Fundamentals
`of RF and Microwave
`
`
`PACKARD
`
`Application Note 57_‘l
`
`[if HEWLETT
`
`RPX—Farmwald Ex. 1041, p 1
`
`RPX-Farmwald Ex. 1041, p 1
`
`

`

`(53 SENSE
`
`Application Note 57-1
`
`
`
`
`
`Fundamentals
`of RF and Microwave
`:NOiiFigure Measurements
`
`Table of Contents
`
`1. Noise Characteristics of Two-port Networks ......................... 3
`Introduction .............................................................. 3
`Kinds of Noise ............................................................ 3
`Thermal Noise .......................................................... 4
`Shot Noise .............................................................. 4
`The Concept of Noise Figure ............................................... 5
`The Importance of Noise Figure Measurement ............................. 6
`Noise Characteristics of Linear Two-port Networks ......................... 7
`Noise Figure With the Straight Line ..................................... 8
`TL. With the Straight Line ................................................ 8
`Noise Figure and Te Compared .......................................... 9
`Gain and Available Gain ............................................... 10
`Measurement of Noise Figure and 'I‘t....................................... 11
`Some Typical Noise Figures .............................................. 12
`
`2. The Measurement of Noise Characteristics ........................... 15
`Noise Sources ............................................................ 15
`
`Noise Figure Meters ..................................................... 16
`ENE Variations with Frequency ........................................ 16
`Cold Noise Source Temperature ......................................... 16
`Second Stage Noise Contribution ....................................... 17
`Frequency Converters .................................................... 17
`Mixers ................................................................. 18
`Local Oscillators ....................................................... 19
`IF Amplifiers .......................................................... 20
`Y-Factor Measurement ................................................... 20
`Hot/Cold Measurement .................................................. 21
`Signal Generator Method ................................................. 22
`
`3. Appendix ............................................................... 2F)
`
`4. Glossary ................................................................ 29
`Symbols and Glossary Terms ............................................. 29
`References ............................................................... :18
`Checklist. Etc. ........................................................... 40
`
`RPX—Farmwald Ex. 1041, p 2
`
`RPX-Farmwald Ex. 1041, p 2
`
`

