Comparison between Active and Passive AC-DC Converters For Low Power
Electromagnetic Self-Powering Systems
A theoretical and experimental study of low power AC-DC converters
Ibrahim Hamed
Main field of study: Electronics Credits: 15 HP
Semester/Year: Spring, 2020 Supervisor: Sebastian Bader Examiner: Jan Lundgren
Course code/registration number: ET107G
Degree programme: Master of Science in Engineering: Electrical Engineering
Electromagnetic based energy harvesting systems such as Variable reluctance energy harvesting systems (VREH) have shown to be an effective way of extracting the energy of rotating parts. The transducer can provide enough power to run an electronic sensing system, but the problem arises in finding an efficient way of rectifying that power to generate a stable energy supply to run a system, which this report will investigate.
Active and passive voltage doublers have proven to be a suitable candidate in solving this issue due to the simplicity and the small footprint. This thesis will aim to compare active and passive voltage doublers under various scenarios in order to understand under which circumstances are active or passive voltage doublers to be preferred. From the conducted experimental measurements, this thesis concluded that active voltage doublers are recommended during high RPMs (>10 RPM) while passive voltage doublers (especially full-wave voltage doubler) is recommended at lower RPMs. Quality of power also plays a significant role in this study. Therefore, measurements have also been done for ripple and rise time. From the measurements, this thesis can conclude that the overall power quality was the best in Full-wave voltage doublers, while Active- voltage doublers had lower ripple than FWVDs at higher current loads.
Keywords: Energy-harvesting, electromagnetic, rectifiers, AC/DC-converters, Active voltage doublers, Passive voltage doublers.
I want to thank my supervisor Sebastian Bader for providing me with guidance and support during this project. I also want to express my gratitude towards Ye Xu for supporting me and giving me some insights into his work related to this thesis, but also for providing me with some of his valuable time.
Finally, I want to thank my family for their support and encouragement but also my friends who helped me throughout my studies.
Abstract... ii
Acknowledgement ... iii
Table of Content ... iv
1. Introduction ... 6
1.1 Background and problem motivation ... 6
1.2 Aim and Objective ... 7
1.3 Scope and limitations ... 8
1.4 Related works ... 9
1.5 Outline ... 10
2. Theory... 11
2.1 Passive voltage doublers ... 11
2.1.1 Half-wave voltage doubler (Greinacher circuit) ... 11
2.1.2 Full-wave voltage doubler (Delon circuit) ... 15
2.1.3 Diode characteristics ... 16
2.2 Active voltage doubler ... 16
2.2.1 Transistor characteristic (MOSFETs) ... 18
2.2.2 Comparator characteristic ... 19
2.3 Impedance matching... 20
3. Methodology ... 21
4.1 Simulation ... 21
4.2 Experimental Analysis ... 23
4. Design and construction ... 26
3.1 Component choice ... 26
3.2 Printed circuit board construction (PCB) ... 28
5. Results and analysis ... 30
5.1 Efficiency measurements ... 31
5.2 Output power measurements ... 33
5.2.1 Maximum Power ... 36
5.2.2 Impedance matching ... 38
5.3 Power quality ... 40
5.3.1 Ripple measurements ... 40
5.4 Active voltage doublers ... 44
6. Conclusion and Discussion ... 46
6.1 Conclusion ... 46
6.1.1 Conclusion - Power and efficiency ... 46
6.1.2 Conclusion - Power quality ... 47
6.2 Ethical considerations and social aspects ... 48
6.3 Future studies ... 49
References ... 50
Appendix A ... 53
Appendix B ... 62
1. Introduction
1.1 Background and problem motivation
In recent years, IoT technology has become an appealing solution for many pioneering industrial applications, thanks to the possibility of enabling data harvesting and condition monitoring for such industrial equipment [1][2]. With today’s advancements in wireless communication infrastructure, wireless network-based industrial automation systems have become an attractive choice for many advanced industrial applications [3].
The problem with such solutions is that many sensor systems still require a wired power supply to function, thereby the benefits of acquiring such wireless communication devices are limited to the traditional wired framework [3]. An example of such limitation occurs when monitoring rotating parts, because of the fundamental difficulty of monitoring such machinery, even providing a wired power supply to the sensor can be difficult [4].
In rotating parts, one can exploit the relative motion of the stationary sensor and the rotation of the rotating shaft to extract energy using a transducer such as an electromagnetic based Variable Reluctance energy harvesting (VREH) transducer [4][5]. Like other energy harvesting solutions, the drawback of relying on such solutions is that additional circuitry is needed in order to rectify the relatively low energy to the sensor. Therefore, an efficient AC/DC converter is required to provide reliable power to the sensor [4], which is the main objective of this thesis.
