The novel solitary electromagnetic wave (SEMW) theory and the novel design methodologies of the switching mode power supply circuit (SMPC) are presented. The SEMW theory was developed as a basic theory of the design of all kinds of the switching mode circuit including SMPC by fusing the physics of semiconductor, nonlinear undulation, and electromagnetic wave. When the SEMW theory is used, the electromagnetic analysis of SMPC becomes possible by using only the real parameters based on the physics. The technologies of the low impedance lossy line (LILL) which is used to the DC line and the matched impedance lossy line (MILL) which is used to the switching line are also presented. They are effective for suppressing the electromagnetic interference. SMPC can be reconfigured to the quasistationary state closed circuit (QSCC) by applying LILL and MILL in accordance with the SEMW theory. No electromagnetic interference exist in QSCC. The buck converter which is one of the most popular DC-DC converters is presented as an example of the method for being reconfigured to QSCC. The conventional design tools which includes SPICE based on the AC circuit theory will be effective for the design and analysis of the inside circuit of QSCC.
The SMPC can be considered to be a kind of the oscillators and
SMPC is a kind of the AC circuit, which is defined by the electromagnetism as the circuit of the EMW. EMW is generated when the electric field or the magnetic field is changed. EMW can travel at quasilight speed through the insulator of the transmission line. According to the Ampère’s circuital law in the electromagnetism, AC current is defined as line integral of the magnetic field around the wire. It has been believed that the switching voltage wave of SMPC consists of many harmonic waves by the idea of the Fourier transform. It is very convincing mathematically. However, this idea should be denied because the switching voltage shape is formed by the charge/discharge action of SEMW generated at the moment on/off of the switching device on the transmission line. When the SEMW theory is used instead of the Laplace transform, the electromagnetic analysis of the transient phenomenon will become easy and accurate.
The SEMW theory was developed by fusing the semiconductor physics, nonlinear undulation physics, and the EMW physics.
Figure
Elementary SMC.
In Figure
SEMW consists of the solitary electric-field wave (SEM) and the magnetic-field wave, which have the same waveform in accordance with the conventional EMW physics. The magnitude of the magnetic-field wave on the voltage source circuit is decided by the characteristic impedance of the transmission line and the magnitude of EMW which depends on the electric permittivity. Therefore, the magnitude of the magnetic-field wave on the transmission line does not depend on the magnitude of the magnetic permeability. The waveform of SEMW was gotten by the calculation based on the semiconductor physics. The shape of the rise part of the signal voltage was calculated by time integral of the waveform of SEW.
Figure
Waveform of SEW and rise part of signal voltage (calculated).
Solitary electric-field wave (SEM)
Rise part of signal voltage
In Figure The similarity between the SEMW and the half of the sine wave which has the frequency of No spectra exist at the frequency band higher than MSF.
In Figure
The developed vector wave equations of SEMW are
As shown in (
The defined wave length (
Figure
Image of SEW and rise part of voltage after turn on of DR.
On power line
On signal line
In Figure
When DR1 is turned off, SEMW is generated only on the signal line. Therefore, the signal line is charged to 0 V from
The fact that the conduction current or charge current which is defined as
Figure
Waveform and shapes on signal line after DR1 is turned on (calculated).
SEW
Rise part of voltage
Signal current
The calculation condition is as follows: the circuit is shown in Figure
In Figure
The static current such as the leakage current and the DC current of the terminal resistance is the conductive current or charge current on SMC. Recently, the static current of the digital circuit which consists of CMOS circuit is becoming negligible.