`

`1. Noise Characteristics of Two-port Networks
`
`Introduction
`Modern reCeiving systems must often process very weak
`signals. but the noise added by the system components
`tends to obscure those very weak signals. Sensitivity.
`SINAD, and noise figure are popular system parameters
`that characterize the ability to process low«level signals.
`Of these parameters, noise figure is unique in that it is
`suitable not only for characterizing the entire system but
`also the system components such as the preamplifier,
`mixer, and IF' amplifier that make up the system. By con-
`trolling the noise figure and gain of system components,
`the designer directly controls the noise figure ofthe overall
`system. Once the noise figure is known. system sensitivity
`can be easily estimated from system bandwidth. Noise
`figure is often the key parameter that differentiates one
`system from another, one amplifier from another, and one
`transistor from another. Such widespread application of
`noise figure specifications implies that highly repeatable
`and accurate measurements between vendors and their
`customers are very important.
`
`The reason for measuring noise properties ofnetworks is
`to minimize the problem of noise generated in receiving
`systems. The noise obscures weak signals. One approach
`to overcome noise is to make the weak signal stronger. This
`can be accomplished by raising the signal power transmit-
`ted in the direction of the receiver, or by increasing the
`amount of power the receiving antenna intercepts, i.e., by
`increasing the aperture of the receiving antenna. Raising
`antenna gain, which usually means a larger antenna, and
`raising the transmitter power are eventually limited by
`government regulations, engineering considerations or
`economics. The other approach is to minimize the noise
`generated within receiver components. Noise measure-
`ments are key to assuring that the added noise is minimal.
`Once noise joins the signals. receiver components can no
`longer distinguish noise in the signal frequency band from
`legitimate signal fluctuations. The signal and noise get
`processed together. Subsequent raising of the signal level
`with gain, for example, will raise the noise level an equal
`amount.
`
`The need for highly repeatable. accurate and meaning-
`ful measurements has. over the years. revealed several
`subtle measurement effects, that require correction fac-
`tors, and a host of noise related terms. These have contrib-
`uted to a mystique about noise figure measurements that
`brings anxiety to the neophyte. The HP 8970A Noise Fig-
`ure Meter uses a microprocessor to perform the tedious
`calculations. and corrects for many subtle effects that were
`formerly accepted as measurement errors or were corrected
`manually by highly skilled people. The major goal of this
`application note is to develop the reader‘s intuitive under-
`standing of noise measurements and to build a general
`
`knowledge about the effects ofnoise. Thus this note. along
`with the 8970A Noise Figure Meter, hopes to remove the
`mystique and replace the neophyte’s anxiety with confi-
`dence, thereby enhancing the art of making proper noise
`figure measurements.
`
`This application note is the first ofa series about noise
`and its measurement in radio frequency equipment. This
`first note discusses the fundamentals of noise measure-
`ment. Much of what is discussed is either background
`material or material that is common to most noise figure
`measurements. Other application notes will discuss more
`specific topics.
`
`The introductory chapter discusses why noise and its
`measurement are important, and the concepts that lead to
`the noise behavior of networks. The next chapter describes
`various measurement methods, old and new. and discusses
`the equipment needed for noise characterization. The
`appendix contains derivations ofseveral noise figure rela-
`tions thatsometimes puzzle the newcomer. The last part of
`this application note is an extensive glossary of noise
`related terms.
`
`The glossary serves several purposes. It is a convenient
`reference to noise figure terms which can be consulted as
`needs arise. The more usual treatment, not followed here,
`progresses from simple terms to more complicated terms or
`most general terms to most particular. Such developments
`pressure the inquisitive reader to read from beginning to
`end rather than to look up terms as his needs arise. Some of
`the terms in the glossary go beyond a dictionary type of
`definition to include considerable background and analy-
`sis. e.g., available gain, insertion gain, power gain and
`transducer gain. Some ofthe descriptions are paraphrased
`from referenced documents in an attempt to increase
`initial comprehension. The reader is encouraged to skim
`through the glossary to see what terms are there and to
`study the various entries in depth as necessary.
`
`A list of references occurs at the end of the glossary.
`Throughout the text of this note, numbers in rectangular
`brackets pertain to that list of references.
`
`Kinds of Noise
`
`The noise being characterized by noise measurements
`consists of spontaneous fluctuations caused by ordinary
`phenomena in the electrical equipment. Two principal
`types of such noise are thermal noise and shot noise.
`Thermal noise arises from vibrations of conduction elec-
`trons and holes due their finite temperature. Some of the
`vibrations have spectral content within the frequency
`
`3
`
`RPX-Farmwald Ex. 1041, p 3
`
`RPX-Farmwald Ex. 1041, p 3
`
`

