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Old 6-Dec-2013, 2:55 AM   #8
mmbridges
Junior Member
 
Join Date: Nov 2013
Posts: 8
Hi GroundUrMast,

It was not obvious to me. However, I have seen the quality your posts and what is obvious to me is your superior knowledge and expertise in the subject matter.

I am new to this subject and am learning a lot hence my going down the Frii's formula Noise figure analysis path. Looks like this topic has been covered quite extensively here and on other sites. I will add one additional view of things but fist another

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DISCLAIMER
1) The following analysis and comparisons are theoretical only and based upon published preamp specs.
2) They do not include multipath or other signal quality effects
3) I understand that for most setups, small improvements in Noise Margin (NM) may end up being irrelevant but for fringe area situations like mine I need to squeeze out every bit of NM improvement I can.
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Since equations tend to make peoples eyes glaze over I decided to create a plot that may provide additional insight. first one more equation:

Let the improvement in Noise Margin obtained from adding a preamp over no using one be expressed as

delta_NM_pa (dB) = 10log(F_sys_no_pa/F_sys_w_pa)

where

F_sys_no_pa = 1+(F_c-1)+(F_stb-1)/A_c

and

F_sys_w_pa=F_pa+(F_c-1)./A_pa+(F_stb-1)./(A_pa*A_c)

and all remaining variables have been previously defined.


delta_NM_pa is a figure of merit that will allow one to see preamp improvements in NM without having to talk about what the absolute NM of the system is. If the absolute NM without a preamp is positive and much greater than delta_NM_pa (i.e. NM_no_pa >> delta_NM_pa and NM_no_pa >0) then the following discussion is moot as a preamp buys you little.

If the absolute NM without a preamp is negative and much smaller than delta_NM_pa (i.e. NM_no_pa << delta_NM_pa and NM_no_pa < 0) then the following discussion is also moot as there is nothing a preamp can do to get you back to having positive NM.

However, if absolute NM without a preamp is 0dB, you are on the edge and a preamp can possibly help. What follows is a discussion of this situation.


Because there are many variables in the delta_NM_pa equation, in order to generate a plot a few variables had to be set. I set the following variables to meet my particular setup:

Single TV, no splitters, 50ft of RG6 one, a Zenith DTT-901 set top box, insertion losses from one coax grounding block and one house main antenna wall plate.

This results in the following two fixed parameters:

NF_stb = 6dB for set top box NF
L_c=-4db for lumped cable and insertion losses

Drum roll...... Here it is:



The above is a contour plot showing delta_NM_pa as a function of preamp NF and preamp gain. contour lines represent levels of constant NM improvement. On this plot I have also placed 7 preamps. A 3D representation of the contour plot would look like a hill with the highest point in the upper left hand corner.

So to perform a sanity check to see if this plot makes sense, lets consider a fictitious preamp with NF_pa=4dB and variable gain that can be adjusted between 0 and infinity. We start with the preamp gain set to G_pa=0dB which is on the x-axis at 4. As we start increasing the preamp gain we move vertically on the plot crossing constant contour lines of increasing NM improvement as we go. What we see is that as the gain is goes to infinity we approach but can not cross the 6dB NM improvement contour. This makes sense because in the limit, the system noise figure without the preamp is

NF_sys_no_pa=set top box NF + cable losses = 6dB + 4dB = 10dB

furthermore the system noise figure with the infinite gain preamp is

NF_sys_w_pa = NF_pa = 4dB.

Consequently the max possible NM improvement for this preamp on this system will be NF_sys_no_pa-NF_sys_w_pa = 10-4 = 6dB.


If we perform a similar test on a preamp with NF_pa=0dB and increase the gain we will find that we approach a constant NM improvement contour of 10dB. This is theoretically the best we could ever do on this system. Similarly if we choose a particularly noisy preamp with NF_pa =1 0dB and crank up the gain, we will never be able to cross the 0dB constant NM improvement contour. As such one will never be able to get a positive noise margin improvement and are better off not using this preamp at all.


Now one other thing about rules of thumb for selecting preamp gain and estimating NM improvement. One quick technique (i.e. one that doesn't involve Frii's formula) to estimate NM improvement from preamp, is to use the infinite gain case (i.e. delta_NM_pa = cable losses + NF_stb - NF_pa). This works very well if you use GroundUrMast's rule of thumb of setting preamp gain to be 5-10dB above the distribution losses(i.e. cable+splitter losses+tuner NF).

Let's see by examining a preamp with NF_pa=1dB. The quick "rule of thumb" based estimate of NM improvement is 10-1=9dB. If we set the preamp gain using the upper end of GroundUrMast's rule of thumb then G_pa=10+10=20dB. To find the actual NM improvement we look at the (1,20) point on the plot an see it would lie on about the 8.7dB contour. This is only 0.3dB off! However, say you simply set the gain equal to the distribution losses (i.e. G_pa=10dB). You would then be on a 6.7dB contour and more like 3.3dB off on the NM improvement estimate. The extra 5-10dB that GroundUrMast adds to the distribution losses when choosing a pre-amp gain is very important.

In general you want your preamp gain to put you in the portion of the contour plot where the contour lines are close to being vertical. This is the equivalent of having the preamp gain being "sufficiently large" to ignore the downstream losses.


Now looking at the various preamps in terms of NM improvement, the Kitztech 200 is the best for my particular setup since I am in a fringe area and have no chance of overloading the preamp. However it is important to note that the top 4 are all within 2 db of each other. The KT200 puts me just 0.5dB away from the maximum theoretical NM improvement which is quite nice if you are like me, and trying to squeeze out every bit of noise margin improvement you can. (Note: I mistakenly plotted the KT200 at 26dB instead of 24dB however when re-ran the calc the deltaNM improvement was still about 9.5dB).

As far as the generality of above contour plot is concerned, it mus be reemphasized that it was produced using a specific set of cable losses and set top box noise figure. Although different systems will have different plots, they will in general have the same shaped contours. The upper left and portion of the plot will have a higher hill top for higher distribution losses.

Last edited by mmbridges; 7-Dec-2013 at 3:27 PM. Reason: spelling and KT200 plot error disclosure
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