1846 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 6, JUNE 2011
Estimation of Coupled Noise in Low Noise PhasedArray Antennas
Mousumi Roy, Student Member, IEEE, and Danielle George, Member, IEEE
Abstract—There is currently a great deal of interest in the useof phased array receivers for radio astronomy. The Square Kilo-meter Array (SKA) project plans to utilize phased arrays in at leastthree different forms: as sparse and dense aperture arrays on theground, and as phased array feeds on dishes. At frequencies abovea few hundred MHz it will be vital to obtain very low noise temper-ature performance from these arrays in order for them to be prac-tical as radio astronomy receivers. Receiver noise coupled betweenantenna elements has been thought to be a significant contributorto overall system noise in such phased arrays. This paper uses fun-damental principles of noisy networks to estimate the noise wavesemanating from the input of each LNA towards the antenna ele-ment. The theory has been implemented using MATLAB, and suc-cessfully used to predict the noise levels emanating from the inputports of two packaged amplifiers. The theory has been applied toan example two-antenna array model. Results from the noise waveanalysis suggest that in reality the coupled noise contribution tosystem noise temperature should be quite small for practical lownoise amplifiers of the type to be used in the SKA.
Index Terms—Noise temperature, wave representation of noise,noise in antenna arrays, low noise amplifiers, LNA, square kilo-metre array, SKA.
I. INTRODUCTION
A VARIETY of antenna elements are expected to be usedfor the Square Kilometre Array (SKA) [1]; each of these
will be coupled, with minimum loss, to a low noise amplifier(LNA). Several thousands of modest size (by astronomy stan-dards) dishes will be equipped with wide band ‘single-pixel’feeds; apart from the wide bandwidth these systems will be sim-ilar to the traditional radio astronomy receptors in use today,and their noise performance can be analyzed in a straightfor-ward manner using well-known techniques. A proportion of thedishes are expected to be equipped with phased array feeds,each comprising of order 100 close-coupled antenna elements.The design of these feeds will draw on the development ex-perience of the APERTIF programme in the Netherlands [2],the ASKAP programme in Australia [3], and the PHAD pro-gramme in Canada [4]. Additionally, a large part of the SKAis expected to consist of multiple ground-mounted dense aper-ture arrays (other radio astronomy projects such as LOFAR [5],
Manuscript received December 30, 2009; revised September 10, 2010; ac-cepted November 02, 2010. Date of publication March 07, 2011; date of currentversion June 02, 2011.
The authors are with the School of Electrical and Electronic Engi-neering, University of Manchester, Manchester M60 1QD, U.K. (e-mail:[email protected]; [email protected]).
Digital Object Identifier 10.1109/TAP.2011.2123054
MWA [6] and PAPER [7] are already using aperture arrays onthe ground). The SKA aperture arrays are expected to be ap-proximately 60 metres in diameter, each consisting of hundredsof thousands of close-coupled antenna elements. At frequenciesabove a few hundred MHz it will be vital to obtain very lownoise temperature performance from these arrays in order forthem to be practical as radio astronomy receivers.
Noise analysis of the phased array feeds and dense aperturearrays is much less straightforward than the single-pixel feedcase. One aspect of the system noise for these arrays that hasreceived much attention is the coupled noise between antennaelements: noise emanating from the input of a low noise am-plifier is coupled into adjacent antennas [8]–[10]. An analysistechnique based on the concept of ‘active impedance’ has beendeveloped by Maaskant et al. [11]. Some results of this anal-ysis suggest that surprisingly high levels of noise may be cou-pled between antenna elements, thus degrading their sensitivity.The work in this paper presents an alternative approach to noiseanalysis of phased arrays. It looks at the coupled noise from thepoint of view of noise waves emanating from the input of eachLNA, considering theory to evaluate these noise levels from theknowledge of the four noise parameters. It is based on the fun-damental principles of noisy networks. The theory has been im-plemented using MATLAB [12], and used to predict the noiselevels emanating from the input ports of two packaged ampli-fiers, after their noise parameters have been determined with ap-propriate tuner measurements. Measurements have then beenperformed to experimentally determine these levels, in termsof effective temperatures, for the two amplifiers. The measuredtemperatures show good agreement with the theoretically pre-dicted values. As such, it can be concluded that the theoreticalapproach is valid.
