A new structure of integrated low-pass LC filter of DC-DC power converter is proposed in this paper. This filter consists in a circular planar coil enclosed between two ferrites substrates. Mn-Zn ferrite has been chosen because of its high permeability and permittivity. In this filter Mn-Zn substrates act not only as a magnetic core but also as a capacitor. In order to reduce the conduction losses in the part of the ferrite used as a capacitor, a particular topology using a blocking layer is proposed. A modelling of the dielectric behaviour of the materials has been performed and injected in a simulation in order to find the resulting LC filter performances and its power range of use. In order to increase the filter efficiency, different solutions have been explored. In particular the inter-turn gap evolution has been optimized to reduce the inter - turn losses. Regarding the bulk losses, BaTiO_{3} blocking layers ha ve been added, either upon the ground or the conductor. In this last case a co-firing ferrite tape has been inserted between turns to increase the LC product. Finally the use of low losses Mn-Zn and BaTiO_{3} has been proposed and the final characteristics (both electrical and dimensional) of our filter have been compared toconventional ones.
Planar LC passive components, such as inductors and capacitors, have been implemented for many years using a variety of substrates, including standard PC boards, ceramics and silicon. This technology has been only used in low power devices (a few W) with working frequencies ranging up to a few GHz [
The aim of this work is to show how Mn-Zn material may be nevertheless used for both their ferromagnetic and dielectric properties in spite of its low resistivity.
The proposed structure to be studied is a distributed LC filter. A spiral coil is sandwiched between two Mn-Zn substrates. To reduce ineluctable substrate losses, different designs have been proposed and additional materials have been used to obtain a filter having a sufficiently high efficiency. In this paper, only conduction losses occurring in the substrates of the LC filter are estimated; hysteresis and eddy-current associated losses are not taken into account.
In the first part of this paper, the equivalent circuit model per unit volume of Mn-Zn ferrite will be established from dielectric measurements. Starting from fixed geometrical sizes of the studied LC filter, distributed volume and inter-turns capacitors will thus been calculated. Effective inductors will be determined by using a finite-elements method simulation. The resulting LC filter performances (cut-off frequency, slope, filter losses ...) will then be estimated in order to provide useful information to propose a final filter design having sufficiently good performances to be integrated in a power converter.
The structure of the filter consists in a planar spiral coil sandwiched in between two ferrite substrates (
Each element of the equivalent circuit model in
The spiral coil has been broken into 2N-cells of half circle connected in series. Each half circle contains the equivalent self-inductance, mutual inductances, series resistance and inter-turns impedance. Values of inductances, mutual inductances are obtained by finite-element method. Inter-turn and volume capacitances are calculated from the Mn-Zn ferrite modelling results.
The electrical properties of ferrites depend on their polycrystalline structure. The grain and insulating grain boundary are the two main components that determine the variation of resistivity and permittivity [
These insulating layers are in practice very thin and exhibit a relatively high electrical capacity [
The equivalent circuit model of
In order to extract the values of the three components of
PARAMETERS | VALUES |
---|---|
Grain size T_{C} µ_{r} (T = 25˚C) µ_{r} (T = 100˚C) B_{S} (T = 25˚C) B_{S} (T = 100˚C) Frequency | 5 µm >200˚C 1800 2600 440 mT 370 mT Up to 500 kHz |
electrodes (diameter: 10 mm). A good fitting has been obtained between simulated and experimental frequency response of the ferrite (in the frequency range of 10 Hz - 1 MHz). Results obtained at T = 20˚C have been reported in
It should be noted that the dielectric equivalent circuit model of other Mn-Zn ferrites (i.e., doped ferrites) may be different from this model. Indeed, a highly resistive layer may be present on the surface of Mn-Zn grains; these resistive layers may be fitted by a supplementary RC-cell [
As Mn-Zn has a sufficiently high relative permittivity, fringing effect can be neglected [
The spiral inductor in between the ferrite substrates is circular. Since the spiral inductor is a distributed structure, our proposed model is based on a distributed model. Several works have already shown that a turn may be represented by a lumped model as reported in
The overall model consists in 2n-circuits connected in series to form a distributed model. The inter-turns impedances between adjacent turns are to be considered, especially by using a high permittivity substrate. They are distributed at the front and the end of the inter-turns, leading to 2(n − 1) inter-turns impedances. To illustrate the principle of this modelling, let us consider a LC filter with 2 turns of
R_{g} (Ω) | R_{gb} (Ω) | C_{gb} (nF) |
---|---|---|
66 | 13 | 16 |
done in
Inductances
Instead of using any analytical formula to calculate both self and mutual inductances, finite-elements method (FEMLAB [
L i = L s i + Σ M i j + − Σ M i j − (1)
Note that in this model, the inductances are assumed to be constant over the frequency range of interest.
Coil resistances
The resistances of each half-turn have been estimated by using the classical relationship as in Equation (2).
R = ρ ⋅ l S (2)
where ρ is conductor resistivity (here copper), l and S are conductor length and cross-sectional area respectively. In the forthcoming LC studied structures, the sizes of the coil conductor will be chosen to avoid any skin effect.
