Implementation of Rapid Prototyping Tools for Power Loss and Cost Minimization of DC-DC Converters

Abstract: In this paper, power loss and cost models of power electronic converters based on converter ratings and datasheet information are presented. These models aid in creating rapid prototypes which facilitate the component selection process. Through rapid prototyping, users can estimate power loss and cost which are essential in design decisions. The proposed approach treats main power electronic components of a converter as building blocks that can be arranged to obtain multiple topologies to facilitate rapid prototyping. In order to get system-level power loss and cost models, two processes are implemented. The first process automatically provides minimum power loss or cost estimates and identifies components for specific applications and ratings; the second process estimates power losses and costs of each component of interest as well as the whole system. Two examples are used to illustrate the proposed approaches—boost and buck converters in continuous conduction mode. Achieved cost and loss estimates are over 93% accurate when compared to measured losses and real cost data. This research presents derivations of the proposed models, experimental validation of the models and demonstration of a user friendly interface that integrates all the models. Tools presented in this paper are expected to be very useful for practicing engineers, designers, and researchers, and are flexible and adaptable with changing or new technologies and varying component prices.


Overview
As dependence on electronic appliances, digital products and computer systems in both industrial and household applications grows, the demand for power electronic converters is increasing.DC-DC converters continue to grow in popularity in all major electronics applications.Given the high demand for these converters, engineers are faced with a major challenge to design them in a very short period of time while still ensuring competitive cost.Rapid prototyping tools for converter development help solve this constraint and thus are of interest as both time-and cost-saving methods.
Existing literature indicates significant research related to power loss estimation of various power electronic components.Loss estimation, for example, is used in [1] to analyze how power loss can be redistributed in a power converter using a modulation technique.Another reason for the need for power loss estimation is when evaluating the effect of different material on device power losses, e.g., [2,3].In other applications, e.g., [4], power loss estimation is central in evaluating the usability of a power electronic converter, and power loss is used as a metric when comparing various converters.Since temperature rise in semiconductors and other power electronic devices is mainly caused by power losses, power losses have also been used for thermal analysis and modeling of power electronic systems, e.g., [5,6].Therefore, power loss estimation is essential for new material, device, and converter evaluation, in addition to comparing various converters and designs where efficiency is a major figure of merit.Modeling of power electronic converters can be improved by loss and cost estimation, such as distributed power converters in a standalone DC microgrid [7], or DC microgrids for electric vehicle charging stations [8].Also, essential application which relies on power converter topology can benefit from loss and cost estimation, like PFC converters for plug-in-hybrid electric vehicles [9], and novel bidirectional DC/DC converter topologies [10].
Several techniques have been implemented to find out power loss or cost models of specific components.A majority of this research has focused on selecting components for power electronic converters, e.g., [11].Extensive research has been conducted for finding specific losses in semiconductors and magnetic components, e.g., [12].Power loss estimation in semiconductors has also been extensively studied, e.g., [6,13] where power losses are correlated with temperature rise in the devices using thermal resistance datasheet values.Topology-specific power loss models also exist, which address specific component losses, e.g., power MOSFET losses in a buck converter [14], or system-level losses, e.g., boost converter [15].Several methods to measure system-level power loss have also been proposed, e.g., [16,17].Power losses in other parts of the converter, e.g., PCB losses [18][19][20] and gate drive losses [21], have been addressed but are only introduced in the Appendix A of this paper.
Cost consideration is the most important factor for industries which mass-produce power electronic converters, to achieve market success and competitiveness by reducing cost [22].However, most existing literature mainly focuses on methods to predict costs of specific systems and avoids generalized cost models of power electronic devices and converters.For example, in [23] the cost models of a battery, inverter and converter were developed on the basis of power ratings of these sub-systems.Cost estimation and reduction techniques have been developed for a single component such as inductor or heat sink in [24].Some cost models are also developed for switch-mode power supplies by considering component power losses, weight, manufacturing process and raw material cost fluctuations [25].
An important application of power loss and cost estimation is design optimization of power electronic converters.With a well-established power loss or cost model of various devices that can form the converter, an optimization problem can be established where the converter's power loss or cost are the figures of merit.Attempts for such analytical design approaches are [26], but mostly focus on power losses, especially semiconductor losses in [26].Cost models and power loss models of specific devices which can be extended for integration in power electronic converters, have been presented in [27] but without converter design optimization.
Therefore, generalized power loss models of major power electronic devices, as well as cost models of these devices, have not been shown in the literature for ease of integration for any power converter topology.For example, textbook models such as those presented in [16,[28][29][30], are presented in an introductory ay where they may not be easily integrated into any power converter topology.Research papers, on the other hand, present very specific models for devices or topologies but rarely provide a flexible model that can be integrated with different power converter topologies.

