"> Gain and Noise Boundaries for NFmin or Unity SWRout – Course Writing Pals

Gain and Noise Boundaries for NFmin or Unity SWRout

Full Characterization of Gain and Noise Boundaries for NFmin or Unity SWRout Operation

M. R. M. Rizk1,4, Ehab Abou-Bakr*,2, A. A. A. Nasser3, El-Sayed A. El-Badawy1 and Amr M. Mahros1,5

Abstract-For a receiver sub-block, Low Babble Amplifier (LNA) is the aboriginal date afterwards the accepting antenna and as a key device, its addition and babble amount (NF) affects the accomplished achievement of the accepting part. In this cardboard we present a abounding graphical decision in agreement of gain, continuing beachcomber arrangement (SWR) and babble for a GaAs HJ-FET transistor in two operating cases; i)NFmin, ii) Accord SWRout. The set of curves and contours presented will accommodate the artist with abundant beheld advice about the transistor operating boundaries and will additionally visually abetment on allotment the adapted analogous credibility for a wideband operation according to the adapted (GT,SWR) for case (i) and (GT,SWRin,NF) for case (ii). Afterwards examples are accustomed for anniversary operating case and absolute via a bake ambit architecture software amalgamation to authenticate the adequacy of the proposed graphical techniques. The after-effects from simulations analyze favourably with the visually estimated values.

  1. INTRODUCTION

Introducing a wide-band LNA with adequate babble amount and accretion depends mainly on allotment a acceptable transistor[1, 2, 3, 4]. Several acknowledged techniques accept been developed in the abstract to beforehand detached transistors with cool low NF and aerial associated accretion [5, 6, 7, 8, 9, 10, 11]. Altered arduous techniques accept been acclimated to accompanying get aerial gain, low babble figure, acceptable ascribe and achievement analogous and absolute adherence at the everyman accessible accepted draw from the amplifier. In 1982, Yarman et al.[12] alien a software based non-linear access adjustment based on their procedural simplified absolute abundance technique. This architecture action is applicative to broadband multistage FET amplifiers with no decisions to be fabricated in advance. It was added able and authentic than alternative accessible CAD methods to accomplish the best optimum accretion and SWR over a predefined bandwidth. This adjustment was afterwards continued by Perennec et al.[13] to optimize the babble amount in alongside with the accretion and mismatch. Capponi et al. [14], bidding the achievement of LNA in ascribe analogous action by allegory the Combined noise-SWR application the accepted ambit ancestors defined for a accustomed alive device. The assurance of the adapted input/output terminations of the alive accessory was explained in [15] back the ability gain, babble figure, and ascribe and achievement conflict constraints are placed on the amplifier. Bengtsson et al. [16] devised a atypical SWR assay action for GaN-HEMT devices. In [17], the operation altitude of a called aerial technology transistor were acclimated forth the archetypal architecture configurations to acquisition a accommodation relations amid the gain, babble amount for the achievement anchorage matching. Recentely graphical methods forth with access methods for anecdotic the abounding accommodation of the called transducer beneath a accustomed set of babble amount and SWR constrains are discussed in [18, 19, 20].

Receivedate

* Agnate author: Ehab Abou-Bakr ([email protected]).

  1. Faculty of Engineering, Alexandria University, Alexandria, Egypt.
  2. The College Institute of Engineering and Technology, El-Behera, Egypt.
  3. Faculty of Engineering, Arab Academy For Science Technology and Maritime Transport, Alexandria, Egypt.
  4. SmartCI, Alexandria University, Alexandria, Egypt.
  5. University of Jeddah, Jeddah 21432, Saudi Arabia.

The (noise, gain, SWR) triplets can be bidding on the Smithchart as circles on both the antecedent and amount absorption accessory planes [21, 22]. Allotment analogous credibility on the Smithchart based on the variations of accretion circles radii reflects on the noise/SWR achievement of the accomplished amplifier circuit. Pre-Knowledge of the transistors abounding accommodation with account to gain, SWR and babble could facilitate the best of the absolute allotment for the targeted architecture goals.

In this paper, two cases of architecture restrictions are taken into consideration; i) NFoperation, ii) accord SWRout. For anniversary of these cases, a formed abstracts abject is acclimated to actualize sets of boundaries for the transducer accretion GT and NF that will acknowledge the abounding operating accommodation o the called transistor. Beheld alternative of the adapted achievement is accessible and abstraction of the adapted analogous credibility for distinct abundance or wideband operation is fabricated simple.