Active and passive voltage doublers circuitry have proven to be a suitable candidate in solving this issue due to the simplicity and the small footprint.
Passive voltage doublers are a variety of voltage multiplier circuits that take AC voltage as input and output a DC voltage with a multiplication of the input amplitude voltage, hence the name “Voltage multipliers.” Voltage multipliers consist of several capacitors and multiple diodes. The diodes are used for separating the positive and negative voltage cycles of the AC input signal, and the capacitors are used for maintaining a DC voltage at the output of the circuitry [6].
In contrast to passive voltage doublers, active voltage doublers use active switches instead of diodes in order to achieve the same voltage conversion.
The goal of this thesis is to compare passive and active voltage doublers in order to determine the best rectifier for usage in electromagnetic self-powering systems.
1.2 Aim and Objective
The project's overall aim is to compare and optimize passive and active voltage doublers for usage in Variable reluctance energy harvesting systems; such systems include a coil for inductive charging and energy harvesting. For this reason, the researched rectifiers will also include an input inductance and DC resistance (DCR) to simulate the input AC voltage of the energy harvester [5].
This study aims to obtain experimental and simulation results in order to evaluate the different voltage doubler rectifiers under conditions expected for the VREH circuitry.
Figure 1. Example illustration of passive voltage doubler usage
The project aims to determine the most suitable rectifier for electromagnetic based energy harvesting systems and determine which circuitry performs better in various scenarios. Due to the importance of minimizing the power loss
in the rectification process, the focus of this study is to examine the maximum power generated by the various voltage doublers.
This thesis will focus on answering the following concrete questions to determine the most suitable voltage doubler for electromagnetic based energy harvesting systems,
• How efficient are passive and active voltage doublers under relevant conditions?
• How is the ripple and rise time affected by the choice of different rectifiers and components?
• Based on the experimental and theoretical studies that have been conducted under which circumstances are active or passive voltage doublers to be preferred?
1.3 Scope and limitations
This study is limited since the performance of the passive and active voltage doublers will only be investigated in connection with the Variable reluctance energy harvester that is based on the following survey called “A Survey on Variable Reluctance Energy Harvesters in Low-Speed Rotating Applications”
[5].
Despite this, the energy harvester is composed of components that are widely used in similar electromagnetic transducers like the inductive pickup coil.
Therefore, comparable results should be expected with similar AC input voltage and frequency when similar electromagnetic energy harvesters are used in combination with the different rectifiers.
Like many other electrical circuits, these types of circuits often change behavior depending on several different variables [7]. As a result, it is difficult to take into consideration all the parameters available, and therefore some variables might be fixed. Because of this, it is important to note that the analyzed rectifiers might not demonstrate their full potential in this paper.
This study will be limited to studying the Delon and Greinacher circuits as passive voltage doublers and the externally powered comparator topology for the active voltage doubler.
1.4 Related works
In this section we will briefly review some related research efforts to enrich the reader’s understanding of the overall problem and to highlight the position of this work in relation to current research.
Several studies have been performed on both passive and active voltage doublers that aim to assess the performance of the different rectifiers in different circumstances. For passive voltage doublers, many different studies like “Optimal Design of a Half-Wave Cockcroft–Walton Voltage Multiplier With Minimum Total Capacitance” [7], have been performed in order to optimize different voltage multipliers (including voltage doublers) by testing different capacitance topologies and values both theoretically but also experimentally.
Similarly, studies have also been performed on active voltage doublers like,
“An Active Voltage Doubling AC/DC Converter for Low-Voltage Energy Harvesting Applications” [8], that also try to evaluate the active voltage doubler both theoretical but also experimentally. The problem relies in finding studies that directly compare passive and active voltage doublers in real-world applications, like in energy harvesting systems.
Despite the need of further research in energy-autonomous systems [4], many studies, including the once mentioned before, does not evaluate the performance of these circuitries in different real-world applications, thus implementing them and guaranteeing their performance is difficult. An example of such difficulty is presented by , "Energy-autonomous On-rotor RPM Sensor Using Variable Reluctance Energy Harvesting" [4], where the article concludes that VREH systems can be used for Energy-autonomous On- rotor RPM Sensor, but the problem relies in finding good rectifiers, that can rectify the relatively small generated power.
This thesis aims to bridge the gap between studies performed on active and passive voltage doubler in relation to electromagnetic energy harvesters to obtain a clearer understanding of which type of rectifier is suitable for electromagnetic self-powering systems.
