Mohr on Receiver Noise Characterization, Insights & Surprises

Transcription

1 Tutorial Mohr on eceiver Noise Characterization, Insights & urprises ichard J. Mohr, PE President,.J. Mohr Associates, Inc. Presented to the Microwave Theory & Techniques ociety of the IEEE Long Island ection

2 Purpose The purpose of this presentation is to describe the background and application of the concepts of Noise Figure and Noise Temperature for characterizing the fundamental limitations on the absolute sensitivity of receivers*. * eceivers as used here, is general in sense and the concepts are equally applicable to the individual components in the receiver cascade, both active and passive, as well as to the entire receiver. These would then include, for example, amplifier stages, mixers, filters, attenuators, circuit elements, and other incidental elements.. J. Mohr Associates, Inc. January 006

3 Approach A step-by-step approach is taken to establish the basis, and concepts for the absolute characterization of the sensitivity of receivers, and to provide the foundation for a solid understanding and working knowledge of the subject. ignal quality in a system, as characterized by the signal-to-noise power ratio (/N), is introduced, but shown to not be a unique characterization of the receiver alone. The origin of the major components of receiver noise and their characteristics are then summarized Noise Figure, F, is introduced which uniquely characterizes the degradation of /N in a receiver. The precise definitions of Noise Figure and of its component parts are presented and illustrated with models and examples to provide valuable insight into the concepts and applications. The formulation for the Noise Figure of a cascade of devices is derived and illustrated by examples.. J. Mohr Associates, Inc. January 006 3

4 Approach (Cont d) The concept of Noise Temperature, T e, is introduced and is shown to be directly derivable from Noise Figure. T e is shown to be a more concise characterization of the receiver alone, by completely eliminating source noise from the equation. Its application is illustrated by examples. The basic methods of measurement of Noise Figure and Noise Temperature are described and compared. Finally, a ummary reviews the material presented, and recommendations are provided for further study. eferences are provided An annotated bibliography follows that is intended to serve as a basis for further study. J. Mohr Associates, Inc. January 006 4

5 Introduction ignal/noise (/N) Characterization Introduction of vacuum tube amplifier Discovered there are limits on achievable signal sensitivity Achievable signal sensitivity in a Communication, adar, or EW receiving system is always limited ambient noise along with the output signal ignal quality is characterized by the final output ignal/noise (/N) ratio Depending on application, /N of at least 0 or 0 db, or more, may be required /N at the input of a receiver is the best it will be Each component in the receiver cascade, while performing its intended function, degrades the output /N. J. Mohr Associates, Inc. January 006 5

6 Introduction (Cont d) Factors Affecting ystem /N In a communication system, /N is a function of: Transmitter output power Gain of Transmit and eceive antennas Path loss eceiver noise - the topic of this presentation To characterize the receiver alone, Friis () introduced Noise Figure which characterized the degradation in /N by the receiver. Noise Figure of a receiver is the ratio of the /N at its input to the /N at its output. J. Mohr Associates, Inc. January 006 6

7 eceiver Noise ummary (Cont d) Thermal Noise (,3) Thermal noise (Johnson Noise) exists in all resistors and results from the thermal agitation of free electrons therein The noise is white noise (flat with frequency) The power level of the noise is directly proportional to the absolute temperature of the resistor The level is precisely e n 4kTB (V ), or 4kT (V /Hz) Where, k is Boltzman s constant.38x0-3 Joules/ºK T is the absolute temperature of the resistor in ºK is the value of the resistance in hms B is the effective noise bandwidth The available noise power is e n /4 ktb At TT 90ºK (the standard for the definition of Noise Figure), kt B 4.00x0 - W/Hz ( dbw/hz dbm/hz -4.0 dbm/mhz) Thermal noise in the resistance of the signal source is the fundamental limit on achievable signal sensitivity. J. Mohr Associates, Inc. January 006 7

8 eceiver Noise ummary (Cont d) hot Noise (4,7) hot Noise was studied by chottky, who likened it to shot hitting a target esults from the fluctuations in electrical currents, due to the random passage of discrete electrical charges through the potential barriers in vacuum tubes and P-N junctions Its noise characteristic is white The power level of the noise is proportional to the level of the current through the barrier In vacuum tube diodes, in temperature-limited operation, shot noise is precisely, i n (f) ei (A /Hz), where I is the diode current and e is the electronic charge.6x0-9 Coulombs Vacuum tube diodes, in temperature-limited operation, were the first broadband noise sources for measurement of receiver noise figure.. J. Mohr Associates, Inc. January 006 8

