The basics.Amplifiers have an input impedance. That is the impedance by which it loads the signal source. The nominal impedance is something else. That is the source impedance that the amplifier is designed for. The input impedance may be much higher than the nominal inpedance.
Amplifiers also have an output impedance. It may be much lower than the nominal impedance. (Consider an audio amplifier for example.)
This page and sub-pages linked to from it discusses RF amplifiers that are designed for use in a 50 ohm system. In other words, the nominal impedance is 50 ohms for input as well as for output. For a power matched amplifier with input impedance as well as output impedance equal to 50 ohms the concept of gain is trivial. A power matched amplifier that provides 20 dB gain will deliver 100 times more power to the load than it absorbs from the source and the voltage on the output will be 10 times higher than the voltage on the input.
There is no need for 50 ohm amplifiers to be matched however. Amplifiers vith very high input impedance may have attractive properties. Such an amplifier has a near infinite standing wave ratio on the input. Return loss close to zero. The voltage across the input is twice as large as for a matched amplifier since no energy is absorbed. Even negative impedances are possible. They provide return gain. (Negative return loss.) The gain when using unmatched amplifiers is defined as the power ratio in a 50 ohm load when driven from a 50 ohm source with respectively without the amplifier.
Noise.A signal source can be the 50 ohm connector of an antenna, a signal generator or something else. All signal sources have a noise floor associated with the temperature of the source. Signal generators are typically at room temperature and have a noise floor of -174 dBm per Hz of bandwidth. An ideal amplifier just amplifies the signals presented by the source. Real world amplifiers also add noise. It is desireable to have amplifiers that add negligible noise compared to the noise present in the signal source itself.
A room temperature source with the temperature 290 K will be degraded by as many dB as given by the noise figure of the system used to receive it. (This is the definition of NF.) It is often assumed that 1 dB is insignificant and for that reason a noise figure of 1 dB is usually considered adequate in terrestrial communication. An amplifier with NF=1dB has a noise temperature of 75 K. The ratio (290+75)/290 = 1.258 which is the power ratio when the actual amplifier that provides a noise power of (290+75) K is compared with an ideal amplifier that does not add any noise at all. 10 * log(1.258) = 1.00 That is the NF.
A good microwave antenna for with a noise temperature of 10 K would need an amplifier with a noise temperature of 2.58 K to only cause a 1 dB degradation ( = loss of S/N.) That corresponds to a noise figure of about 0.0038 dB. Very low noise temperatures can be observed with good antennas that are used in space communication, radio astronomy and among radio amateurs for EME, signals reflected off the moon.
Read this article AMPLIFIER NOISE TEMPERATURES by Chuck MacCluer W8MQW for a more stringent presentation of the noise problem in amplifiers. Chuck has also made this table available: Conversion for Noise Temperature Te (K) to Noise Figure de KB2AH
Conventional measurements of amplifier noise figures.Automatic noise figure meters have been available since at least Jan 1961. That is the oldest description of the automatic Noise Figure Meter type 113B in my possession. It was manufactured in Sweden by Magnetic AB. At that time vacuum diodes or gas discharge tubes were used as noise sources. Today the automatic instruments use semiconductor diodes.
This document by Chuck MacCluer W8MQW MEASURING NOISE FIGURES presents the basic theory for noise figure measurements. Automatic or manual.
The measurement of a preamp's noise figure, or noise temperature, was discussed by Rainer Bertelsmeier, DJ9BV Myths and Facts about Preamp Tuning in Dubus long ago. Agilent has made this article available: http://cp.literature.agilent.com/litweb/pdf/5952-3706E.pdf
In all, the use of a standard instrument such as an Agilent HP8970A NF measuring set in conjunction with a HP346A 6dB ENR Noise Source can give serious errors and tuning an amplifier for the optimum reading may not lead to the optimum noise figure. The most important error is caused by the variation of the source impedance between hot and cold states. This problem should be eliminated by use of isolators/circulators. The absolute accuracy could be lower, but different amplifiers would have the same error provided that they all have a bandwidth well above the bandwidth of the NF meter.
Measurement of noise figures using Linrad.The most important measurement is the one we do while tweaking the amplifier for optimum performance. By measuring S/N for a signal that is sent through a room temperature attenuator one can totally eliminate the problem of impedance changes between hot and cold. There is only one temperature and the signal is present all the time.
A similar method has been available since 50 years or more, but not much used. Tweak amplifiers for minimum noise in FM mode on a stable, but weak carrier. This is an old clever method. Much better than using NF meters. It guarantees the optimum result - but it will not give any information about the absolute NF value. It is useful for comparing amplifiers however although one has to take into account that real life FM detectors are not ideal so one has to make sure that the signal level is the same all the time.
When using Linrad (version 03-41 or later) one can select to display S/N in the S-meter graph. S is computed with a narrow bandwidth using the baseband filter while N is computed from the full bandwidth of the hardware while excluding narrowband signals (spurs that may be present.) The signal can be evaluated in a narrow enough bandwidth to avoid any noise contribution. Since the noise is measured at the full bandwidth all of the time this method is a factor of four faster than conventional NF meters with a noise head because with them 50% of the time is spent on each of the noise head states and the result is a difference between two power levels. With a stable sine-wave, the power level can be evaluated with a very small uncertainty since very little noise would be present within the very small evaluation bandwidth for the signal. There is a pitfall however. One has to make sure that the frequency response is flat over the selected measurement bandwidth. When tuning selective preamplifiers one would tune for a narrower bandwidth rather than for a lower NF when comparing a signal at the passband center with the noise power over a wide bandwidth. For this reason one may need to use fairly small measurement bandwidths.
When evaluating the noise floor by use of a weak signal it is of course essential that the amplitude of the test signal does not vary with time. With normal commercial signal generators this is not a problem. One can do absolute measurenments by sending the signal through an attenuator and by varying the temperature of the attenuator.
The method and a first measurement of the NF of an amplifier using the PSA4-5043 MMIC from Minicircuits was presented here july 16 2012. using Linrad-03.41pre.
This link A study of several low noise amplifiers with Linrad-03.41 discusses the method in more detail.
It is repeated with better accuracy here: A study of several low noise amplifiers with Linrad-03.42
Tweaking low noise amplifiers.When tweaking amplifiers in a way that changes the frequency response one would get incorrect results if the noise bandwidth of the measurement system is larger than the flat bandwidth of the amplifier being optimized.
It will not be a good idea to use the 1.8 MHz bandwidth of a rtl-sdr for optimizing the frequency determining components in LNAs. Tuning currents and voltages is fine - and fast however.
By selecting a fairly narrow bandwidth for the noise measurement one can get NF directly on the S/N graph to use for tweaking amplifiers for optimum performance. For details, look here: Linrad as a NF meter. The differences in S/N directly give the system NF with a vey high accuracy but only if interferences can not leak into the test object or some other point in the signal path. The measurements with Linrad as a NF meter are not consistent with the results from using Linrad for hot/cold measurements. There are errors up to 0.1 dB which is far above the expected accuracy. Using water to keep the temperature constant requires some skill in water-proofing. These mesurements give the NF for a SWR of about 1.5 due to water inside the attenuator. Better screening in some cases and replacement of old cables having connectors with silvered center pins are other problems that affected the results. The link shows that accurate results are possible, and gives an idea on the problems one might encounter when trying to measure low noise figures very accurately.
This link S/N differences at 50 ohms. is a repetition of the experiment in the previous link. Here the attenuator is a precision attenuator carefully matched to 50 ohms. S/N is also measured at SWR=1.5.