Receive System Calculations
NOTE:  "log" is logarithm to the base 10, or log10

System Noise Figure
("cascaded")

NFs = 10 log (Fs) dB

where:
    NFs = system noise figure, and
    Fs = system noise FACTOR.
and:
    Fs = F1 + [(F2 - 1)/G1] + [(F3 - 1)/G1*G2] + [(F4 - 1)/G1*G2*G3] + ...

    where:
    Fs = system noise FACTOR,
    F1 = noise FACTOR of the first stage,
    F2 = noise FACTOR of the second stage, etc.

    G1 = gain of the first stage as actual multiplier, NOT in dB,
    G2 = gain of the second stage as actual multiplier, NOT in dB,
    In each case, remember to subtract the loss of interconnecting circuitry, coaxial cable, or whatever, following the gain stage before entering the gain in the formula! If working in dB, merely subtract the loss in dB from the Gain in dB before converting, as below.

NOTES:

1. If one knows a noise FIGURE (NF), the noise FACTOR (F) is calculated F = 10NF/10

or, on your scientific calculator, divide NF by 10, take inverse log of the result to find F.

2. If one knows a gain in dB (GdB), the gain multiplier is calculated G = 10GdB/10

or, on your scientific calculator, divide GdB by 10, take inverse log of the result to find G.


Minimum Discernable Signal

This "rule of thumb" MDS formula is widely used by system engineers, but it does not accurately calculate the actual value for the"minimum" discernable signal level, especially for very sensitive systems. Go HERE for an excellent discussion of this subject.

MDS = [-174 + NFs + 10 log (BWHz)] dBm

where:

    BWHz = system (generally IF) bandwidth in HZ

System Input Intercept Point
("cascaded")

IPs = {[20/(n - 1)] log (1/S)} dBm

where:
    S = 10 [-(n-1)IP1/20] + 10 [-(n-1)IP2/20] + 10 [-(n-1)IP3/20] + ...
and:
    n = order of intercept (usually only 2nd and 3rd are specified for any given equipment)
    IPx = nth-order intercept point of the "xth" active element "reflected" out to the system input.

    An "active" element is any stage having gain, a Noise Figure, and intercept points. Gain can be either positive or, in the case of an active element exhibiting loss, negative.

    "Reflected" means the INPUT intercept point (for amplifiers, the output IP in dB minus the gain in dB) plus any attenuations and minus any gains between the input of that active stage and the system input.


System Dynamic Range
for third order intercept (IP3) situation

DR = [2 (IPs - MDS)/3] dB


Level of System Intermod
for third order intercept (IP3) situation

IM = [3MS - 2IPs] dBm

where:
    MS is the level in dBm of the strongest signal within the passband of interest.

Comments:

The generalized formulas presented here have been used successfully to design new and characterize existing receive systems used in a variety of actual non-amateur applications, as well as several of my own HAM systems. In practice, I generally limit my calculations to IP3.

The most difficult parameter to find for HAM gear is the intercept point specification. I have badgered manufacturers' technical representatives at trade shows and hamfests, as well as telephonic and snail-mail queries to manufacturers' US offices. It is often a daunting task which can yield little or no results. Most times an "estimate" made by a staff design engineer is the best one can do. It is not uncommon to ask for this information only to have the manufacturer's representative ask, "What is an intercept point?" Good luck!

Field measurements have verified calculations in a sufficient number of instances to provide a high confidence level regarding the above formulae. Nevertheless, caveate emptor, and if you identify anomalies, please advise!

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