9 eceiver Noise ummary (Cont d) Flicker (/f) Noise (4,7) Flicker Noise appears in vacuum tubes and semiconductor devices at very low frequencies Its origin is believed to be attributable to contaminants and defects in the crystal structure in semiconductors, and in the oxide coating on the cathode of vacuum tube devices Commonly referred to as /f noise because of its low-frequency variation Its spectrum rises above the shot noise level below a corner frequency, f L, which is dependent on the type of device and varies from a few Hz for some bipolar devices to 00 MHz for GaAs FETs. J. Mohr Associates, Inc. January 006 9

10 eceiver Noise ummary (Cont d) Comparison of Levels of Major Components of eceiver Noise 000 Mean quare Noise Voltage(V ) 00 0 Jitter Precision Bipolar Jitter HF Bipolar Jitter MFET hot Noise, I DC 0.0A, Voltage across 50 hms: 8x0-8 V /Hz Thermal Noise, 90ºK, 50 hms: 8x0-9 V /Hz Jitter GaAsFET.E00.E0.E0.E03.E04.E05.E06.E07.E08.E09 Frequency (Hz). J. Mohr Associates, Inc. January 006 0

11 F / N / N Noise Figure, F Definition* () i i N GN i N GkT B GkT B GkT N B F is the Noise Figure of the receiver i is the available signal power at the input is the available signal power at the output N i kt B is the available noise power at the input T is the absolute temperature of the source resistance, 90 ºK N is the available noise power at the output, and includes amplified input noise N is the noise added by the receiver G is the available gain of the receiver B is the effective noise bandwidth of the receiver *The unique and very precise definition of Noise Figure and its component parts makes provision for a degree of mismatch between component parts of a receiver chain which is often necessary for minimum Noise Figure. J. Mohr Associates, Inc. January 006

12 Noise Figure Example, elating Noise Figure to ensitivity What level of input signal, i, is required for an output /N 0 db in a receiver with NF 6 db, and B0. MHz? From definition of F: N F N GkT B and so, FGkT B Input sensitivity is evaluated by referring the output noise, N, to the receiver s input, i.e. N Ni FkT B G N i (dbm) NF(dB)KT (dbm/mhz)0 Log B(MHz) dbm For a desired /N of 0 db, i must be at least: i -8 dbm0 db -08 dbm. J. Mohr Associates, Inc. January 006

13 Definition of Factors in Noise Figure Available Input ignal Power ( i ) i is the signal power that would be extracted from a signal source by a load conjugately* matched to the output of the source i.e.: E i E 4 i is dependent only on the characteristics of the source, specifically it is independent of the impedance of the actual load, L. For a load, L, the delivered power is less than the available power, but the available power is still i. * For simplicity and without loss of illustrative value, ideal transformers and reactive elements are not included in models here since they are loss-free and do not directly contribute to receiver Noise Figure. J. Mohr Associates, Inc. January 006 3

14 Definition of Factors in Noise Figure (Cont d) Available utput ignal Power, is the power that would be extracted by a load conjugately matched to the output of the network, i.e.: E Network E C E 4 C is dependent only on the characteristics of the network and its signal source, and the impedance match at its input is independent of the actual load, L, on the network For a load, L, the delivered power will equal the available output power, for L the delivered power will be less than the available output power, but the available output power is still Available output is maximum achievable when input is matched to. J. Mohr Associates, Inc. January 006 4

15 Definition of Factors in Noise Figure (Cont d) Available Gain*, G G i Definition is applicable to both active and passive devices G is independent of impedance match at output G is dependent on impedance match at the input In general, G is: Less than, or equal to, the maximum available gain Equal to the maximum available gain when source is matched to the input Greater than, or equal to, the insertion gain May be less than, greater than, or equal to, one (unity) *When used herein, G will always refer to the available gain. J. Mohr Associates, Inc. January 006 5

