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See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/282851710 Design of a Low Noise Amplifier Using the Quarter Wave Transformers Matching Technique in the Frequency Band [9-13] GHz Article in International Journal on Communications Antenna and Propagation · August 2015 DOI: 10.15866/irecap.v5i4.7065 CITATIONS READS 0 288 3 authors: Islam Toulali Mohammed Lahsaini 1 PUBLICATION 0 CITATIONS Mohammadia School of Engineers SEE PROFILE 8 PUBLICATIONS 11 CITATIONS SEE PROFILE Lahbib Zenkouar Mohammadia School of Engineers 42 PUBLICATIONS 54 CITATIONS SEE PROFILE All content following this page was uploaded by Mohammed Lahsaini on 16 November 2015. The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately. International Journal on Communications Antenna and Propagation (I.Re.C.A.P.), Vol. 5, N. 4 ISSN 2039 – 5086 August 2015 Design of a Low Noise Amplifier Using the Quarter Wave Transformers Matching Technique in the Frequency Band [9-13] GHz I. Toulali1, M. Lahsaini2, L. Zenkouar3 Abstract – Low noise amplifier (LNA) constitutes one of the essential component in wireless communication systems. It is used especially for designing different types of communication receivers. The main function of LNA is to provide sufficient gain to overcome noise of other blocks. Amplifier design requires a matching circuit of impedance to have a low noise, achieve maximum power transfer and have minimum reflection. This paper presents a low noise amplifier that operates over the frequency range [9-13] GHz and adopts quarter-wave transformers impedance matching technique. Simulation and synthesis are made by using CAD software (ADS: Advanced Design System) addressed to simulations of RF circuits and which is developed by Agilent®. The proposed LNA is designed in HEMT process. As a result, the amplifier is unconditionally stable and achieves a 20 dB gain and a good impedance matching over the working frequency range of [9-13] GHz. Copyright © 2015 Praise Worthy Prize S.r.l. - All rights reserved. Keywords: Low Noise Amplifier (LNA), Matching Network, Microstrip, Quarter Wave Transformer, Transmission Lines I. This paper is organized as follows. The first part introduces the microstrip technology used to design the amplifier. The second part gives an overview of the fundamentals parameters. The third and fourth sections present the chosen matching technique. The fifth section discusses the simulation results, which demonstrate the feasibility of the proposed technique. The last section summarizes the gist of the study results. Introduction In the fields of terrestrial radio and radar, microwave applications have been expanding rapidly over the last decades. Many new application areas have emerged due to technological advances, particularly in the domain of mobile communication systems of the new generation like UMTS, LTE and satellite navigation [1]. Such telecommunication systems consist of a large assembly of circuits, which are themselves produced using active or passive components [2]. Nowadays, researches focuses mainly on designing competitive microwave circuits with certain technical requirements and offering benefits such as reduction of size and cost. The low noise amplifier (LNA) device is a powerful module for the RF receiver. Thus, the performance analysis and optimization of its characteristics is the objective of our study. Most circuits working in the frequency range [9-13] GHz are made by planar technology [3]. This technique consists of engraving the circuit elements on a suitable dielectric substrate. Therefore, several topologies and LNA design methods have been proposed based on different manufacturing technologies and associated to various applications [4]-[7]. In this paper, a RF amplifier is proposed and developed by considering two transistors in cascade and employing the matching method based on quarter wave transformers. The dimension of microstrip lines are calculated and optimized to achieve the impedance matching and optimum performance of amplifier. Some parameters design including gain, noise figure, and stability are used as performance indicators. II. The Microstrip Line The geometry of a microstrip line is shown in Fig. 1. A conductor of width W is printed on a thin, grounded dielectric substrate of thickness d and relative permittivity ; a sketch of the field lines is shown in Fig. 2. The mode of propagation along a microstrip line is not pure transverse electromagnetic (TEM) [8], [9]. The effective dielectric constant of a microstrip line is given approximately by [10]: ≃ +1 + 2 −1 2 1 1+ (1)) The effective dielectric constant can be interpreted as the dielectric constant of a homogeneous medium that equivalently substitutes the air and dielectric regions of the microstrip line, as shown in Fig. 3 [8]. The characteristic impedance can be calculated by the formulas below according to the dimensions of the microstrip [8]: Copyright © 2015 Praise Worthy Prize S.r.l. - All rights reserved 248 I. Toulali, M. Lahsaini, L. Zenkouar = ⎧ ⎪ ⎨ ⎪ ⎩ 60 8 + 4 for ⁄ ≤1 for ⁄ ≥1 (2) 120 [ ⁄ + 1.393 + 0.667 ( ⁄ + 1.444)] The source and load reflection coefficients should be chosen as: = ∗ (3) = ∗ For a bilateral transistor ( ≠ 0), the input and output reflection coefficients are given by [11]: = Fig. 1. Geometry of the microstrip transmission [8] + 1− (4) = , where , transistor. and + 1− are the S-parameters of the III.3. Stability The circuit design requires taking into consideration the factor of stability. The aim objective is to avoid amplifier oscillation when we try to optimize the gain. The quadrupole is unconditionally stable if: Fig. 2. Electric and magnetic field lines [8] | | ≤ 1 and | |≤1 (5) To express the conditions to the unconditional stability, we use the Rollet factor K as defined by the following expression: = Fig. 3. Equivalent geometry, where the dielectric substrate of relative permittivity is replaced with a homogeneous medium of effective relative permittivity [8] 1−| | −| | +| | 2| − | (6) and: ∆ = S S − S S . The necessary and sufficient stability criteria are: > 1 and |∆|< 1, the quadrupole is then unconditionally stable. In addition, it is possible to adjust simultaneously the input and output [14]. If this condition is not verified |∆| > 1 where | | < 1, the quadrupole can be stable for certain impedances. In this way, it is said to be conditionally stable. In general, if < −1: a simultaneous adaptation is impossible, the quadrupole is unstable and therefore unusable as an amplifier. Another stability coefficient is defined by the expression (7), if > 1 the circuit is unconditionally stable [14]: III. Fundamentals of the Matching Network A model of a single stage amplifier including input and output matching networks is represented in Figure 4 [11]. III.1. Power Gain After the amplifier design the evaluation of the gain is essential. Power gains of a 2-ports circuit network, like the one shown in Fig. 4, are defined by scattering parameters and classified into 3 types of gain: operating gain, transducer gain and available gain [12]. = IV. III.2. Matching Condition | 1−| | ∗ − Δ| + | | (7) Impedance Matching Maximum transducer power gain is obtained by the conjugate match [13]. The impedance matching plays an important role in the microwave circuit design. Copyright © 2015 Praise Worthy Prize S.r.l. - All rights reserved Int. Journal on Communications Antenna and Propagation, Vol. 5, N. 4 249 I. Toulali, M. Lahsaini, L. Zenkouar Fig. 4. Equivalent circuit of a single stage amplifier Designing a microwave amplifier with an improper impedance matching will influence the stability of the circuit and reduce its efficiency. In fact, the use of adaptive devices is related to several objectives. The most important factors are a maximum power transfer. In other words, the output impedance of the matching circuit must be equal to the complex conjugate value of the load impedance. It is also important to have a reflection coefficient as low as possible or a standing wave ratio near unity, and a noise matching [15]. There are different types of matching network to microwave amplifiers. The first technique is based on the use of lumped elements [16]. However, these elements are not very suitable to wide bands. Therefore, several methods which are more adapted to microwave frequency domain are used. They are based on distributed elements such as quarter wave lines [13]. One way to adapt an antenna or more, generally a circuit is to insert a quarter-wavelength line between the load impedance and the input impedance line, and to choose an adequate characteristic impedance. It is one of the simplest technique of doing impedance matching in a narrow band [17]. The impedance transformers generally comprise a cascade of uniform quarter wave line sections. Discontinuities result from different jumps of impedance, such as a change in the width of the microstrip line. During the selection of the matching