`

`band of interest and contribute noise to the signals. Shot
`noise arises from the quantized nature of current flow.
`
`to within 10% up to 1000 GHz. Since 100 GHz covers most
`electrical equipment. the simple expression, kTB, will be
`used.
`
`Thermal Noise
`
`Thermal noise refers to the kinetic energy of a body of
`particles as a result of its finite temperature. If some parti-
`cles are charged [ionized], vibrational kinetic energy may
`be coupled electrically to another device if a suitable
`transmission path is provided. The power available, i.e.
`the maximum rate at which energy can be removed from
`the body, is kTB where k is Boltzmann’s constant [1.38
`MOT?a joules/kelvin ), T is the absolute temperature. and B
`is the bandwidth of the transmission path [18, 26]. The
`units of kTB are usually joules/second which are the
`same as watts.
`
`A brief examination of kTB shows that each of the fac-
`tors makes sense. Boltzmann's constant 1: gives the aver,
`age mechanical energy per particle that can be coupled out
`by electrical means per degree oftemperature. Boltzmann's
`constant is related to the universal gas constant IR of the
`gas law that states pv=NRTL R gives the energy per mole
`of gas per degree, but k gives the average energy per parti-
`cle per degree. The ratio R/k is equal to the number of
`particles in a mole which. of course. is Avogadro's number
`(6.02 x1046). Boltzmann's constant is thus a conversion
`constant between two forms of expressing energy — in
`terms of absolute temperature and in terms of joules.
`
`That the power available should depend directly on
`temperature is obvious. The more energy that is present in
`the form of higher temperature or larger vibrations, the
`more energy that it is possible to remove per second.
`
`That bandwidth should be part of the expression is, per-
`haps, not immediately obvious. Consider the example of a
`transmission band limited to the 10 to 11 Hr. range. Then
`only that small portion of the vibrational energy in the 10
`to 11 Hz band can be coupled out. The same amount of
`energy applies to the 11 to 12 Hr. hand :because the energy
`is evenly distributed across the frequency spectrum). If,
`however, the band were 10 to 12 Hz, then the total energy of
`the two Hz range, twice as much. is available to be coupled
`out. Thus it is reasonable to have bandwidth, B, in the
`expression for available power.
`
`It should be emphasized that kTB is the power available
`from the device. This power can only be coupled out into an
`optimum load, Le. a complex-conjugate impedance that is
`at absolute zero so that it does not send any energy back.
`
`The thermal noise power available. kTB. although de-
`pendent on bandwidth, is independent of frequency. The
`glossary gives a more exact expression that shows the very
`slight frequency dependence of the power available. The
`power density is constant to within 1% up to 100 GHz. and
`
`4
`
`It might seem that the power available should depend on
`the physical size or on the number of charge carriers. i.e.,
`the resistance. A larger body, after all, contains more total
`energy per degree and more charged particles would seem
`to provide more paths for coupling energy. It is easy to
`show with a counter example that the power available is
`independent of the size or of the resistance. Consider a
`system consisting of a large object at a certain tempera-
`ture, electrically connected to a small object at the same
`temperature. If there were a net power flow from the large
`object to the small object, then the large object would
`become cooler and the small object would become warmer.
`This violates our common experience— not to mention the
`second law of thermodynamics. So the power from the
`large objectmust be the same as thatfrom the small object.
`The same reasoning applies to a large resistance and small
`resistance instead of a large and small object.
`
`This brings up the point that if a source of noise is
`emitting energy it should be cooling off. Such is generally
`the case, but for the problems in electrical equipment, any
`energy removed by noise power transfer is so small that it
`is quickly replenished by the environment at the same rate.
`This means that sources of noise are in thermal equili-
`brium with their environment.
`
`For a more thorough treatment ofthermal noise, consult
`the references by Johnson | 18l and Nyquist |26I.
`
`Shot Noise
`Shot noise is caused by the quantized and random
`nature of current flow. Current is not continuous but
`quantized, being limited by the smallest unit of charge
`le=1.6 x1049 coulombs}. Particles of charge, furthermore.
`also flow with random spacing. The arrival of one unit of
`charge at a boundary is independent of when the previous
`unit arrived or when the succeeding unit will arrive. When
`dc current 10 flows. the average current is l”, but that does
`not indicate what the variation in the current is or what
`frequencies are involved in the random variations of cur—
`rent. Statistical analysis of the random occurrence of par-
`ticle flow yields (see, for example, Van der Ziell33]! thatthe
`mean square current variations are uniformly distributed
`in frequency and have a spectral density of
`
`
`inzm :29 I0 Aux/Hz
`
`11.1:
`
`This formula holds for those frequencies which have peri~
`ods much less than the transit time of carriers across the
`device. More exactly. the period must be much less than the
`width of each current pulse. The noisy current flowing
`
`RPX—Farmwald Ex. 1041, p 4
`
`RPX-Farmwald Ex. 1041, p 4
`
`

