I understand what you're saying here, however it seems to assume that the amplifier isn't introducing any noise of it's own into the signal. Plus it also seems to assume that the amplifier has a linear response, both across signal levels and across the 950-1450 band. Also missing from the discussion, is where do you put the amplifier, which I think is very important.
Of course amplifiers introduce noise, but so do receivers, LNBs and dishes. Even receivers have variable gain stages (AGC) and this does not come for free, either. The important part is to have the gain where it belongs. Lots of gain in a LNB is good. Modern LNBs typically have around 60 dB of gain and are very affordable. I haven't seen one post here where someone complained this was bad, too much, etc. But the moment when someone suggests adding an amplifier with say 15 dB of gain for some fraction of a LNB cost, alarm bells start ringing everywhere. I think there are misconceptions of what noise and noise floors are and how they relate to receiving the highest quality signal.
In the best case a dish will have sufficient signal gain and sufficient shielding of terrestrial noise and interference to deliver a decent signal to the LNB. Also in the best case the LNB will have a low noise factor, so it doesn't deteriorate the received SNR by a significant amount, and enough gain to ensure the SNR is maintained all the way to the receiver.
The receiver should also have a low equivalent input noise floor, but the design of receivers is always a compromise. Low noise detectors generally have a limited dynamic range over which they can operate, usually far less than the signal environment. So an AGC normally precedes the detector to better match the signal environment to the detector's limited dynamic range. If we stress the AGC with too much or too little signal, we will have suboptimal performance from the detector. Just as an aside, a wide dynamic range AGC is generally a tougher design problem than a fixed-gain amplifier.
Before proceeding, we first need to recall that noise combines non-coherently in a RMS process. If the noise floor input to the next component in the receiving chain happens to be the same as that component's equivalent noise floor, we will lose 3 dB of SNR. Ouch. What we really want is the input noise floor to be significantly higher than that component's noise floor. For example, if the input noise floor is 20 dB above the component's equivalent noise floor, noise combining will result in a 0.04 dB loss of SNR. That's a lot more tolerable. If there is a greater spread, the loss will be even less.
Whether the above component is an amplifier or a receiver, noise combining works pretty much the same way. If we ever allow the noise level output by the LNB to even approach the equivalent noise floor of any component in the signal chain, we're going to lose SNR. This includes any amplifiers, switches, splitters and the receiver. The gain of modern LNBs is roughly standardized to ensure that modern receivers have enough signal that the LNB's output noise floor is sufficiently above the receiver's noise floor. That way noise combining is negligible for a 'typical' cable run and switching system.
With longer cable runs, and often non-powered switches, the signal is attenuated along with the LNB's output noise floor. FTA systems pass the LNB output from 950-2150 MHz and often only 950-1450 MHz. The higher the frequency the more the attenuation. If the attenuated noise floor approaches the equivalent noise floor of the receiver we will start to lose serious amounts of SNR. If LNBs had higher gain, this would be less of a problem. But then we would risk overloading a receiver with shorter cable runs.
Let's look at a 36 MHz bandwidth transponder. The theoretical thermal noise floor for this bandwidth at room temperature is around -90 dBm. You can't do better than that. I haven't run calibrated measurements on my receivers, but they appear to have equivalent noise floors around -80 dBm. None of them want more than about -30 dBm of input level. My LNBs output a noise floor around -50 to -60 dBm in that bandwidth. That's about right because I am unlikely to see more SNR than would overload my receivers.
Let's take OP's concern about 200' of cable. For 100' of cable, RG-6 will attenuate 6 dB @ 950 MHz, 7 dB @ 1450 MHz and 9 dB @ 2150 MHz. RG-11 does better for the same length, but not incredibly: 4 dB at 950 MHz, 5 dB @ 1450 MHz and 6 dB @ 2150 MHz. At 1450 MHz that means I would lose 14 dB with RG-6 and 10 dB with RG-11. A LNB noise floor of -60 dBm would become -74 dBm with RG-6 and -70 dBm with RG-11. Without any amplifier I would lose about 1 dB of SNR with RG-6 and 0.8 dB with RG-11 because of noise combining in the receiver. Is RG-11 that much better?
But let's say I put in a 15 dB gain amplifier with the same equivalent noise floor as the receiver (-80 dBm). Decent amplifiers are better. I will lose 0.04 dB of SNR at the amplifier right off the bat. But the receiver will only degrade the SNR by 0.03 dB because the noise floor comes in much higher with the amp, and there is less noise combining. This is a total SNR degradation of 0.07 dB. That's a lot better than even RG-11 alone. How much is the difference? About the same as sawing off 1' from your 10' dish.
To answer your question about where to put the amplifier: as close to the LNB as possible. Good amplifiers can easily tolerate the hottest LNB you're likely to come across. They can't make up SNR that is already lost in a cable by putting them downstream. But if you were running an extremely long cable, spaced amplifiers might make sense.