Some similar work has been previously described in radio-as-tronomy [13], where the authors estimate the equivalent noisetemperature in terms of the noise current flowing through thesource impedance, when source inductive feedback is used in anamplifier design to obtain a better VSWR. However, the deriva-tion is valid only when the input side is matched for maximumgain. The theory developed as part of this paper is more generalin the sense that it is based on no assumptions about the tech-nology of the amplifier, and is valid for any noisy two-port.
Much work has previously been carried out to determine thenoise levels emanating from the input of LNAs. Engen and Wait[14], [15] have published significant work in deriving a formulafor the effective temperature at the input port of an LNA, .In their theoretical approach, they have expressed it in termsof both the amplifier’s noise and scattering parameters. Theyhave also outlined a method to directly measure of an
ROY AND GEORGE: ESTIMATION OF COUPLED NOISE IN LOW NOISE PHASED ARRAY ANTENNAS 1847
Fig. 1. Wave representation of a linear noisy two-port, from [20].
Fig. 2. Rothe-Dahlke model of a linear noisy two-port, from [21].
LNA. Wait, Randa and Walker [16], [17] have carried out fur-ther measurements of the reverse temperature. Since isnot normally used to determine the four noise parameters, Randaand Wait use the measurements as an independent check of themeasured noise parameters. Weatherspoon and Dunleavy’s [18]work provides equivalent results, but rely on extremely accuratemeasurements, which will be particularly difficult to achieve forthe ultra low noise amplifiers required by the SKA. This workdiffers in that rather than rely completely on measurements, wehave used well-established theoretical techniques to determinethe noise amplitudes. However, as mentioned previously, thesetheoretical predictions have then been verified by measurementson two packaged amplifiers in the laboratory and very goodagreement has been found between the theoretical predictionsand the measured results.
Section II describes the theoretical principles that havebeen used to estimate the noise temperatures. Measurementtechniques used to verify the theory have then been discussedin Section III. Results of noise measurements on two packagedamplifiers have been presented in Section IV, alongside theircomparison to the theoretical values. Finally, in Section V,the theoretical principle has been used to estimate the amountof noise coupling between adjacent antennas in a low noisephased array system like the SKA.
II. THEORY
Wave representation of noise in linear two-ports was origi-nally proposed by Bauer and Rothe [19], and further work wasdone by Penfield [20]. In this representation, a noisy two-portis replaced by two uncorrelated noise-wave sources in the for-ward and reverse direction, and , respectively, at the inputof the noise-free two-port, as shown in Fig. 1. These sourcesare related to the noise voltage and current sources, and , ofthe Rothe-Dahlke model [21], shown in Fig. 2, through the re-lations:
(1)
(2)
(3)
where is a normalizing impedance.
The noise wave sources and are associated with tem-peratures and defined by
(4)
(5)
where is Boltzmann’s constant and is the frequency in-terval. For our scenario, we are interested in evaluating the tem-perature of the noise wave travelling from the input of anLNA towards the antenna, plus any component of the temper-ature of the noise wave reflected back from the input ofthe two-port. Penfield has provided closed-form expressions ofthese temperatures in terms of the four noise parameters as well[20]:
(6)
(7)
These equations are simple to use, however they are valid onlywhen the noise waves are normalized to the optimum sourceimpedance of the two-port. This is the ideal noise-match condi-tion, when the noisy two-port is looking into an impedance of
at its input. Under this condition, the correlation compo-nent of noise generated by the correlation between the forwardand the reverse wave vanishes [20]. However, phased array feedslike the SKA can be very sensitive to this correlated noise, soin the relevant computations, this noise correlation componentmust be taken into account. The work done by Meys [22] andWedge and Rutledge [23] are significant in this context. In theseformulations, two correlated noise waves are used, the advan-tage being that the noise waves are normalized to an arbitraryreal characteristic impedance of the surrounding transmissionline or waveguide elements.