`

`through a load resistance forms the power variations
`known as shot noise.
`
`Other random phenomena occur that are quantized in
`nature and can be statistically analyzed in the manner of
`shot noise. Examples are the generation and recombina-
`tion of hole/electron pairs in semiconductors lG-R noise},
`and the division of emitter current between the base and
`collector in transistors (partition noise].
`
`A very important source of noise occurs in avalanche
`diodes because such devices are used as reference sources
`for measurement. Here a carrier achieves enough energy
`so that, upon collision with the crystal lattice. it is able to
`generate another hole/ electron pair. Some mobile carriers
`generate two pairs, some three, and then those can gener-
`ate other pairs, etc. The multiplication factor for the free-
`charge generation varies randomly and is also quantized.
`The noise power associated with the avalanche diode tends
`to be inversely proportional to current and somewhat
`dependent on frequency. The noise power vs. frequency
`relation depends on the current being conducted tsee Haitz
`| 11.12|i.
`
`Thus there are many causes ofrandom noise in electrical
`devices. Noise characterization usually refers to the com-
`bined effect from all the causes in a component. The com-
`bined effect is often referred to as ifit all were caused by
`thermal noise. Referring to a device as having a certain
`noise temperature does not mean that the component is
`that physical temperature, but merely that its noise power
`is equivalent to a thermal source of that temperature.
`
`The noise of this application note does not include
`human generated interference. although such interference
`is very important when receiving weak signals. This note
`is not concerned with noise from ignition. sparks, or with
`undesired pick-up of spurious signals. Nor is this note con
`cerned with erratic disturbances like electrical storms in
`
`the atmosphere. Such noise problems are usually resolved
`by techniques like relocation, filtering. and proper shield-
`ing. Yet these sources of noise are important here in one
`sense — they upset the measurements of the spontaneous
`noise this note is concerned with. For this reason, accurate
`noise figure measurements must often be performed in
`shielded rooms.
`
`at the output. Thus the noise figure of a network is the
`decrease or degradation in the signal-to-noise ratio as the
`signal goes through the netwurk. A perfect amplifierwould
`amplify the noise at its input along with the signal. (The
`source of input noise is often thermal agitation of free
`electrons in the atmosphere acting like signal to the ampli-
`fier.) A realistic amplifier. however, also adds some extra
`noise from its own components and degrades the signal—to-
`noise ratio. A low noise figure means that very little noise
`is added by the network. The concept of noise figure only
`fits networks that process signals — ones that have at least
`one input port and one output port. This note is mainly
`about two-port networks.
`
`It might be worthwhile to mention what noise figure
`does not characterize. Noise figure is not a quality factor of
`networks with one port; it is not a quality factor oftermi-
`nations or ofoscillators. Oscillators indeed generate noise
`and have their own quality factors like "carrier to noise
`ratio" and “single-sideband phase noise in a one hertz
`bandwidth. X hertz from the carrier". But receiver noise
`generated in the sidebands of the local oscillator that
`drives the mixer, acts like noise that gets added by the
`mixer. Such added noise increases the noise figure of the
`receiver.
`
`Noise figure also has nothing to do with modulation. ltis
`independent ofthe modulation format and ofthe fidelity of
`modulators and demodulators. Noise figure is, therefore,
`unlike SINAD, which is often used to indicate the qualr
`ity of FM receivers.
`
`Noise figure should be thought of as separate from gain.
`Once noise is added to the signal, subsequent gain ampli-
`fies signal and noise together and does not change the
`signalvto—noise ratio.
`
`Noise figure serves best for the low-signal-level portions
`of a system. It is normaily not a useful quality of high-
`power stages. Once the signal level achieves a high level,
`added noise is usually small in comparison and is no
`longer a source of aggravation or uncertainty. In analysis
`this shows up in the cascade effect tsee glossary]. The
`effect on noise figure of noise added by a device toward the
`output ofa system is divided by the gain that precedes that
`device. Since preceding gain is large by the time the signal
`reaches the high-power stages. the effect of added noise is
`small.
`
`The Concept of Noise Figure
`Before showing the importance of accurate noise mea-
`surement. itis necessary to define the most popularquality
`factor for noise performance, noise figure. Harold Friis | 7]
`defined the noise figure F ofa network to be the ratio ofthe
`signal-to-noise ratio at the input to the signaltonoise ratio
`
`Figure l-l(a) shows an example situation at the input
`of an amplifier. The depicted signal is 40 dB above the
`noise floor. Figure 1-l(b) shows the situation at the
`amplifier output. The amplifier’s gain has boosted the sig-
`nal by 20 dB. It also boosted the input noise level by 20 dB
`and then added its own noise. The output signal is now
`only 30 dB above the noise floor. Since the degradation
`
`5
`
`RPX—Farmwald Ex. 1041, p 5
`
`RPX-Farmwald Ex. 1041, p 5
`
`

