However, dBc/Hz is the power referenced to the carrier and I'm not sure what that is in this case.
I suspect the carrier in this case is the average optical power, which they may be thinking of as a many-terahertz carrier.
some authors present system noise floor measurements in units of dBc/Hz. Is this wrong since in this case there's no carrier?
It's not clear to me why somebody would choose those units for a noise floor. It may be wrong, but I'd want to see the context where you read it to say for sure.
I find that the trace on the RF spectrum analyzer shows harmonics as a series of peaks. The levels between peaks is at the same level as the background level (i.e. when there is no signal input). Can we therefore infer that the RIN at these points (i.e. if we integrate from 10 Hz, say, up to the 1st harmonic) is equal to or less than the system RIN?
In the RIN measurements I've seen, there are no measurable harmonics, just a single peak related to the laser's intrinsic relaxation oscillation frequency. Are you testing with a modulation signal applied to the laser? Most RIN measurement's I've seen were done with the laser operated CW, and I'd think the results are easier to interpret for a CW optical signal.
In general spectrum analyzers have a noise floor, but I wouldn't call it "RIN", because it is not "relative intensity" --- it doesn't change in proportion to the optical power. The measurement system noise is a fixed "floor" and you can't measure power spectral density below that floor. So whenever the trace is down at the noise floor, you're not measuring anything about the device you are testing, just the capabilities of the analyzer.
General comment
The RIN measurement is fairly difficult to do. Unless the laser has very bad performance you need a very low-noise detector, very low-noise preamplifier, and a very sensitive spectrum analyzer (with a low noise floor). You will want to test the noise floor of your whole receiver system (detector, preamplifier, spectrum analyzer) before measuring your laser to be sure you know when you're measuring the laser behavior and when you're just seeing instrument noise.
Edit
To follow up your questions in comments:
Sorry I'm not familiar with RIN measurements on pulsed lasers. But the units of dBc/Hz make a lot more sense now --- they're just talking about the fundamental of the pulse signal as the carrier.
The measurements I'm familiar with, you're most interested in the peak frequency in the RIN spectrum. I don't think you could do this with a pulsed laser because you'd have to pulse at a higher frequency than the RIN peak, which would also be beyond the modulation capabilities of the laser. But maybe there are tricks I'm not aware of.
I will suggest that for a pulsed RIN measurement, you don't need the bias tee, though you might want a blocking capacitor for the sake of your SA input. The peak of the fundamental of the pulse signal gives you the laser signal power that you'd be measuring the noise relative to.
is it fair to say then that the laser has equal or better noise performance?
I'd say it this way: if the laser noise is too small to measure on your detector/SA system, then the measurement system is not adequate to measure the noise of that laser.
how would you recommend characterising the system noise floor?
Typically, you turn on the photodetector and pre-amp, but don't apply any laser signal. Then take a sweep on the spectrum analyzer, using the exact settings you'll use for your measurement. This gives the combined floor for the detector plus the SA.
You should be able to display this for comparison to your laser RIN measurements by just using the save-trace features of the SA, without any need for calculations.
I doubt if I can cover all your questions, but I'll give it a try:
Well, what if I'm using a fixed-frequency signal? Fupper and Flower would be the same value, right? So does that mean B=0? So a fixed frequency signal can't carry any data? So what am I missing?
A single frequency signal would be a continuous tone. It's amplitude would never change. It would just continue on repetitively forever. As such, it would not convey any information.
When you start modulating your carrier, the spectrum of your signal is no longer a single frequency. According to the amplitude modulation formula, the spectrum of the modulated signal is the convolution of the carrier (a single frequency) and the modulating signal (typically, containing energy in some band about 0 Hz).
Therefore the modulated output signal contains energy in a band around the carrier, not just at the single (carrier) frequency.
We know that's not true, AM radio does it.
Each AM station delivers energy not just at the carrier frequency, but in a band around that frequency. An AM radio broadcast is not an example of a single-frequency signal.
It's plainly obvious that I can cram way more bits into 2.4*10^9 cycles/second than I can with just 1/sec.
Certainly you could. However, if you simply modulated your 2.4 GHz carrier with an information signal spanning 2.4 GHz, the bandwidth of the resulting signal would be nearly 2.4 GHz. The energy in the signal would be spread from 1.2 to 3.6 GHz.
There is a way to get around this though...
