Calculation of Capacitance of the Rectangular Coaxial Lines with Offset Inner Conductor by Strong FEM Vladimir V. Petrovic 1 and Žaklina J. Mančić 2 Abstract – In this paper, capacitance per unit length of rectangular coaxial transmission lines with offset nonzero- thickness inner conductor, having an isotropic and anisotropic dielectric, using strong FEM formulation is calculated. The results were compared with the results obtained by the weak FEM and commercial software FEMM, which uses node-based first-order basis function. Based on that, appropriate conclusions are made. Keywords – Quasi-static analysis, Finite element method, Strong FEM formulation, lines with rectangular cross section, offset inner conductor, isotropic and anisotropic dielectric, capacitance per unit length. I. INTRODUCTION Problem of capacitance per unit length of square or rectangular lines calculation, especially lines with offset inner conductor is topical in theory and practice. The paper [1] gives a review of the literature, dealing with this task and it performs the calculation of capacitance of the rectangular coax line with offset inner conductor by using the weak FEM formulation [2]. This paper deals with calculation of capacitance per unit length of square and rectangular coaxial lines filled with isotropic and anisotropic dielectric by using strong FEM formulation [3-6]. The results are compared with those obtained by weak FEM [1] and by commercial software FEMM [6]. FEM is a very suitable method for the analysis of closed polygonal structures and it can be simply used for analysis of geometries with anisotropic dielectrics, unlike the methods that use Green’s function (e.g., MoM or EEM) for which an additional complicated step of anisotropic Green’s function determination is needed [7]. Besides classifying FEM into strong and weak formulation, this method can be classified as a node-based [1,6,8,9] and non node-based (with hierarchical basis functions) [2-5, 10-12]. Node-based FEM can be found much more often than non node-based FEM. However, weak FEM formulation is usually presented in the literature, while strong formulation can rarely be found. In weak FEM formulation, only function’s continuity condition is exactly satisfied, whereas in strong FEM formulation, boundary conditions for the both function and its first derivative are satisfied exactly [2-5,10-12]. In this paper are obtained for the third order basis functions ( 3 n ). II. BRIEF DESCRIPTION OF THE STRONG FEM FORMULATION FEM approach in this paper is based on hierarchical strong basis functions of higher (arbitrary) order that are constructed by using mutual multiplication of 1D strong basis functions [13]. Consider a two-dimensional domain, uniform with respect to z-axis, Fig. 1, filled with linear inhomogeneous dielectric without free charges, in which the distribution of electrostatic potential, (, ) Vxy , is the unknown function. Let the problem be of the closed type: on one part of the domain boundary ( 1 C ), boundary conditions of the first kind (given V ), and on the rest of the boundary ( 2 C ), boundary conditions of the second kind (given / V n ), are imposed (Fig.1). (Boundary condition of the second kind here is equivalent to given / n D V n .) Differential equation for (, ) Vxy can be defined with: div ( grad ) 0 S S V , (1) In previous equation div S and grad S denote surface divergence and gradient, respectively. Calculation domain is divided into M sub-domains (elements) in FEM solution of Eq. (1). Exact solution (, ) Vxy is expressed as a linear combination of basis functions with unknown coefficients, 1 N j j j V f af . Fig. 1. Two-dimensional calculation domain divided into elements. The system of linear algebraic equations for unknown coefficients is obtained by applying the weak Galerkin formulation [14, 15], and it is defined with: [ ][ ] [ ] ij j i K a G , , 1, , ij N = , (2) where ε grad grad d ij i j S K f f S , 2 0 d i i n C G fD l . (3) 1 Vladimir V. Petrovic is with the Robert Bosch, GmbH, Reutlingen, Germany , e-mail [email protected]2 Žaklina J. Mančić is with the Faculty of Electronic Engineering, University of Niš, Aleksandra Medvedeva 14, 18000 Niš, Serbia, e- mail [email protected].
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Calculation of Capacitance of the Rectangular Coaxial
Lines with Offset Inner Conductor by Strong FEM Vladimir V. Petrovic
1 and Žaklina J. Mančić
2
Abstract – In this paper, capacitance per unit length of
rectangular coaxial transmission lines with offset nonzero-
thickness inner conductor, having an isotropic and anisotropic
dielectric, using strong FEM formulation is calculated. The
results were compared with the results obtained by the weak
FEM and commercial software FEMM, which uses node-based
first-order basis function. Based on that, appropriate conclusions
are made.