`

`in signal—to-noise ratio is 10 dB, the amplifier has a 10 dB
`noise figure.
`
`IEEEJ adopted 290K as the standard temperature [6! for
`determining noise figure. Then equation lI-2l becomes
`
`40
`
`'E
`E. -m
`‘5 —an
`s
`E4”
`-1
`
`2.5
`
`us
`qulncinHfl
`ill
`
`2.7
`
`40
`
`E
`’33 -an
`z —oo
`gaw
`420
`an
`
`2-:
`
`2.5
`FWIGHII
`11’]
`
`Figure 1~1. Typical signal,r and noise tenets vs. frequency
`(a) at an amplifier's input and (b) at its output. Note that
`the noise level rises more than th e signal (eve! due to added
`noise from amplifier circuits. This reiatioe rise in noise
`tenet is expressed by the amplifier noise figure.
`
`Note that ifthe input signal level were 5 dB lower :35 dB
`above the noise floor) it would also be 5 dB lower at the
`
`output (25 dB above the noise floor}. and the noise figure
`would still be 10dB.Thus noise figure is independentofthe
`input signal level.
`
`A somewhat subtle effect will now be described. The
`degradation in a network’s signal-to-noise ratio is depen-
`dent on the temperature of the source that excites the
`network. To see why that is true, the ratio of the signal-to-
`noise ratios, i.e.. the noise figure, is
`
`Si/N-l
`
`SU/N0
`
`Si/Ni
`
`Gasza + 6,, Ni)
`
`Na+ GaN-l
`
`GuNi
`
`ll-2l
`
`represent the signal and noise levels
`where S,- and Ni
`available at the input to the device under test [DUTL S,U
`and N“ represent the signal and noise levels available at
`the output, N“ is the noise added by the DUT, and Ga is the
`available gain of the DUT. Equation t1v2) shows the
`dependence on noise at the input Ni . The input noise level
`is usually thermal noise from the source and is referred to
`by kTB. Friis |7I suggested a reference source temperature
`of290K {denoted by To l, which is equivalent to 16.806 and
`62.3"F. This temperature is close to the temperature seen
`by receiving antennas directed across the atmosphere at
`the transmitting antenna. The powerspectral density kT,,,
`furthermore. is the even number 4.00 2110—2.I watts per hertz
`of bandwidth (-174 dBm/Hzl. The IRE (forerunner of the
`
`6
`
`N, + k'l‘u BGfl
`= ——
`lrrn B0,,
`
`as;
`
`which is the definition of noise figure adopted by the IRE.
`
`Noise figure is generally a function of frequency but it is
`usually independent of bandwidth (50 long as the mea-
`surement bandwidth is narrow enough to resolve varia-
`tions with frequency). Noise powers Na and Ni ofequation
`{1-21 are each proportional to bandwidth. But the band-
`width in the numerator of ll-Zl cancels with that of the
`denominator — resulting in noise figure being indepen-
`dent of bandwidth.
`
`In summary. the noise figure of a DU'I‘ is the degrada~
`tion in the signal-to-noise ratio as a signal passes through
`the DUT. The specificinput noise level for determining the
`degradation is that associated with a 290K source temper-
`ature. The noise figure of a DUT is independent of the
`signal level so long as the DUT is linear. Because of the
`need for linearity, any AGC circuitry must be deactivated
`for noise figure measurements.
`
`The IEEE Standard definition of noise figure, eq il-Jh,
`states that noise figure is the ratio of the total noise power
`output to that portion of the noise power output due to noise
`at the input when the input source temperature is 290K. It
`is obviously related to the Friis definition by the above
`arguments.
`
`The Importance of Noise Figure
`Measurement
`
`The signal-to-noise ratio at the output of receiving sys-
`tems is a very important criterion in communication sys-
`tems. We frequently experience the difficulty oflistening to
`a radio signal in the presence of noise. The ability to inter-
`pret the audio information, however. is difficult to quantify
`because it depends on such human factors as familiarity
`with language, the nature of message, fatigue, training,
`and experience. Noise figure and sensitivity are measure-
`able figures of merit. Noise figure and sensitivity are
`closely related [sec Sensitivity in the glossary). For digital
`communication systems, a quantitative reliability mea
`sure is often stated in terms of bit error rate (BER) or the
`
`probability Pie! that any received bit is in error. BER is
`related to noise figure in a non-linear way. As theS/N ratio
`decreases gradually, for example, the BER increases sudv
`denly near the noise level where 1's and We become con;
`fused. Noise figure shows the health ofthe system but BER
`shows whether the system is dead or alive. Figure 1-2,
`which shows the probability of error vs. signal-to-noise
`ratio for several types ofdigital modulation, indicates that
`
`RPX—Farmwald Ex. 1041, p 6
`
`RPX-Farmwald Ex. 1041, p 6
`
`

