Several great responses have been left already, so I'll try not to repeat things too much. Here's a simplified "visual" representation of the relationship between signal and noise. I don't know if this helps any, but there's a chance this might make things clearer for some people...
In the following graphs, the progression moves from left to right.
- The (dark blue) line running across the graph represents the TV signal level.
- The red hashed area at the bottom represents the thermal noise floor (ambient noise that is naturally present everywhere).
- The different gray sections indicate the part of the system that is causing signal or noise levels to go up or down. The alternating grays are only for visual clarity and have no significance beyond that.
- The entire chain can be thought of as two parts: 1) stuff that happens between the transmitter and your address; and 2) stuff that happens between "the air" at your address and your TV.
Noise Margin is best thought of as a Signal to Noise Ratio (SNR). In the following graphs, the Noise Margin is the difference between the signal line (dark blue) and the noise floor (black line on top of hashed marks). I'll explain the distinction between NM and SNR toward the end of this post.
Let's first take a look at a simple example. This first chart represents what happens when there is a very strong line-of-sight signals coming from the transmitter, and all that is needed is a simple indoor antenna.
1) For the given transmitter's ERP (assuming adjustments for the broadcaster's antenna pattern are already included), the line-of-sight propagation loss in this example is minimal, so a very high Noise Margin is available "in the air" at the given address.
2) Since this example is assuming an indoor antenna, there's going to be some signal loss due to building penetration.
3) The indoor antenna will have a little bit of gain, so that improves the signal level slightly. This also improves NM and SNR because antennas pick up the signal without raising the noise.
4) The cable between the antenna and the TV will have a little bit of loss associated with it (depends on cable quality and length).
5) As the signal enters the TV, the tuner circuitry has a Noise Figure associated with it. This indicates how much the tuner itself will degrade the signal before it reaches the part of the logic that actually decodes and displays the picture. This Noise Figure must be taken into account when estimating the amount of "usable" signal that actually gets to the decode/display circuitry.
6) When the net residual Noise Margin is greater than 0, then the TV signal can theoretically be decoded and watched. In reality, it's better to have a buffer of at least 5 to 10 dB residual NM so that the setup does not show blocking artifacts and/or drop-outs at every little fluctuation (e.g., blowing trees, rain, airplanes, etc.) or when there's interference (e.g., multipath, power lines, etc.).
In this next example, we'll look at a more difficult situation. In this case, the transmitter might be far away or behind 1Edge or 2Edge diffraction obstacles. By the time the signal reaches the given address, the signal is very weak. A very good antenna and pre-amp are needed to recover a usable signal.
1) The TV transmission might start strong, but terrain and distance might bring the signal down to barely usable levels. In this example, the Noise Margin is actually a negative value because the desired signal is down at the level of the noise floor.
2) In this case, an outdoor high-gain antenna is needed. There is no building loss, so the first thing we encounter is the antenna gain. It will need to be a high-gain antenna too. This pulls the signal back up to a level where we have a positive Noise Margin again.
3) There will be a short run of cable between the antenna and the pre-amp, so a tiny bit of loss is shown. If the amp is not mast-mounted, and is placed further down the chain (like in the attic or closer to the TV), this loss will increase, and will ultimately hurt the Noise Margin.
4) Then we hit the pre-amp. All pre-amps have a Noise Figure associated with them, which means they will degrade the signal a bit in the process of boosting it. At the pre-amp's output, both the signal and the noise floor have been boosted, so the Noise Margin remains about the same (minus the Noise Figure of the amp).
5) From this point on, the Noise Margin remains essentially constant. Cable losses, splitter losses, and receiver Noise Figures do not hurt the Noise Margin any more. Since the signal has been boosted to a high level, these downstream losses are no longer driving the signal into the thermal noise floor.
6) If the net downstream losses (and Noise Figures) happen to be greater than the net gain provided by the amp, you might be back into a situation where the Noise Margin starts to degrade again. For extremely long cable runs or other special circumstances, it may be required to install a secondary amp in the chain to minimize the loss of Noise Margin. There are several complications when doing this, so it's not recommended unless absolutely necessary.
Everyone should note that the antenna is the ONLY element in the system that helps you GAIN Noise Margin.
A pre-amp does not change the intrinsic gain of the antenna. Amps boost the signal and noise floor simultaneously, so a crappy signal going into an amp will yield a strong, but even crappier signal (because of the amp's Noise Figure) at its output.
Do not be fooled by lousy antennas that include a built-in amp and claim to be high-gain antennas. The amp's gain does NOT count toward the gain of the antenna itself.Difference between SNR and NM
SNR is generally defined as the ratio between desired signal power and the power of the noise floor. The minimum required SNR for any communication system depends on the details of its design and signal structure. Modulation type, symbol rate, error correction codes, Turbo codes, Viterbi encoding, and dozens of other design considerations ultimately affect what SNR is needed to make the system work.
For example, ATSC requires a theoretical minimum of about 15 dB SNR in order to get a TV picture. NTSC requires about 27 dB SNR (with analog, it's a very subjective matter to decide what is "watchable", but this is roughly where you get a picture with "some snow").
There are other systems (like GPS) that can work even when the SNR values are negative. These signals have a very high "processing gain" that make it possible to decode it even when it is buried well below the noise floor. The desired signal can actually have less power than the ambient thermal noise and still be used.
NM, on the other hand, is generally defined as the amount of signal relative to the minimum threshold for operation. On a dB scale, the 0 dB point is at the theoretical boundary between working and not working. Positive dB numbers mean the system should work with some margin for error. Negative dB numbers mean the system should not work because the signal level is deficient by that many dB.
If we used SNR to compare ATSC and NTSC, we'd have two different number scales to deal with. We'd have to mentally keep track of the minimum SNR thresholds for each signal type and do a lot of quick math in our heads.
If we use NM to compare ATSC and NTSC, it's a lot easier to tell how well we're doing relative to the minimum operating thresholds. It also reduces some of the confusion caused by the differences in power levels. Many people believed that digital coverage was going to be worse than analog coverage because a lot of transmitters were broadcasting with significantly less power. However, less power does not mean less coverage.
The average person will not know the different operating thresholds for each signal type, so providing numbers for field strength, dBm, SNR, or ERP often leads to increased confusion for some people.