Like Penfield, Meys defines both the forward and reversewaves at the input, and additionally defines a temperatureassociated with the correlated component , the magnitudeand angle of which are given by
(8)
(9)
Both the approaches discussed so far consider noise wavesat the input of the two-port. Wedge and Rutledge [23] outlinedanother approach to look into the problem by considering noisewaves and at the input and output, respectively, of the noisytwo-port, as shown in Fig. 3. As is observed, if the two-port isrepresented by the S-parameter matrix S, then the waves in Meysand Penfield’s approach are incorporated in the equation by
(10)
whereas the waves in Wedge and Rutledge’s approach are givenby
(11)
1848 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 6, JUNE 2011
Fig. 3. Wedge representation of a linear noisy two-port, from [23].
The noise powers delivered to the terminations in a 1-Hzbandwidth, and , and the correlation power givenin terms of the noise and S-parameters of the two-port are [23]:
(12)
(13)
(14)
is the noise temperature of the two-port multiplied bythe gain of the two-port (considering a 1-Hz bandwidth). It canbe observed that the correlation power in (14) becomes zero ifboth and are zero.
Though both the Meys’ and Wedge and Rutledge’s represen-tations consider the correlated noise, we prefer to use the latterfor our purpose owing to the following reasons:
i) Expressions of the noise powers in equations (12)–(14)include the S-parameters making computations easier.
ii) is the deliverable noise power to the input termina-tion (in our case an antenna element) in a 1-Hz bandwidth[23], which is basically the quantity we are interested in.Let C1 be the temperature associated with this deliverablenoise power .
iii) It might be of interest to know the noise temperatures C2of the two-port at the output as well, which is given by
straightaway.iv) Circuit simulation softwares like ADS [24] calculate
noise powers based on this approach, thus verification bysimulation, if required, becomes considerably easier.
It should be reiterated that any of the three approaches dis-cussed above can be used for determination of the effective tem-perature of the reverse noise wave emanating from the input portof any noisy two-port, each with its limitations. However, theWedge and Rutledge’s approach is chosen here because of itscompleteness and the advantages discussed above.
III. VERIFICATION
A. Measurement of Noise Coming Out From the LNA InputPort
To verify that the noise coming out from the input port of theDUT was indeed equal to the theoretically calculated value ofC1, we used the experimental set-up shown in Fig. 4. This set-upis very similar in principle to the set-up used in [16] and [17].
Fig. 4. Experimental set-up for determination of the effective temperature ofthe reverse noise wave emanating from the DUT.
However, whereas in [16], a standard radiometer has been used,we used a standard noise figure meter, model HP8970B, as anoise power receiver. The noise figure meter was set to displaynoise power ratio in dB, relative to 290 Kelvin. Thus it is givenby
(15)
where is the temperature associated with the unknown powerspectral density and is expressed in Kelvin. Since the DUT wasconnected in a reverse manner, this was also the effective reversenoise temperature we wanted to determine. Accuracy of themeasurements was limited to some extent by the noise figure ofthe instrument, which was of order 6 dB. Addition of a low noisepreamplifier improved this. An isolator was connected beforethe preamplifier, as shown. Calibration was done with a standardAgilent noise diode, model 346B, connected to the isolator port1. Inclusion of the isolator in the measurement set-up, betweenthe DUT and preamplifier, removed the following sources of er-rors:
i) The noise wave emanating from the input of the preampli-fier, reflected by the input of the DUT and sent back to themeasurement system. This contribution would be smallin the case of low input reflection coefficient of the DUTand/or a very low noise preamplifier. This effect couldalso be theoretically corrected for, but then the noise pa-rameters of the preamplifier would have to be known. Theuse of an isolator previous to the preamplifier eliminatedthis requirement. Any noise coming out of the preampli-fier input would be absorbed by the matched termination(50 ) at port 3 of the isolator. For an ideal isolator thenoise parameters are well determined and it was neces-sary only to know the magnitude of the reflection coeffi-cient of the DUT.
ii) The portion of the noise wave emanating from the inputof the DUT which is reflected back by mismatch at theinput of the preamplifier. Together, these two effects cangive rise to a standing wave pattern.