`

`reduction in noise figure has about the same effect as
`increasing the antenna diameter by 10%. But increasing
`the diameter could change the design and significantly
`raise the cost of the antenna steering mechanism and sup-
`port structure.
`
`Noise Characteristics of Linear
`
`Two-Port Networks
`
`Although noise figure was described above, a deeper
`treatment of noise behavior is helpful to understand and
`clarify the man},Ir noise figure terms and concepts in popu-
`lar use, as well as to conceive, analyze, and refine noise
`measurement setups.
`
`At the low power levels of concern here. amplifiers, mix-
`ers, input stages of receivers. passive networks. and tran-
`sistors operate in the linear region. This means the power
`out is proportional to the power in. Ifthe input signal is set
`to zero, but the source impedance remains, the powerinput
`to devices is thermal noise from the source impedance.
`Linear devices will exhibit a straight line power output
`characteristic vs. source temperature as pictured in
`Figure 1-3.
`in Figure 1-3, the Y axis indicates the noise
`power at the output ofa DUT and the X axis indicates the
`absolute temperature of the source impedance that excites
`the DUT. At the origin of the X axis, where the source
`
` 0
`
`Sum 1mm lit}
`
`Tl
`
`Figure 1-3. The straight-line power output us. source
`temperature characteristic of linear, two-port devices. For
`a source impedance with a temperature of absolute zero,
`the power output consists soieiy of added noise Na from the
`device under test (BUT). Forothersoarcetemperatures the
`power output is increased by thermal noise from the source
`amplified by the gain-bandwidth characteristic of the
`BUT.
`
`RPX—Farmwald Ex. 1041, p 7
`
`f,
`
`BER changes by several orders of magnitude for only a few
`dB change in signal-to-noise ratio.
`
`it
`
`thdaililvnlEnur-l’lll°-.‘3.'3‘.‘i’.'i“i.
`
`10"“ a
`
`5 1012141513 21122 2:26
`GI'I'II' to None Hath - ldfl]
`
`Figure 1-2. Probability of error, Pfe), as a function of
`carrier-tortoise ratio, C/ N (which can be interpreted as
`signal-to-noise ratio}, for various kinds ofdigitai modula-
`tion. From Kamila Feher. DIGITAL COMMUNICA-
`TIONS: Microwave Applications, @1981, p. 71. Reprinted
`by permission of PrenticevHaii, Inc, Engiewood Cliffs,
`N. J.
`
`As explained above, the output signal—to-noise ratio
`depends on two things — the input signal-to-noise ratio
`and the noise figure. In terrestrial systems the input
`signal‘to-noise ratio is a function ofthe transmitted power,
`transmitter antenna gain, atmospheric transmission coef-
`ficient. atmospheric temperature. receiver antenna gain,
`and receiver noise figure. Lowering the receiver noise fig-
`ure has the same effect on the output signal-to—noise ratio
`as improving any one of the other quantities.
`
`At the system design level, consider the example of low-
`ering a receiver’s noise figure from 10 dB to 7 dB by adding
`an ordinary-quality, low-noise preamplifier in front of the
`receiver's mixer. This has the same effect on the signal-to-
`noise ratio as doubling the transmitter power. Doubling
`the transmitter power, if allowed, often doubles the price
`—more expensive than the ordinary low’noise preamp.
`
`In the case ofa production line that produces receivers, it
`may be quite easy to reducethe noise figure 1 dB by adjust-
`ing impedance levels or selecting transistors. That 1 dB
`
`RPX-Farmwald Ex. 1041, p 7
`
`

