International Journal of Electrical and Computer Engineering (IJECE) Vol.
No.
February 2017, pp.
ISSN: 2088-8708.
DOI: 10.
11591/ijece.
Modeling and Structure Optimization of Tapped Transformer Abdelhadi Namoune1.
Azzedine Hamid2.
Rachid Taleb3 Electrical Engineering Department.
University of Science and Technology of Oran-Mohamed Boudiaf Laboratoire dAoElectronique de Puissance Appliquye (LEPA).
Oran.
Algeria Electrical Engineering Department.
Hassiba Benbouali University Laboratoire Gynie Electrique et Energies Renouvelables (LGEER).
Chlef.
Algeria
Article Info
ABSTRACT
Article history:
In this paper, a simplified circuit model of the tapped transformer structure has been presented to extract the Geometric and technology parameters and offer better physical understanding.
Moreover, the structure of planar transformer has been optimized by using changing the width and space of the primary coil, so as to enlarge the quality factor Q and high coupling coefficient K.
To verify the results obtained by using these models, we have compared them with the results obtained by employing the MATLAB Very good agreement has been recorded for the effective primary inductance value, whereas the effective primary quality factor value has shown a somewhat larger deviation than the inductance.
Received Jun 1, 2016 Revised Aug 23, 2016 Accepted Dec 11, 2016 Keyword:
Geometrical parameters High coupling coefficient Quality factor Tapped transformer Technological parameters Copyright A 2017 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Abdelhadi Namoune.
Electrical Engineering Department.
University of Science and Technology of Oran-Mohamed Boudiaf.
Laboratoire dAoElectronique de Puissance Appliquye (LEPA).
Faculty de Gynie Electrique.
BP 1505 El-mAonaouar.
Oran.
Algeria.
Email: namoune.
abdelhadi@gmail.
INTRODUCTION
Transformers are exploited in RFIC .
adio-frequency integrated circui.
functions in place of two inductors in disparity circuits to acquire superior Q .
uality facto.
while absorbing less expire region .
They are also utilized for solitary to differential signal translation, impedance matching, signal pairing and phase dividing.
A transformer is shaped when two spiral coils, or inductors, magnetically combine due to their close proximity.
This reasons the impedance levels, distincted as the ratio of the terminal voltage to the current flow, to modify between coils .
The transformer characteristics comprise the self-inductance, series resistance, mutual coupling coefficient, substrate capacitances, self resonating frequencies, symmetry and die region.
Alike to inductor, the type of transformer structure influences these characteristics and is selected based on the application usage the transformer is intended for.
The three ordinary transformer configurations are shown in Figure 1.
Figure 1.
illustrates a tapped structure consisting of an inner winding and an outer winding.
Mutual combination between adjacent conductors contributes mostly to the selfinductance of every coil.
The structure is not often useful as the mutual inductance is small due to very small coupling .
Figure 1.
shows two spirals interwound in the equal plane.
The interwound spirals guarantee electrical characteristics of primary and secondary are equal, including the similar number of turns.
The transformer terminals are situated in opposite sideAos permiting easy access for layout .
Figure 1.
shows two spirals stacked in divide metal planes.
The advantage of the structure is an abridged generally region since it is implemented in different metal layers.
The flux linkage between the two windings advances due to the close coupling.
The coupling coefficient.
K, can be as high as 0.
9 for a stacked structure .
However, the use of separate metal planes consequences in an asymmetry between the primary and secondary coils Journal homepage: http://iaesjournal.
com/online/index.
php/IJECE A ISSN: 2088-8708 caused by the diverse thickness and metal characteristics of the planes.
This layout is suitable for small frequency action as big capacitance between coils due to the overlap results in a low SRF .
elf resonating frequencie.
Figure 1.
Transformers Physical Structures .
Tapped .
Interleaved .
Stacked An on-chip transformer model is needed for chip technologies.
Modeling and design of on-chip inductors and transformers is presented in .
Each inductor is constructed with one metal spiral or winding.
On-chip transformers, consisting of various windings, may be designed in different ways.
The tapped transformer design is chosen for various causes.
This structure simply permits for any ratio of NP: NS, but in return, due to the large relative distance between windings of the two spirals it consequences in a awfully small coupling coefficient.
Clearly, because of including straight relations between two spirals there is a superior possibility of circulating tall levels of noise between parts of the circuit that use magnetic coupling.
On the other hand, due to low surface area between the two inductors, the resulted parasitic capacitance is extremely small which consequences in tall self resonance frequency .
