Design of a Low Noise Amplifier Using the Quarter Wave Transformers Matching Technique

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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
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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.
Chun-Chieh Chen, Yen-Chun Wang, 3.1–10.6 GHz ultrawideband LNA design using dual-resonant broadband matching
technique, AEU - International Journal of Electronics and
Communications, Volume 67, Issue 6, June 2013, Pages 500-503.
Kargaran, E.; Khosrowjerdi, H.; Ghaffarzadegan, K.; Kenarroodi,
M., "A novel high gain two stage ultra-wide band CMOS LNA in
0.18μm technology," in Circuits and Systems for Communications
(ECCSC), 2010 5th European Conference on , vol., no., pp.90-92,
23-25 Nov. 2010.
Yi-Jing Lin; Hsu, S.S.H.; Jun-De Jin; Chan, C.Y., "A 3.1–10.6
GHz Ultra-Wideband CMOS Low Noise Amplifier With CurrentReused Technique," in Microwave and Wireless Components
Letters, IEEE , vol.17, no.3, pp.232-234, March 2007.
Shih-En Shih; Deal, W.R.; Yamauchi, D.M.; Sutton, W.E.; WenBen Luo; Yaochung Chen; Smorchkova, I.P.; Heying, B.;
Wojtowicz, M.; Siddiqui, M., "Design and Analysis of Ultra
Wideband GaN Dual-Gate HEMT Low-Noise Amplifiers," in
Microwave Theory and Techniques, IEEE Transactions on ,
vol.57, no.12, pp.3270-3277, Dec. 2009.
D. M. Pozar, Microwave Engineering, (3 edition, New york:
JohnWiley & Sons, Inc., 2011).
R. K. Mongia. I. J. Bahl. P. Bhartia. J. Hong, RF and Microwave
Coupled-Line Circuits, (Second Edition, 53-80: ARTECH House,
INC, 2007).
Ibahl, I. J. and Trivedi, D. K, A Designer’s Guide to Microstrip
Line, Microwaves, Vol.16, (pp. 174–182, May 1977).
G. Gonzalez, Microwave transistor amplifiers, Analysis and
Design (2e édition, Prentice Hall, 1996).
E. Henry Fooks, R. A. Zakarevičius, Microwave engineering
using microstrip circuits, (New York: Prentice Hall, 1990).
C. Gentili, Microwave Amplifiers and Oscillators, (N.Y: McgrawHill edition, 1987).
D. 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.
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