The called alive accessory for our assay is the GaAs HJ-FET transistor NE3210S01 from Renessa Electronics [24]. The transistor is potentially ambiguous at VDS= 2V, ID= 10mAin the abundance acerbity beneath 8.6 GHz [26, 27]. So, by administering the assay in a ambit aloft this abundance (9-12)GHz, no added ambit basal is adapted to drive the transistor to its codicillary adherence region. As a result, the (NFmin) and their agnate (Γopt) provided in the architect datasheet are acclimated anon afterwards any modifications. Added average dataset that is not provided in the datasheet, is acclimated in our investigation. This was accessible by application the departure advantage provided by the Advanced Architecture Systems (ADS) from Keysight technologies [25].

This arrangement is organized as follows: Afterwards archetype and simulation assay are presented in section.2 for demonstrating the acceptance of the graphical accretion boundaries and the arty of SWR on them for NFmin operation. In section.3, the abstraction of correlating noise, accretion and SWR on a distinct blueprint application NF boundaries are presented and aided by addition afterwards example. The cessation is discussed in section.4.

  1. GAIN BOUNDARIES FOR NFMIN OPERATION

All the basal formulas acclimated in the presented assay is listed in Table.1.

In [22], three expressions for the accretion are provided. These are; the transducer accretion (GT), the accessible accretion (GA) and the operating ability accretion (GP). The architecture of a bake amplifier requires utilizing one or added of these accretion belief to ability the adapted architecture goals. Graphically, all the ahead mentioned types can be represented as circles on the Smithchart. However, allotment which accretion blazon to use in the design, depends on the transistor blazon and the adapted architecture criterion.

+j1.0

 

+j0.5

 

GP circles

+j2.0

 

+j0.2

+j5.0

 

0.0∞

 

-j0.2

As the ambit CP increases, the Amount of GP decreases

 

-j5.0

 

-j0.5

-j2.0

 

-j1.0

Figure1.For NFmin operation, Altered operating accretion circles acquired by alteration the GP agency in (15)

 

Table1.Basic equations acclimated in the analysis

 

Γin−Γâˆ-

C1 = |S11 −∆Sâˆ-|(10)

 

Γb=S

  1. GA

 

1 −ΓinΓS

gA=

2(11)

 

Γout−Γâˆ-

|S21|

 

Γb=L

(2)

g Câˆ-

 

1 −ΓoutΓL

CP=P 2

(12)

 

S12S21ΓS

1 + gP(|S22|2 −|∆|2)

 

Γin= S11 + 1 −S Γ

(3)

I

P

 

S12S21ΓS

rP=22

 

Γout= S22 + 1 −S Γ

(4)

1 + gP(|S22|

−|∆|)

(13)

 

SWR= 1 + |Γa|(5)

in1 −|Γa|

C2 = |S22 −∆Sâˆ-|(14)

GP

 

SWR= 1 + |Γb|(6)

out1 −|Γb|

gP=

|S21

(15)

|2

 

GT=

1 −|ΓS|2

|1 −ΓsS11|2

|S21|2

1 −|ΓL|2

|1 −ΓLΓout|2

. (7)

1 −|S11|2 −|S22|2 + |∆|2

2|S21S12|

(16)

 

CA=

gACâˆ-

(8)

G= |S21|I2

 

1 + gA(|S11|2 −|∆|2)

I

Pmax

|S12

(K−

|

K −1)(17)

 

1 −2K|S21S12|gA+ |S12S21|2g2

NF = NFmin+

4rn|ΓS−Γopt|2

(18)

 

rA=

1 + gP

(|S11

(9)

|2 −|∆|2)

(1 −|ΓS

|2)|1 + Γ

opt|2

 

  1. (b)

Figure2.Distribution of SWRout over operating accretion circles for NFmin operation at 12 GHz a) A 3D representation with baby ethics of SWRout displayed in lighter colors, b) A even appearance of the aforementioned amount with absolute ethics of SWRout on the blush bar.

2.1. Arty SWR on GT Boundaries for a Wideband, NFmin Operation

Considering the aloft choices, the mutual acreage of the Accessory Beneath Assay (DUT) aversion the acceptance of GT circles. Also, targeting a NFmin operation armament ΓS=Γoptand this prevents the acceptance of GA circles. As a result, GP circles in the ΓL plane of the Smithchart were used.

 

16

14

1212 GHz11 GHz 10 GHz9 GHz

10

8

6

Best accessible G

T

Minimum accessible G

T

2

1212.51313.51414.51515.51616.5

Operating accretion (G )

P

Figure3.GT vs. GP, area GTmin ≤GT≤GTmax regions for frequencies 9,10,11,12 GHz are apparent in solid and dotted curve respectively.

For a assertive abundance of operation, alteration the amount of the GP agency in (15) will aftermath altered circles for the operating accretion as apparent in Figure.1. Anniversary point on the ambit of these circles represent a different amount of ΓLthat can be acclimated for analogous according to the adapted architecture goals. For added assay of the accessory capabilities, SWR accompanying to these ethics can be imposed on these circles. For illustration, abandoned the SWRout levels are imposed in Figure.2 area lighter blush regions represent lower ethics of SWRout. Although these are the adapted regions to body our architecture around. However, for a wideband operation, extensive the adapted GT could anticipate allotment analogous credibility from these regions.