The advantages are short port-to-port capacitance and tall Lp and Ls but have the disadvantages of organism asymmetric and have short coupling coefficient, approximately around 0.
3 to 0.
In this paper, square shaped tapped transformer has been studied.
Section 2.
extract the geometrical and technological parameters of the tapped transformer.
Section 3, an equivalent-circuit model of tapped transformers is presented.
In Section 4, the structure has been optimized by changing the geometrical and technological parameters of the tapped transformer, to enlarge the quality factor Q and high coupling coefficient K.
Moreover, simulation results will be compared with calculation results.
Finally, a conclusion is drawn in Section 5.
TAPPED TRANSFORMER
Figure 2 illustrate the cross Section view beside the thickness of a typical tapped transformer The outer diameter OD is distinct as the outmost distance between two parallel segments.
The inner diameter ID is distinct as the intimate distance between 2 parallel segments.
The width is W, the spacing is S.
The example device in Figure 2 has Np=Ns = 2 turns .
, .
Tm=tp Auox Dielectric (Co.
Primary coil Secondary coil Silicon substrate Asub Ausub Figure 2.
Cross Section View of a Tapped Transformer with the Definition of the Main Geometrical and Technological Parameters IJECE Vol.
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The planned transformer model obtains into explanation an amount of geometrical parameters.
They are abridged in Table 1 .
, .
Table 1.
Geometrical Parameters of the Tapped Transformer Symbol Geometrical Parameters Number of primary turns Number of secondary turns Wire length of the primary turns Wire length of the secondary turns Width of the metal conductor of the primary turns Width of the metal conductor of the secondary turns Thickness of the metal conductor of the primary turns Thickness of the metal conductor of the secondary turns Space between metal conductor of the primary turns Space between metal conductor of the secondary turns Inner diameter of the transformer Outer diameter of the transformer Technological parameters must be cautiously measured in the enlargement of the model so that it can be legal for an amount of different processes parameters .
, .
Table 2 presents a list of the technological parameters, which are considered in the planned model .
ee Figure .
Table 2.
Technological Parameters of the Tapped Transformer Symbol Technological Parameters Distance between the substrate and the .
rimary, secondar.
lower face
Substrate thickness Equivalent relative permittivity of the dielectric between substrate and conductor
Equivalent relative permittivity of the substrate Substrate resistivity Auox
Ausub
Asub
TRANSFORMER MODEL
A lossy transformer can be modeled with an inductor and a resistor in series for each coil representing the dominating series losses as shown in Figure 3.
From the model, the characteristics of the tapped transformer can be illustrated .
The impedances of the primary and secondary coils are:
Z11 A Rp A j.
Z 22 A Rs A j.
The inductances of the primary and secondary windings are:
Lp A ImAZ11 A A .
Ls A ImAZ 22 A A .
The quality factors of the windings are:
Qp A ImAZ11 A ReAZ11 A .
Qs A ImAZ 22 A ReAZ 22 A .
Modeling and Structure Optimization of Tapped Transformer (Abdelhadi Namoun.
A ISSN: 2088-8708 To explanation for the inadequate coupling suitable to metal ohmic loss, substrate dissipation, parasitic capacitance and outflow, several parameters are defined .
The quality factor represents the power of the magnetic coupling and M is the mutual inductance between the primary and secondary coils as distinct in Equation 7.
For a completely joined transformer, the quality factor is harmony.
But in a characteristic process.
K is between 0.
3 and 0.
9 for monolithic transformers .
The relation between coupling coefficient.
K, and mutual inductance.
M, is illustrated in Equation 8.
Z12 Z 21
A j.
kA Lp .
Z11
Z22
Figure 3.
A Lossy Transformer Model The model for a tapped transformer is exposed in Figure 4.
This model comprises two A models, one for each coil.
The A model contains the series inductance (L.
, the series resistance (R.
, the series capacitance (C.
, the transformer to substrate capacitance (Co.
, and the substrate resistance (Rs.
and capacitance (Cs.
The transformer model also includes the spiral-to-spiral capacitances (Co.
and the mutual inductance (M).
The substrate coupling elements Rsi and Csi are neglected from the use of a patterned ground shield .
Sub Csi Sub Csi Rsi Rsi Cov Cox Cox Cox Cox Cov Csi Rsi Sub Rsi Csi Sub Figure 4.
Physical Representation of Equivalen Circuit Model Parameters for Transformer .