Keywords – Quasi-static analysis, Finite element method,
Strong FEM formulation, lines with rectangular cross section,
offset inner conductor, isotropic and anisotropic dielectric,
capacitance per unit length.
I. INTRODUCTION
Problem of capacitance per unit length of square or
rectangular lines calculation, especially lines with offset inner
conductor is topical in theory and practice. The paper [1]
gives a review of the literature, dealing with this task and it
performs the calculation of capacitance of the rectangular
coax line with offset inner conductor by using the weak FEM
formulation [2]. This paper deals with calculation of
capacitance per unit length of square and rectangular coaxial
lines filled with isotropic and anisotropic dielectric by using
strong FEM formulation [3-6]. The results are compared with
those obtained by weak FEM [1] and by commercial software
FEMM [6]. FEM is a very suitable method for the analysis of
closed polygonal structures and it can be simply used for
analysis of geometries with anisotropic dielectrics, unlike the
methods that use Green’s function (e.g., MoM or EEM) for
which an additional complicated step of anisotropic Green’s
function determination is needed [7]. Besides classifying FEM
into strong and weak formulation, this method can be
classified as a node-based [1,6,8,9] and non node-based (with
hierarchical basis functions) [2-5, 10-12]. Node-based FEM
can be found much more often than non node-based FEM.
However, weak FEM formulation is usually presented in the
literature, while strong formulation can rarely be found. In
weak FEM formulation, only function’s continuity condition
is exactly satisfied, whereas in strong FEM formulation,
boundary conditions for the both function and its first
derivative are satisfied exactly [2-5,10-12]. In this paper are
obtained for the third order basis functions ( 3n ).
II. BRIEF DESCRIPTION OF THE STRONG FEM
FORMULATION
FEM approach in this paper is based on hierarchical strong
basis functions of higher (arbitrary) order that are constructed
by using mutual multiplication of 1D strong basis functions
[13]. Consider a two-dimensional domain, uniform with
respect to z-axis, Fig. 1, filled with linear inhomogeneous
dielectric without free charges, in which the distribution of
electrostatic potential, ( , )V x y , is the unknown function. Let
the problem be of the closed type: on one part of the domain
boundary ( 1C ), boundary conditions of the first kind (given
V ), and on the rest of the boundary ( 2C ), boundary
conditions of the second kind (given /V n ), are imposed
(Fig.1). (Boundary condition of the second kind here is
equivalent to given /nD V n .) Differential equation
for ( , )V x y can be defined with:
div ( grad ) 0S S V , (1)
In previous equation divS and gradS denote surface
divergence and gradient, respectively. Calculation domain is
divided into M sub-domains (elements) in FEM solution of
Eq. (1).
Exact solution ( , )V x y is expressed as a linear combination
of basis functions with unknown coefficients,
1
N
j jj
V f a f
.
Fig. 1. Two-dimensional calculation domain divided into elements.
The system of linear algebraic equations for unknown
coefficients is obtained by applying the weak Galerkin
formulation [14, 15], and it is defined with:
[ ][ ] [ ]ij j iK a G , , 1, ,i j N= , (2)
where
ε grad grad dij i jS
K f f S ,
2
0 di i nC
G f D l . (3)
1Vladimir V. Petrovic is with the Robert Bosch, GmbH,
Reutlingen, Germany , e-mail [email protected] 2Žaklina J. Mančić is with the Faculty of Electronic Engineering,
University of Niš, Aleksandra Medvedeva 14, 18000 Niš, Serbia, e-
Control of Photon Energy Sharing for Photovoltaic Power Charge in Power Grid of Optic Fiber With Enhanced
Effectiveness Jovan Shikoski1, Juli Zlatev2, Tinko Eftimov3, Georgi Stanchev4
Abstract – In the following article have been reviewed two
methods of photon energy charge with: Optical splitter and Optical switch, with purpose of smart Sensors charging. Energy efficiency was analysed and compared.
Optical power, Optical fibre, Power IR laser, Photovoltaic power converter PPC-4E.