As you say in the middle quote above, the amplifier should affect the noise the same as the signal, provided that it has a linear response, however there will be noise added by the amplifier, and it seems to me that this will always lower the S/N. Of course this brings in the "completely negligible effect" phrase, and I think that it could be negligible if you have a high quality amplifier, and it is " Properly applied" as you say, however I don't really think that an off the shelf consumer amplifier plunked into the signal line at random can do anything but lower the S/N.
I don't have any knowledge about the design of these in-line amplifiers, but I'd have to guess that there is an optimum range of signal (including noise) level that it will amplify in a linear fashion, and that there will be some level at which some degree of clipping or attenuation will occur, and this non-linearity would seem likely to attenuate the signal more than the noise, although perhaps only on the stronger signals where it is less important.
In the bigger scheme of things -30 dBm is around 9 mV into 75 ohms. Even with the design objective of a low noise factor, there's plenty of supply voltage available to an amp (13 to 18V) where overload isn't a major consideration. I've come across a few terrible amplifiers that hit the circular file in a ns, but for the most part amps have proved very tolerant (and linear) of whatever I've thrown. Designing a good amp is a lot easier than most people think. Designing a good LNB is a lot tougher. Given the LNBs often used in FTA, I'm surprised there isn't more outrage about the marginally performing ones.
But the linearity across the 950-1450 band is also an important issue. This can do some very strange things to the signal that the receiver ends up using. I'm not positive about the cause of the strange things I've seen, but I THINK that it must have something to do with the AGC you mention. Ie if the AGC is acting on the signal level in the whole 950-1450 band, but the amplification is greater say in the lower end of the band, then signal in the upper end of the band can actually go down to zero on noise and marginal signals.
Precisely why a sloped (compensating) amplifier is normally a good thing. If the spectrum is flat coming out of the LNB, it will still be pretty flat at the end of a long cable with a sloped amplifier. That way the receiver will see the same level across the band and that will likely lead to more consistent performance. AGCs can be implemented in different ways. They don't have to act across the full LNB bandwidth.
On to the issue that wasn't mentioned, ie where do you put the amplifier? Since the LNBs already amplify the signal, and most likely are a higher quality than the amplifier in a consumer inline amplifier, I really have a hard time seeing any advantage to putting the amplifier out at the dish, and likewise, the AGC amplifier circuitry in the receivers is most likely higher quality than the inline amp, plus all the damage has been done by the time you get the signal to the receiver, so putting the amp near the receiver clearly is usually unlikely to help (I've seen a couple situations where it did help). Intuitively (I've really never felt the need to try an inline amp at this position), I think that the only place it makes sense would be mid-way between the dish and receiver. Ie a point where both signal and noise may have dropped down to levels where the amplification of the inline amp would bring the level back up to near where it was when it left the lnb, hopefully without introduction of much new noise.
I wouldn't assume the LNB amplifier and/or the receiver AGC is necessarily better in noise performance than in an inline amplifier. The amplifier is an extremely easy design with the integrated components available today. There is a lot more to designing a good LNB or receiver.
But anyway, I think how useful the inline amp ends up being depends a lot on the quality of the amp. Since you've seen to have had success with them, I'm curious what brand amps you've used? I've been thinking of moving one of my dishes to a point where I'd be adding another 50' or so of coax, which will put me out past the 300' mark, which is where I think that an inline might become advantageous, however if I do this, I want to get a high quality amp, as I've observed that cheap amps have seemed to be next to useless.
So I'd be interested in recommendations for a good quality inline, and opinions on whether my mid run positioning opinion seems logical.
At the moment I like the Channel Master duals, partly because they're easy to mount and everything I have comes in pairs. I recently picked up some very inexpensive JVIs that appear to have the same specs, and put one on a dish last night. I haven't nit picked it, yet, but it looked about the same on the spectrum analyzer as the CMs.
The best place for an inline is at the LNB, unless you have an extremely long cable and the gain required is too much up front.
Also, slightly off topic, but a topic which influenced some of my comments above... I've noticed that the pass-thrus of receivers seem to have amplification, some better than others. I am curious whether this amplification is prior to the AFC of the receivers, or if it is part of the AFC? And does this amplification only affect the signal coming out of the passthru, or is it actually the first stage of amplification for the receiver itself? I've seen or read things that have suggested both sides of all both questions, so I'm curious.
Depending on the receiver, the pass-through may or may not have a gain stage. I would be surprised if there was an AGC in the loop. Generally I'd generally prefer to have a little more gain elsewhere in the system and run through a splitter than take a pass-through off a receiver. But properly implemented it shouldn't be a problem. My Pansat 9200HD has two pass-throughs: the first is for the DVB tuner and that seems ok. The second from the DVB-S2 tuner (original card, not the new one) is terrible.