16 Definition of Factors in Noise Figure (Cont d) Available Gains f Elementary Networks Gain of eries esistor Gain of hunt esistor E H E E G E G E E 4( E i 4 E is greatest when ) E >> E G G H ( E H H E i H ) 4 4 is greatest when H H << H H H The gains of the resistor networks are less than one (), and are often expressed instead as a power loss ratio, L /G, which is then >; only G will be used here.. J. Mohr Associates, Inc. January 006 6

17 . J. Mohr Associates, Inc. January Definition of Factors in Noise Figure (Cont d) esistor L-ection Network Available Gains f Elementary Networks (Cont d) ) ( with maximum a is Gain ) )( ( 4, ) ( 4 G G G E E H E i L i E Available gain of L-ection is seen to be the product of the gains of the series section ( and ) and the shunt section ( in parallel with series connection of and )

18 Definition of Factors in Noise Figure (Cont d) Available Gains f Elementary Networks (Cont d) -Port Network Γ Network E G M G G M Γ G M Γ Where: Γ is the reflection coefficient of relative to the input characteristic impedance of the network G M is the maximum available gain of the network, i.e. the available gain with a matched input, Γ 0. J. Mohr Associates, Inc. January 006 8

19 Definition of Factors in Noise Figure (Cont d) Effective Noise Bandwidth, B Noise bandwidth, B, is defined as the equivalent rectangular pass band that passes the same amount of noise power as is passed in the usable receiver band, and that has the same peak in-band gain as the actual device has. It is the same as the integral of the gain of the device over the usable frequency band, i.e.: G( f ) B df G 0 Where: B is the effective noise bandwidth G(f) is the gain as a function of frequency over the usable frequency band G is the peak value of in-band gain Typically, B is approximately equal to the 3 db bandwidth. For greatest sensitivity, B should be no greater than required for the information bandwidth.. J. Mohr Associates, Inc. January 006 9

20 Definition of Factors in Noise Figure (Cont d) Available Input Noise Input noise, N i, is defined as the thermal noise (Johnson Noise () ) generated in the resistance of the signal source The input mean-square noise voltage is expressed concisely as (3) : Where i e ni is the mean-square noise voltage of the Thevinin voltage source, in V /Hz K is Boltzman s constant.38x0-3 Joules/ºK T is the absolute temperature of the resistor in ºK In noise figure analysis, standard temperature is T 90ºK is the resistance, in hms B is the effective noise bandwidth The available noise power, N i (W), from the resistor is: With T at 90ºK, N i 4.00x0 - W/Hz dbw/hz -74.0dBm/Hz -4.0 dbm/mhz N e n 4 kt 4kT B 4 B i kt B. J. Mohr Associates, Inc. January 006 0

21 Definition of Factors in Noise Figure (Cont d) Thermal Noise Models (Cont d) Thevinin Voltage Model Norton Current Model e n e n N 4kTB 4kTB 4 ktb i n g i n N 4KTgB 4KTgB 4g ktb Where: e n is the mean-square noise voltage of the Thevinin voltage source, in V /Hz i n is the mean-square noise current of the Norton current source, in A /Hz K is Boltzman s constant.38x0-3 Joules/ºK T is the absolute temperature of the resistor in ºK In noise figure analysis, standard temperature is T 90ºK is the value of the resistance, in hms g is the value of the conductance, in mhos B is the effective noise bandwidth, in Hz N is the available noise power, in W. J. Mohr Associates, Inc. January 006

22 Definition of Factors in Noise Figure (Cont d) Thermal Noise Models (Cont d) Will network of resistors provide more noise power than ktb? eries Voltage Model hunt Current Model e n e n i n i n g g e n N e n e n 4kTB( 4( ) 4kTB( ) ktb ) i N i i 4kTB( g n n n 4kTB( g g 4( g g ) g ) ktb ) Available noise power from network of resistors at T is still just ktb. J. Mohr Associates, Inc. January 006

23 Definition of Factors in Noise Figure (Cont d) Thermal Noise Models (Cont d) eries resistors at different temperatures e n e n T T e n 4kB N e n [( ) T ( T T )] kt B G e e 4( E n n k( T 4kB( T ktb k( T ) T ) B T ) T ) B When T T, the second term in N - disappears and N - kt B When T T, the term k(t -T )B may be considered the excess available noise power of the source resistor,. For noise calculations, the excess available noise power may be treated as though it was signal The excess noise power is then attenuated by the term, /( ), which is recognized as the gain of the series resistor, and the attenuated result adds to the kt B, power at the output* *When T <T, then N - <kt B. J. Mohr Associates, Inc. January 006 3