`

`temperature is absolute zero, electron vibrations in the
`source impedance are nonexistent and the noise power
`output from the DUT consists solely of noise generated
`within or added by the DUT, Na. For any other source
`temperature T3, the clectrou vibrations in the source act
`like signal to the DUT with available input noise power
`density, kTs watts/Hz (k is Boltzman's constant =1.3B
`xiii—23 joules/kelvin). IsT,3 is about —174 dBm/ Hz at room
`temperature. The input noise power gets amplified by the
`gainbandwidth product ofthe DUTto form additional out-
`put noise power, bringing the total output to Na+kT,GaB.
`The straight-line characteristic of noise power output ver-
`sus source temperaturehas slope kGB and Y—axic intercept
`N 3.
`
`Noise Figure With the Straight Line
`The straight-line characteristic is a complete description
`of noise performance. But such graphs are difficult to
`communicate. It is more common to find one or two figures
`of merit. One obvious figure of merit for this case is gain
`(proportional to the slope of the straight line). A second
`figure of merit, popularized in the 1940’s and 50’s, is noise
`figure. Systems of that era were terrestrial, and the noise
`received by antennas corresponded to atmospheric temp-
`eratures 1 about 290K ). For this reason, noise figure concen-
`trates on describing the noise chartacteristic at a lource
`temperature of 290K (Figure 1-4). The basis for defining
`noise figure is equation [1-3) which was already discussed
`but is repeated here
`
`, N, + kToBG,
`k'l‘oBGa
`
`(1-3)
`
`This equation shows that noise figure I", is the ratio oftotal
`noise power output, to that portion of the power output
`engendered by the 290K source temperature {the height of
`the shaded area in Figure 1-4). As indicated in the glos-
`sary, the numerical ratio is sometimes called noise factor
`and the ratio in dB is called noise figure. More often, how-
`ever, “noise figure” is used for both forms. There should be
`no confusion as to which is being considered because the
`units “dB” accompany the result of taking 10 log (ratio).
`
`T,3 With the Straight Line
`Satellite receivers began to come into beingin the 1960's
`and input noise levels to antennas fell toward the back-
`ground temperature of deep space (=4K). Device technol-
`ogy, furthermore, improved to the point where the noise
`added was less than 25% of kTaGBB (noise figures less than
`1 dB). For some of these applications, noise figure and its
`reference to 290K, has given way to another figure ofmerit,
`Te, the effective input noise temperature. Consider that a
`completely noise-free device, one that adds no noise of its
`own, would have a straight-line noise characteristic that
`goes through the origin as shown in Figure 1-5. If the
`Y-axis intercept, Na, of the actual DUT is projected horiz-
`
`8
`
`
`
`Figure 1-4. Noise figure shows the behavior at standard
`temperature To (=290K). Noise figure is the ratio ofthe total
`power output (Na + kToBGu) to that portion that is due to
`the amplified input noise power (I: TaBGa). Noise figure is
`usually expressed in dB.
`
`
`
`Figure 1-5. Effective input noise temperature T, shows
`how hot the source impedance driving a perfect {noise-free}
`device would have to be to contribute the some noise as the
`added noise of the DUT. It also turns out that —Te is the
`chxis intercept of thc‘strnight-line noise characteristic.
`
`zontally to the ideal device characteristic and then pro-
`jected down, the point Te occurs on the X axis. In other
`words, '1‘e is the source temperature whose noise power,
`multiplied by the gain-bandwidth product, equals the
`noise added.
`
`Another interpretation of Te is to translate the ideal
`straight-line characteristic {the one that goes through the
`origin) to the left until it is superimposed on the actual
`DUT characteristic. The distance of left translation is T,.
`
`RPX—Farmwald Ex. 1041, p 8
`
`RPX-Farmwald Ex. 1041, p 8
`
`

`

`This also means the extrapolated X~axis intercept of the
`DUT straight-line characteristic is the negative of Te.
`
`Te is a much better quality factor pertaining to noise
`than N 3 because Na is directly dependent on the gain of the
`DUT. N.l is affected. for example, by gain that occurs
`toward the output of the DUT after a lot of gain at the
`input. Such gain varies the slope of the straight line and
`the Y-axis intercept. Na, but not the X-axis intercept, 7T...
`
`The above descriptions of Te and F referred to the gain-
`bandwidth product of the DUT. The power measurement
`equipment at the output was assumed to be broadband
`Consider, however. having a narrowband, tunable power
`meter. Then the bandwidth and frequency of measurement
`are determined by the power meter. Different straight-line
`noise characteristics would likely be measured for differ-
`ent power meter frequencies showing that T9 and F are
`functions of frequency. The slope of the straight line is
`proportional to the bandwidth of power meter, the gain of
`the power meter. and the gain ofthe DUT. The characteris-
`tic at an individual frequency is often emphasized by the
`
`term “spot noise figure”. Very broadband noise figures are
`sometimes distinguished by the term “average noise
`figure”.
`
`Noise Figure and Te Compared
`When people learn that noise figure and Te characterize
`the noise performance ofdevices. they often feel compelled
`to select one of those figures of merit as the more useful. But
`there is no dominant use of one term over the other. For
`terrestrial applications, noise figure is almost universally
`used. This is probably due to tradition and due to'I‘e having
`inconveniently large numerical values (:600 to 300010.
`For space applications, however, T9 is more common. The
`range ofvalues forTe(:35 to 150K I is more convenient and
`has adequate resolution. Noise figure is approximately 0.5
`to 1.5 dB for space applications.