From the above, it has been shown that the following three kinds of the electric current on SMC were clarified by the SEMW theory. The first electric current can be gotten by a line integral of the magnetic field of SEMW around the conductor of the transmission line in accordance with the Ampère’s circuital law, and it travels at quasilight speed. The second electric current can be gotten by a line integral of the magnetic field of the flow of the electrostatic energy, and it is not the wave but it drifts at quasilight speed by being pulled out of SEMW. The third electric current is the conductive current or charge current. The average drift speed of the charge (
When SMPC is used for the IT equipment or the multimedia equipment, the almost load current of SMPC which consists of the second current and the third current is included slightly. Therefore, the test condition of SMPC should be recreated to this condition. The second electric current and the third electric current cannot cause electromagnetic disturbance or EMI because they are not the wave. The help of SEMW is necessary whenever the second electric current moves or changes. The third electric current cannot be changed to the EMW or SEMW because its drift speed is quite slower than the traveling speed of EMW or SEMW. And, in addition, it cannot change quickly by itself without the help of SEMW. Therefore, only the first current can cause electromagnetic disturbance or EMI only. The voltage droop, bounce, surge, and electromagnetic noise will be suppressed by simply attenuating the first current or SEMW on SMC.
Figure
Elementary circuit of buck converter.
The major circuit parameters in Figure
Major circuit Parameters.
UDCL | 500 mm length, 20 mm width | Transmission line formed by double-sided PCB of FR4 |
SDCL | 100 mm length, 20 mm width | |
RDCL | ≧100 mm, few ten millimeters width | |
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Q1 | Absolute maximum drain to source voltage: 30 V |
Power MOSFET of RJK0305DPB (RENESAS) |
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VS | 12 V | |
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VOUT | 5 V | |
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Output current | 20 A |
Figure
SEW and voltage after Q1 is turned on (calculated).
SEW on SDCL
Rise part of voltage at point A
In Figure
SEW and voltage after Q1 is turned off (calculated).
SEW on UDCL
Drain voltage of Q1
In Figure
As above, when the SEMW theory is used, the electromagnetic analysis of SMPC becomes possible by using only parameters according with the physics.
When the component which is similar to the ideal voltage source is located near the power MOSFET, it is expected that the vibration after Q1 is turned on/off will not arise. The electromagnetic disturbance or EMI will be suppressed by being configured to the transmission line and adding the absorption loss when the characteristic impedance is not zero. Such function cannot be actualized by the capacitor. The development of the low impedance lossy line (LILL) was started for such needs.
Figure
Cross-section of LILL chip.
In Figure
The novel characteristic equations for the simulation of the transmission coefficient (
Figure
The prototype of LILL16 for using on PCB.
Prototype
Configuration
Appearance of test
In Figure
Figure
In Figure
Calculation condition.
Appearance capacitance of etched aluminum foil | 33.9 |
Dielectric constant of alumina | 8.5 |
Conductivity of conductive polymer | 12,000 S/m |
Conductivity of carbon graphite | 72,727 S/m |
Appearance ratio of capacitance | 0.8 |
Shortening ratio of effective line length | 0.45 |
Effective chip width | 1 mm |
Effective chip length | 14 mm |
Thickness of alumina layer on etching surface | 22.8 nm |
Thickness of conductive polymer layer | 1 |
Thickness of carbon graphite layer | 0.92 |
Effective thickness of void in etching layer | 0.8 |
Electromagnetic coupling between terminals |
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Figure
Characteristics of LILL for applying SMPC (calculated).
The calculation condition is shown in Table
Calculation condition.
Effective chip width | 2 mm |
Thickness of alumina layer on etching surface | 34.3 nm |
Thickness of high viscosity conductive layer | 20 |
Widh of LILL | 4 mm |
Length of LILL | (Chip Length) + 6 mm |
Rated voltage | 24.5 V |
Rated current | 25 A |
Others are same as the calculation condition of
LILL for using to SMPC will be sealed by the heat hardener.
The cross-section of the chip and configuration of the on-board MILL for SMPC are similar to those of the on-board LILL shown in Figures
SEMW exists on SDCL and L1 in the elementary circuit of the buck converter shown in Figure
Figure
Image of SEW traveling on MILL.
In Figure
The magnitude of SEW on MILL is
According to the definition of the electromagnetism, the signal voltage on MILL is
In (
The compensation voltage by the attenuation of SEW which is shown by the dash line in Figure
From (
From (
This phenomenon can be explained also in a qualitative manner. That is, the DC level does not attenuate on the metal plate, and the wave length is maintained on the transmission lines having the homogeneous medium which are connected to each terminal of MILL when SEMW is considered to be a kind of Soliton.