Substrate impedances
Both resistances and capacitances of the ferrite substrates are calculated by using the fitting parameters of
{ R g 2 = K R ⋅ R g 1 R g b 2 = K R ⋅ R g b 1 C g b 2 = K C ⋅ C g b 1 (3)
where K R = 2 ⋅ ( S 1 S 2 ) ⋅ ( h 2 h 1 ) and K C = 1 2 ⋅ ( S 2 S 1 ) ⋅ ( h 1 h 2 ) .
S_{2} is the area below the half-turn and S_{1} the area of electrode disk, h_{2} is the height of the ferrite between the half-turn and ground plane and h_{1} the height between the electrode disks. Factors 2 and 1/2 in the expression of K_{R} and K_{C} stand for the fact that resistances and capacitances are equally distributed at each end of the half-turn.
Calculation of section S_{2} is done with the following expressions:
{ S 2 = w ⋅ l i l i = 1 2 ⋅ π ⋅ [ 2 ⋅ R i + i ⋅ w + ( i − 1 ) ⋅ s ] . (4)
R_{i} is the inner radius of the spiral coil and l_{i} the mean length of each half-turn with i = 1 to 2n.
Inter-turns impedances
The calculation of the inter-half-turn parameters is not quite easy. The co-planar electrodes of the tested sample have to be transformed into parallel plate electrodes by using the theory of conformal transformations developed in [
K ′ R = 2 ⋅ K ( k ) K ( k ′ ) and K ′ C = K ( k ′ ) 2 ⋅ K ( k ) (5)
where K(k) is the complete integral of first kind with modulus k, and K ( k ′ ) is the complete integral of the first kind taken in the complementary modulus k ′ .
The modulus k is given by the following expression:
{ k = tanh [ π ⋅ s 4 ⋅ h ] tanh [ π ⋅ ( w + 0.5 ⋅ s ) 2 ⋅ h ] k ′ = 1 − k ² (6)
Using all these constants the parameters R_{g}_{2}, R_{gb}_{2} and C_{gb}_{2} of inter-half-turn are given by:
{ C g b 2 = 1 2 ⋅ [ C g b 1 ⋅ K ( k ′ 2 ) K ( k 2 ) ⋅ K ( k 1 ) K ( k ′ 1 ) ⋅ l 2 i l 1 ] R g 2 = 2 ⋅ [ R g b 1 ⋅ K ( k 2 ) K ( k ' 2 ) ⋅ K ( k ′ 1 ) K ( k 1 ) ⋅ l 2 i l 1 ] R g 2 = 2 ⋅ [ R g 1 ⋅ K ( k 2 ) K ( k ′ 2 ) ⋅ K ( k ′ 1 ) K ( k 1 ) ⋅ l 2 i l 1 ] (7)
where l_{2i} is the mean length of inter-half-turn and l_{1} the transversal length of the electrodes of the tested sample.
l 2 i = 1 2 ⋅ π ⋅ [ 2 ⋅ R i + ( i + 1 ) ⋅ w + i ⋅ s ] (8)
with i = 1 to 2(n − 1).
All the parameters of the filter can be now computed.
First simulations were performed by using the following physical and electrical parameters reported in
As expected, a large amount of power losses takes place in both ferrite substrate and inter-turns areas, justifying that the Mn-Zn ferrites have never been used as capacitors. As an illustration, the filter efficiency, excluding magnetic and eddy current losses, has been calculated versus output power in
Buck | Spiral | Ferrite |
---|---|---|
Frequency: 100 kHz | Number of turns: 9 | Permeability: 1800 |
Duty cycle: 0.5 | Internal radius: 5 mm | Permittivity: 6.5 × 10^{4} |
Input voltage: 200 V | Track thickness: 0.2 mm | Thickness: 1 mm |
Load: 10 to 40 Ω | Track width: 1 mm |
Power losses originating from the electrical conduction of the Mn-Zn substrate are located in the substrate bulk and in the inter-turns areas. The repartition of these losses has been estimated and revealed that these losses decrease versus inter-turns index, as indicated in
In order to reduce the electrical conduction losses, mainly located in the first turns, new simulations have been performed in which the inter-turns distances have been chosen to depend on the turn index. The inter-turns distance evolution law has been chosen linear and exponential successively in order to reduce the inter-turns losses. The chosen laws are detailed in
The resulting losses have been reported in
In spite of the reducing in the power losses induced by the modification of the coil design, the resulting filter efficiency is no longer acceptable. New structures have therefore been proposed in
Turn index | 1 | 2 | 3 |
---|---|---|---|
Substrate losses (%) | 77 | 8.5 | 1.3 |
Inter-turn losses (%) | 11 | 1.4 | 0.2 |
Inter-turn gaps law (mm) | |
---|---|
Constant | 1 |
Linear | (23.5 − 2.5 × i)/7 |
Exponential | 3 × exp[−0.256 × (I − 1)] |
Inter-turn gap evolution law | Filter efficiency (%) |
---|---|
Constant | 37 |
Linear | 59 |
Exponential | 63 |
“blocking” layers have been added in between the Mn-Zn substrates and the ground plates. In structure 3, these blocking layers have been put in between the coil and the Mn-Zn substrates. These layers have to exhibit a sufficiently high permittivity (in order to keep the advantage of Mn-Zn) and also a higher resistivity. Among available materials exhibiting such characteristics, BaTiO_{3} has been chosen. As already done with Mn-Zn, a dielectric characterisation has been performed. The most suitable electrical model able to describe the experimental behaviour of BaTiO_{3} is the same as those obtained with our Mn-Zn samples. The results obtained with a 130 µm-thick commercial (standard) BaTiO_{3} film has been reported in
In structure 3, the air gap between the two Mn-Zn substrates has been increased (+200 µm = BaTiO_{3}), leading to a decrease in the corresponding inductance L, and thus in the product LC.