network, some factors should be considered such as complexity, bandwidth, and necessary adjustment according to the desired application. V. Then, if an intermediate section of transmission line with a characteristic impedance and a quarter / wavelength long is connected between the main line and the load, as illustrated in Fig. 5. Fig. 5. Quarter wave transformers [1] The impedance presented to the main line would be equal to [17]: / = (9) The adaptation condition is verified if: / = . This implies that: = , therefore the transmission line is well suited [17]. The total reflection coefficient is given by [17]: 1 = 1+( (10) ) Fig. 6 shows the plot of | | versus , we see that a single section quarter-wave transformer provides a perfect match for a given frequency [17]. Quarter Wave Transformers V.1. General Theory For a transmission line of the characteristic impedance and length l, the input impedance can be written as follow in [1]: + + = (8) such as: = = 2 Fig. 6. Characteristic bandwidth of a quarter-wave transformer for a single section Copyright © 2015 Praise Worthy Prize S.r.l. - All rights reserved Int. Journal on Communications Antenna and Propagation, Vol. 5, N. 4 250 I. Toulali, M. Lahsaini, L. Zenkouar It is a narrow band match. The design of multi sections circuits increase the bandwidth [17]. + ( )= Theory of small reflections Fig. 7 shows a quarter-wave transformer and the different transmission and reflection coefficients. ( + ) + ( + ) +⋯ We have represented the relation to calculate the impedance for a Butterworth response. The binomial function is defined by [17]: ( )= 1+ ( =2 ) (17) such as: − + =2 The transmission and reflection coefficients are given by relations [17]: − + / / =1+ ; − + = =1+ / / =1+ =1+ / − ; = − / − + − + = / / = 2 / / + 2 + = + + =0 ( )= 1+ = = (11) = + + + ⋯+ (18) we have: (12) = Using the mathematical approach: (13) / − + = So, the amplitude of the total reflected wave of the quarter-wave transformer is given by [17]: = for: The relation which links the characteristic impedance and the load impedance to the impedances characterizing the multi-section transformer is calculated from the following formula [17]: Fig. 7. A microwave circuit with two reflecting junctions [17] = (16) ≃ 1 2 the ratio of impedance is obtained by: +… =2 (19) (14) + V.2. Approximate theory for multisection quarter-wave transformers The study of the total reflection coefficient requires making approximations to simplify the final formula. These approximations give the general relation which are used to calculate the characteristic impedances of a multi-section quarter-wave transformer as shown in Fig. 7 [17]. The first approximation consists on representing the coefficient as follows: The Broadband Matching Technique To achieve adaptation we will study the case of three λ sections of length as shown in Fig. 8. Fig. 8. A three sections quarter-wave transformer ( )= + …+ + + The equivalent characteristic impedances obtained by applying the Eq. (19) are given by: (15) = − + ( = 0,1, … , ) = The second approximation assumes that the transformer is symmetrical, which means that the reflection coefficients may be grouped in pairs. In this case (15) becomes: (20) = = Copyright © 2015 Praise Worthy Prize S.r.l. - All rights reserved (21) (22) Int. Journal on Communications Antenna and Propagation, Vol. 5, N. 4 251 I. Toulali, M. Lahsaini, L. Zenkouar VI. circuit. ADS is also the professional software used by leading companies in the wireless communication and networking. The low noise amplifier specifications are as follows: Center frequency of 11 GHz; Source and load impedance: Design and Simulation of the Low Noise Amplifier VI.1. Configuration of the Matching Circuit The design process adopted in this article is based on three essential steps. First, type of transistor to be used was determined; we opted for the HEMT transistor (AFP 02 N2-00) of Alpha Industries ®. Then the choice of circuit topology is made. Afterwards, the matching circuit is established. The proposed LNA comprises two transistors separated by a transmission line, and an inter-stage matching networks which are located in the input and output [11]. The implementation of the method is very simple. We represented the input and output impedances of the amplifier which demonstrated that the impedances are far from the center of the Smith chart at 11 GHz. The block of impedance transformation was used to adapt the impedance at 11 GHz, it represents the transmission