1.5 Outline
The report will be divided into mainly six different chapters. In chapter 2, the paper will describe the theory behind passive and active voltage doublers and the behavior they exhibit, which will be backed by peer-reviewed journals.
Chapter 3 will present the methodology that will be used followed by chapter 4 which will describe the prototype construction and implementation.
Finally, chapter 5 will present the obtained results from experimental and theoretical studies, followed by a chapter discussing and concluding the results.
2. Theory
This chapter will be devoted to describing the relevant theories behind passive and active voltage doublers. Before going into the specifics of the theories, this chapter will discuss the difference between the two types of rectifiers.
The main difference between active and passive voltage doublers is the rectification method that is being utilized. In passive voltage doublers, diodes are commonly used as a “switch” to separate the positive and negative voltage cycles of the AC input signal. Meanwhile, the active voltage doublers use a combination of a MOSFET and a comparator to mimic the conventional P-N junction diode [8].
2.1 Passive voltage doublers
Passive voltage doublers can be categorized into mainly two distinct types of voltage doublers. The first type is called half-wave voltage doubler, and it rectifies the voltage to the output during either the positive or negative half- cycle [6], hence the name “half-wave”.
In contrast to half-wave voltage doublers, full-wave voltage doubler rectifies the voltage to the output during both the positive and negative half-cycle [9], hence the name “full-wave”.
2.1.1 Half-wave voltage doubler (Greinacher circuit)
Half-wave voltage doubler, also known as the Greinacher circuit is a voltage multiplier circuit that consists of two capacitors and two diodes [6]. The rectifier is composed of a voltage clamper followed by a peak-detector. The voltage clamper unbiases the AC potential making it only output positive voltage, that is then cascaded into the peak-detector that charges a capacitor during the positive half-cycle.
Figure 2. Illustration of the Greinacher circuit
Figure 2 illustrates the Half-wave voltage doubler.
In the illustrated circuit, C1 and D1 forms the voltage clamper and while D2 and C2 forms the peak detector of the voltage doubler. Diode D1 conducts during the negative half-wave cycle, which charges capacitor C1 with the input amplitude voltage (Red). During the positive cycle, diode D2 conducts and thus, charges capacitor C2 with the input voltage plus the voltage across C1, making the output voltage at C2 double the input amplitude voltage (Blue).
Thereby, rectifying the AC voltage to DC voltage.
It is good to note that the Greinacher circuit is equivalent to stage one half-wave Cockcroft voltage multiplier, therefore, allowing us to examine the circuitry using derivations from similar studies [7].
According to formulas obtained from similar optimization attempts [7], the Greinacher circuit will not provide an ideal DC voltage because of the nature of reactive circuitries. Instead, there will be a voltage drop and ripples exhibited by the circuit when a load is added, which will alter the DC output voltage.
Due to this issue, the efficiency of such circuits will be affected.
Luckily, this behavior can be predicted thanks to prior studies regarding Cockcroft voltage multipliers [7]. In accordance with earlier studies performed on the Cockcroft voltage multiplier, the voltage drop and the ripple demonstrated by the half-wave voltage doubler depend on multiple factors like total capacitance, AC frequency, and output current that is being drawn [7].
Figure 3. Illustration of the typical waveform of Greinacher circuit output reproduced from [7])
The circuit output behavior is illustrated in figure 3. The behavior can be described by equations 1-4, according to earlier studies performed on Cockcroft-Walton voltage multipliers [7]
𝑋 = 2𝑛 ∗ 𝐸𝑝𝑘− 𝐼𝐿
𝑓∗𝐶𝑡𝑜𝑡
𝑛(8𝑛3+9𝑛2+𝑛)
6 (1)
∆𝑉𝑜= 𝐼𝐿
𝑓∗𝐶𝑡𝑜𝑡
𝑛(4𝑛3+3𝑛2−𝑛)
3 (2)
𝛿𝑉𝑜= 𝐼𝐿
𝑓∗𝐶𝑡𝑜𝑡∗ 𝑛2(𝑛 + 2) (3)
𝐼𝑚𝑝𝑡𝑜𝑡 = 8𝑛4+9𝑛3+𝑛2
6∗𝑓∗𝐶𝑡𝑜𝑡 (4)
Similar to the presented illustration, magnitude X represents the average output voltage of the half-wave voltage doublers (or the Greinacher circuit), variable ∆𝑉𝑜 represents the voltage drop and 𝛿𝑉𝑜 is the voltage ripple demonstrated by the circuitry.
Note that equation 1-4 is only valid when all the capacitor values are equal, refer to [7] for other design configurations.