What about fractional differences? Waveforms are analog in nature, so we could have a 1Hz signal and a 1.5Hz signal. Likewise at the high frequency range. Say 2.4GHz minus 0.5Hz. There is an infinite amount of space between 1 and 1.5. Could not 1Hz and 1.001Hz serve as two separate channels?
They can, but only by trading off the SNR term in the Shannon-Hartley formula for the bandwidth term. That is, the formula shows there's two ways to increase the capacity of the signal: Increase the bandwidth or increase the signal to noise ratio.
So if you had an infinitely high signal to noise ratio, you could use 0.001 Hz of bandwidth to carry as much information as you like.
But in practice, the log function around the SNR means that there are diminishing returns for increasing SNR. Beyond a certain point, large increases in SNR provide little improvement in channel capacity.
Two typical ways this is used:
In multilevel AM coding, instead of just sending the carrier or not sending it in a bit interval, you might have 4 different amplitude levels that can be sent. This allows two bits of information to be encoded in each bit interval and increases the bits per Hz by a factor of two. But it requires a higher SNR to be able to consistently distinguish between the different levels.
In FM radio broadcasting, the broadcast signal bandwidth is broader than the audio signal being carried. This allows the signal to be received accurately even in low SNR conditions.
Could not 1Hz and 1.001Hz serve as two separate channels? In terms of practicality I realize this would be difficult, nearly impossible to measure this difference with modern electronics
In fact it's quite easy to distinguish 1 Hz from 1.001 Hz with modern electronics. You simply need to measure the signal for a few thousand seconds and count the number of cycles.
So in that sense, shouldn't there be an infinite amount of bandwidth between two frequencies?
No. Between 1.00 Hz and 1.01 Hz there is exactly 0.01 Hz of bandwidth. It doesn't need to be counted in whole numbers of Hertz, but there's only as much bandwidth between two frequencies as the difference between those frequencies.
Edit
From what you're saying, the B in the Shannon equation has nothing to do with carrier frequency? This is modulation bandwidth only?
Essentially yes. B is the bandwidth, or the range of frequencies over which the signal spectrum has energy.
You could use a 1 MHz band around 10 MHz, or a 1 MHz band around 30 GHz, and the channel capacity would be the same (given the same SNR).
However in the simplest cases, like dual-sideband AM, the carrier tends to sit in the middle of the signal band. So if you have a 1 kHz carrier, with dual-sideband AM, you can only hope to use the bandwidth from 0 to 2 kHz.
Single-sideband obviously doesn't follow this rule.
An information signal spanning 2.4GHz, what does this mean?
I mean that the spectrum contains energy over a 2.4 GHz band.
If you had a narrow band filter and an RF power detector, you could detect energy in the signal at any frequency within the band.
are you taking about the carrier wave now?
No. The carrier is a single frequency. The complete signal contains energy over a band of frequencies around the carrier. (Again, single-sideband pushes all the signal to one side of the carrier; also, suppressed-carrier AM eliminates most of the energy at the carrier frequency)
As N->0, C will approach infinity. So in theory an infinite amount of data can be encoded into a single wave?
In principle, yes, by (for example) varying the amplitude in infinitely small steps and infinitely slowly.
In practice, the SNR term has that log function around it, so there are diminishing returns for increasing SNR, and also there are fundamental physical reasons that the noise never goes to 0.
Best Answer
Dynamic range refers to the difference between the maximum signal a system can handle and the noise floor for a specific system configuration. If the gain of the system is fixed, there is no difficulty with this definition. If the gain of the system can be varied, then the dynamic range becomes a function of the system gain. The use of the word "dynamic" means that it refers to the system capability in processing a signal at one point in time, in other words for one specific gain. Since the gain can only be varied statically, you cannot claim increased dynamic range by having a variable gain. For example, if you have a 10-bit A/D converter in the system, the dynamic range is generally taken as approximately 6 dB X the number of bits or 60 dB in this case. If you put a variable gain amplifier (say with 0 to 40 dB gain in front of this A/D converter, you can't claim the dynamic range of the system is increased by 40 dB. The advantage of the variable gain amplifier is the ability to set the system dynamic range over a given voltage range. For example, if the maximum input of the A/D converter is 10 volts, then the dynamic range of the system with the variable gain amplifier can be shifted from 10 millivolts to 10 volts with the amplifier gain set to 0 dB, to 0.1 millivolts to 100 millivolts with the amplifier gain set to 40 dB. In both cases, the dynamic range remains at 60 dB but the static range has increased to 100 dB.