NOISE FIGURE
Noise Figure is important because it allows the comparison of devices on the basis of how much noise the device adds to the signal as it transits from input to output. All other things being equal, devices which add the least noise are preferable.
Receiver Noise: The ideal limit of a receiving system's sensitivity is determined by the noise present at its input. That is, signals that are below the noise (negative signal-to-noise ratio) are masked by the noise. In practice, however, the receiving system itself generates noise, and it is this noise that limits system sensitivity. A term called Noise Factor (F), is used as a figure of merit to define how closely the ideal is approached. The noise factor for an ideal device would be one; it would add no noise. Noise Factor is defined by:
F= (Si/Ni)/(So/No)
Where: Si/o = Signal power in/out
Ni/o= Noise power in/out
Noise Figure (Nf) is the Noise Factor expressed in dB:
Nf = 10 log F
Noise is a temperature related phenomenon. At absolute zero (-273°C/0K) electron activity stops as does the production of noise. You may know of attempts to reduce noise in receiving systems by cooling the receiving amplifiers. Noise is also related to bandwidth (B). The narrower the bandwidth the less noise. You may have noticed this when switching between modes on a receiver, say from AM/6 KHz B, to SSB/2.4 KHz B to CW/500 Hz B. At each decrease in B the noise drops. Noise power can be expressed as a function of temperature and bandwidth by:
Pn = kTB
Where k = Boltzman's constant, 1.374 x 10 -23 joule/K
T = Absolute temperature, K (Room temp = 290K)
B = Bandwidth, Hz
Notice that noise is directly related to bandwidth. After converting the Pn to dB (10 log Pn) the importance of using the narrowest bandwidth can be easily seen. Reducing the bandwidth by half will gain 3 dB in signal-to-noise. Changing from 2.4 KHz to 1.8 KHz gives a 1.2 dB increase; reducing to 500 Hz produces a whopping 6.8 dB improvement.
Noise Factor can and often is expressed in terms of kTB. Substitution in the first equation gives
F = (Si/kTB)/(SiG/No) = No/GkTB
Where G = gain of the device; So = SiG
The GkTB term represents the minimum noise at the measurement temperature and bandwidth. In an ideal amplifier, No would equal GkTB and the F value would be 1 (0 dB noise figure).
Noise Figure Measurement: Noise Figure is difficult to measure without using sophisticated measurement tools such as a noise figure meter or a spectrum analyzer [1] and is normally beyond the capability of the individual amateur. Some groups, especially VHF and above aficionados, have purchased noise figure measuring equipment. Noise figure measurement is also offered at some VHF/UHF gatherings. Lacking a noise figure meter or spectrum analyzer, the measurement can be made with an excess noise source and a power meter. An excess noise source is a diode which has been calibrated to produce a given amount of noise. Argon gas tubes or more recently avalanche diodes are used. A common device is the Hewlett Packard HP346A which produces 5 to 7 dB of excess noise, depending upon frequency, in the 10 MHz to 18GHz range. The measurement involves reading the noise output of the receiver or device with the excess noise source off and then on; these two values are called N1 and N2. The two values along with the excess noise ratio (ENR) is then used to calculate the noise figure from the following [2]:
Nf = ENR - 10 log(N2/N1 -1)
Practical application: Even though measuring noise figure is difficult, and most of us will have to use the manufacturers specifications in our calculations, tuning an amplifier for best noise figure is possible with a gated (modulated) wideband noise source. A method is described in the ARRL Handbook that uses a simple home made noise source [3]. Knowing the noise figure of a receiver or amplifier does not divulge the receiving system noise figure which must also include the antenna connectors, transmission line and any devices connected in that path. At VHF and above, lowering the system noise figure is extremely beneficial, because, at those frequencies atmospheric noise is low enough that the limiting factor in receiver sensitivity will almost always be the receiving system. At HF, however, atmospheric noise is high enough such that it will exceed the system noise of a well designed station, therefore, atmospheric noise becomes the limiting sensitivity factor. In a practical sense this means that it is not worthwhile to put a low noise figure amplifier in front of an HF receiving system, but it may pay to do so at VHF and above.
Cascaded Noise Figure Calculations. VHF/UHF receiving systems often consist of four basic items; an antenna, preamplifier, transmission line, and receiver. By using the expression below we can determine the overall noise figure for the system. This allows us to do some "what if" calculations involving preamplifier gain, noise figure and transmission line loss which help determine how much performance to purchase in these two areas. The cascaded three stage noise figure is determined by:
Fc = F1 + (F2 - 1)/G1 + (F3 - 1)/G1G2 + ...
