmission speed.

Also more narrow bandwidth become more sensitive to precise tuning on exact frequency and requires more longer time to detect signal.

Even given receiver/bandwidth sensitivity I just can't see how the signal attenuates the same no matter if the power is spread over 100Hz or 1,000,000Hz. Help me out here.

The signal attenuated because less power arrived on the same size antenna placed at longer distance. This is happens because radiated power is flying as a sphere from transmitter, so if you want to not loss signal power on longer distance, you're needs to use more large antenna to collect the same signal power. If you use antenna with the same effective surface, you will get smaller part of power.

See picture:


As you can see, the same power from transmitter is distributed across more large surface area at longer distance.

Signal bandwidth and carrier frequency doesn't matter here. When you calculate RF path loss, you're just calculate relation between two surface areas - for a sphere with radius equals to the specific distance and for receiver antenna.

When using antenna with high directivity, you can use the same calculations for entire sphere as used for isotropic radiator just apply antenna gain correction for transmitter power at specific direction.