With that being said, it is also important to note that the above presented equations have been obtained using the following assumptions. Which might not reflect the circuitry behavior in non-ideal scenarios [7].
• The duration it takes the capacitors to charge and discharge is much smaller than the period of the input ac voltage.
• The total charge, which flows in the n stage is n times smaller than the total charge that flows in the first stage, which is valid as long as the voltage drop and ripple isn’t bigger than the output voltage.
For half-wave voltage doubler (Cockcroft stage 1), n variable can be set to n=1, giving us the following simplified equations,
𝑋 = 2 ∗ 𝐸𝑝𝑘− 𝐼𝐿
𝑓∗𝐶𝑡𝑜𝑡∗ 3 (5)
∆𝑉𝑜 = 𝐼𝐿
𝑓∗𝐶𝑡𝑜𝑡∗ 2 (6)
𝛿𝑉𝑜= 𝐼𝐿
𝑓∗𝐶𝑡𝑜𝑡∗ 3 (7)
𝐼𝑚𝑝𝑡𝑜𝑡 = 3
𝑓∗𝐶𝑡𝑜𝑡 (8)
We can see that the load current (𝐼𝐿), frequency (𝑓), and total capacitance (𝐶𝑡𝑜𝑡) of the presented equations 5-8, manifest a vital role in the behavior of the voltage output of the circuitry.
According to [7], at fixed frequency and capacitance, the voltage doubler can be simplified to an ideal voltage source with a voltage that’s two times the input amplitude (2*𝐸𝑝𝑘) potential connected with impedance (𝐼𝑚𝑝𝑡𝑜𝑡). It is important to keep in mind that in electromagnetic based energy harvesting systems, such assumptions might not generate accurate results since the input voltage is not ideal.
2.1.2 Full-wave voltage doubler (Delon circuit)
Full-wave voltage doubler, also known as the Delon circuit is a voltage multiplier circuit that consists of two capacitors and two diodes, initially developed by J. Delon [9]. The rectifier is composed of two stacked peak detectors, where each detector operates at its own half-cycle.
Figure 4. Illustration of the Delon circuit
During the first positive half-cycle of the AC input potential, diode D1 will conduct and charge capacitor C1 to the input amplitude voltage (Red). At negative half-cycle diode D2 will, in turn, conduct and charge C2 with the same amplitude voltage (blue), thus rectifying the AC voltage to DC voltage with two times the amplitude voltage across capacitors C1 and C2.
As previously mentioned, the main difference between half-wave and full- wave voltage doubler is mainly that half-wave voltage doublers only utilize half of the AC cycle to rectify the voltage. Meanwhile, the full-wave voltage doubler utilizes the whole cycle for rectification.
Another critical difference is that because half-wave voltage doubler only utilizes half the AC cycle, the ripple has the same frequency as the input frequency. In contrast, the ripple in full-wave voltage doublers has double the frequency of the input frequency, thus making the full-wave voltage doubler more favored due to the improved power quality.
2.1.3 Diode characteristics
Diode characteristics play a significant role in determining the efficiency of passive voltage doublers. Therefore, this sub-chapter will be devoted to explaining some important characteristics to look for when designing such circuitry for power efficiency [8].
According to several studies performed on active voltage doublers, like [8], the main disadvantage of relying on traditional P-N junction diodes is that there is a forward voltage needed in order to get current to flow through the diode.
This forward voltage creates a voltage drop across the diode, which leads to power loss in the circuitry [8]. Therefore, it is crucial to minimize the forward voltage drop of the diode by choosing low forward voltage diodes with fast- recovery time for best performance.
Schottky diodes have proved to be suitable for such applications due to the low forward voltage and fast recovery time [10]. The main disadvantage of choosing this type of diodes compared to other diodes is the high reverse leakage current, which limits Schottky diodes to relatively low current applications [10].
2.2 Active voltage doubler
Active voltage doublers are analogous to passive voltage doublers. However, instead of using passive diodes, active voltage doublers use controlled switches that mimic the traditional diode [8][11].
Figure 5. Illustration of a controlled switch
Figure 5 illustrates the controlled switch, which works by letting a comparator compare the voltage between the source and the drain of the MOSFET. When the source voltage is larger than the drain voltage of the NMOS, the comparator outputs a positive voltage that switches the NMOS on, thus, letting current pass through the MOSFET [8][11]. When the comparator instead senses that the drain voltage is larger than the source voltage, the comparator outputs a negative voltage which discharges the NMOS, which turns off the MOSFET [8][11]. In this manner, the controlled switch behaves like an ideal diode [8].