I. INTRODUCTION
At a high level of electric and high-frequency interferences and extreme meteorological conditions, explosive surrounding and more it is not appropriate for the sensors to get charged with copper conductors or standard photovoltaics [1,2]. Lately there is a trend optic fiber to be used for photon energy conduction in the range of 100mW~2W, generated by a laser diode for the charge of remote smart sensors [3,4]. For that purpose there are specialized photovoltaic power converters being offered with a convertor for coupling to optical fiber [5,6] (PPC-E – for 12.6 and 4V).
The article reviews the possibility of optical power sharing on two photovoltaic convertors PPC-4E with the purpose of autonomous charging of two separated smart sensors, positioned at a distance from each other.
The sharing of optic power, coming from the IR laser, to the relevant photovoltaic inputs have been made by passive optical splitter [7]. The main task of the following release is to present alternative mesh for sharing of optic power, which must have better energy characteristics by specific consumption in the grid circle and conditions of exploitation. There is also algorithms for controlling of the both types of grid charging.
In addition in the following article both circles of optic power sharing have been analyzed. The main purpose is to compare their energy efficiency as well the conditions in which the suitable method could be used. .
II. PRINCIPLE OF OPERATION
А. Optical system for distribution of photon power with an optical splitter
A splitter with two outputs has been chosen with the purpose of receiving more energy at the outputs, which has to be delivered to the corresponding photovoltaic by a multi- mode optic fiber 62.5 μm. The sharing energy at the splitter 1x2 is equal at every output (each 50%) with a loss of 3.83dB.
In the Figure 1 was represented a block diagram of an optical system for optical energy sharing with optical splitter. Microcontroller in the smart sensor SS, parallel with his main functions, observes the condition of the Li- ion battery. When the electric tension of the battery reduces to a level of 3V, there is a request for recharging to the central controller transmitted through the optical transmitter on the channel for data CF (optical communication fiber). The central controller switches on and manages the powerful IR laser diode PLD through PLDD driver. The photon energy from the laser, occurred on the entry of the optical splitter OSP, splits equal on both exits. The light energy, through optical fibers PF (electric cable), distributes simultaneously to both photovoltaic converter PPC-4E, then transforms in electric energy and both charger devices BBC in the sensors start charging the batteries. Until the charging process lasts, DC- DC converters supply the sensors with electrical energy, that comes from the entry 1 (the voltage of photovoltaic). DC- DC converters have been designed to automatically switch and use the voltage of entries 2 (voltage of the batteries), when the voltage of entries 1 are zero (voltage of photovoltaic). That happens, when the charging of the batteries is over. As opposition of the sensor, which requests starting of charging process, the battery of the other sensor is not empty, but after the powerful laser switches on, the photon energy, delivered to the optical splitter, enters equally to the both photovoltaic cells and the both batteries are starting to recharge simultaneously. The battery with the higher voltage at the beginning of the process will charge to 4,2 V earlier and the sensor SS2 indicates to the central, that the battery is fully charged. The central controller CC checks the ID address of the relevant sensor and confirms, that this sensor has not gave request for charging and continues with the charging. When the battery is charged to the level of active mode of sensor SS2, he receives an energy trough DC- DC converter of the photovoltaic, but if the sensor is in sleep mode, then the delivered energy of the photovoltaic would be spend inefficient. In the moment when the central controller receives
1Jovan Shikoski is with the Faculty of Telecommunications atTechnical University of Sofia, 8 Kl. Ohridski Blvd, Sofia 1000,Bulgaria.
2Juli Zlatev is with the Faculty of Telecommunications atTechnical University of Sofia, 8 Kl. Ohridski Blvd, Sofia 1000,Bulgaria.
3Tinko Eftimov is with University of Telecommunications andPost, 1 Stefan Mladenov sreet, Sofia 1700, Bulgaria.
4Georgi Stanchev is with the Faculty of Mechanical Engineeringat Technical University of Sofia, 8 Kl. Ohridski Blvd, Sofia 1000,
output signal from the relevant sensor, that the battery is fully charged, the charging process disconnects.
In Figure 2 has been described the specified algorithm of operating of the grid.
B. Optical system for distribution of photon power with optical switch
The difference between optical splitter compared with optical switches is, that the photon energy is sharing simultaneously and equal to all of the exits by the splitters and the full energy is distributed only in one output channel, which is the focus of the mirror, by the switches.