24 Noise Figure f Elementary Networks ptimum ource Impedance for Minimum Noise Figure Each component in a receiver cascade can be characterized by an available Noise Figure (F) and available gain (G) The available noise figure of each component is dependent only on its source impedance within the receiver chain Every component having a noise figure has an optimum noise figure which is achieved when it is supplied from its optimum source impedance The optimum source impedance for components is not always the same as required for maximum gain, and so there will be an optimum input mismatch In such cases, although the operational available output signal is reduced, the available output noise is reduced proportionally more. J. Mohr Associates, Inc. January 006 4

25 Noise Figure f Elementary Networks (Cont d) F of eries esistor F of hunt esistor, T E E, T E, T E H, T H F N GkT T T E B G Where, G kt Noise figure is minimum when E B Gk( T T GkT B E E ) B >> E F N GkT B kt H TH T G H Where, G B Gk( T T GkT B H Noise figure is minimum when H ) B << H. J. Mohr Associates, Inc. January 006 5

26 Noise Figure f Elementary Networks (Cont d) Attenuators, Lossy Line ections, T E Γ Lossy Network G M,T X N N ktx B Gk( T TX ) B TX F GkT B GkT B T G Γ Where G is: G GM G Γ M By inspection, F is least when G is greatest ( is matched to the characteristic input impedance of the network Γ 0 ). J. Mohr Associates, Inc. January 006 6

27 Noise Figure f Elementary Networks (Cont d) Active Devices implified noise model for active devices references all noise sources to input e ni e nd i nd,t G N utput noise power, N, referenced to input is: N N i i e kt ni end i 4 nd Ni end ind F Ni 4kT F is minimum when 4kTo e nd i nd e 4 nd i nd and is, F e kt nd. J. Mohr Associates, Inc. January 006 7

28 Noise Figure f Elementary Networks (Cont d) Example, Active Device Find optimum noise figure and required source impedance for amplifier with input voltage and current noise sources for the amplifier specified as: e n.6x0-8 V /Hz and, i n 4x0-3 A /Hz F is minimum when Therefore : F.6x0 4x0 8 3 e nd 00 hms i nd and is, F -8.6x0 ; NF 3dB -3 (.38x0 )(90)(00) e kt nd. J. Mohr Associates, Inc. January 006 8

29 Cascade Formula for Noise Figure Noise Figure, F for cascade of or more devices G, F G, F i KT B G i N F G KT B G G i N G N 0 N G G F kt B(F -)G kt B GG F kt B ( F ) GkT F GG kt B In general, for cascade of n devices: B F F G F n F F G F3... G G F G G n... G n. J. Mohr Associates, Inc. January 006 9

30 Cascade Formula for Noise Figure (Cont d) ptimization Example In the example on lide 8, it was determined that the amplifier has an optimum noise figure, NF, of 3 db when operated from a source impedance of 00 hms. When operating from a source of 50 hms, what is the best way to optimize for best noise figure? Using the cascade approach, the analyses below illustrate two optimization approaches. Which is best? ptimize with series 50 hm resistor ptimize with input step-up transformer E,T F F F G, T E NF F dB E :, T NF F F F 3dB G esistors in input matching networks adversely impact noise figure!. J. Mohr Associates, Inc. January

31 Cascade Formula for Noise Figure (Cont d) G (db) T, T e ºK F (db) G (atio) G -k (atio) F* (atio) () () ignal ource (3) Example, eceiver Cascade Component No.:. () () (3) (4) (5) (6) (7) Line Losses F dB (4) BPF (5) Preamp (6) Line Losses (7) Mixer IF Ampl cvr *For a resistive element, F TX T G. J. Mohr Associates, Inc. January 006 3