Since ΓS=Γoptfor a NFmin operation, a graphical affiliation (GT vs. GP) will accommodate a pre- architecture advice about the limitation of the called transistor. Figure.3 explains this by allegorical GTmin ≤GT≤GTmax over a ambit of GP for the called abundance points, the solid curve represent GTmax while the dotted curve accord to GTmin . In actuality a database was complete for this amount that accommodate all ethics of ΓL‘s that accord to anniversary GP value. Afterwards on, this database will be actual advantageous in allotment adapted analogous credibility for wideband operation. A quick attending to the amount revels that if targeting a wideband operation the adapted GT should not beat GTmax of the accomplished frequency. For example, the transistor cannot accomplish GT college than 12.73 dB for a called abundance of 12 GHz.

However, designing for a acceptable SWRin and SWRout requires added alternation amid GT and SWR. This is apparent in Figure.4 area beheld affirmation of the accessory operating boundaries are clear. The complete database is continued by appearance the contours of both SWRin and SWRout on the GT boundaries at NFmin operation. Since lighter colors announce bigger ethics of SWR, it is accessible that for this authentic transistor, the SWRin and SWRout are worse for lower frequencies. Also, the administration of the blush stripes are askew for SWRin and accumbent for SWRout, this is an adumbration that, for this authentic transistor, allotment an adapted GP and its consecutive ΓL‘s could aftereffect in a connected amount of SWRin forth the absolute bandwidth.

As an archetype to emphasise on application Figure.3 to architecture a wideband LNA operating at its NFmin, a targeted 12.7 dB is called for analogy in the ambit of 9-12 GHz. From Figure.4, the blush curve reveals that the minimum SWRout=1 agnate to this GT akin belongs to a 12GHz operation. Then, the accompanying ΓLpairs for frequencies 9,10,11,12 GHz are fetched for analogous purpose as apparent in Figure.5(a). The displayed ΓLpairs on the artisan blueprint of Figure.5(b) were acclimated by ADS to assemble analogous circuits to verify the accepted SWR. the acquired simulation after-effects are listed in Table.2 and compares favourably with those listed in Figure.5(a).

 

16351650

 

1430

1225

12 GHz 11 GHz 10 GHz 9 GHz

10

20

8

15

 

14

12

12 GHz

10

8

 

11 GHz

 

10 GHz

 

45

40

35

9 GHz30

25

20

 

6615

10

10

44

55

 

2

12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 SWRin

Operating accretion G

P

(a)

2

12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 SWRout

Operating accretion G

P

(b)

 

Figure4.Imposing the contours of both SWRin and SWRout on the GT boundaries at NFmin operation,

  1. for SWRin and b) for SWRout

+j1.0

 

+j0.5

 

+j2.0

 

+j0.2

 

12 GHz

 

11 GHz 10 GHz

 

  1. GHz

+j5.0

 

0.0∞

11 GHz

 

(a)

 

-j0.2

9 GHz

-j0.5

  1. GHz

-j1.0

(b)

 

-j2.0

 

-j5.0

 

Figure5.a) Extracting the basal ΓLpairs from the complete database for the apparent called point of operation according to the targeted GT ans SWR, b) Smithchart representation of the extracted ΓL pairs

 

  1. NF BOUNDARIES FOR A UNITY SWROUT

For the action of an achievement conjugate analogous (ie. ΓL=Γâˆ-

 

), GA= GT and a accord SWRout is

 

produced. All ethics of ΓSthat corresponds to a authentic GA amphitheater gives the aforementioned amount of SWRin.

This is apparent in Figure.6 area a curve of SWRin is imposed on GA= GT circles. The tip of the cone

in Figure.6(a) corresponds to ΓSpoint that will aftermath a accompanying conjugate bout (ie. ΓS=Γâˆ- &

 

ΓL=Γâˆ-

) area (SWRin= SWRout=1).However, this amount abandoned cannot associate the (GT,NF,SWR)

 

triplets to accord a abounding decision acumen of the accessory adequacy in this case of operation.

  1. GT, SWRin and NF Alternation for SWRin=1

Figure.7(a) allegorize the aberration of SWRin forth a ambit of GA= GT ethics area at SWRin=1, a accompanying conjugate analogous occurs. The abstracts in Figure.7(a) alongside GA= GT ethics and their agnate NF are acclimated to assemble a database to advice acute the NF boundaries apparent in Figure.7(b). For a SWRout=1 operation, this amount can be acclimated to visually adumbrate both NF and SWRin for any targeted GT. Since, the apparent credibility on the artifice represent SWRin=1 for anniversary selected

 

Table2.ADS simulation abstracts after-effects afterwards alone analogous the IMN and OMN according to the analogous credibility in Figure.5(a).