Above-mentioned function of MILL was confirmed by the experiment [
Figure
Characteristics of MILL for applying SMPC (calculated).
The calculation condition is shown in Table
Calculation condition.
Appearance capacitance of etched aluminum foil | 0.49 |
Appearance ratio of capacitance | 0.9 |
Shortening ratio of effective line length | 0.6 |
Effective chip width | 0.2 mm |
Thickness of alumina layer on etching surface | 1.024 |
Thickness of high viscosity conductive layer | 50 |
Effective thickness of void in etching layer | 0.3 |
Electromagnetic coupling between terminals |
|
Rated voltage | 24.5 V |
Rated current | 25 A |
Others are same as the calculation condition of LILL shown in Figure
MILL for applying SMPC will be sealed by the heat hardener.
Figure
Improved circuit of buck converter.
In Figure
The circuit parameters in Figure
Circuit parameters.
UDCL1 | Stem trace: 10 mm length, 100 mm width |
Transmission line formed by outer layers of four-layer PCB of FR4 |
UDCL2 | 20 mm length, 60 mm width | |
SDCL1 | 10 mm length, 60 mm width | |
RDCL1 | 20 mm length, 30 mm width | |
RDCL2 | 20 mm length, 30 mm width | |
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SDCL2 | 20 mm length, 60 mm width | Transmission line formed by abutting outer layer and inner layer of four-layer PCB of FR4 |
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Q1 | Maximum DC voltage: 27 V |
POL IC of R2J20751NP (RENESAS) |
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D1 | Maximum average forward current: 30 A |
30SLJQ030 (IR) of Schottky barrier diode |
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L1 | Inductance: 800 nH |
CEP125NP-0R8NC-UD (SUMIDA) |
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C1 | 100 |
Bulk capacitor |
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Switching frequency | ≧1 MHz | |
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VS | 12 V | |
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VOUT | 5 V | |
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Output current | 20 A |
Figure
Characteristics of LL1 on PCB (calculated).
LL1 has two power terminals and two ground terminals. The calculation condition is the following: the characteristics of LILL shown in Figure
In Figure
Figure
Characteristics of LL2 on PCB (calculated).
The calculation condition of LL2 is the following: the power terminal number 1 is connected to the power trace of RDCL1, the power terminal number 2 is connected to the branch trace of RDCL2, and the ground terminal number 1 and number 2 are connected to the ground plane, respectively. The other condition is same as that of the characteristics of LL1 shown in Figure
Figure
Characteristics of ML1 on PCB (calculated).
ML1 has two power terminals and two ground terminals. The calculation condition is the following: the characteristics of ML1 shown in Figure
Figure
SEW on SDCL after Q1 is turned on (calculated).
Point C on SDCL1
Point D on SDCL2
The waveform of SEW is calculated by (
Calculation condition.
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0.877 |
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0.568 |
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0 |
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−5.25 ns |
Relative permeability of transmission line | 1 |
Dielectric constant of transmission line | 4.35 |
ML1 | MILL32 |
Dielectric constant of MILL32 | 8.5 |
In Figure
Figure
Rising part of line voltage after Q1 is turned on (calculated).
Point C on SDCL1
Point D on SDCL2
The rising part of line voltage at the point C on SDCL1 is calculated by time integral of SEW on SDCL1. The rising part of line voltage at the point D on SDCL2 is calculated by time integral of SEW on SDCL2 which has the magnitude of SEW on SDCL1 in accordance with the function of MILL shown in Section
Figure
SEW on UDCL after Q1 is turned off (calculated).
SEW at point B on UDCL2
SEW at point A on UCDL1
The waveform of SEW is calculated by (
Calculation condition.
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13.17 |
LL1 | LILL16 |
Dielectric constant of LILL16 | 8.5 |
Others are same as the calculation condition of the waveform of SEW shown in Figure
In Figure
Figure
Line voltage after Q1 is turned off (calculated).