The active voltage doubler that is going to be presented in this work has a similar topology to the full-wave voltage doubler. Instead of using P-N junction diodes, the voltage doubler uses controlled switches that behaves more like ideal diodes than what traditional diodes do.
Figure 6. Illustration of the active voltage doubler
Figure 6 illustrates the active voltage doubler, which consists of two controlled switches and two capacitors. The working principle of this circuitry is similar to the Delon circuit, which is composed of mainly two half-wave rectifiers [11].
The controlled switch that is located at the positive side of the active voltage doubler consists of a PMOS and a comparator whose negative input is
connected to the AC input source. The PMOS switches on, only when its gate terminal voltage is below its negative threshold voltage. On the opposite side, the controlled switch consists of an NMOS and a comparator whose negative input is also connected to the input source. The NMOS switches on when its gate terminal voltage is above its positive threshold voltage. According to [11], PMOS and NMOS are used in order to reduce the power requirements for the comparators.
During the first positive half-cycle of the AC input voltage, the drain terminal will have a higher voltage than the source terminal of the PMOS. This makes the comparator at the positive side of the active voltage doubler output a negative voltage that switches the PMOS on. While the p-type MOSFET is on, current and voltage can pass through, thus, charging the capacitor C2 with the peak voltage.
At the negative-half cycle of the AC voltage, the source terminal voltage of the NMOS will be higher than the drain-terminal, making the comparator located at the negative side of the circuit output a positive voltage. The positive voltage of the comparator switches then the n-type MOSFET on, allowing capacitor C1 to charge up to the peak voltage of the AC voltage source. This rectifies the AC voltage to DC voltage, allowing us to acquire double the peak input voltage across capacitor C1 and C2.
In order to avoid reverse current through the body diode, the MOSFETs needs to be connected in the correct orientation demonstrated in figure 6 [8][11]. With correct MOSFET orientation, the body diode can forward current to the capacitors and thereby help the capacitor to pre-charge at start-up [8][11].
When designing active voltage doublers, the choice of MOSFETs and comparator can affect the overall performance of the circuitry, therefore this work will present some key parameters to keep in mind when designing such rectifiers.
2.2.1 Transistor characteristic (MOSFETs)
Due to the nature of semiconductor devices, a transistor has a significant impact on the overall performance of active voltage doublers, especially in efficiency and power requirements. Therefore, it is important to choose the right transistor characteristics depending on the application requirements.
In order to turn on a MOSFET, a specific gate-source voltage is needed. This threshold voltage plays an essential role in determining the power requirement needed, especially in self-starting setups.
Since the active voltage doubler uses a combination of PMOS and NMOS located in the positive and the negative side of the circuit, the power requirement for self-starting is lowered.
Meaning that for self-start to happen, theoretically, the minimum input voltage required is half the threshold voltage (in an ideal case) according to previous studies conducted using cross-coupled topology [11].
Another critical aspect to consider when choosing different types of MOSFETs is the on-resistance, which is the resistance that appears between the drain and source when the MOSFET is open. Minimizing this resistance can minimize the power loss generated by the resistance.
Larger MOSFETs with large silicon-area tend to have lower on-resistance [11].
The problem with these types of MOSFETs apart from the increased footprint, is the increase of input and output capacitance, making it harder to maintain high speed and low power consumption [11].
2.2.2 Comparator characteristic
Beside from aiming to maintain low power consumption of the comparators, comparator hysteresis is also a vital characteristic to look for [9]. Comparator hysteresis is the voltage difference required between the two comparator terminals in order to trigger the comparator.
In energy harvesting systems subjected to noise, one might consider choosing a comparator with some hysteresis in order to eliminate oscillations caused by the noise in the input voltage. These oscillations often result in additional power loss in the circuitry; therefore, it is crucial to consider the amount of noise the rectifier will be susceptible to.
Thanks to previous studies, equations can be derived to explain the behavior of hysteresis in active voltage doublers. According to [8], the following formula can be used to determine the output voltage of the active voltage doubler depending on various variables, including comparator hysteresis.
𝑉ℎ𝑦𝑠+ 𝑅𝑂𝑁𝜔𝐶(𝑉𝑐0+ 𝑉ℎ𝑦𝑠)sin(2𝛽)
2 = 𝑅𝑂𝑁𝜔𝐶 ∗ 𝑐𝑜𝑠2(𝛽) ∗ √𝑉𝑖𝑛2 − (𝑉𝑐0+ 𝑉ℎ𝑦𝑠)2 (9) 𝛽 = arctan(𝜔(𝑅𝑠𝑜𝑢𝑟𝑐𝑒+ 𝑅𝑂𝑁)𝐶) (10)
Where, 𝑉ℎ𝑦𝑠 is the hysteresis voltage, 𝑉𝑐0 is the capacitance output voltage, 𝑅𝑂𝑁 is the on-resistance of the transistor and finally 𝑅𝑠𝑜𝑢𝑟𝑐𝑒 is the series resistance at the source.