The experiments in the article are made for optical switch with 1 input and 2 outputs with 62,5 μm multi-mode optical fiber. The losses on the first exit are 0,58 dB and for the second 0,35 dB. The maximal optic power, which is the
limit of working conditions for the switch is 500mW with light length of 850nm. The switch time from one to another position is 8 ms. The control system of the switch is digital through l2C or TTL interface. The block diagram of distribution of photon energy with optic switch is described in Figure 3. When the smart sensor SS1 sends request for charging to the base station, the main controller CC manages the optical switch through I2C interface and aims the mirror to the outputs of the optic fibre to the direction of the relevant sensor. With the help of the driver PLDD the main controller switches on and manages the powerful IR laser diode PLD with maximal power of 500mW. Compared to the splitter, the optic switch delivers the whole photon energy through the optic fibre to the photovoltaic of the relevant smart sensor. When the battery is charged to 4,2 V, the smart sensor sends a signal to the main station thorough the optic fibre for communication CF, the central controller stops the power laser and the process of charging interrupts. The same process replays by the charging of the other sensor. The frequency of charging of the smart sensor in the grid depends on the time of charging of the batteries. Because the charging of the sensors is successive, it is necessary the sensors to be chosen with different by discharging of the
batteries or with phase displacement by the charge process, in order for the system to charge them just in them with energy. The main target is to avoid the situation of charging both of them simultaneously. For the optimisation of the charging time the battery must start to be charging from the moment of voltage under 3,5 V (0,2 V under the nominal value). From big importance by the design of this type of sensor system is
Fig. 2. Algorithm for optical grid with splitter
Fig. 1. Optical grid with splitter
the consumption and the time of active regime of the sensors to be distributed without critical situations, where the both sensors must be charged simultaneously.
The block algorithm which describes the work principles of the optic system for sharing of photon power with optical switch is shown in the Figure 4.
III. DESIGN INSTRUCTION
At the beginning of the design of the optic sensor grid must be evaluated the main energy losses as a sum of the losses of every single component from the pick tail of the powerful laser to the photovoltaic device [8]:
as they follow: nconnector =2 is the number of connectors from the sensor to the base station, Bconnector=0,5dBare the losses in the connectors, nsplice = 2- number of the weld seams in the optic fiber Bsplice= 0,1 dB- those are the losses in the welds of the optic fiber, bf = 2,7 dB/km are the losses for a kilometer through multimode 62,5 μm optic fiber with light with length of the wave of 808nm [9]. The length of the optic fiber in
centimeters in “z”, measured in kilometers. BS are the losses in the optic distributor as it follows: optic splitter -BS=3,83dB and optic switch BS=0,58dB for the first one and BS= 0,35 dB for the second output. From the equation (1) the main energy loss for the optic system with splitter is B=6,38 dB, for optic system with optic switch is BS=3,13dB for the first and BS=2,9dB for the second output.
The energy design of the optic system is a response of the following equation:
PVS PBP += [dBm] (2)
here PS is the optical power of the source of light, in our experiment IR laser, B- the main energy losses in the optic system and PPV -The optic power on the input of the devices of photovoltaic converter. From equation (2) for the calculation of the provided optic power in the system we receive the following condition:
Fig. 3. Optical grid with a switch
Fig. 4. Algorithm for optical grid with a switch
BPP SPV −= [dBm] (3)
The IR laser with optic power of 1W (30 dBm) has been
chosen for the optic system of sharing of photon energy with passive splitter, where every photovoltaic have inputs power of PPV= 23,6 [dBm]. In the optic system with optic switch, the power of the IR laser has been reduced to 500mW (27dBm). When we add the losses in (3), we receive the optic power PPV= 23,9 [dBm] in the first output of the photovoltaic and PPV= 24,1 [dBm] on the input of the second.
We convert the power from dBm to W with the following equation:
10)(
10.1)(
mWP
mWP mW = (4) After the convert from (4), by the system with splitter with
input optic power of 1W, every photovoltaic of the equipment receives P(mW)= 229 mW. For a system with switch and adjusted power of 500mW input optic power, the hardware of the first photovoltaic receives P(mW)=251mW and at the input of the second P(mW)= 257 mW optic power.
In the Table 1we can see the dependency between the maximum output electric power with adjusted different levels of experimental power on the input of the photovoltaic [6].