line of a characteristic impedance Z equal to 50 Ω and an adequate electrical length. This line can eliminate the imaginary part of the impedance to adapt. After that a matching block designed by the quarter wave transformer was used to approach the center of the Smith chart. And finally, we integrated a terminating line at the input and the output of the circuit. We have calculated the parameters of the circuit defined by the characteristic impedance and the electrical length using the smith chart and the impedances shown in Tables I and II. Then, we have simulated the circuit constituted by the physical parameters. These parameters was obtained by using some techniques of ADS, LineCal is the tool for converting the electric parameters to physical parameters. The final circuit is shown in Fig. 9 and analyzed using the ADS software relying on the Sparameters of the transistor [18]. We opted for the ADS software because it is the world’s leading electronic design automation software for RF and microwave = = 50 ; The characteristic impedances of the three sections quarter wave transformer are represented in the two following tables The topology of the final circuit is shown in Fig. 9. VI.2. Results and Discussion Figures 10 and 11 represent the amplifier simulation results on the frequency band [9-13 GHz]. Tuning and optimization tools of ADS software have been used to optimize results. The gain S shows an acceptable power transfer, about 20 dB from 10 GHz to 13 GHz. Around 9 GHz, the gain reaches its maximum value which is equal to 22 dB. The reverse transmission coefficient S of the amplifier is less than -35 dB over the band of interest. Figure 11 clearly shows the usefulness of the input and output matching circuit. The results are quite acceptable with losses in return of about -32 dB and -40 dB respectively on the input and output. Figure 12 shows the stability factor (StabFact1). The simulated K factor is greater than 4, which accomplishes the necessary and sufficient conditions for unconditional stability. Fig. 13 represents the plot of noise figure in contrast with the frequency. The simulated NF varies between 1 and 1.7 dB over the frequency range [9-13] GHz. The value of the lowest Fmin is 0.7 dB obtained at 9 GHz as shown in the figure. A comparison of the results with those of other researchers [19]-[22] is shown below. TABLE I IMPEDANCES OF THE INPUT 59.27 98.74 164.49 TABLE II IMPEDANCES OF THE OUTPUT 53.02 This work [19] [20] [21] [22] Frequency (GHz) [9-13] [10-12] [7-12] [8-12] [10-12] 63.24 75.43 TABLE III SUMMARY OF THE LNA PERFORMANCE S (dB) S (dB) S (dB) S (dB) < -32 >20 < -40 <- 35 <-25.75 >14.10 <-25.28 <-33.43 <-9 >12 <-15.12 <-10 >15 <-10 <-19.35 >20 <-32.93 <-37.63 Copyright © 2015 Praise Worthy Prize S.r.l. - All rights reserved Noise figure(dB) >1.25 >2 >2.9 - Technology HEMT FET FET CMOS HEMT Int. Journal on Communications Antenna and Propagation, Vol. 5, N. 4 252 I. Toulali, M. Lahsaini, L. Zenkouar Fig. 9. General diagram of the modeled amplifier Copyright © 2015 Praise Worthy Prize S.r.l. - All rights reserved Int. Journal on Communications Antenna and Propagation, Vol. 5, N. 4 253 I. Toulali, M. Lahsaini, L. Zenkouar 40 dB(S(2,1)) dB(S(1,2)) 20 0 -20 -40 -60 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 freq, GHz Fig. 10. Transmission coefficients and -10 dB(S(1,1)) dB(S(2,2)) -20 -30 -40 -50 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 12.0 12.5 13.0 12.0 12.5 13.0 freq, GHz Fig. 11. Reflection coefficients and 9 MuPrime1 Mu1 StabFact1 8 7 6 5 4 3 2 9.0 9.5 10.0 10.5 11.0 11.5 freq, GHz Fig. 12. Stability factor 1.8 F_dB NFmin_dB 1.6 1.4 1.2 1.0 0.8 0.6 9.0 9.5 10.0 10.5 11.0 11.5 freq, GHz Fig. 13. Noise figure Copyright © 2015 Praise Worthy Prize S.r.l. - All rights reserved Int. Journal on Communications Antenna and Propagation, Vol. 5, N. 4 254 I. Toulali, M. Lahsaini, L. Zenkouar VII. edition, New york: John Wiley & Sons, 2001). [18] J. F. White, High Frequency Techniques - An Introduction to RF and Microwave Engineering, (pp.172-177: Wiley-IEEE Press, 2004). [19] Lahsaini, M., Zenkouar, L., Bri, S., Broadband impedance matching techniques for microwave amplifiers [10-12] GHz, (2013) International Review on Modelling and Simulations (IREMOS), 6 (3), pp. 953-961. [20] K. E. Christina Lessi, An X-Band Low Noise Amplifier Design for Marine Navigation Radars, International Journal of Communications, Network and System Sciences, vol. 7, no. 3, pp. 75-82, 2014. [21] Cheng-Chi Yu, Jiin-Hwa