However, even with the use of an isolator, the following noisecomponents would remain:
Component 1: Noise generated by the matched termination(50 ) at port 3 of the isolator, reflected by the input of theDUT, and incident on the measurement system.Component 2: Noise generated by the matched termination(50 ) at the output of the DUT transmitted to the input. In
ROY AND GEORGE: ESTIMATION OF COUPLED NOISE IN LOW NOISE PHASED ARRAY ANTENNAS 1849
case of an amplifier however, if the reverse transmission issmall, this can be neglected.
Thus, the total noise incident on port 1 of the isolator wasgiven by the sum of the noise from the DUT input, component1 and component 2. The input mismatch of the isolatorwas another potential source of measurement error, so this wasaccounted for in the calculations. This is discussed in detail inSection IV.
The noise parameters of amplifiers are not always providedby the manufacturers. Without the noise parameters, it was notpossible to determine the value of C1 theoretically using themethod described in the previous section. Therefore tuner mea-surements were performed to extract the noise parameters of theDUT when they were not provided. The procedure we used isdetailed below.
B. Tuner Measurements to Determine the Noise Parameters
As is well known, noise parameters of any circuit are usu-ally determined by analyzing the variation of the measurednoise figure as a function of source impedance. The sourceimpedance is varied by connecting the input terminal to a tuner,the impedance of which can be adjusted, either manually orelectronically.
The least-square fit curve is then determined for the mea-sured values of the noise figure. Ideally, only four measurementsshould be enough to determine the four unknown noise param-eters. Various approaches and computer algorithms have beendeveloped previously to improve the accuracy of the best-fit.One such approach [25] uses a set of redundant measurements(seven instead of four) to calculate four new parameters A, B, Cand D from the measured noise figure. Based on this principle,we developed a programme using the National Instruments Lab-VIEW software [26]. To improve the accuracy our programmetook into account two more parameters before estimating thenoise parameters—the gain of the input network (the tunerin our set-up) and its output reflection coefficient, from the prin-ciple described in [27].
This required measurement of two of the S-parameters of thetuner circuit, more specifically its forward transmission coeffi-cient and the output reflection coefficient, and ,respectively, using a standard vector network analyzer. A simpleswitch configuration was used to switch the connection betweenthe noise figure meter and the VNA. The block diagram for thisset-up is shown in Fig. 5. As can be seen, switches S1 and S2could be effectively used to
a) connect the tuner to the noise diode on one side and theDUT on the other side, which were already connected tothe noise figure meter—to measure the noise figure of thetuner and DUT.
b) connect only the tuner to the VNA—to measure its outputimpedance (input impedance when seen from the DUT),and also and .
The noise figure meter and the VNA were calibrated to thepoints where they connect to the switches. The measured noisefigure, the gain of the tuner , and magnitude and angle ofthe output reflection coefficient of the tuner, , were thenused as input parameters to the LabVIEW programme to obtainthe four noise parameters. These were then used to obtain the
Fig. 5. Experimental set-up for determination of noise figure of the DUT andthe impedance presented by the tuner.
Fig. 6. Measured minimum noise figure and noise figure of ZX60-2522-M andZX60-3018-G amplifiers.
values of the effective temperatures of the reverse noise wave C1theoretically (using the MATLAB programme discussed previ-ously).
IV. RESULTS
Tuner measurements and S-parameter measurements oftwo Mini Circuits packaged amplifiers ZX60-2522M [28]and ZX60-3018-G [29] were carried out, using the methodoutlined in [25], to determine their noise parameters. ForZX60-2522M, measurements were performed at a DC biasof 5 V. For ZX60-3018-G, the DC bias was 12 V. The fournoise parameters, the noise figure and the S-parameters of theamplifiers measured by the tuner are presented in Figs. 6 to 11.The relevant values were then used to calculate the value ofthe effective temperature of the reverse noise wave C1 theoreti-cally.