Proposed Approach and Contribution
This paper presents a building-block approach, as demonstrated in Figure 1, towards modeling power loss and the cost of power electronic converters.Power loss models are based on converter voltage, current, power, and frequency ratings and operating conditions along with basic datasheet information.Cost models are based on average prices related to component ratings obtained using an extensive market survey and surface-fitting tools.It is important to note that component technology and cost profiles change over time as a result of changes in material and manufacturing techniques and thus this paper intends to develop power loss and cost modeling methodologies that can evolve with time and changes in technology.
The paper focuses on the building-block approach of the modeling of power loss and the cost of power electronic converters to achieve minimum power loss and cost design instead of the model Energies 2016, 9, 509 3 of 35 construction of single component.The proposed method provides a new tool and effective way where assembles the circuit from parts to an entirety to evaluate the power loss and cost of an entire converter.The overall process used in rapid prototyping tools for cost and power loss models in optimization and component-specific modes as proposed here is illustrated in Figure 2. The target of the models is to minimize the estimation error when comparing actual component power loss and cost values with the measured power losses or actual cost.Their main advantage is the ability to evaluate a large number of possible component combinations and achieve almost instantaneous cost and loss estimates.Thus a large quantity component library is generated as the basement of the models and the web based program of the rapid prototyping tool ensures the component library is up to date along with the newest marketing price and technology.From customer perspective, once the converter topology is chosen and desired power loss and cost are typed into the GUI interfacing panel, the rapid prototyping tool is able to search, chose the appropriate component and assemble the converter rapidly to save the time of customer to search and evaluate the component.Also, the rapid prototyping tool is able to optimize the results to minimize the power loss and cost with the change of the custom parameters such as topology, total cost and power loss.
Energies 2016, 9, 509 3 of 35 The paper focuses on the building-block approach of the modeling of power loss and the cost of power electronic converters to achieve minimum power loss and cost design instead of the model construction of single component.The proposed method provides a new tool and effective way where assembles the circuit from parts to an entirety to evaluate the power loss and cost of an entire converter.The overall process used in rapid prototyping tools for cost and power loss models in optimization and component-specific modes as proposed here is illustrated in Figure 2. The target of the models is to minimize the estimation error when comparing actual component power loss and cost values with the measured power losses or actual cost.Their main advantage is the ability to evaluate a large number of possible component combinations and achieve almost instantaneous cost and loss estimates.Thus a large quantity component library is generated as the basement of the models and the web based program of the rapid prototyping tool ensures the component library is up to date along with the newest marketing price and technology.From customer perspective, once the converter topology is chosen and desired power loss and cost are typed into the GUI interfacing panel, the rapid prototyping tool is able to search, chose the appropriate component and assemble the converter rapidly to save the time of customer to search and evaluate the component.Also, the rapid prototyping tool is able to optimize the results to minimize the power loss and cost with the change of the custom parameters such as topology, total cost and power loss.Rapid prototyping tools for DC-DC converters are of main interest here due to the converters' simplicity, wide range of their applications and since the methodology for developing models is of main interest rather than actual topologies.The paper focuses on the building-block approach of the modeling of power loss and the cost of power electronic converters to achieve minimum power loss and cost design instead of the model construction of single component.The proposed method provides a new tool and effective way where assembles the circuit from parts to an entirety to evaluate the power loss and cost of an entire converter.The overall process used in rapid prototyping tools for cost and power loss models in optimization and component-specific modes as proposed here is illustrated in Figure 2. The target of the models is to minimize the estimation error when comparing actual component power loss and cost values with the measured power losses or actual cost.Their main advantage is the ability to evaluate a large number of possible component combinations and achieve almost instantaneous cost and loss estimates.Thus a large quantity component library is generated as the basement of the models and the web based program of the rapid prototyping tool ensures the component library is up to date along with the newest marketing price and technology.From customer perspective, once the converter topology is chosen and desired power loss and cost are typed into the GUI interfacing panel, the rapid prototyping tool is able to search, chose the appropriate component and assemble the converter rapidly to save the time of customer to search and evaluate the component.Also, the rapid prototyping tool is able to optimize the results to minimize the power loss and cost with the change of the custom parameters such as topology, total cost and power loss.Rapid prototyping tools for DC-DC converters are of main interest here due to the converters' simplicity, wide range of their applications and since the methodology for developing models is of main interest rather than actual topologies.Rapid prototyping tools for DC-DC converters are of main interest here due to the converters' simplicity, wide range of their applications and since the methodology for developing models is of main interest rather than actual topologies.The paper proceeds as follows: Section 2 shows generalized component-level power loss models.Section 3 discusses the application of generalized power loss models for several power electronic converters.Section 4 explains the concept behind cost model development and illustrates these models.Section 5 shows experimental results that validate the developed models.Section 6 explains rapid prototyping tools for model-based power loss minimization and presents tools for cost minimization.Section 7 concludes with the summary remarks and future work.

Generalized Component-Level Power Loss Models
Generalized power loss models of power electronic components are derived based on equivalent circuit models of each major component by considering component non-idealities and parasitic elements.The models presented here stem from existing models in textbooks and foundational research papers, e.g., [13,19,[28][29][30] and others.Therefore, this Section is a summary of such models, while Section 3 presents these models when massaged for specific buck and boost converter topologies.

MOSFET Losses
In power electronic converters, MOSFETs operate as switching elements.Figure 3 shows a MOSFET model with its non-idealities.The paper proceeds as follows: Section 2 shows generalized component-level power loss models.Section 3 discusses the application of generalized power loss models for several power electronic converters.Section 4 explains the concept behind cost model development and illustrates these models.Section 5 shows experimental results that validate the developed models.Section 6 explains rapid prototyping tools for model-based power loss minimization while Section 7 presents tools for cost minimization.Section 8 concludes with the summary remarks and future work.

Generalized Component-Level Power Loss Models
Generalized power loss models of power electronic components are derived based on equivalent circuit models of each major component by considering component non-idealities and parasitic elements.The models presented here stem from existing models in textbooks and foundational research papers, e.g., [13,19,[28][29][30] and others.Therefore, this Section is a summary of such models, while Section 3 presents these models when massaged for specific buck and boost converter topologies.

MOSFET Losses
In power electronic converters, MOSFETs operate as switching elements.Figure 3 shows a MOSFET model with its non-idealities.The MOSFET PCM [28] is: where ID is represented as shown in Figure 4 when the MOSFET operates as a switch.IDrms can be computed by Switching losses of MOSFETs are mainly divided into two parts, PON(M) and POFF(M).Because only steady state efficiency is concerned, voltage overshoot and diode reverse recovery effect won't be considered.The total switching loss PSW is thus [31]: where for a fixed fsw: The MOSFET P CM [28] is: where I D is represented as shown in Figure 4 when the MOSFET operates as a switch.I Drms can be computed by The paper proceeds as follows: Section 2 shows generalized component-level power loss models.Section 3 discusses the application of generalized power loss models for several power electronic converters.Section 4 explains the concept behind cost model development and illustrates these models.Section 5 shows experimental results that validate the developed models.Section 6 explains rapid prototyping tools for model-based power loss minimization while Section 7 presents tools for cost minimization.Section 8 concludes with the summary remarks and future work.

Generalized Component-Level Power Loss Models
Generalized power loss models of power electronic components are derived based on equivalent circuit models of each major component by considering component non-idealities and parasitic elements.The models presented here stem from existing models in textbooks and foundational research papers, e.g., [13,19,[28][29][30] and others.Therefore, this Section is a summary of such models, while Section 3 presents these models when massaged for specific buck and boost converter topologies.

MOSFET Losses
In power electronic converters, MOSFETs operate as switching elements.Figure 3 shows a MOSFET model with its non-idealities.The MOSFET PCM [28] is: where ID is represented as shown in Figure 4 when the MOSFET operates as a switch.IDrms can be computed by Switching losses of MOSFETs are mainly divided into two parts, PON(M) and POFF(M).Because only steady state efficiency is concerned, voltage overshoot and diode reverse recovery effect won't be considered.The total switching loss PSW is thus [31]: where for a fixed fsw: Switching losses of MOSFETs are mainly divided into two parts, P ON(M) and P OFF(M) .Because only steady state efficiency is concerned, voltage overshoot and diode reverse recovery effect won't be considered.The total switching loss P SW is thus [31]: where for a fixed f sw : Energies 2016, 9, 509 5 of 35 The gate loss P G is usually observed at C gs [17]: Thus, total power losses in a MOSFET are:

Diode Losses
Diodes in power electronic converters act as rectifiers and uncontrolled switches.Figure 5 shows a diode model with its non-idealities.
Energies 2016, 9, 509 5 of 35 The gate loss PG is usually observed at Cgs [17]: Thus, total power losses in a MOSFET are:

Diode Losses
Diodes in power electronic converters act as rectifiers and uncontrolled switches.Figure 5 shows a diode model with its non-idealities.The diode conduction loss PCD is modeled as: where typical values of VD0 and RD are: There are two switching losses of a diode-turn-on loss and turn-off loss.The turn-on loss is usually ignored because the diode starts conducting from an off-state.PSWD is thus [6]: rr rr sw P QV f  (10) and the total diode power loss is:

Inductor Losses
An inductor stores energy in its magnetic field.Figure 6 shows an inductor with non-idealities and Figure 7 shows a typical inductor current waveform in a DC-DC converter.The diode conduction loss P CD is modeled as: where typical values of V D0 and R D are: There are two switching losses of a diode-turn-on loss and turn-off loss.The turn-on loss is usually ignored because the diode starts conducting from an off-state.P SWD is thus [6]: Q rr V rr f sw (10) and the total diode power loss is:

Inductor Losses
An inductor stores energy in its magnetic field.Figure 6 shows an inductor with non-idealities and Figure 7 shows a typical inductor current waveform in a DC-DC converter.
Energies 2016, 9, 509 5 of 35 The gate loss PG is usually observed at Cgs [17]: Thus, total power losses in a MOSFET are:

Diode Losses
Diodes in power electronic converters act as rectifiers and uncontrolled switches.Figure 5 shows a diode model with its non-idealities.The diode conduction loss PCD is modeled as: where typical values of VD0 and RD are: There are two switching losses of a diode-turn-on loss and turn-off loss.The turn-on loss is usually ignored because the diode starts conducting from an off-state.PSWD is thus [6]: rr rr sw P QV f  (10) and the total diode power loss is:

Inductor Losses
An inductor stores energy in its magnetic field.Figure 6 shows an inductor with non-idealities and Figure 7 shows a typical inductor current waveform in a DC-DC converter.The core loss PCORE is usually obtained by the Steinmetz equation [16,32] to be: Note that modified Steinmetz equations are also common for core loss estimation, but if core loss coefficients are not supplied in a datasheet, a constant RC can be used and PCORE is estimated as: The Steinmetz equation is used as an example, but the methodology is intended to support other forms of loss models.This is clear by using either Equation (12) or Equation (13) and can extend to more detailed models.Resistive losses can also be estimated as shown in [16,32], DCR and ACR are provided by datasheets or manufacturers:

Capacitor Losses
Capacitors are major storage elements in power electronic converters and their typical nonidealities are shown in Figure 8. Two major power losses in the capacitor are those in its AC and DC resistances [33].Pac is: while Pdc is: Total power loss of the capacitor is thus:  The core loss P CORE is usually obtained by the Steinmetz equation [16,32] to be: Note that modified Steinmetz equations are also common for core loss estimation, but if core loss coefficients are not supplied in a datasheet, a constant R C can be used and P CORE is estimated as: The Steinmetz equation is used as an example, but the methodology is intended to support other forms of loss models.This is clear by using either Equation (12) or Equation (13) and can extend to more detailed models.Resistive losses can also be estimated as shown in [16,32], DCR and ACR are provided by datasheets or manufacturers: Total power loss of an inductor is thus:

Capacitor Losses
Capacitors are major storage elements in power electronic converters and their typical non-idealities are shown in Figure 8.The core loss PCORE is usually obtained by the Steinmetz equation [16,32] to be: Note that modified Steinmetz equations are also common for core loss estimation, but if core loss coefficients are not supplied in a datasheet, a constant RC can be used and PCORE is estimated as: The Steinmetz equation is used as an example, but the methodology is intended to support other forms of loss models.This is clear by using either Equation (12) or Equation ( 13) and can extend to more detailed models.Resistive losses can also be estimated as shown in [16,32], DCR and ACR are provided by datasheets or manufacturers: Total power loss of an inductor is thus:

Capacitor Losses
Capacitors are major storage elements in power electronic converters and their typical nonidealities are shown in Figure 8. Two major power losses in the capacitor are those in its AC and DC resistances [33].Pac is: while Pdc is: Total power loss of the capacitor is thus:  Two major power losses in the capacitor are those in its AC and DC resistances [33].P ac is: while P dc is: Total power loss of the capacitor is thus: P dc is small as compared to P ac as capacitors are mainly used to pass current ripple, thus P dc it is frequently ignored.

Power Loss Models for Several Converters
Equations explained in the previous section are common in the literature, but are rarely presented for specific converter topologies.In this section power loss models for boost and buck converter in continuous conduction mode (CCM) and flyback converter in discontinuous conduction mode (DCM) are explained in detail.These converters are used as examples due to their common use in any applications and their simple construction and analysis.All generalized equations are reformulated in terms of input and output parameters and datasheet information.

Boost Converter in CCM
A typical non-ideal boost converter is shown in Figure 9 followed by derivations for power losses in main boost converter components operating in CCM.
Energies 2016, 9, 509 7 of 35 Pdc is small as compared to Pac as capacitors are mainly used to pass current ripple, thus Pdc it is frequently ignored.

Power Loss Models for Several Converters
Equations explained in the previous section are common in the literature, but are rarely presented for specific converter topologies.In this section power loss models for boost and buck converter in continuous conduction mode (CCM) and flyback converter in discontinuous conduction mode (DCM) are explained in detail.These converters are used as examples due to their common use in any applications and their simple construction and analysis.All generalized equations are reformulated in terms of input and output parameters and datasheet information.

Boost Converter in CCM
A typical non-ideal boost converter is shown in Figure 9 followed by derivations for power losses in main boost converter components operating in CCM.

MOSFET Losses
PCM is obtained from Equation ( 1) and can be estimated [34] as: To calculate PSW, IDon and IDoff can be obtained from Figure 7: Thus, PON(M) and POFF(M) are calculated as:

Diode Losses
PCD and PSWD are obtained using Equations ( 7) and (10) as:  

MOSFET Losses
P CM is obtained from Equation ( 1) and can be estimated [34] as: To calculate P SW , I Don and I Doff can be obtained from Figure 7: Thus, P ON(M) and P OFF(M) are calculated as: 3.1.2.Diode Losses P CD and P SWD are obtained using Equations ( 7) and (10) as: Energies 2016, 9, 509 8 of 35 3.1.3.Inductor Losses P CORE , P DCR and P ACR can be calculated as: 3.1.4.Capacitor Losses P loss(Capacitor) is obtained using Equation ( 17) as:

Buck Converter in CCM
A typical non-ideal buck converter is shown in Figure 10.

Buck Converter in CCM
A typical non-ideal buck converter is shown in Figure 10.