With the following equation, one can determine the maximum allowed hysteresis voltage for a specific output voltage at one end of the active voltage doubler (𝑉𝑐0).
For systems with no hysteresis, the formula can be simplified further to [8], 𝑉𝑐0= 𝑉𝑖𝑛∗ cos(𝛽) = 𝑉𝑖𝑛
√1+(𝜔(𝑅𝑠𝑜𝑢𝑟𝑐𝑒+𝑅𝑂𝑁)𝐶)2 (11)
2.3 Impedance matching
Impedance matching play a significant role when it comes to understanding maximum power transfer in different electrical circuits, therefore this chapter will briefly talk about how impedance matching can be used in order to maximize the power output of the different circuitries.
In basic AC analysis one can determine that inductive and capacitive components have reactive parts that generate resistances that depend on frequency and component values. These reactive parts are complex (complex numbers), which allows them to behave in a reactive way enabling them to change the relationship between current and voltage (phase difference).
When different reactive parts are added together, they can either increase the total impedance of the circuit or cancel each other allowing the circuitry to normalize as if DC voltage is applied. The extra impedance that can be generated from reactive parts contributes to power loss, thereby for maximum power these reactive parts must cancel each other (ignoring the load and source resistance matching).
Capacitors have a negative reactive part which allows them to counteract inductive components that have positive reactive parts. When right component values are chosen under the right designated frequency the circuitry reaches maximum power output (ignoring the load and source resistances).
𝑍𝑆 = 𝑍𝐿∗ → 2𝜋𝑓𝐿 = 1
2𝜋∗𝐶𝑡𝑜𝑡 (12)
3. Methodology
The following research will focus on answering the concrete questions presented in chapter two by using a deductive based approach. In this approach, the basics of the evaluated circuitries will be presented using peer- reviewed journals to show the latest developments in the subject. The observed theories will then be complemented and evaluated using simulations and experimental analysis to verify and answer the problem statement.
In the experimental analysis, a PCB prototype was constructed in order to validate the theories in the real world. The prototype will utilize available commercial hardware, carefully selected for optimum results, which will be discussed in the next chapter.
Apart from verifying and answering the problem statement, the experimental analysis will also help to determine the validity and reliability of the theories presented by this paper, which can help raise any issues when dealing with electromagnetic based energy harvesting systems.
The next sub-chapters will be devoted to describing the methodology used for simulation of the circuitries and measurement of the prototype.
4.1 Simulation
The simulations have been performed using LTspice for passive voltage doublers and TINA-TI for active voltage doublers, which can be found at [20][21].
To simulate electromagnetic based energy harvesting systems, a non-ideal voltage source will be used. The voltage source consists of an ideal AC voltage source cascaded with an inductor and a resistor. The inductor will simulate the inductance of an electromagnetic based energy harvesting coil, followed by its internal resistance. The peak voltage, frequency, inductance, and internal resistance values of the non-ideal voltage source have been chosen using prior experimental studies performed on real VREH circuitry.
From initial simulations preformed, several diodes and MOSFET models have been selected in order to determine potential components for the experimental prototype.
Each voltage doubler circuitry purposed in the theoretical chapter, have been simulated with a non-ideal voltage source. The simulations of the circuitries
have been performed in order to collect data on efficiency, power output, power input, ripple, and raise time under various loads and frequencies.
For efficiency and power calculations, different current loads have been evaluated at constant input voltage and frequency. The rectifiers have also been evaluated under a range of frequencies ranging from 1 to 140 Hz under constant current load.
Quality of power that is being delivered is also a significant part of this thesis;
therefore, a range of capacitor values have been evaluated for ripple and initial raise time, under no load. Different fixed capacitor values have also been evaluated under a ranging load current, for their power quality.
The power efficiency calculations have been performed using the following formula,
η = 𝑃𝑜𝑢𝑡
𝑃𝑖𝑛 ∗ 100 =
1
𝑇∫ 𝑉0𝑇 𝑂𝑈𝑇(𝑡)∗𝐼𝑂𝑈𝑇(𝑡)𝑑𝑡 1
𝑇∫ 𝑉0𝑇 𝐼𝑁(𝑡)∗𝐼𝐼𝑁(𝑡)𝑑𝑡 ∗ 100 (12)
The raise time have been calculated by measuring the time it takes for the different circuits to go from 10% to 90% of the steady state average voltage.
