Simulation of MEMS transformer on a Chip

For the case of MEMS transformer, some assumptions are also adopted to simplify the complex model and reduce the calculating time. On the geometry, the circular cross-section of connecting wires is simplified as a hexagon to reduce the number of elements. On the material property, the relative permittivity, relative permeability and magnetic loss tangent are also assumed as frequency-independent constants.

Fig. 4.20 and Fig. 4.21 show the models of MEMS transformer and the dummy PCB. The convergence curve of simulation with the model of MEMS transformer is shown in Fig. 4.22. The maximum magnitude delta S decreases when the number of tetrahedra increases, which indicates that the simulation has a converged solution. When the number of tetrahedra reaches 39606, the maximum magnitude delta S is 0.0086597, which is less than a half of default value. And when the number of tetrahedral reaches 74443, the maximum magnitude delta S is 0.0021021, which is a tenth of the default value. Considering the solving efficiency, the model is meshed into about 40000 tetrahedra.

Fig. 4.23 shows the simulated self-inductance and leakage inductance of coils of

MEMS transformer with the air core and magnetic core of 1 M Fe3O4 nanofluid.

Comparing to the measured results, the simulated results shows that the parasitical capacitance is underestimated so that a higher resonance frequency is obtained, and the simulated inductances at the frequency of 100MHz are lower than the measured. Fig.

4.24 shows the simulated coupling coefficient of MEMS transformer with the air core and magnetic core of 1 M Fe3O4 nanofluid. With the present of magnetic core of 1 M Fe3O4 nanofluid, the coupling coefficient increases slightly but still poor.

Fig. 4.25 and Fig. 4.26 show the simulated resistance and quality factor of coils of MEMS transformer with the air core and magnetic core of 1 M Fe3O4 nanofluid. The measured resistance is higher than the simulated, and it is speculated that the high resistance results from the bad contact between bonding wires and copper pads. Due to the lag between the magnetization of material and the external magnetic field, with the present of magnetic core of 1 M Fe3O4 nanofluid, the resistance increases and the quality factor decreases.

4.5 Discussions

As shown in Fig. 2.10, it illustrates the characteristic of super-paramagnetism of Fe3O4 nanofluid. Thus, the Fe3O4 nanofluid is applied as the magnetic core to reduce the

material and the external magnetic field, the resistance increases as a function of frequency, which results in a low quality factor. The reasons of lag are speculated as follow:

1. On the macroscopic view, a nanoparticle can be regard as a small magnetic dipole as shown in Fig. 4.27(a). While the external magnetic field is applied, the directions of the magnetic dipoles will turn to the direction of external magnetic field and produce a non-zero total magnetic dipole moment as shown in Fig. 4.27(b). Once the external magnetic field is removed, the directions of the magnetic dipoles will turn to random directions due to the Brownian motion, and the total magnetic dipole moment will reduce to zero in a short time.

2. On the microscopic view, a nanoparticle is composed of numerous magnetic dipoles as shown in Fig. 4.28(a). These magnetic dipoles are also influenced while the external magnetic field is applied as shown in Fig. 4.28(b). Once the external magnetic field is removed, the directions of the magnetic dipoles will turn to random directions, and the total magnetic dipole moment will reduce to zero in a short time.

Therefore, when the frequency of alternate external magnetic field is high enough, which means that the alternate time of magnetic field is smaller than the relaxation time, the lag will occur and cause the increase of resistance.

For the reasons mentioned above, the lag results in the increase of resistance. And the resistance increases faster and larger than that of inductance. Finally, the quality factor decreases with the present of Fe3O4 at high frequency.

Fig. 4.1 The schematic measurement of self inductance and leakage inductance

Fig. 4.2 The effective circuit model of real inductors containing the series resistance and parasitic capacitance

Fig. 4.3 The self-inductance of coils of transformers with different magnetic cores

Fig. 4.4 The leakage inductance of coils of transformers with different magnetic cores 60

65 70 75 80

0 20 40 60 80 100

Leakage Inductance (nH)

Frequency (MHz)

Air 0.25M 0.5M 0.75M 1M Solid

Fig. 4.5 The coupling coefficient of transformers with different magnetic cores 80

82 84 86 88 90

0 20 40 60 80 100

Coupling Coefficient (%)