Consequently, a complementary ferromagnetic material has been used to reduce this induced inconvenient. A low temperature co-firing ferrite tape (ferrite powder in organic matrix-LTCC-ESL 40012) has been chosen first of all for its interesting physical properties and secondly because it may be easily adapted to our complex structure (tapes which may be easily cut and hot-pressed to obtained the desired design and thickness). Physical data and the fitting parameters obtained on a 280 µm-thick sample have been reported in
Using successively structure 1 to 4, the filter efficiency has been estimated. In these simulations, an exponential inter-turns gaps law has been applied. The corresponding filter efficiencies are given in
All the structures show the same behaviour: the higher the output Buck power, the higher the corresponding efficiency.
R_{g} (Ω) | R_{gb} (MΩ) | C_{gb} (nF) |
---|---|---|
116 | 3.8 | 24 |
T_{C} | µ_{r} (F = 100 kHz) | R_{g} (Ω) | R_{gb} (Ω) | C_{gb} (nF) |
---|---|---|---|---|
350˚ | 450 | 12 | 1.6 × 10^{10} | 22 |
The goal of the BaTiO_{3} layers is to strongly reduce the power losses in Mn-Zn substrates in both volume and also inter-turns areas. In structure 2, only volume losses are reduced, while in structure 3 both volume and inter-turns losses are reduced, justifying that the structure 3 has a better efficiency (close to 90% at 1 kW − duty-cycle = 0.5).
As shown in this simulation, the losses reduction provided by the magnetic LTCC is not as high as expected. Moreover, keeping the air gap free may allow a complementary use of this gap. As an example, if the cooling of the DC converter is obtained by the use of a cooling fluid, this fluid may be injected in this gap to extract the heat produced by the filter.
As already mentioned, the spiral conductor is not, whatever the chosen structure, sufficient to carry 1 kW from the power supply to the load. New simulations have to be performed, using a suitable conductor cross section.
By using a 200 V power supply, carrying 3 kW leads to a spiral conductor of 3 mm^{2} (taking 5 A/mm^{2}). New simulations have been performed with this new conductor sizes. In
Electrical characteristics of such LC filters have been reported in
F_{c} (−3 dB) (kHz) | Slope (dB/decade) | Attenuation at 100 kHz (dB) | Size (cm^{3}) | Weight (g) | |
---|---|---|---|---|---|
LC filter using an air inductor and a plastic capacitor | 43 | −40 | −4.87 | 186 | 431 |
LC filter using a Mn-Zn inductor and a plastic capacitor | 43 | −40 | −4.87 | 25.5 | 180 |
Our LC planar studied filter | 45 | −180 | −3.7 | 14.7 | 81 |
Optimized filter with low loss ceramics materials | 33 | −180 | −11.5 | 14.7 | 81 |
filter while C to the total capacitance. As clearly shown in this table, our proposed LC filter is less heavy and bulky as conventional LC structures using discrete L and C components.
New optimizations are actually in progress to provide LC planar filters with lower cut-off frequencies in order to be used in DC-DC converters working at 10 - 20 kHz.
Mn-Zn ceramic substrates have been used in this work for both their high permeability and permittivity. Already largely used as core material, the goal of this study was to show that Mn-Zn may also be used as a capacitor in a DC-DC power converter integrated LC filter. The topology of this power filter is mainly composed of a circular coil between two Mn-Zn substrates. In order to reduce the Mn-Zn induced conduction power losses, the use of a blocking layer, such as BaTiO_{3}, has been proposed. Modelling and simulation were used to estimate the filter electrical characteristics. Results have shown that a combination of Mn-Zn and BaTiO_{3} ceramics materials allows the conception of power LC filters (a few kW) with a satisfactory efficiency. Future investigations are focused on the optimization of the filter design and the use of new synthesized materials in order to increase this efficiency.
The authors would like to thank T. LEBEY for his useful discussions.
Coulibaly, S., Malec, D., Bley, V., Mary, D. and Schlegel, B. (2017) New Use of Mn-Zn Ferrite Material in Power Electronics Integrated LC Filters. Engineering, 9, 993-1007. https://doi.org/10.4236/eng.2017.912059