TABLE I Electrical power by different levels of optic power for photovoltaic
PPC-4E
Optical Power (mW)
50
100
250
500
750
1000
1500
Pmax (mW)
17.6
34.8
86
168
240
304
432
Vmp (V)
4.4
4.4
4.3
4.2
4
3.8
3.6
Imp (A)
4
8
20
40
60
80
120
IV. CONCLUSION
When the time of voltage release by the batteries are almost the same, the usage of optic splitter as a sharing of photon energy is the better solution, because it gives the opportunity for simultaneously recharging of all batteries in the optic grid. The bigger amount of the sensors will need a splitter with bigger number of outputs, which comes with higher optic power of the supply laser. The usage of more powerful laser is considered as a disadvantage, because they are more expensive and the increase of the optic power leads to the destruction of the structure of the optic fiber [10]. That’s why there is a limit of the optic power through the fibers and it will limit the number of the sensors. A disadvantage of this method of sharing of energy could be the ineffective usage of the energy from the sensors, which need to charge their battery, but they are in sleep mode.
The usage of optic switch as sharing of optic power is the better decision, when the times of discharge are different and
it is possible every single battery to be charged separately. Compared to the splitters, the optic switch sharing the optic power discrete to every fiber, which allows the usage of laser lower power supply. This makes this type of system more energy effective. Because of the limitation of the power to 500mW, the working power of the switch, the usage of microcontroller and sensors is necessary. The biggest effort comes with the management of the time for charging of the separate sensors and the avoidance of the situation, when two or more sensors must be charged simultaneously. With bigger number of sensor this issue grows definitive. The possible solution could be made with the software with the building of command structure between the sensors in the optic system. That means, that the sensors which have more time in active mode must be with higher priority for recharging in compare with others, which are higher time in sleep mode.
From the analysis and the comparison of the both models for sharing of photon energy can be noted, that the system with optical splitter is technically easier for construction and maintenance and also cheaper.
The method of sharing of optic power with optic switch has better energy effectiveness in the following aspect: the whole optic energy is used for charge, the supply laser is two times less powerful, the effective moment power by the separate sensors is a little bit higher, because of the lower losses in the switch.
V. REFERENCES
[1] JDSU, Photonic power solutions for sensor applications, December, 2006.
[2] J.G. Werthen, M.J. Cohen, T.C. Wu, and S. Widjaja, ELECTRICALLY ISOLATED POWER DELIVERY FOR MRI APPLICATIONS, Photonic Power Business Unit, JDSU, Milpitas, CA, United States, Proc. Intl. Soc. Mag.
[3] Furey J., Anaheim, CA (US), Power over optical fiber systems, Ulllted States Patent Application Publication, No.: US 2009/0016715 A1, Jan. 15, 2009.
[4] Wilson C., Kawasaki (JP); Chee S.S., Kokubunji (JP); Nutt L., Houston, TX (US); Yamate T.,Yokohama (JP); Kamata M., Kawasaki (JP); Methods and apparatus for photonic power conversion downhole, Ulllted States Patent, No.: US 7,696,901 B2, Apr. 13, 2010.
[5] JDSU, Photovoltaic power converter, 12 V (PPC-12E), datasheet, December 2006.
[6] JDSU, Power Over Fiber Kit PPM-500-K, April 2014. [7] JDSU, Power Over Fiber, March 2014. [8] Mitzev C., Dimitrov K., Optical Communications seminar
[10] Seo K., Nishimura N., Shiino M., Yuguchi R. and Sasaki H., Evaluation of High-power Endurance in Optical Fiber Links, Furukawa Review, No. 24, 2003.