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STRUCTURE OPTIMIZATION
Space and Width of the Primary Coil of the Tapped Transformer The width and the space between turnAos lines of primary coil can influence the inductance and quality factor of tapped transformers.
Figure 5 shows the space Sp and width Wp of a tapped transformer.
When varying the width and space of primary coil, the inductance, quality factor and coupling coefficient will also be changed so as the parasitic capacitance.
For the tapped transformer, if the outer diameter and number of turns is fixed, equal summation of width Wp and space Sp leads to approximately the equal region of the tapped transformer, which is a thought in tapped transformer design.
Also, the summation constant of width and space .
rimary coi.
are optimized, together verify the performance of the tapped transformer.
Primary Secondary Figure 5.
Tapped Transformer Structure .
he Indication of width and Space of Primary Coi.
Four tapped transformer structures are considered by care the summation of width and space of the primary coil at 25AAm.
The width and space of primary coil are 9 16AAm, 13 12AAm, 17 8AAm, and 21 4AAm.
The number of turns (Np and N.
of these four tapped transformers is fixed at 2 and OD outer diameter is 250AAm.
Figure 6 shows the four structures of tapped transformer.
:W S= .
AAm .
:W S= .
AAm .
:W S= .
AAm .
:W S= .
AAm Figure 6.
The Four Structure of Tapped Transformers with width Plus Space (Wp S.
as: .
9 16AAm, .
13 12AAm, .
17 8AAm, .
21 4AAm Figure 7 shows the inductance Lp and quality factor Qp of primary coil of these four structures.
The value primary inductances of these four structures are approximately the equal.
Above 5 GHz, the value primary inductances show divergence for the reason that of the diverse element parasitic.
For the primary quality factor Qp, it is obvious that the structure with the summation of width and space (Wp Sp= 17AAm 8AA.
achieve the major quality factor.
Figure 8 shows the result for the highest value primary inductance can achieve for a square tapped transformer having the thickness of metal tp, the widths of primary coil between 2 and 20 AAm and .
p / W.
ratios between 0.
1 and 0.
haracteristic devise values for primary coil of tapped transforme.
It must be renowned that tapped transformers, still although of easy realization, eat a lot of on-wafer region, and wary optimization to contain the top magnitude inductance and quality factor.
This optimization must think a known primary inductance value, frequency of action and the technology parameter used to create the tapped Modeling and Structure Optimization of Tapped Transformer (Abdelhadi Namoun.
A ISSN: 2088-8708 (Wp S.
=21AAm 4AAm (Wp S.
=13AAm 12AAm (Wp S.
=17AAm 8AAm (Wp S.
=9AAm 16AAm Inductance of the primary coil "Lp(H)" Quality Factor of the primary coil "Qp" (Wp S.
=21AAm 4AAm (Wp S.
=17AAm 8AAm (Wp S.
=9AAm 16AAm (Wp S.
=13AAm 12AAm Frequency F(H.
Frequency F(H.
Figure 7.
Primary Inductance Lp and .
Primary Quality Factor Qp as a Function of Frequency of these Four Structures (Wp S.
Tp/W p=0.
Tp/W p=0.
Tp/W p=0.
Tp/W p=0.
Inductance Lp (H) W idth of primary coil .
Figure 8.
Results for the Primary Inductance of Tapped Transformer having the Width Wp between 2 and 20 AAm and the Thickness of Metal tp defined by the tp / Wp Ratios between 0.
1 and 0.
Effect of Geometrical Parameters To evaluate the inductance of the primary turn of a tapped transformer, we employ the experimental formula .
, .
Lp A 37,5.
A0 .
N p2 .
AD 2
OD A 14.
E OD.
A14,5.
OD A 13.
AD A E
k A1A E E 37,5.
N .
N .
AD 2 E
where Np is the number of primary turns.
Ns is the number of secondary turns.
OD is the outer diameter.
ID is the inner diameter.
W is the track width, and S is the line-to-line spacing.
In addition (W and S), outer diameter (OD) is another important geometrical parameter determining the coupling coefficient value and surface employ of the tapped transformer.
Figure 9 shows how coupling coefficient K varys with changing outer diameter OD and number of turns of primary coil Np.
The spacing of primary coil Sp can be fixed to 2m, the width of primary coil Wp can be fixed to 10m and the frequency f IJECE Vol.
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can be fixed to 5 GHz.
bigger outer diameter and augment number of turn Np product in elevated coupling coefficient K.