MOSFETs Losses
PCM is obtained from Equation (1) and can be estimated [30] as: To calculate PSW, IDon and IDoff can be obtained from Figure 7 and VDS as in Equation ( 23).Thus, PON and POFF are calculated as:

Diode Losses
PCD and PSWD are obtained by referring Equations ( 7) and ( 10) as:

MOSFETs Losses
P CM is obtained from Equation (1) and can be estimated [30] as: To calculate P SW , I Don and I Doff can be obtained from Figure 7 and V DS as in Equation ( 23).Thus, P ON and P OFF are calculated as: 3.2.2.Diode Losses P CD and P SWD are obtained by referring Equations ( 7) and (10) as: Energies 2016, 9, 509 9 of 35 3.2.3.Inductor Losses P CORE , P DCR and P ACR can be calculated as: 3.2.4.Capacitor Losses P loss (Capacitor) is obtained using Equation ( 17) as:

Flyback Converter in DCM
Flyback converters are widely used in DCM.A non-ideal flyback converter in DCM is shown in the Figure 11.For the sake of illustration, the MOSFET switching period was considered as T ON + T OFF = 0.8T S as shown in Figure 12.

Inductor Losses
PCORE, PDCR and PACR can be calculated as:

Flyback Converter in DCM
Flyback converters are widely used in DCM.A non-ideal flyback converter in DCM is shown in the Figure 11.For the sake of illustration, the MOSFET switching period was considered as TON + TOFF = 0.8TS as shown in Figure 12.
PCM in the flyback converter is described in [30,35] as:

Flyback Converter in DCM
Flyback converters are widely used in DCM.A non-ideal flyback converter in DCM is shown in the Figure 11.For the sake of illustration, the MOSFET switching period was considered as TON + TOFF = 0.8TS as shown in Figure 12.
PCM in the flyback converter is described in [30,35] as:

MOSFET Losses
T ON " 0.8T S pV out `VF q V F (43) Energies 2016, 9, 509 10 of 35 P CM in the flyback converter is described in [30,35] as: For a flyback converter in DCM, I Don is zero but I Doff and P SW are determined using [35,36] and Figure 13 as: For a flyback converter in DCM, IDon is zero but IDoff and PSW are determined using [35,36] and Figure 13 as: 0.9 Figure 13.Inductor switching waveform.

Diode Losses
PCD and PSWD of the flyback diode are calculated as:  [34,36,20] as: where: Primary PRpri and secondary PRsec resistive power losses are calculated [21] as:

Capacitor Losses
Form Equation (17), Ploss(Capacitor) is calculate as:   [20,34,36] as: where: Primary P Rpri and secondary P Rsec resistive power losses are calculated [21] as: - The main components in the snubber branch are R sn , C sn and D sn .R sn and C sn form a clamp unit.P clamp is represented as [35]: or: Snubber diode conduction loss P CDsn is obtained from Equation (7) as: while P SWDsn is obtained as: Total snubber circuit power loss is the summation of snubber diode power loss and power loss in the clamp unit.Therefore, all power loss equations for the three different converter examples are derived based on datasheet information and converter ratings.Results that validate the derived models are shown in Section 5 where experimental prototypes are used to measure the total loss in the converter.

Major Component Cost Models
A large database of cost information for multiple elements was compiled from common manufacturers' and suppliers' data.The two main sources of this data were Digikey [37] and Mouser Electronics [38], where searches were performed for MOSFETs, diodes, capacitors, and inductors of specific rating ranges.Search filters were applied to achieve such range limits, and the database is compiled and available for public use [39].Since multiple options exist for different power, voltage, current, and/or device value rating (e.g., inductance and capacitance), the average cost for each component at a certain rating combination was found by considering these multiple options.This database was input to MATLAB to create interpolated graphs and find a mathematical relationship between cost and component ratings.Cost per quantity was also considered.The impact of time on cost is not considered due to availability of present prices only.Some other costs such as costs resulting from auxiliaries, heat sinks, fan/clod plates, etc are also not considered because they are beyond the scope of this work, where the focus is mainly on methodology.

MOSFETs
SiC and GaN type semiconductor cost is still varying rapidly due to continued production improvements, thus to demonstrate the methodology we focus on Si.To create a MOSFET cost model Cost M , a large database was prepared using V DS , I D and cost.α i coefficients are as listed in Table 1, but it should be noted that these coefficients vary across a certain range and the values shown are selected to achieve the best fit for specific components used in Section 5. Figures 14 and 15 show the mathematical relationship for this database.Cost M is represented as:

Diodes
A diode cost database was prepared using VB, IF and cost where Figures and 17 show the interpolated cost surfaces while the mathematical model is shown in Equation (60) and its coefficients are shown in Table 2.

Diodes
A diode cost database was prepared using VB, IF and cost where Figures and 17 show the interpolated cost surfaces while the mathematical model is shown in Equation (60) and its coefficients are shown in Table 2.

Diodes
A diode cost database was prepared using V B , I F and cost where Figures and 17 show the interpolated cost surfaces while the mathematical model is shown in Equation (60) and its coefficients are shown in Table 2.

Diodes
A diode cost database was prepared using VB, IF and cost where Figures 16 and 17 show the interpolated cost surfaces while the mathematical model is shown in Equation (60) and its coefficients are shown in Table 2.

Capacitors
A capacitor cost (CostC) database for electrolytic capacitors was prepared using C, VC and cost where Figures 20 and 21 show the interpolated cost surfaces while the model is shown in Equation (62) and its coefficients are shown in Table 3. Different material of capacitor will lead to different cost, but electrolytic capacitor is chosen as an example to illustrate the methodology: Cost D pV B , I F q " j"2 ÿ j"0

Inductors
Inductor cost data is compiled based on L, I L and cost.

Capacitors
A capacitor cost (CostC) database for electrolytic capacitors was prepared using C, VC and cost where Figures 20 and 21 show the interpolated cost surfaces while the model is shown in Equation (62) and its coefficients are shown in Table 3. Different material of capacitor will lead to different cost, but electrolytic capacitor is chosen as an example to illustrate the methodology:

Capacitors
A capacitor cost (CostC) database for electrolytic capacitors was prepared using C, VC and cost where Figures 20 and 21 show the interpolated cost surfaces while the model is shown in Equation (62) and its coefficients are shown in Table 3. Different material of capacitor will lead to different cost, but electrolytic capacitor is chosen as an example to illustrate the methodology: Cost L pL, I L q " χ `µsinpυπLI L q `φe ´pωI L q 2 (61)

Capacitors
A capacitor cost (Cost C ) database for electrolytic capacitors was prepared using C, V C and cost where Figures 20 and 21 show the interpolated cost surfaces while the model is shown in Equation ( 62) and its coefficients are shown in Table 3. Different material of capacitor will lead to different cost, but electrolytic capacitor is chosen as an example to illustrate the methodology:

Flyback Coupled-Inductor Core
Typical core materials include silicon steel, iron powder and ferrites.A ferrite material core is used in the selected transformer to demonstrate the methodology.Two types of cores, gapped and ungapped, are considered in the proposed cost model with a frequency range between 50 KHz and 500 KHz.High frequency cores which are used for radio or telecommunications application are excluded.The cost core cost model was prepared using fsw, AL and cost.Figures 22 and 23 show the interpolated CostCO surfaces while the mathematical model is shown in Equation (63) and its coefficients are shown in Table 4.