Though the amplifiers operate over a larger frequency range,only results over the frequency range of 1–2 GHz have beenpresented here. This is because the isolator used in the reversenoise measurement set-up only worked in this frequency range,and thus the reverse measurements had to be restricted to thisfrequency range only. For better comparison purposes, datapoints have been taken at 100 MHz intervals. For the reversemeasurements, the amplifiers were connected reversely asdescribed in Section III, and the actual effective temperaturesat the inputs were measured. Suitable preamplifiers were used
1850 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 6, JUNE 2011
Fig. 7. Measured noise resistances of ZX60-2522-M and ZX60-3018-G am-plifiers.
when necessary. The results for these measurements are tab-ulated in Tables I and II, respectively. The various quantitiestabulated are defined by the following expressions, followingthe definition of the various noise components in Section III:
where is the input reflection coefficient of the isolator.A comparison of the calculated (‘Total’) and measured valuesof the effective temperature of the reverse noise wave showsthat they are in good agreement. This proves the validity of thetheoretical approach. Figs. 12 and 13 show the correspondinggraphs. Fig. 14 shows the measured noise temperatures of thetwo amplifiers—it can be observed that for both the amplifiers,
Fig. 9. Measured forward gain of ZX60-2522-M and ZX60-3018-G amplifiers.
Fig. 10. Measured input and output reflection coefficients and reverse gain ofthe ZX60-2522-M amplifier.
Fig. 11. Measured input and output reflection coefficients and reverse gain ofthe ZX60-3018-G amplifier.
ROY AND GEORGE: ESTIMATION OF COUPLED NOISE IN LOW NOISE PHASED ARRAY ANTENNAS 1851
Fig. 12. Comparison of calculated and measured effective temperatures of thereverse noise wave for the ZX60-2522-M amplifier.
Fig. 13. Comparison of calculated and measured effective temperatures of thereverse noise wave for the ZX60-3018-G amplifier.
the effective temperatures of the reverse noise waves are farless than the noise temperatures of the amplifiers. Also, thecomponent E1’ and E2’ are negligible in comparison to C1’.
V. APPLICATION OF PROPOSED THEORY TO SKA
Based on the observed agreement between the predicted andmeasured effective temperatures of the noise wave emanatingfrom the input of two commercially available amplifiers, as de-tailed in the Section IV, it can be concluded that the theoret-ical approach is valid, and can be used to determine the level ofnoise emanating from the input of any noisy two-port, as long asthe four noise parameters and the input reflection coefficient areknown. This approach can thus find significant application in theSquare Kilometer Array project which plans to utilize phasedarrays. As mentioned previously, the coupled noise between an-tenna elements, i.e., noise emanating from the input of a lownoise amplifier and coupled into adjacent antennas, then passingthrough their associated LNAs into the beamformer, has beenone aspect of the system noise for these phased arrays that hasreceived much attention. Thus, if the noise parameters and the
Fig. 14. Measured noise temperatures of the ZX60-2522-M and ZX60-3018-Gamplifiers.
TABLE ICALCULATED AND MEASURED EFFECTIVE TEMPERATURES OF THE REVERSE
NOISE WAVE FOR ZX60-2522M
TABLE IICALCULATED AND MEASURED EFFECTIVE TEMPERATURES OF THE REVERSE
NOISE WAVE FOR ZX60-3018G
input reflection coefficient of an LNA in a single receiver chain,and the coupling between two adjacent elements are known, thepresent theory can be used to calculate the noise emanating fromthe input of the LNA, and the levels of the coupled noise, re-spectively. To elucidate this, a step-by-step approach is taken,outlined below:
1852 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 6, JUNE 2011
TABLE IIIMEASURED NOISE PARAMETERS OF ASTRON LNA IN THE SKA FREQUENCY
RANGE OBTAINED FROM [31]
i) First, we consider an LNA which has been designed forthe SKA application, and for which the noise parametersare available.
ii) Next, the temperature C1 associated with the reversenoise wave is then calculated for this LNA.
iii) Finally, a previously-used antenna S-parameter set is thenused to determine the maximum amount of noise that willbe coupled into an adjacent antenna in an example twoelement array system.