32 ystem Noise Temperature Formulations Derivation In low-noise systems and with low source temperature, T <<T, treatment in terms of noise temperature (7), rather than noise figure, is frequently preferred. Derivation follows. utput noise power level, N, for system operating from source at T is: N FGkT BGkT B(F-)GkT B With a source temperature at T, N GkT B(F-)GkT BGkB(T T e ) Where T e (F-)T is defined as the effective input noise temperature of the receiver*. The total equivalent noise temperature of the system referenced to its input terminals is T Y T T e. *T e is more concise than F in defining the noise performance of a receiver in that it is independent of source temperature.. J. Mohr Associates, Inc. January 006 3

33 ystem Noise Temperature Formulations, (Cont d) ystem ensitivity Analysis Using Noise Temperature ignal source is antenna, pointed at sky with effective temperature, T a 30ºK. eceiver system noise figure is NF0.5dB, F.:. The equivalent noise temperature of the receiver is: T e (.-)9035.4ºK Therefore effective system noise temperature is: T Y T a T e (3035.4)65.4 ºK Equivalent input system noise is*: N -74(dBm/Hz)0 log(65.4/90) dbm/hz *The term: -74(dBm/Hz) is the thermal level for 90ºK; the term: 0 log(65.4/90), corrects for a system noise temperature of 65.4 ºK. J. Mohr Associates, Inc. January

34 . J. Mohr Associates, Inc. January ystem Noise Temperature Formulations (Cont d) Cascade Formulation For cascade of n devices the noise temperature of the cascade is, e Y n n n n n n e e T T T T G G G T G G T G T T T G G G F G G F G F F T F T T is; the system,including the source at Noise Temperature of The ) ( 3 3

35 ystem Noise Temperature Formulations (Cont d) Example eceiver Analysis Ta30ºK () () (3) (4) (5) (6) Gain (db) Gain atio F(dB) T(ºK) Te(ºK)* Line Loss *For a resistive element, Preamp Line Loss T e T G Postamp J. Mohr Associates, Inc. January 006 Line Loss CV Te Te 3 Te 4 Te 5 Te 6 Te Te G GG GG G3 G... G4 G... G x x5.9x x5.9x0.989x x5.9x0.989x5.x00 () () (3) (4) (5) (6) K 35

36 Measurement of Noise Figure ignal Generator Method (5,7) ignal Generator DUT Power Meter Procedure Tune ignal generator over frequency to measure output variation of power From data, determine B (lide ) Turn signal generator off, and note output noise power level, N FGkT B Turn signal generator on and tune to frequency of maximum G; adjust its level to i to just double output indication, to N Then G i FGkT B, and F i /kt B NF(dB) i (dbm)4-0 log B(MHz) Example B0.5 MHz, (-3 db MHz) i -90 dbm Therefore: NF(dB)-904-(-3)7 db. J. Mohr Associates, Inc. January

37 Measurement of Noise Figure (Cont d) Calibrated Noise ource Method (Y Factor) (7) Calibrated T H, T C ource DUT Power Meter Y kt H B kt C B N N H C FT FT T T H C T T ; TH T F N H FGkT B(T H -T )kbg N C FGkT B(T C -T )kbg T Y T Y C Example: T H 0,90ºK (argon source), T C 300ºK Measured Y factor: Y9 db (7.94:) Then, F 4.94; NF( db) 0 log(4.94) 6. 9dB J. Mohr Associates, Inc. January

38 Measurement of Noise Figure (Cont d) Comparison of Measurement Methods Advantages Disadvantages ignal Generator Method Accurate results even with significant out-of-band responses Useful for measurement of devices with high noise figure equires separate measurement of B Not easily adaptable to automatic measurements Noise ource Method Does not require separate determination of B Measurement is simple and straight-forward Lends itself to automatic measurements Capabilities of available noise sources don t allow measurement of devices with high noise figure equires correction for presence of out-of-band responses. J. Mohr Associates, Inc. January

39 Presentation ummary The background and application of the concepts of Noise Figure and Noise Temperature for characterizing the fundamental limitations on the absolute sensitivity of receivers were set forth in a step-by step approach and illustrated with examples to provide insight into the concepts. The origin of the major components of receiver noise, and their characteristics were summarized. ample Noise Figure and Noise Temperature analyses of receiver systems were illustrated. The basic methods of measurement of Noise Figure and Noise Temperature were described and compared. eferences and a Bibliography follow. The Bibliography is intended to serve as a basis for further study.. J. Mohr Associates, Inc. January