Point B on UDCL2
Point A on UDCL1
In Figure
Figure
SEW on SDCL after Q1 is turned off (calculated).
Point C on SDCL1
Point D on SDCL2
The waveform of SEW is calculated by (
In Figure
Figure
Falling part of line voltage after Q1 is turned off (calculated).
Point C on SDCL1
Point D on SDCL2
In Figure
According to the electromagnetism, the electromagnetic disturbance or EMI does not arise when the electromagnetic field of SMC is in the stationary state or the quasistationary state. According to the SEMW theory, when the traveling time (
Normally, the electromagnetic effect of the wire can be ignored on QSCC. When the accurate analysis of the transmission delay of the wire is necessary, the easy method using the element of the capacitance and the resistance can be applied like a design method of on-chip interconnection. The conventional AC circuit theory, the circuit simulator such as the SPICE, and the state space averaging method for the analysis of the stability control of SMPS can be used effectively on QSCC. The switching frequency can be increased till the limit of the switching device because the rise time of the switching voltage is kept to intrinsic rise time of the power MOSFET by LILL. The power loss consists of the static loss and the electromagnetic loss. The generation of SEMW, bounce, surge, and vibration cause electromagnetic loss. The electromagnetic loss will also be reduced by being configured to QSCC. The higher the switching frequency, the higher the performance of LILL and MILL. The more the switching frequency, the higher the performance of LILL and MILL. Therefore, the switching time of the device is desired to be faster. The size, weight, the turn-around time from design to delivery, the cost for manufacturing, and the reliability will be improved by configuring SMPC to QSCC.
The SEMW theory and the design methodologies of SMPC were presented in this paper. When the SEMW theory is used, the electromagnetic analysis of SMPC becomes possible by using only parameters based on the physics, not by the equivalent circuit which is formed by the arbitrary idea. LILL and MILL technologies were presented also in this paper. LILL is effective for suppressing the electromagnetic noise and the spike on UDCL after the transistor is turned on. In addition, LILL provide the ideal DC source near the switching transistor. The MILL is effective for suppressing the electromagnetic noise and the spike on SDCL on SMPC after the transistor is turned on/off.
Three kinds of the electric current on SMC were presented. The first electric current is gotten by the line integral of the magnetic field of SEMW based on the Ampère’s circuit law, and it travels at quasilight speed. The second electric current is the flow of charge current of the transmission line or others and the value of the line integral of the magnetic field of the electrostatic energy around the conductor in accordance with the Ampère’s circuit law. And the third electric current is the conductive current or charge current. The average drift speed of the charge (
The methodology for reconfiguring SMPC to QSCC was presented. SMPC can be configured to QSCC by applying LILL and MILL because the electromagnetic boundary line of QSCC is formed by them. The buck converter which is one of the most popular DC-DC converters was configured to QSCC as an example. Normally, the electromagnetic effect of the wire can be ignored on QSCC. When the accurate analysis of the transmission delay of the wire is necessary, the easy method using the element of the capacitance and the resistance can be applied like a design method of on-chip interconnection. The conventional design tools which includes SPICE based on the AC circuit theory will be effective for the design and analysis of the inside circuit of QSCC. The state space averaging method for the analysis of the stability control of SMPS will become more reliable when SMPS is reconfigured to QSCC. The more the switching frequency, the higher the performance of LILL and MILL. Therefore, the switching time of the device is desired to be faster earnestly. The size, weight, the turn-around time from design to delivery, the cost for manufacturing, and the reliability will be improved by configuring SMPC to QSCC. The other application examples cannot be presented because of space limitation. They will be presented in the future by utilizing the suitable opportunity. The challenge for the commercialization of these technologies by getting the investment is the immediate issue for our venture company. Mathcad 15 and Excel were used for all calculations.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The LILL was prototyped since 2008 by using the Clevios offered by Heraeus in Germany, the etched aluminum foil offered by Japan Capacitor Industrial Co., Ltd., and some production equipment offered by Kohzan Corporation in Japan.