This is described in two separate sections below. It is im-portant to bear in mind that for the SKA phased array appli-cations we are mainly concerned with determining estimates ofthe maximum noise that can be coupled between the antennas inthe array, from a knowledge of the typical noise parameters ofLNAs that will be used in these applications. Any assumptionor generalization that has been made is based on this criterion.
A. Calculation of Noise Emanating From a Single ChainTowards the Antenna
The study done by Bhaumik and George [30], [31] summa-rizes the reported measured data from different LNA teamsinvolved in SKA. It reports the noise parameters and inputmatch of a single-ended LNA designed by the SKA team atASTRON (ASTRonomisch Onderzoek in Nederland—theNetherlands Foundation for Research in Astronomy), over afrequency range of 1 GHz to 1.6 GHz. We choose this particularLNA as an example for our present purpose because of thefollowing reasons:
i) The design has been based on Avago Technology’s GaAspHEMT device, ATF54143, and such pHEMT devicesfrom Avago (ATF54143, ATF35143) have indeed beenpopular choices for LNA designs in the SKA frequencyrange in the recent years [30].
ii) A noise temperature value of 35 K has been achieved overthe frequency range of 1–1.6 GHz in the least. The studyby Bhaumik and George [30] also shows that noise tem-perature levels of 35–40 K at room temperature have beenachieved by more than one team in the SKA frequencyrange. Thus, this particular LNA designed by ASTRONcan serve as a very good example for our present purpose.
The measured noise parameters and the input reflection coef-ficient for this LNA, as reported in [31], are tabulated in Table IIIover 1–1.6 GHz. The approximate values of the input reflectioncoefficient have been obtained from a plot presented in [31].
Now, using the formula from (12), we can calculate the noisepowers associated with the reverse noise waves emanating from
Fig. 15. Effective temperatures of the reverse noise wave and the coupled noise.
the input sides of these LNAs. It is repeated here for conve-nience. Division of this value by the Boltzmann’s constant kwould give the associated noise temperatures.
(16)
From this equation, it can be seen that we have all the infor-mation we need to calculate the noise power, except the phaseof the input reflection coefficient . Since the magnitudes ofboth (assuming a value of 10 dB) and are in the rangeof 0.1, the component is in the order of 0.01. Thus,for simplicity, we assume that can be approximated by
.In these calculations, we assume that the LNAs are unilateral.
This assumption should be quite valid for amplifiers which willactually be used in the SKA. In circumstances where a very ac-curate estimate of the reverse noise is required, or the reversegain cannot be neglected, the process outlined in [18] can beused, but of course with all the added complexities of the mea-surements involved (which can be particularly difficult whenultra low noise amplifiers are used, like in SKA).
Column 2 in Table IV summarizes the calculated effectivetemperature values of the reverse noise wave for the LNA thathas been considered, and the bold curve in Fig. 15 shows the plotof this temperature with respect to frequency. It can be observedfrom the graphs that levels of reverse noise are below 33 K forthe frequency of operation of phased array receivers in the SKA.It is certain that the actual amplifiers used in LNA designs for theSKA will have similar or improved noise and S-parameters, andthus the levels of noise will be similar to the present estimation,or lower.
B. Estimation of Coupled Noise to an Adjacent Receiver Chain
For a phased array system, if the coupling between adjacentantennas is known, the portion of the reverse noise from asingle chain which gets coupled back into the receiver systemthrough an adjacent antenna can also be determined, providedthe coupling coefficients are known. Fig. 16 illustrates thisconcept for a simple two-element array, which has also been
ROY AND GEORGE: ESTIMATION OF COUPLED NOISE IN LOW NOISE PHASED ARRAY ANTENNAS 1853
TABLE IVMEASURED NOISE WAVE FOR THE ASTRON LNA AND THE CORRESPONDING
COUPLED NOISE
Fig. 16. A two-element array to illustrate the noise coupling.