Frequency (MHz)

Air 0.25M 0.5M 0.75M 1M Solid

Fig. 4.6 The resistance of coils of transformers with different magnetic cores

Fig. 4.7 The quality factor of coils of transformers with different magnetic cores

Fig. 4.8 The quality factor of coils of transformers with different magnetic cores at low

Fig. 4.9 The self-inductances and leakage inductances of coils of MEMS transformer with the air core and magnetic core of 1 M Fe3O4 nanofluid

35 37 39 41 43 45

0 20 40 60 80 100

Inductance (nH)

Frequency (MHz)

Air_L Air_Lsc 1M_L 1M_Lsc

Fig. 4.10 The coupling coefficient of MEMS transformers with the air core and magnetic core of 1 M Fe3O4 nanofluid

3 5 7 9 11 13 15

0 20 40 60 80 100

Coupling Coefficient (%)

Frequency (MHz)

Air 1M

Fig. 4.11 The resistance of coils with the air core and magnetic core of 1 M Fe3O4

nanofluid 0

0.5 1 1.5 2 2.5

0 20 40 60 80 100

Resistance (ohm)

Frequency (MHz)

Air 1M

Fig. 4.12 The quality factor of coils with the air core and magnetic core of 1 M Fe3O4 nanofluid

0 2 4 6 8 10 12 14 16

0 20 40 60 80 100

Quality Factor (U)

Frequency (MHz)

Air 1M

Fig. 4.13 The HFSS model of transformer on a capillary

Fig. 4.14 The convergence curve of simulation with the model of transformer on a capillary

0 0.004 0.008 0.012 0.016 0.02

20 21 22 23 24 25 26

Max Magnitude Delta S

Number of Tetrahedra (x10000)

Convergence

Fig. 4.15 The simulated self-inductance of coils of transformers with different magnetic

Fig. 4.16 The simulated leakage inductance of coils of transformers with different

Fig. 4.17 The simulated coupling coefficient of transformers with different magnetic cores

80 82 84 86 88 90

0 20 40 60 80 100

Coupling Coefficient (%)

Frequency (MHz)

Air 0.25M 0.5M 0.75M 1M

Fig. 4.18 The simulated resistance of coils of transformers with different magnetic cores

Fig. 4.18

Fig. 4.19 The simulated quality factor of coils of transformers with different magnetic cores

Fig. 4.20 The HFSS model of MEMS transformer with the PCB

Fig. 4.21 The HFSS model of dummy PCB

Fig. 4.22 The convergence curve of simulation with the model of MEMS transformer 0

0.01 0.02 0.03 0.04

2 3 4 5 6 7 8 9

Max Magnitude Delta S

Number of Tetrahedra (x10000)

Convergence

Fig. 4.23 The simulated self-inductance and leakage inductance of coils of MEMS transformer with the air core and magnetic core of 1 M Fe3O4 nanofluid 35

37 39 41 43 45

0 20 40 60 80 100

Inductance (nH)

Frequency (MHz)

Air_L Air_Lsc 1M_L 1M_Lsc

Fig. 4.24 The simulated coupling coefficient of MEMS transformer with the air core and magnetic core of 1 M Fe3O4 nanofluid

3 5 7 9 11 13 15

0 20 40 60 80 100

Coupling Coefficient (%)

Frequency (MHz)

Air 1M

Fig. 4.25 The simulated resistance of coils of MEMS transformer with the air core and magnetic core of 1 M Fe3O4 nanofluid

0 0.4 0.8 1.2 1.6 2

0 20 40 60 80 100

Resistance (ohm)

Frequency (MHz)

Air 1M

Fig. 4.26 The simulated quality factor of coils of MEMS transformer with the air core and magnetic core of 1 M Fe3O4 nanofluid

0 2 4 6 8 10 12 14 16

0 20 40 60 80 100

Quality Factor (U)

Frequency (MHz)

Air 1M

(a)

(b)

Fig. 4.27 The macroscopic view of Fe3O4 nanoparticles: (a) without a magnetic field; (b) with a magnetic field.

(a)

(b)

Fig. 4.28 The microscopic view of Fe3O4 nanoparticles: (a) without a magnetic field; (b) with a magnetic field.