Figure 7. Illustration of simulated half-wave voltage doubler
Figure 7 illustrates the simulated half-wave voltage doubler with the corresponding values of the inductor and DC resistance used in all simulations (632mH and 180.5ohm). With the aim of providing a fair comparison between the experimental and simulated circuitries, same diode models and MOSFETs have been used in the simulations.
Like demonstrated on figure 7, at the output of the circuitry a current source has been added in order to simulate the current draw of the connected system.
The same following setup illustrated in figure 7 have also been used for other circuitries, but instead of using the same component models other component models have also been evaluated like the presented prototype in chapter three.
4.2 Experimental Analysis
To mimic electromagnetic based energy harvesting systems, a real VREH transducer setup was used with the corresponding simulated input inductance and DC resistance.
Figure 8. Illustration of the VREH transducer, the image is reproduced from [5]
Figure 8 illustrates the VREH electromagnetic transducer; the VREH transducer setup consists of a toothed wheel with an electromagnetic pickup coil and a magnet. When the toothed wheel rotates, the reluctance between the geared wheel and the coil changes, thus providing us with an alternating current, which can then be supplied into the PCB prototype for experimental measurements [5].
Figure 9. Illustration of the VREH pickup coil followed by magnets
Similar to the measurements attained from the simulations, this paper will aim to provide efficiency and power calculations using a range of load currents at constant input voltage amplitude and frequency which will be controlled by adjusting the angular velocity of the wheel. Due to limited time available, this thesis will not conclude any efficiency and power calculations under a range of frequencies in constant power draw.
Because mechanical setups often lack measurement accuracy, multiple mechanical cycles are needed in order to get reliable data. This is time consuming especially at relatively low RPM/frequencies. All measurements have been performed at 10 RPM which corresponds to an average input AC frequency of 16 Hz and an average amplitude of 1.61 volts. For reliable results 100 mechanical cycles was recorded for each individual measurement.
In order to measure the power efficiency of the various voltage doublers, input power and output power of the prototype needs to be acquired.
Figure 10. Illustration of the experimental setup
For measuring input power, a modified version of a precision current measurement device called “uCurrent Gold” was used [22]. The uCurrent device works by outputting a voltage that changes in relation to the measured current. In this study the uCurrent device was set to a ratio of 9.99mA/1.0075V for best results. The current measuring device was connected between the transducer and the voltage doublers, allowing us to measure the current going from the transducer to the rectifiers
Apart from obtaining current measurements, voltage measurements are also needed in order to calculate the input power. This is done by using a logic analyzed called Logic Pro 16 made by Saleae [23]. The Logic pro controller is a logic analyzer that can measure both analog and digital signals at high sampling rates (1kHz in this paper) [23]. In this study the Logic analyzer is used for measuring the input voltage but also the voltage exhibited by the uCurrent device.
For measuring the output power, an N6705C DC Power Analyzer with N6784A module was used in constant current load configuration (CC load) [24]. In this configuration the power analyzer can draw constant current with varying voltage applied at the output, thus allowing us to obtain comparable results as the executed simulations. Due to the limitations of the power analyzer, the minimum power draw that could be achieved was 10uA and the maximum power draw was around 2mA before the negative overload voltage was reached (the rectifier voltage drop bigger than the output voltage).
When measuring active voltage doublers, same equipment was used but with an additional +-5v external power supply for the comparators. The current flowing through the comparator power supply was also partially measured using a multimeter with the aim of getting some insights on how much current is flowing to the comparators.
4. Design and construction
In this paper, an experimental prototype was constructed in order to verify and compare the theories presented in chapter two, which will be used to answer and discuss the presented problem statements.
The prototype design consists of mainly two various parts, the first part is the choice of components and the second part is the Printed Circuit Board (PCB) construction.
3.1 Component choice
As previously mentioned, the components for the prototype have been selected from commercially available components on the market.
The choice of components is based on earlier conducted studies and initial simulations that have been performed. In order to provide a fair comparison between the active and passive voltage doublers, same capacitor value and capacitor type have been chosen.
Aluminum polymer capacitors with a value of 100uF have been picked for all rectifiers in order to minimize the capacitance impedance at relatively low frequencies [12].
Initial simulations have also been conducted on the passive voltage doublers in order assess multiple diode models for their efficiency and power output.
Based on these simulations, two different diodes have been selected due to their efficiency and maximum power output.