Yang, Hsiao-Hua Yeh, and Lien-Chi Su, "A Broadband Low Noise Amplifier for X-band Applications," Progress In Electromagnetics Research Symposium Proceedings, pp. 541-543, 2011. [22] M. Z. L. Lahsaini, "Coupled Lines Filters for Broadband Impedance Matching of Microwave," International Journal of Engineering and Technology (IJET), 6 (4), pp. 1940-1950, 2014. Conclusion In this article, we have done a description of important parameters during designing an amplifier. Besides, we have also given an overview of the impedance matching theory. The circuit presented is designed by distributed elements and it is dedicated to the reception stage of a radar or satellite communication system operating in the frequency range [9-13] GHz. It is adapted by the three sections quarter wave transformers technique, with the aim of achieving high performance features. The simulations allowed obtaining promising results that show the effectiveness and ease of using the design approach. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] Authors information D. K. Misra, Radio-Frequency and Microwave Communication Circuits; Analysis and Design, second edition., Wiley-Blackwell, (John Wiley & Sons, Inc., Hoboken, New Jersey, 2004). François de Dieuleveult, Olivier Romain, Electronique appliquée aux hautes fréquences, (2ème édition, Paris, Dunod, 2008). Bihan, M. Contribution à l’étude des dispositifs planaires microondes à ferrites pour des applications en télécommunications, Thèse de Magister, Université de Tlemcen. Algérie: 59-64, 2006. 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Woods, Reappraisal of the unconditional stability criteria for active 2-port networks in terms of S parameters, IEEE Trans. Circuits Syst., vol. CAS-23, pp. 73-81, Feb.1976. Xiaorong Zhao, Honghui Fan, Feiyue Ye , Sheng He, Haijun Huang, "Design of a LNA in the frequency band 1.8-2.2GHz in CMOS," Wseas Transactions On Circuits And Systems, Vol. 14, No. E-Issn: 2224-266x, Pp. 100-108, 2015. S. K. S. Shreyasi, Analysis of Different Matching Techniques for Microwave Amplifiers, International Journal of Engineering Trends and Technology (IJETT), Volume 9 Number 12, pp. 625632, 2014. R. E. Collin, Foundations for Microwave Engineering (2nd 1 Electronic and Communication Laboratory,Mohammadia School of Engineers, EMI, Mohammed V University, Agdal, Rabat, Morocco. Tel: (+212) 0674937607. E-mail: [email protected] 2 Electronic and Communication Laboratory,Mohammadia School of Engineers, EMI, Mohammed V University, Agdal, Rabat, Morocco. Tel: (+212) 0671385808. E-mail: [email protected] 3 Electronic and Communication Laboratory, Mohammadia School of Engineers, EMI, Mohammed V University, Agdal, Rabat, Morocco. Tel: (+212) 0537687150, Fax: (+212) 0537778853. E-mail: [email protected] Islam Toulali was born in Rabat, Morocco, in 1990. She studied mathematics and physics at Ibn Ghazi Higher School Preparatory Classes in Rabat, Morocco. And obtained the engineer degree in telecommunications and networks from National School of Applied Sciences in 2014,Oujda,Morocco. She is preparing her PhD in Mohammadia School of Engineers, Mohammed V University, Agdal, Rabat, Morocco. Her research interests include Microwave Circuits and Systems. Mohammed Lahsaini was born in SidiSlimane, Morocco, in 1984. He received the Bachelor's degree in Physics from Faculty of Sciences, Rabat, Morocco, in 2008 and Master's degree in Telecommunication and Microwave Devices from National School of Applied Sciences, Fes, Morocco, in 2011. He is currently pursuing his PhD degree in Mohammadia School of Engineers, Mohammed V University, Agdal, Rabat, Morocco. His research interests include Microwave Circuits and Transmission and Reception Systems. Lahbib Zenkouar, was born in Meknes, Morocco. He received the Doctoral degree in CAD-VLSI from University of Sciences and Techniques of Languedoc, Montpellier, France and Ph.D. Sciences and Techniques in Telecommunication from Institute of Electricity of Montefiore, Liege, Belgium, He is currently Leader of research team TCR of the Laboratory Electronic and Communication -LEC- and Professor at Electrical Engineering Department, Mohammadia School of Engineers, Mohammed V University, Agdal, Rabat, Morocco. His research interests focuses on the design of Microwave Circuits and Systems and Information Technology. Copyright © 2015 Praise Worthy Prize S.r.l. - All rights reserved Int. Journal on Communications Antenna and Propagation, Vol. 5, N. 4 255 View publication stats