Polynomial-Based Extraction Procedure for
Determination of HEMT Noise Wave Temperatures Vladica Đorđević
1, Zlatica Marinković
2, Olivera Pronić-Rančić
2 and Vera Marković
2
Abstract – The noise wave model defines relationships between
the noise wave parameters and the noise parameters. As the
noise wave model is related to device intrinsic circuit and
available measured transistor noise parameters are related to the
whole device, the noise wave parameters are usually extracted
using time-consuming optimization procedures in circuit
simulators. In this paper, a new, faster and more efficient
extraction procedure based on using polynomial functions is
presented. The detailed validation of the proposed procedure is
done by comparison of the transistor noise parameters of the
entire circuit, obtained by using the noise wave parameters
extracted by the proposed approach, with the measured
Mixer Linearization in Direct Conversion Receiver Aleksandar Atanasković1, Aleksandra Đorić2 and Nataša Maleš-Ilić1
Abstract – In this paper, the linearization of the mixer in direct conversion receiver is performed by the technique that exploits the baseband signals. The signals for linearization are formed and processed in digital domain, set on the appropriate amplitude and polarity and inserted at the mixer. The linearization effects of the applied linearization method on the third- and fifth-order nonlinearities are observed for the case when the signals for linearization are driven at the transistors' drain of the RF stage differential pair in the Gilbert mixer cell. Additionally, the effects of I/Q signal imbalances on the linearization of the mixer are examined. Analysis are performed for two types of the signal – ideal I/Q signal without imbalances and I/Q signal with imbalance effect (up to 30% amplitude imbalance and 50 degrees phase imbalance). Tests were performed for two different input signal power levels and for two cases of frequency spacing between signals.
Keywords – Direct Conversion, Mixer, Linearization method, I/Q imbalances.
I. INTRODUCTION
The direct-conversion receivers (DCRs), also known as zero-IF receivers, over the last decade have become popular alternative approach to the classical heterodyne architecture in the development of RF integrated circuits (ICs) in modern wireless communication systems. The DCR architecture has become an attractive solution for the commercial applications due to its exquisite characteristics, such as low-cost, low-power, wide bandwidth, and highly integration with RF circuitry. On the other hand, linearity of the receiver become necessary feature and mixer is one of the influential components which can determine system performances. The mixers have frequency-conversion/demodulation function in RF and microwave receivers. The major goals of the mixer design are to minimize conversion loss, noise figure and intermodulation distortion.
Different techniques for the mixer linearization have been deployed, such as predistortion, feedforward, a technique based on transconductance cancelation of the third-order, techniques based on the insertion of the second harmonic and/or the difference frequency signal in the analogue domain [1-5].
The technique applied in this paper for the mixer linearization uses the modified signal in the baseband which is a low-frequency product of the second-order nonlinearity
of a nonlinear system induced by the useful baseband signal, [6], [7]. The in-phase I and quadrature-phase Q components of the signal are digitally processed in order to create adequate signals for linearization, which are tuned in amplitude and polarity and injected at the mixer cell.
The effects of the proposed linearization method are examined through the simulation process for QAM signal at two input power levels , where I and Q components are single tones with frequency interval between spectral components of 0.2 MHz and 2 MHz. Additionally, the impact of the imbalances of the I and Q signals on the intermodulation products is investigated. Output power levels of the fundamental signal, as well as levels of the third- and fifth-order intermodulation products, are observed in terms of the amplitude and phase mismatch of the I and Q signals.
II. THEORETICAL APPROACH
The direct-conversion receivers translate the desired RF spectrum directly to DC using a local oscillator (LO) which frequency is equal to the RF-carrier frequency of the desired signal. The mixed output is the signal that is downconverted directly to the baseband, so that the IF stage is not required. Figure 1 shows the schematic diagram of the direct-conversion receiver including the mixer linearization circuit.
The theoretical approach of the proposed linearization technique is based on the nonlinearity of the transistor output current [7-9]. The in-phase, I and quadrature phase, Q components are extracted at the demodulator output in the receiver to be adequately processed in the baseband to create signals for linearization:
2 2mod ( , )BB f I Q I Q= = + (1)
The formed linearization signals are separately adjusted in amplitude and polarity { }e oa across two branches, as
indicated in Figure 1. Indexes, e and o in subscript are related to the signals prepared for the insertion in the mixer cell through the serial LC circuit. According to the analysis performed in [6-9], the second order nonlinearity of the transistor in the mixer cell leads to the interference of the injected baseband signal for linearization and fundamental signal, which generates additional third-order nonlinear products that may suppress the original intermodulation products distorted by the transistor nonlinear characteristic.