Freq

GT

NFmin

NF

SWRin

SWRout

9GHz

12.742

0.31

0.31

2.472

3.073

10GHz

12.710

0.32

0.32

2.438

2.319

11GHz

12.751

0.33

0.33

2.434

1.869

12GHz 12.760 0.34 0.34 2.379 1.033

  1. (b)

Figure6.3D representation of SWRin over a ambit of GA=GT circles a) Isometric view, b) Plan view

frequency, it is visually bright that a SWRin= SWRout=1 is absurd for a wideband, collapsed accretion design.

For a wideband, collapsed accretion operation with SWRout=1.Figure.7(b) reveals that GT collapsed max=

GT max 12GHz is the best amount of GT to attain a collapsed accretion throughout the bandwidth. The

previously complete database can be acclimated to back ΓS, ΓLthat will aftermath the visually targeted

(GT, SWRout, NF) triplets from Figure.7(b). As an example, a targeted wideband operation (9-12 GHz)

with GT=13.9 dB is called for demonstration, Figure.8 present the basal ΓS, ΓLfor the visually

selected point. this point was called to accord the targeted GT for a accompanying conjugate matching

at 12 GHz with NF≤1.4 dB. the antecedent and amount analogous credibility for the called frequencies are shown

in Figure.9. Again, ADS was acclimated to verify the estimated (GT, NF, SWR) triplets by amalgam alone analogous networks application ΓSand ΓLlisted in Figure.8. Table.3 present the simulation after-effects which compares agreeably with the visually estimated values.

Table3.ADS simulation abstracts after-effects afterwards alone analogous the IMN and OMN according to the analogous credibility in Figure.8.

Freq

GT

NF

SWRin

SWRout

9 GHz

13.96

1.34

3.06

1.02

10 GHz

13.98

1.33

2.34

1.01

11 GHz

13.93

1.37

1.88

1.01

12GHz 13.95 1.33 1.12 1.03

  1. CONCLUSION

In this paper, authentic graphical assay to analyze the called accessory capabilities in the NFmin and SWRout=1 cases was presented. For the aboriginal case; a set of GT abuttals curves and contours can be visually acclimated to analyze the accepted ethics of SWRin SWRout for a targeted GT at NFminoperation. While for the additional case; NF abuttals curves were acclimated to visually adumbrate the NF, SWRin levels for

 

6

Simultaneous conjugate analogous point

10Γ =Γ* , Γ =Γ* , for 9,10,11,12 GHz

 

4.5

 

5

9 GHz

S in L

out

4

 

410 GHz

8

3.5

 

  1. GHz

3

  1. GHz

2

1

 

6

4

2

12 GHz11 GHz 10 GHz 9 GHz

 

3

2.5

2

1.5

 

0

11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5

Transducer accretion G

T

(a)

 

0

12.5 13 13.5 14 14.5 15 15.5 16 16.5

Transducer accretion G

T

(b)

 

SWRin

 

Figure7.a) Distribution of SWRin over a ambit of GT, b) NF boundaries for frequencies 9, 10, 11, 12 GHz

Figure8.Extracted ΓS, ΓLfrom the complete database for the apparent called point of operation. achievement conjugate analogous that will aftereffect a SWRout=1. For both cases, a abounding database was formed to

be acclimated in the abstraction of the agnate analogous absorption coefficients for any visually targeted

operating points. The architecture and application of this database was begin to accomplish abortion credibility abstraction accessible and accurate. And As declared by [19] “ItcanbeconcludedthatthenearfuturemicrowavetransistorisexpectedtobeidentifiedbythePerformanceDataBaseswhereallpossibleLNAdesignscanbeoverviewedusingthefulldevicecapacity.

REFERENCES

  1. Friis, H.T.,”Noise Figures of Radio Receivers,” Proceedings of the IRE, Vol. 32, No. 7, 419-422, 1944.
  2. Collins, C.E. et al.,”On the altitude of SSB babble amount application sideband cancellation,” IEEE Transactions on Instrumentation and Measurement, Vol. 45, No. 3, 721-727, 1996.
  3. Collantes, J.M. et al.,”Effects of DUT conflict on the babble amount characterization: a allusive assay of two Y-factor techniques,” IEEE Transactions on Instrumentation and Measurement, Vol. 51, No. 6, 1150-1156, 2002.

 

+j1.0

+j1.0

 

+j0.5

 

+j2.0

 

+j0.5

 

+j2.0

 

+j0.2

 

10 GHz

 

12 GHz

 

+j5.0

 

+j0.2

 

12 GHz

  1. GHz

 

10 GHz

 

9 GHz

 

+j5.0

 

9 GHz

11 GHz

 

0.0∞

0.0∞

 

-j0.2

-j5.0

-j0.2

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