Flyback Coupled-Inductor Core
Typical core materials include silicon steel, iron powder and ferrites.A ferrite material core is used in the selected transformer to demonstrate the methodology.Two types of cores, gapped and ungapped, are considered in the proposed cost model with a frequency range between 50 KHz and 500 KHz.High frequency cores which are used for radio or telecommunications application are excluded.The cost core cost model was prepared using fsw, AL and cost.Figures 22 and 23 show the interpolated CostCO surfaces while the mathematical model is shown in Equation (63) and its coefficients are shown in Table 4.

Flyback Coupled-Inductor Core
Typical core materials include silicon steel, iron powder and ferrites.A ferrite material core is used in the selected transformer to demonstrate the methodology.Two types of cores, gapped and ungapped, are considered in the proposed cost model with a frequency range between 50 KHz and 500 KHz.High frequency cores which are used for radio or telecommunications application are excluded.The cost core cost model was prepared using f sw , A L and cost.Figures 22 and 23 show the interpolated Cost CO surfaces while the mathematical model is shown in Equation (63) and its coefficients are shown in Table 4.

Flyback Coupled-Inductor Core
Typical core materials include silicon steel, iron powder and ferrites.A ferrite material core is used in the selected transformer to demonstrate the methodology.Two types of cores, gapped and ungapped, are considered in the proposed cost model with a frequency range between 50 KHz and 500 KHz.High frequency cores which are used for radio or telecommunications application are excluded.The cost core cost model was prepared using fsw, AL and cost.Figures 22 and 23 show the interpolated CostCO surfaces while the mathematical model is shown in Equation (63) and its coefficients are shown in Table 4.     Cost models presented here were evaluated based on two criteria.The first criterion is that an analytical form is available for the cost model, i.e., polynomial, trigonometric, exponential, etc. in order to integrate this model with other mathematical and optimization tools.The second criterion is that the R 2 value for each model, which is a measure between 0 and 1 of how well does the model match discrete data points, is acceptable.An R 2 value that is closer to 1 is desired.The second criterion is essential when dealing with cost modeling of power electronic devices since their ratings are not available as continuous options; for example, MOSFET ratings of 50 V and 100 V exist, but not necessarily at 63.5 V, and the surface fit provided applies to the continuous range.All R 2 values of the proposed models are shown in Table 5, and are all acceptable except for MOSFETs whose cost model's R 2 value is low.To mitigate this case, a locally weighted scatterplot smoothing (LOWESS) model was established to achieve an R 2 = 0.9436 for CostM but does not have an explicitly model equation like the polynomial one.Also, note that that exact cost estimates of specific components can be obtained if coefficients are changed within the specified ranges shown in Tables 1-4.

Results
Basic boost, buck and flyback converters were experimentally developed to test the power loss and cost models presented here.Bus bar losses are not considered since the experimental prototype is at a power level that does not require bus bar.More bus bar losses information can be found in [40].All parasitic elements and specific test condition examples are given in Table 6. Figure 24 shows the board housing both the boost and buck converters (flyback converter not shown).Cost models presented here were evaluated based on two criteria.The first criterion is that an analytical form is available for the cost model, i.e., polynomial, trigonometric, exponential, etc. in order to integrate this model with other mathematical and optimization tools.The second criterion is that the R 2 value for each model, which is a measure between 0 and 1 of how well does the model match discrete data points, is acceptable.An R 2 value that is closer to 1 is desired.The second criterion is essential when dealing with cost modeling of power electronic devices since their ratings are not available as continuous options; for example, MOSFET ratings of 50 V and 100 V exist, but not necessarily at 63.5 V, and the surface fit provided applies to the continuous range.All R 2 values of the proposed models are shown in Table 5, and are all acceptable except for MOSFETs whose cost model's R 2 value is low.To mitigate this case, a locally weighted scatterplot smoothing (LOWESS) model was established to achieve an R 2 = 0.9436 for Cost M but does not have an explicitly model equation like the polynomial one.Also, note that that exact cost estimates of specific components can be obtained if coefficients are changed within the specified ranges shown in Tables 1-4.

Results
Basic boost, buck and flyback converters were experimentally developed to test the power loss and cost models presented here.Bus bar losses are not considered since the experimental prototype is at a power level that does not require bus bar.More bus bar losses information can be found in [40].All parasitic elements and specific test condition examples are given in Table 6. Figure 24 shows the board housing both the boost and buck converters (flyback converter not shown).6 are extracted from datasheets of the components used in the experimental setup and which are IRFP4332PBF MOSFET, AIRD-03-101K inductor, MURF860G diode, and EEU-EB2D221 capacitor in the boost converter and IRFP240 MOSFET, AIRD-03-101K inductor, MURF860G diode, and EEU-EB2D221 capacitor in buck converters, and IRFP240 MOSFET, Q4338-BL flyback transformer, EGP10G Diode, and EEU-EB2D221 capacitor are used in the flyback converter.

Power Loss Model Verification
To validate the power loss models derived in Section 3, each of the three converters was tested under the conditions shown in Table 6, along with various output voltages and currents varied with the duty ratio.Power losses were measured by deducting the output power of the converter from its input power.Gate drive losses can be measured, but were not considered since the gate drive power supply was separate in the experimental setup and the gate drive losses do not contribute to the experimental system-level verification.Voltage divider and current sensor in the prototype consume much less power than main power losses, thus they are not taken into consideration.Figures 25-27 show experimental results of each converter at the specified test conditions in Table 6.Input and output voltage and current were measured to obtain totally converter loss to verify converter scopelevel power loss.All measurements are under zero offset condition and using calibrated probes to ensure measurement accuracy.Parasitic elements shown in Table 6 are extracted from datasheets of the components used in the experimental setup and which are IRFP4332PBF MOSFET, AIRD-03-101K inductor, MURF860G diode, and EEU-EB2D221 capacitor in the boost converter and IRFP240 MOSFET, AIRD-03-101K inductor, MURF860G diode, and EEU-EB2D221 capacitor in buck converters, and IRFP240 MOSFET, Q4338-BL flyback transformer, EGP10G Diode, and EEU-EB2D221 capacitor are used in the flyback converter.