40 eferences () Friis, H.T., Noise Figures of adio eceivers, Proc. f the IE, July, 944, pp 49-4 () Johnson, J. B. Thermal Agitation of Electricity in Conductors, Physical eview, July, 98, pp (3) Nyquist, H. Thermal Agitation of Electric Charge in Conductors, Physical eview, July, 98, pp. 0-3 (4) Joshua Israelsohn. Noise 0, EDN January 8, 004, PP (5) tanford Goldman. Frequency Analysis, Modulation and Noise. McGraw- Hill Book Company, Inc., 948 (6) Van der Ziel, Aldert. Noise:ources, Characterization, Measurement, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 970 (7) D. C. Hogg and W. W. Mumford, The Effective Noise Temperature of the ky, The Microwave Journal, March 960, pp J. Mohr Associates, Inc. January

41 Bibliography Agilent Application Notes The following 5 Agilent Application Notes are highly recommended for study and reference. Together, they provide excellent material on noise figure and noise temperature. They progress from the background of noise and receiver sensitivity, through a summary of computer-aided design of amplifiers for optimum noise figure, description of measurement setups and techniques, including analysis of measurement uncertainty. They include comprehensive lists of references. They can be ordered from the Agilent web site. Fundamentals of F and Microwave Noise Figure Measurements, Application Note 57- Noise Figure Measurement Accuracy- The Y-Factor Method, Application Note 57-0 Hints for Making uccessful Noise Figure Measurements, Application Note 57-3 Noise Figure Measurement of Frequency Converting Devices, Using the Agilent NFA eries Noise Figure Analyzer, Application Note 487 Practical Noise-Figure Measurement and Analysis for Low-Noise Amplifier Designs, Application Note J. Mohr Associates, Inc. January 006 4

42 Bibliography (Cont d) Text Books van der Ziel, Aldert. Noise: ources, Characterization, Measurement, Prentice- Hall, Inc., Englewood Cliffs, New Jersey, 970.-Everything you ever wanted to know about noise but were afraid to ask. The classic text on the subject. Covers noise and noise models for devices, at a high technical level tanford Goldman. Frequency Analysis, Modulation and Noise. McGraw-Hill Book Company, Inc., 948. I Norman Dye and Helge Granberg. adio Frequency Transistors, Principles and Applications, EDN eries for Design Engineers, Motorola eries in olid tate Electronics. Contains examples of noise figure analysis models of amplifier stages. J. Mohr Associates, Inc. January 006 4

43 Background Bibliography (Cont d) Johnson, J. B. Thermal Agitation of Electricity in Conductors, Physical eview, July, 98, pp This is the classic paper on measured thermal noise in resistors. It showed that the mean square thermal noise voltage at the terminals of a resistor were proportional to the magnitude of the hmic value of its resistance and to its absolute temperature. The noise voltage is referred to as Johnson noise in his honor. Nyquist, H. Thermal Agitation of Electric Charge in Conductors, Physical eview, July, 98, pp This is the classic paper companion paper to the Johnson Paper which related the Johnson noise to the fundamental laws of thermodynamics and arrived at the famous, KTB Friis, H.T., Noise Figures of adio eceivers, Proc. f the IE, July, 944, pp This is the classic paper on Noise Figure. It should be reviewed as an excellent example of a concise presentation of an important concept.. J. Mohr Associates, Inc. January

44 Background (Cont d) Bibliography (Cont d) Harold Goldberg. ome Notes on Noise Figure, Proc. f the IE, ctober, 948, pp The paper is a tutorial based on the Friis paper. It carefully explores the basics concepts of noise figure and illustrates their application, progressing from elementary networks to low-noise vacuum tube amplifier configurations. The paper s approach served as a model for this presentation. Kurt tern. Fundamentals of Electrical Noise, Presentation to the IEEE MTT ection of Long Island NY, January, 004. This reviews the basics of noise figure and its measurement. It includes detail of automatic measurement setups and of available test equipment. The presentation is available on the web site for the LI NY MTT Chapter of the IEEE Joshua Israelsohn. Noise 0, EDN January 8, 004, PP Good summary on thermal, shot, and jitter noise.. J. Mohr Associates, Inc. January