In a tapped transformer, such as the one in design, the coupling coefficient between the primary and secondary coils is small.
Figure 10 shows the coupling coefficient K as a function of number of turns Np and different spacing Sp, different width Wp of the primary coil for a tapped transformer.
For the unchanged space and width of the primary coil, there is a big development in coupling coefficient K as number of turn W p=6AAm & Sp=2AAm W p=8AAm & Sp=2AAm W p=6AAm & Sp=3AAm W p=8AAm & Sp=3AAm Coupling coefficient k Outer diameter OD .
Number of turns of primary coil Np Figure 9.
Outer Diameter OD Versus Number of Turns of Primary Coil Np for a Tapped Transformer and a given Coupling Coefficient Value K Number of turns Np Figure 10.
Coupling Coefficient K as a Function of Number of Turns Np and different Metal Trace Width Wp, and Spacing Sp for a Tapped Transformer Effect of Substrate Thickness and Substrate Resistivity The influence of the substrate resistivity and the substrate thickness on the performance of a 5.
2 nH nominal tapped transformer is analyzed.
Two different substrate resistivities were simulated: low resistivity silicon (LR-S.
4 W.
cm and high resistivity silicon (HR-S.
at 7 KW.
Two different substrate thicknesses were also simulated.
Tsub = 300 AAm and Tsub = 500 AAm.
The results are shown in Figure 11.
Increasing the thicknesses from 300 to 500 AAm does not augment significantly the primary quality factor, mostly since the resistance of the substrate is limited by the skin effect.
The peak of the primary quality factors at 2.
5 GHz and 5.
5 GHz.
On the additional hand, rising the resistivity of the substrate can augment the primary quality factor, signifying that at very elevated frequency the substrate connected losses are the controling ones when employing thick substrate (Tsub > 200 AA.
LR-Si & Tsub=300AAm LR-Si & Tsub=500AAm HR-Si & Tsub=300AAm HR-Si & Tsub=500AAm Inductance of the primary coil "Lp(H)" Quality Factor of the primary coil "Qp" LR-Si & Tsub=300AAm LR-Si & Tsub=500AAm HR-Si & Tsub=300AAm HR-Si & Tsub=500AAm Frequency F(H.
Frequency F(H.
Figure 11.
Primary Inductance and .
Primary Quality Factor as Function of the Frequency for different Substrate Resistivity (LR Ae Low Resistivity and HR Ae High Resistivit.
and different Substrate Thicknesses (Tsub=300 AAm and Tsub=500 AA.
Modeling and Structure Optimization of Tapped Transformer (Abdelhadi Namoun.
A ISSN: 2088-8708 Comparisons Between Calculation and Simulation Results Figure 12 illustrate a comparison of the effective values of the primary inductance Lp and primary quality factor Qp of tapped transformer taked by the calculation of the parameters physical model and by simulation results by MATLAB.
Calculation Simulation Calculation Simulation Quality Factor of the primary coil "Qp" Inductance of the primary coil "Lp(H)" Frequency F(H.
Frequency F(H.
Figure 12.
Comparison between Calculated and Simulated Results .
Primary Inductance and .
Primary Quality Factor of a Tapped Transformer A good accord between the calculated and simulated primary inductance value was also achieved in the holder of tapped transformer.
A vaguely bigger calculated inductance value was achieved compared with the simulated results.
The calculated inductance value at 3 GHz frequency is 10.
45 nH.
The simulated inductance value at 3 GHz frequency is 7.
96 nH.
The maximum primary quality factor value achieved by calculating the parameters of the equivalent model of tapped transformer was 16.
82 and was achieved at 2.
2 GHz frequency.
The maximum primary quality factor value obtained by simulation was 13.
15 and was obtained at 2.
6 GHz frequency.
CONCLUSION
In this paper, an equivalent circuit model has been presented to study the tapped transformer.
This model presents a great physical perception of the tapped transformer and can be utilized to remove the geometric and technology parameters.
The correctness of the circuit model is definited by contrasting its consequence with MATLAB simulation result.
Also, the physical structure of tapped transformer has been optimized to obtain improve performance.
By contrasting the MATLAB simulation results of diverse structures, the quality factor of tapped transformer is optimized by using appropriate, outer diameter, inner diameter, width, space, substrate thickness and substrate resistivity.
The preferred tapped transformer specifications recognized by the designer are transformed into suitable geometrical parameter without neglecting the process parameter.
REFERENCES