Power Loss Model Verification
To validate the power loss models derived in Section 3, each of the three converters was tested under the conditions shown in Table 6, along with various output voltages and currents varied with the duty ratio.Power losses were measured by deducting the output power of the converter from its input power.Gate drive losses can be measured, but were not considered since the gate drive power supply was separate in the experimental setup and the gate drive losses do not contribute to the experimental system-level verification.Voltage divider and current sensor in the prototype consume much less power than main power losses, thus they are not taken into consideration.Figures 25-27 show experimental results of each converter at the specified test conditions in Table 6.Input and output voltage and current were measured to obtain totally converter loss to verify converter scope-level power loss.All measurements are under zero offset condition and using calibrated probes to ensure measurement accuracy.
Tables 7-9 show power loss estimates of each converter under different duty ratios.It is clear from Tables 5-7 that the error in estimating power losses using the derived models is less than 8% leading to more than 92% accuracy.More accurate measurements and models would still be of very high value for rapid prototyping, but the achieved model-based estimation error is very satisfactory for evaluating various design options.Among the sources of estimation error are approximations, e.g., R C (when not in a datasheet), and limited measurement accuracy.
Energies 2016, 9, 509 17 of 35  show power loss estimates of each converter under different duty ratios.It is clear from Tables 5-7 that the error in estimating power losses using the derived models is less than 8% leading to more than 92% accuracy.More accurate measurements and models would still be of very high value for rapid prototyping, but the achieved model-based estimation error is very satisfactory for evaluating various design options.Among the sources of estimation error are approximations, e.g., RC (when not in a datasheet), and limited measurement accuracy.Tables 7-9 show power loss estimates of each converter under different duty ratios.It is clear from Tables 5-7 that the error in estimating power losses using the derived models is less than 8% leading to more than 92% accuracy.More accurate measurements and models would still be of very high value for rapid prototyping, but the achieved model-based estimation error is very satisfactory for evaluating various design options.Among the sources of estimation error are approximations, e.g., RC (when not in a datasheet), and limited measurement accuracy.Tables 7-9 show power loss estimates of each converter under different duty ratios.It is clear from Tables 5-7 that the error in estimating power losses using the derived models is less than 8% leading to more than 92% accuracy.More accurate measurements and models would still be of very high value for rapid prototyping, but the achieved model-based estimation error is very satisfactory for evaluating various design options.Among the sources of estimation error are approximations, e.g., RC (when not in a datasheet), and limited measurement accuracy.

Cost Model Verification
In order to validate the cost models proposed in Section 3, prices of the parts used were compared to prices generated from the mathematical models for the MOSFET, diode, inductor, and capacitor utilized.The flyback coupled inductor model was split into wire and cores due to their abundant information, thus similar core and wire to the Q4338-BL model are used for cost validation.Cost figures of these components were generated based on Equations ( 59)-( 63), and results are compared to estimated prices in Table 10.Results in Table 10 are shown to have less than 5% error and thus the cost models established prove that the results are more than 95% accurate.The accuracy of the cost model was improved with the help of interpolated graphs and surface fitting tools.Since cost of components changes with technology and manufacturing trends, the methodology presented here can be applied for future technologies or with a refined, more comprehensive database.

Optimal Design Selection Approach
The main objective of establishing power loss models in Sections 3 and 4 is to achieve the capability of selecting the "right components" in a converter.Such components can be selected based on a figure of merit, or an optimization objective function.These figures of merit include two main factors which are (1) minimum power loss; and (2) minimum cost.While co-optimizing for both can establish a Pareto front for acceptable local minima of cost and power loss, the next sections optimize for either power loss or cost, independently.Co-optimization is left for future work and is a natural next step of this paper.
In order to find component combinations that can optimize a figure of merit, a direct search optimization is performed with priority given to the component with most influence on the figure of merit being optimized.In both power loss and cost optimizations, inductors are given priority-(1) In power loss optimization, the impact of inductors on ripple and other components' power losses is very significant; (2) in cost optimization, inductors tend to be the most expensive components.Figure 28 demonstrates the overall high-level direct search optimization performed.Sections 6.2 and 6.3 present approaches for two different figures of merit being power loss and cost, respectively.

Minimum Power Loss Designs
Power loss models developed here are combined with converter ratings to automatically produce system-level minimum power loss and select the right components.This procedure reduces the manual effort in calculating component power losses to select a combination of components that minimizes power losses.Components are selected in the order that affects selection of other components-For example, selecting the inductor in a boost converter comes as a priority as it affects the losses in semiconductors and capacitor as the inductor determines the input current ripple.In order to search for components with compatible voltage and current ratings which are set by the designer, minimum inductance and capacitance values in addition to MOSFET and diode ratings for boost and buck converters in CCM are calculated based on [41,42], while component ratings are double the converter ratings even though this factor can be modified.The resulting minimum power loss does not guarantee low cost but selects components leading to a minimum converter power loss from the available database.A pseudo-code is shown below as an example for inductor selection for minimum inductor power loss and similar logic is applied to other components.Figure 29 shows a flowchart for the minimum power loss rapid prototyping tool.The procedure shown in Figure 29 is integrated into a user-friendly GUI developed in MATLAB for rapid-prototyping.The user enters the converter type, currently boost or buck converter, and sets the operating points and basic specifications of the converter such as desired output voltage ripple and switching frequency, then receives suggested components based on the minimum combined

Minimum Power Loss Designs
Power loss models developed here are combined with converter ratings to automatically produce system-level minimum power loss and select the right components.This procedure reduces the manual effort in calculating component power losses to select a combination of components that minimizes power losses.Components are selected in the order that affects selection of other components-For example, selecting the inductor in a boost converter comes as a priority as it affects the losses in semiconductors and capacitor as the inductor determines the input current ripple.In order to search for components with compatible voltage and current ratings which are set by the designer, minimum inductance and capacitance values in addition to MOSFET and diode ratings for boost and buck converters in CCM are calculated based on [41,42], while component ratings are double the converter ratings even though this factor can be modified.The resulting minimum power loss does not guarantee low cost but selects components leading to a minimum converter power loss from the available database.A pseudo-code is shown below as an example for inductor selection for minimum inductor power loss and similar logic is applied to other components.Figure 29 shows a flowchart for the minimum power loss rapid prototyping tool.

Start
Get input and output parameters; The procedure shown in Figure 29 is integrated into a user-friendly GUI developed in MATLAB for rapid-prototyping.The user enters the converter type, currently boost or buck converter, and sets the operating points and basic specifications of the converter such as desired output voltage ripple and switching frequency, then receives suggested components based on the minimum combined power loss.This GUI is shown in Figures 30 and 31 for buck and boost optimal component selection, respectively.In order to validate the optimal component selection based on minimum converter power losses, all selected components based on compatible ratings were evaluated manually.Power losses highlighted as gray background in Tables 11 and 12  Note that a separate GUI has also been developed for component-specific evaluation as shown in Figure 32, where the effect of specific parameters and component choices can be visualized in terms of power loss.Note that a separate GUI has also been developed for component-specific evaluation as shown in Figure 32, where the effect of specific parameters and component choices can be visualized in terms of power loss.