Where N# is stage noise factor and G# is stage gain factor. Note: If noise figures and gain are given in dB, they must be converted using F = 10Nf/10. A scientific programmable calculator makes short work of the numbers; a program for HP (RPN) calculators is available which takes entry in dB.
Notice how important the noise figure of the first device after the antenna is in establishing the overall system noise figure.
System Block Diagram
For example, say a 144 MHz station uses a preamplifier with 10 dB gain, 20dBm IPo3 and a 2.5 dB noise figure, 75 feet of RG-213 cable and a receiver with a noise figure of 8 dB. Seventy five feet of RG-213 @ 144MHz results in a loss of 2.0 dB; add .1 dB for each connector for a total cable loss of 2.2 dB. Cable noise figure is equal to the absolute value of the cable loss (2.2dB), cable gain is equal to cable loss (-2.2 dB). Positioning the amplifier at the antenna terminals yields a system noise figure of 4.35 dB; positioning the amplifier at the receiver end of the cable yields a noise figure of 5.83 dB. From the performance standpoint locating the amplifier at the antenna is best, however, that installation is more complicated than locating the amplifier at the receiver. As you can see from the equation above, gain is also a factor in determining the overall noise figure. For instance, changing the antenna mounted amplifier gain from 10 to 15 dB lowers the noise figure to 3.18 dB.
Dynamic range considerations: In achieving a lower noise figure by installing a preamplifier ahead of the receiver we have also changed the dynamic range of the system. Consideration of the effect on the overall system is appropriate as selection of the gain and dynamic range of the amplifier, or the choice of cable are dependent upon overall system specifications; trade-offs can be made. Lets assume four different cases, which are:
Case 1 -10 dB gain amplifier at antenna
Case 2 - 15 dB gain amplifier at antenna
Case 3 - No amplifier
Case 4 - 10 dB amplifier and low loss transmission line, .75 dB for 75 feet including connectors.
Example calculations for case 1 follow with the results of all case calculations tabulated in the table below. Establish the minimum discernible signal for a SSB signal (2.4 KHz bandwidth) for each of the cases. For case 1:
MDS = Nf + 10 log B - 171
= 4.35 + 10 log 2400 - 171
= -132.8 dBm
Dynamic Range can be calculated from the spur free dynamic range equation:
SFDR = 2/3 (IPi3 - MDS)
To calculate the input third order intercept point (IPi3) requires that the intercept points of the system be summed back to the antenna port. This can be calculated using the cascaded intercept point summation equation [4], however, for simple systems algebraic addition will suffice. Using the fact that IPo (output intercept point) = IPi + G (gain), where both are in dB, the system IPi can be approximated. Assume that the receiver IPi3 is 0 dBm.
Case 1 - for the antenna mounted preamplifier:
IPi3 » IPi(rx) - G(cable) - G(amp)
IPi3 » 0 - (-2.2) - 10 = -7.8 dBm
Calculating dynamic range for the above yields:
SFDR = 2/3 (IPi3 - MDS)
Case 1 2/3 (-7.8 - (-132.8)) = 83.3 dB
Nf MDS IPi SFDR
dB dBm dBm dB
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Case 1 4.35 -132.8 -7.8 83.3
Case 2 3.18 -134.0 -12.8 80.8
Case 3 10.5 -126.7 +2.2 90.8
Case 4 3.85 -133.4 -9.3 82.7
2 Meter System Table
From the table you can see that, in this case, paying the cost for very low loss cable is likely not worth the expense as almost the same performance can be obtained from the 15 dB amplifier and RG-213 cable. The advantage of an amplifier to noise figure improvement is apparent, however, the system IP suffers. Notice that having the higher dynamic range amplifier ahead of a mediocre receiver does not help the system dynamic range. If you are local to another 2 meter station, you may not want to give up the 10 dB in dynamic range. Having a sensitive system that is constantly overloaded will not do. Improvement in the receiver may be in order, such as by using a down converter with an HF receiver (which may have a higher IP) or modifying the VHF receiver input stage or first mixer. Although we have not covered the antenna as part of the system, consideration should also be given to increasing the gain of the antenna, or placing strong signals in a pattern null to achieve desired performance.
73, Kevin/W3DAD
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[1] Slater, Carla, "Spectrum-Analyzer-Based System Simplifies Noise Figure Measurement," RF Design, Dec 93, pp24-32
[2] Hewlett Packard Application Note 57, Noise Figure Primer, 1965, pp 2-3
[3] ARRL Handbook for Radio Amateurs, ARRL, 1994, p 25-31
[4] Gross, Brian P. WA7TDB, "Calculating the Cascade Intercept Point of Communications Receivers",, Ham Radio, August 1980, p 50