1Aleksandar Atanasković and Nataša Maleš-Ilić are with theFaculty of Electronic Engineering, University of Niš, Serbia,Aleksandra Medvedeva 14, 18000 Niš, Serbia, E-mail: [aleksandar.atanaskovic, natasa.males.ilic]@elfak.ni.ac.rs
2Aleksandra Đorić is with the Innovation Centre of AdvancedTechnology, Niš, Serbia, Bulevar Nikole Tesle 61, 18000 Niš,Serbia, E-mail: [email protected]
Fig.1. Schematic diagram of the DCR with the mixer linearization circuit
III. LINEARIZATION RESULTS
The linearization was applied to the Gilbert mixer that is used in the direct conversion receiver (Figure 1). The impact of the performed linearization method on the intermodulation products reduction was analysed through the simulation process in ADS for the mixer cell that uses transistor MOSFET model. The linearization was carried out for the ideal case where I and Q components have equal amplitudes and phase difference of 90 degrees.
The mixer cell was tested for QAM modulated signals that comprise the I and Q single tone baseband components. The frequency spectrum of such a signal contains two spectral components and we considered two cases, when the spectral components are separated by 0.2 MHz and 2 MHz.
The carrier frequency of the input signal is 1 GHz as well as the frequency of the local oscillator. Linearization of the mixer was performed for the cases when the input power of the RF carrier is PinRF = -20 dBm and -30 dBm, while the power of the signal from the local oscillator is PinLO = -3 dBm.
The optimization process of the adjustable parameters of the linearization signals was performed to reduce the third-order intermodulation products, IM3 and to restrain the fifth-order intermodulation products, IM5 at the levels below the suppressed IM3 products.
Figures 2 and 3 show the intermodulation products, IM3 and IM5, before and after the applied linearization method. After applied linearization, suppression of the IM3 products is around 12 dB for higher power level and both frequency spacing. For lower power, the IM3 products are improved about 22 dB for 0.2 MHz frequency spacing and 8 dB for 2 MHz signal separation. On the other hand, the IM5 products are aggravated, but they are still below linearized IM3 products.
a) b)
Fig 2. Intermodulation products before and after the linearization forPinRF = -20 dBm, PinLO = -3 dBm: a) IM3 i b) IM5
a) b)
Fig 3. Intermodulation products before and after the linearization forPinRF = -30 dBm, PinLO = -3 dBm: a) IM3 i b) IM5
IV. EFFECTS OF I/Q IMBALANCES
In ideal case, the signal from the local oscillators in the I and Q channels have equal amplitude and phase difference of -90 degrees, as depicted in Figure 1. When the asymmetry occurs, the amplitudes and phases of the LO signals in the channels deviate from the values in the ideal case. In practice, I channel is defined as a reference (0 degrees phase, amplitude value 1).
The signal at the mixer input is in the form:
( ) ( ) ( ) ( ) ( )ttQttItX ccRF ω−ω= sincos (2) where cω is the carrier frequency. Imbalance is characterized by amplitude (α) and phase shift ( θ ) of the signal from the local oscillator XLO in Q branch as:
( )θ+ωα−= tX LOLO sin (3)
Then, the IQ imbalanced signal at the mixer output can be written as follows:
( ) ( )tItI BB =
( ) ( ) ( ) ( ) ( )[ ]θ−θα= sincos tItQtQBB (4)
In 3D figures, 4 and 5, the output power of the fundamental signal for both, input power levels and signal spacing, in terms of amplitudes and phases misalignment of the I and Q components is presented. Figures clearly indicate that output power levels stay almost unchanged with the increase of the parameters α and θ for the considered signal separation and input signal levels.
Figures 6 to 9, represent the IM3 and IM5 products after the linearization when IQ imbalances are considered. For low level of IQ imbalances ( 5%α < , deg3<θ ) the IM3 products after the linearization retain almost unaltered in case of 0.2 MHz signal spacing. When signal spacing is 2 MHz, the IM3 products are less susceptible to the amplitude and phase changing, especially for lower considered power. In the cases of greater IQ imbalances, values of the IM3 products after the linearization are approaching the levels of the IM3 products before the linearization. As far as the IM5 products are concerned they slightly increase with the rise of the IQ imbalances, but they still stay below the linearized IM3 products considered under the same imbalance conditions.