Minimum Cost Designs
Another rapid prototyping tool is developed to achieve minimum cost of essential components for boost and buck converters as example applications.Component selection for minimum cost is done sequentially for different components based on converter ratings only.A short list of components that satisfy the converter ratings and values for inductance and capacitance is established, and components with minimum cost are selected.This selection is not necessarily optimal in terms of efficiency but ensures minimum cost based on the available database.The optimal-cost component selection pseudo-code is below and the flowchart is shown in Figure 33.

Minimum Cost Designs
Another rapid prototyping tool is developed to achieve minimum cost of essential components for boost and buck converters as example applications.Component selection for minimum cost is done sequentially for different components based on converter ratings only.A short list of components that satisfy the converter ratings and values for inductance and capacitance is established, and components with minimum cost are selected.This selection is not necessarily optimal in terms of efficiency but ensures minimum cost based on the available database.The optimal-cost component selection pseudo-code is below and the flowchart is shown in Figure 33.Two GUIs were developed to implement rapid prototyping based on cost models with one GUI targetting minimum converter cost and the other targeting component-specific cost models.Screenshots of the tool designed for rapid prototyping to achieve minimum converter cost are shown in Figures 34 and 35 for buck and boost converters, respectively.Tables 13 and 14 show manual validation of these results based on the short list of components that meet the converter specifications in the available database.Results in Figures 34 and 35 are highlighted in Tables 13 and 14 for minimum cost.The component-specific GUI is shown in Figure 36.Two GUIs were developed to implement rapid prototyping based on cost models with one GUI targetting minimum converter cost and the other targeting component-specific cost models.Screenshots of the tool designed for rapid prototyping to achieve minimum converter cost are shown in Figures 34 and 35 for buck and boost converters, respectively.Tables 13 and 14 show manual validation of these results based on the short list of components that meet the converter specifications in the available database.Results in Figures 34 and 35 are highlighted in Tables 13 and 14 for minimum cost.The component-specific GUI is shown in Figure 36.

Get input and output parameters
As can be seen in the GUI screenshots and manual validations, the rapid prototyping tools holding all power loss models and cost models from Section 2 are very valuable for practicing engineers and researchers.These GUIs can be conveniently adjusted to include different component types, various technologies for specific components, and a growing database of component with adjustable cost and prices.While models running behind the GUIs may not be all inclusive of all losses in buck and boost converters, the presented methodology and MATLAB platform is very scalable and flexible.Engineers, designers, and researchers can iteratively and manually study the effect of different component parameters, e.g., MOSFET RDS,on, on converter efficiency using the componentspecific mode, or can rely on built in minimum cost or loss searches in the optimization mode.As can be seen in the GUI screenshots and manual validations, the rapid prototyping tools holding all power loss models and cost models from Section 2 are very valuable for practicing engineers and researchers.These GUIs can be conveniently adjusted to include different component types, various technologies for specific components, and a growing database of component with adjustable cost and prices.While models running behind the GUIs may not be all inclusive of all losses in buck and boost converters, the presented methodology and MATLAB platform is very scalable and flexible.Engineers, designers, and researchers can iteratively and manually study the effect of different component parameters, e.g., MOSFET R DS,on , on converter efficiency using the component-specific mode, or can rely on built in minimum cost or loss searches in the optimization mode.Two GUIs were developed to implement rapid prototyping based on cost models with one GUI targetting minimum converter cost and the other targeting component-specific cost models.Screenshots of the tool designed for rapid prototyping to achieve minimum converter cost are shown in Figures 34 and 35 for buck and boost converters, respectively.Tables 13 and 14 show manual validation of these results based on the short list of components that meet the converter specifications in the available database.Results in Figures 34 and 35 are highlighted in Tables 13 and 14 for minimum cost.The component-specific GUI is shown in Figure 36.
As can be seen in the GUI screenshots and manual validations, the rapid prototyping tools holding all power loss models and cost models from Section 2 are very valuable for practicing engineers and researchers.These GUIs can be conveniently adjusted to include different component types, various technologies for specific components, and a growing database of component with adjustable cost and prices.While models running behind the GUIs may not be all inclusive of all losses in buck and boost converters, the presented methodology and MATLAB platform is very scalable and flexible.Engineers, designers, and researchers can iteratively and manually study the effect of different component parameters, e.g., MOSFET RDS,on, on converter efficiency using the componentspecific mode, or can rely on built in minimum cost or loss searches in the optimization mode.

Conclusions
This paper presents power loss and cost models of major power electronic components which can be further aggregated into power electronic converters.The proposed models are expected to aid designers in making preliminary useful estimates which help to decide specific components that can achieve desired system power loss and cost.Cost models are found based on an extensive survey of commercial devices followed by cost surface fitting.Power loss models are based on generalized forms that are reformulated to reach converter-specific models.Power loss models presented here are based on non-idealities and parasitic elements including PCB and gate drive losses to develop to achieve higher accuracy.The presented models are shown to be over 93% accurate.All models are integrated into MATLAB-based rapid prototyping tools designed for either minimum power loss or minimum cost component selection.With a large database, hundreds or thousands of various component options can be evaluated in minutes to achieve model-based component selection for optimized converter designs.The implementation of these tools with supplier databases is of major future interest, and extending the models to other applications and converters such as DC/AC inverters and AC/DC rectifiers can be achieved using the methodologies proposed here.Future work will include open-access web-based GUIs and possible linking to major supplier databases for up-todate component lists that eliminate obsolete parts, and up-to-date prices.
Author Contributions: Amruta V. Kulkarni is the first author of this paper whose Master's thesis work focused on the topic of the paper; she performed the literature review to find all related cost and loss model equations, applied these equations to specific converter topologies, and built the rapid prototyping tools; she also established the original component database.Weiqiang Chen helped to perform the hardware validation of models and double checked the accuracy of cost and loss models in addition to database data; he was responsible for paper submission and revision.Ali M. Bazzi provided the original idea for this paper, and provided guidance and mentoring on how to achieve the rapid prototyping tools; he was the research and academic advisor of Amruta V. Kulkarni and the advisor of Weiqiang Chen.

Conclusions
This paper presents power loss and cost models of major power electronic components which can be further aggregated into power electronic converters.The proposed models are expected to aid designers in making preliminary useful estimates which help to decide specific components that can achieve desired system power loss and cost.Cost models are found based on an extensive survey of commercial devices followed by cost surface fitting.Power loss models are based on generalized forms that are reformulated to reach converter-specific models.Power loss models presented here are based on non-idealities and parasitic elements including PCB and gate drive losses to develop to achieve higher accuracy.The presented models are shown to be over 93% accurate.All models are integrated into MATLAB-based rapid prototyping tools designed for either minimum power loss or minimum cost component selection.With a large database, hundreds or thousands of various component options can be evaluated in minutes to achieve model-based component selection for optimized converter designs.The implementation of these tools with supplier databases is of major future interest, and extending the models to other applications and converters such as DC/AC inverters and AC/DC rectifiers can be achieved using the methodologies proposed here.Future work will include open-access web-based GUIs and possible linking to major supplier databases for up-to-date component lists that eliminate obsolete parts, and up-to-date prices.
Author Contributions: Amruta V. Kulkarni is the first author of this paper whose Master's thesis work focused on the topic of the paper; she performed the literature review to find all related cost and loss model equations, applied these equations to specific converter topologies, and built the rapid prototyping tools; she also established the original component database.Weiqiang Chen helped to perform the hardware validation of models and double checked the accuracy of cost and loss models in addition to database data; he was responsible for paper submission and revision.Ali M. Bazzi provided the original idea for this paper, and provided guidance and mentoring on how to achieve the rapid prototyping tools; he was the research and academic advisor of Amruta V. Kulkarni and the advisor of Weiqiang Chen.