used previously in [11]. Noise waves andcorrespond to LNA1 in a receiver chain, and noise wave
and correspond to LNA2 in an adjacentreceiver channel. If the scattering parameters of the coupledantenna system are known, the part of coupledto receiver 2, , can be determined. To illustrate thiswith our example, we consider that both receiver chains usethe same LNA that we have considered here. So, in this case,
. We choose to use the same S-parame-ters (normalized to 50 ) for the antenna system as specified in[8], which are as follows:
(17)
From this set of S-parameters, it can easily be calculated thatthe coupling between adjacent channels is 12.7%. Thus the max-imum values of the coupled noise from one receiver channelto the adjacent channel can be calculated. Column3 in Table IV summarizes these results, and the dashed curvein Fig. 15 shows the plot of this coupled noise temperature asa function of frequency. It is observed that the maximum pos-sible coupled noise is very small and in the order ofa few Kelvin for low noise amplifiers of the type to be used inthe SKA.
Important to note in this context is that to be of practical use inSKA, the radiation efficiency of the antennas has to be high. Assuch, from the principle of reciprocity, most of the noise comingout from the input port of the LNA in a receiver chain towardsthe antenna will be radiated into space, rather than be coupledto adjacent antennas.
The analysis in this section suggests that for the very lownoise amplifiers that will be used for the SKA, the amount ofnoise coupled between antennas will be relatively small, gener-ally a few Kelvin at most. There is another important observa-tion that surfaces from the present work. It has been observedthat the effective temperature of the reverse noise wave depends
heavily on the value of the noise resistance. Thus, the impor-tance of a low value of the noise resistance for the SKA LNAdesigns cannot be overemphasized.
VI. CONCLUSION
A theory to evaluate the level of noise emanating from theinput of any noisy two-port has been described, based on thefundamental principles of noisy networks. This has been usedto estimate the level of noise that will be coupled between an-tenna elements in a phased array receiver of the type expectedto be used in the SKA project. The theory can be used to find theeffective temperature of noise emanating from the input of anylow noise amplifier, irrespective of the technology. The theoryhas been implemented using MATLAB, and used to predict thenoise levels emanating from the input ports of two commerciallyavailable packaged amplifiers, after their noise parameters havebeen determined with appropriate tuner measurements. Mea-surements have then been performed to experimentally deter-mine the effective noise temperature levels at the input ports ofthe two amplifiers. The measured effective temperatures showgood agreement with the theoretically predicted values. As such,it can be concluded that the theoretical approach is valid, andcan be used to determine the level of noise emanating from theinput of any noisy two-port, as long as the four noise parametersand the input reflection coefficient of the two-port are known.
The theory has been applied to an example two-antennaphased array system discussed in [5], using reported measuredvalues of noise parameters of an LNA designed by ASTRONfor the SKA [31]. Results from this noise wave analysis suggestthat the coupled noise contribution to system noise temperaturein SKA phased array receivers should be quite small, especiallysince the LNAs which will be finally used in the SKA appli-cations will have either similar or improved noise parametersthan those analyzed in this paper.
ACKNOWLEDGMENT
The authors would like to acknowledge Dr. S. Bhaumik forhis help with the measurements. The authors would also like tothank Mr. N. Roddis of the SKA Program Development Officefor useful discussions about the SKA.
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Mousumi Roy (S’09) was born in Siliguri, India. Shereceived the B.Tech. degree in electronics and com-munication engineering from West Bengal Univer-sity of Technology, India, and the M.Sc. degree incommunication engineering from the University ofManchester, Manchester, U.K., where she is currentlyworking toward the Ph.D. degree.
She is currently with the Microwave and Commu-nication Systems research group, University of Man-chester. Her field of research is comprised of designof MMIC-based low noise transceiver systems.
Danielle George (M’00) is a Senior Lecturer withthe School of Electrical and Electrical Engineering,University of Manchester, Manchester, U.K. Sheis the U.K. Lead Academic in the field of lownoise amplifier research and has worked on anumber of international radio astronomy telescopeprojects including the square kilometer Array andthe EU-funded FARADAY One Centimetre Radio100-beam Array programme. She was part of thetechnical team to develop the low frequency instru-ment (LFI) for the successfully launched PLANCK
Space Telescope. Her research collaborations include Rolls Royce, The Euro-pean Space Agency, The Indian Space Research Organization and The ChineseAcademy of Science for Space Studies.