a) b)
Fig. 4. Output power of the fundamental signal for signal spacing 0.2 MHz in terms of I/Q imbalances : a) PinRF = -20 dBm,
Fig. 5. Output power of the fundamental signal for signal spacing 2 MHz in terms of I/Q imbalances: a) PinRF = -20 dBm, PinLO = -3 dBm; b) PinRF = -30 dBm, PinLO = -3 dBm
a) b)
Fig. 6. Intermodulation products of the direct converted mixer for signal spacing 0.2 MHz, PinRF = -20 dBm, PinLO = -3 dBm: a) IM3;
b) IM5
a) b)
Fig. 7. Intermodulation products of the direct converted mixer for signal spacing 0.2 MHz, PinRF = -30 dBm, PinLO = -3 dBm: a) IM3;
b) IM5
a) b)
Fig. 8. Intermodulation products of the direct converted mixer for signal spacing 2 MHz, PinRF = -20 dBm, PinLO = -3 dBm: a) IM3;
b) IM5
a) b)
Fig. 9. Intermodulation products of the direct converted mixer for signal spacing 2 MHz, PinRF = -30 dBm, PinLO = -3 dBm: a) IM3;
b) IM5
V. CONCLUSION
This paper describes the linearization method that uses the modified baseband signals for the Gilbert mixer linearization in direct conversion receiver. The main role of this mixer is direct conversion of the input signal carrier frequency to the baseband. The test was performed for the QAM signal whose I and Q components are sinusoidal signals and the spectrum
contains two frequency components separated for 0.2 MHz and 2 MHz. The proposed linearization method utilizes the I and Q signals that are adequately processed in the digital domain at the receiver with the aim to form the signals for linearization. Linearization effects are examined for different input power levels and different frequency spacing between the signal spectral components. The signals for linearization are fed at the transistors' drain of the RF stage differential pair in the Gilbert cell. It should indicate that very good results are achieved in the reduction of the third-order mixer nonlinearity. The fifth-order intermodulation products are deteriorated, but they are still kept at the levels below the linearized IM3 products. Additionally, it is shown that the low-levels of IQ misalignment have almost negligible effect on the linearization results, especially in case of 2 MHz spacing between signals. Also, we analyse the grade in which the linearization effects deteriorate with the increasing imbalance.
ACKNOWLEDGEMENT
This work was supported by the Ministry of Education, Science and Technological Development of Republic of Serbia, the projects number TR-32052.
REFERENCES
[1] Y. Kim, Y. Kim, and S. Lee, “Linearized mixer using predistortion technique”, IEEE Microw. Wireless Compon. Lett., vol. 12, no. 6, pp.204–205, 2002.
[2] T. J. Ellis, “A modified feed-forward technique for mixer linearization”, IEEE MTT-S Int. Dig., pp. 1423–1426, 1998.
[3] K-H Liang, C-H Lin, H-Y Chang, and Y-J Chan, “A New Linearization Technique for CMOS RF Mixer Using Third-Order transconductance Cancellation”, IEEE Microwave аnd Wireless Components Letters, vol. 18, no. 5, pp.350-352, 2008.
[4] S. Ock, Y.Yang and B. Kim, “New Linearization Method for Mixer”, Journal of the Korean Physical Society, vol. 39, no. 1, pp. 1-3, 2001.
[5] S. Lou, H. C. Luong, “A Linearization Technique for RF Receiver Front-End Using Second-Order-Intermodulation Injection“, IEEE Journal of Solid-state circuits, vol. 43, no. 11, pp.2404-2412, 2008.
[6] A. Đorić, N. Maleš-Ilić, A. Atanasković, B. Milovanović, “Mixer Linearization by Modified Baseband Signals”, Sinteza 2016, Conference Proceedings, Belgrade, Serbia, 2016 (accepted for publication).
[7] J. C. Pedro and J. Perez, “Accurate simulation of GaAs MESFET’s intermodulation distortion using a new drain-source current model,” IEEE Trans. Microwave Theory Tech., vol. 42, pp. 25–33, January 1994.
[8] J. P. Aikio and T. Rahkonen, “Detailed distortion analysis technique based on simulated large-signal voltage and current spectra”, IEEE MTT Trans Microwave Theory Tech., vol. 53, pp. 3057–3065, 2005.
[10] A. Heiskanen, J. Aikio, and T. Rahkonen, “A 5-th order Volterra study of a 30W LDMOS power amplifier”, ISCAS'03- International Symposium on Circuits and Systems, Conference Proceedings, Vol. 4, pp. 616–619, Bangkok, Thailand, 2003.