Conflicts of Interest:
The authors declare no conflict of interest.

Abbreviations
The following abbreviations are used in this manuscript:  Trace power loss Ptrace [17] is calculated as: where Lstray can be estimated in μH as: As presented in [17], stray capacitance is estimated as: and PCstray is: The total PCB power loss PPCB is thus: Trace power loss P trace [17] is calculated as: As presented in [17], stray capacitance is estimated as:

Figure 1 .
Figure 1.Example illustration on how to aggregate component level models into a system ($: Cost, η: Efficiency).

Figure 2 .
Figure 2. Procedure for the proposed rapid prototyping tools.

Figure 1 .
Figure 1.Example illustration on how to aggregate component level models into a system ($: Cost, η: Efficiency).

Figure 1 .
Figure 1.Example illustration on how to aggregate component level models into a system ($: Cost, η: Efficiency).

Figure 2 .
Figure 2. Procedure for the proposed rapid prototyping tools.

Figure 2 .
Figure 2. Procedure for the proposed rapid prototyping tools.

Figure 10 .
Figure 10.Buck converter topology for power loss model.

Figure 10 .
Figure 10.Buck converter topology for power loss model.

Figure 16 .
Figure 16.Diode cost model for one unit.

Figure 14 .
Figure 14.MOSFET cost model for one unit.

Figure 16 .
Figure 16.Diode cost model for one unit.

Figure 16 .
Figure 16.Diode cost model for one unit.

Figure 16 .
Figure 16.Diode cost model for one unit.

Figure 18 .
Figure 18.Inductor cost model for one unit.

Figure 18 .
Figure 18.Inductor cost model for one unit.

Figure 18 .
Figure 18.Inductor cost model for one unit.

Figure 20 .
Figure 20.Capacitor cost model for one unit.

Figure 22 .
Figure 22.Flyback core cost model for one unit.

Figure 20 .
Figure 20.Capacitor cost model for one unit.

Figure 20 .
Figure 20.Capacitor cost model for one unit.

Figure 22 .
Figure 22.Flyback core cost model for one unit.

Figure 20 .
Figure 20.Capacitor cost model for one unit.

Figure 22 .
Figure 22.Flyback core cost model for one unit.

Figure 22 .
Figure 22.Flyback core cost model for one unit.

Figure 24 .
Figure 24.Experimental setup for the buck and boost converters.

Figure 28 .
Figure 28.High-level block diagram of proposed figure of merit optimization.

Figure 28 .
Figure 28.High-level block diagram of proposed figure of merit optimization.

Figure 29 .
Figure 29.Flowchart of the minimum power loss tool.

Figure 30 .
Figure 30.Minimum power loss selection (optimization mode) for a buck converter example.

Figure 29 .
Figure 29.Flowchart of the minimum power loss tool.

Figure 30 .
Figure 30.Minimum power loss selection (optimization mode) for a buck converter example.

Figure 30 .
Figure 30.Minimum power loss selection (optimization mode) for a buck converter example.
are those for minimum power loss components and confirm results shown in Figures30 and 31.Other examples are shown in the Appendix B.

Figure 32 .
Figure 32.Component-specific power loss model for a boost converter example.

Figure 32 .
Figure 32.Component-specific power loss model for a boost converter example.

Figure 34 .
Figure 34.Minimum cost selection (opt.mode) for a buck converter.

Figure 33 .
Figure 33.Optimization technique implementation for cost model.

Figure 34 .
Figure 34.Minimum cost selection (opt.mode) for a buck converter.

Figure 36 .
Figure 36.GUI for component cost estimates in component-specific mode.

P trace " I 2
trace R trace (B1) while the stray inductance loss P Lstray is obtained[25] as:P Lstray " I trace L stray ˆdi dt ˙(B2)where L stray can be estimated in µH as:L stray " 2 ˆ10 ´4 L e

Table 1 .
Coefficients for the MOSFET cost model equation.

Table 1 .
Coefficients for the MOSFET cost model equation.Figure 14. MOSFET cost model for one unit.

Table 1 .
Coefficients for the MOSFET cost model equation.Figure 14. MOSFET cost model for one unit.

Table 1 .
Coefficients for the MOSFET cost model equation.Figure 14. MOSFET cost model for one unit.

Table 2 .
Coefficients for the diode cost model equation.
Inductor cost data is compiled based on L, IL and cost.Figures18 and 19

Table 2 .
Coefficients for the diode cost model equation.

Table 2 .
Coefficients for the diode cost model equation.
Inductor cost data is compiled based on L, IL and cost.Figures18 and 19

Table 2 .
Coefficients for the diode cost model equation.
Inductor cost data is compiled based on L, IL and cost.Figures18 and 19

Table 3 .
Coefficients for the capacitor cost model equation.

Table 3 .
Coefficients for the capacitor cost model equation.

Table 3 .
Coefficients for the capacitor cost model equation.

Table 3 .
Coefficients for the capacitor cost model equation.

Table 4 .
Coefficients for the core cost model equation.

Table 5 .
Surface fitting evaluation of cost models.

Table 4 .
Coefficients for the core cost model equation.

Table 5 .
Surface fitting evaluation of cost models.

Table 6 .
Example testing conditions and parasitic elements in experimental prototypes.

Table 7 .
Estimated and measured power loss in boost converter.

Table 8 .
Estimated and measured power loss in buck converter.

Table 7 .
Estimated and measured power loss in boost converter.

Table 8 .
Estimated and measured power loss in buck converter.

Table 7 .
Estimated and measured power loss in boost converter.

Table 8 .
Estimated and measured power loss in buck converter.

Table 7 .
Estimated and measured power loss in boost converter.

Table 8 .
Estimated and measured power loss in buck converter.

Table 9 .
Estimated and measured power loss in flyback converter.

Table 10 .
Detailed cost comparison for power components.
This GUI is shown in Figures30 and 31for buck and boost optimal component selection, respectively.
Flowchart of the minimum power loss tool.This GUI is shown in Figures30 and 31for buck and boost optimal component selection, respectively.
Figure 36.GUI for component cost estimates in component-specific mode.