The DSF01S30SL diode made by Toshiba has shown to provide high efficiency at different current loads [13]. Meanwhile, the CTS05S40 diode, also made by Toshiba has shown to provide the maximum power output at a range of current loads [14]. Note that the diode models have been simulated on both the Delon and Greinacher circuit for fair comparison. Information regarding the other diodes that have been evaluated can be found in appendix A, with their respective efficiency and power output at different current loads.
For active voltage doublers, earlier studies have shown that larger MOSFETs often have lower on-resistance, but also have larger input/output capacitance [11]. According to [11] the increase in input/output capacitance of the MOSFETs makes maintaining low power consumption difficult. This observation plays a key role in finding the limits of how efficient these circuits can achieve.
Therefore, two types of MOSFET pairs have been chosen with attention to the MOSFET size.
The first pair of MOSFETs consist of a NMOS and PMOS with smaller MOSFET size compared to the second pair. Similar set of MOSFETs can often be found in earlier studies performed on active voltage doublers like, [8]. In this study, the first pair of MOSFETs will consist of a Si1499DH PMOS and a Si1442DH NMOS made by Vishay Intertechnology [15][16].
The second pair of MOSFETs is composed of a SI4838BDY NMOS made by Vishay Intertechnology and an IRF7410TRPBF PMOS made by Infineon Technologies, this pair of MOSFETs have significantly larger die size than the previously mentioned pair and it is often named Power MOSFETs[17][18].
Another key thing to remember when choosing diverse types of MOSFETs is the threshold voltage required in order to open the gate, this depends on several factors like the comparator voltage source or in the case of self-start the input voltage like previously mentioned (in chapter 2.2). In this paper the chosen components have a gate to source threshold voltage of about 1 V.
For the active voltage doubler comparators, the same type of comparator has been used in order to provide a fair comparison. A TLV3702 from Texas Instruments have been chosen because of the zero-hysteresis voltage and the small power consumption [19].
3.2 Printed circuit board construction (PCB)
The PCB prototype consisted of a 100x100mm 2-layer board divided into mainly 6 different sections for each circuitry, see figure 7.
Figure 11. Illustration of the PCB prototype design
To the left of the illustrated PCB in the above figure, we have two active voltage doublers, the top one consists of the two small MOSFETs, and the bottom one is composed of the large size MOSFET pair. On the opposite side of the PCB illustrated in figure 11, we have four passive voltage doublers were each passive voltage doubler (half wave and full wave) utilizes two different diodes mentioned in the previous sub-chapter. The first two passive-voltage doublers utilize the CTS05S40 diode, while the other two circuits use the DSF01S30SL diode.
The passive voltage doublers is composed of mainly two different inputs and two different outputs, the inputs are used for the AC input voltage and the outputs are used for measuring the DC output voltage. On the other hand, the active voltage doubler utilizes 5 different inputs and only two outputs, the inputs are used for the AC voltage source but also for comparator power supply and ground which is used for minimizing the interference on the PCB.
It is important to note that the prototype is only constructed in order to serve for experimental purposes, thus the PCB might not reflect the optimal design for small footprint. For best results, the PCB was constructed in such a way in order to minimize the trace impedance by maximizing the possible width without sacrificing the signal integrity, the maximal trace width used is 3 mm.
5. Results and analysis
In this section we will summarize the obtained results from both the performed simulations and the conducted experimental analysis on the prototype. This chapter will be divided into primarily four sub-chapters, which will discuss obtained data on efficiency, output power, ripple and rise time.
All simulated and experimented circuitries use 100uF capacitors with an input inductance of 632mH and an internal resistance of 180.5 ohm. Note that no experimental results have been obtained from the active voltage doubler with the large MOSFETs due to the difficulty of getting reliable rectification, therefore also no simulation results will be presented in this chapter.
For easier navigation through the graphs and results, the naming of the different circuits analyzed in both experimental and simulated circuits are abbreviated.
For example, HWVD1 stands for Half-wave voltage doubler with diode type DSF01S30SL. Whereas FWVD2 stands for Full-wave voltage doubler with diode type CTS05S40. The same abbreviation goes for active voltage doublers, ACVD1 for active voltage doublers with the smaller MOSFET pair and ACVD2 for the larger MOSFET pair.
5.1 Efficiency measurements
Efficiency measurements play a significant role in determining suitable rectifiers in different scenarios; therefore, this paper will first present the simulated results and then present the collected data from the experimental efficiency measurements.
Figure 12. Simulation result, Efficiency vs Current load, at 1.6142V amplitude at frequency 16 Hz (10 RPM)
Figure 12 shows the efficiency vs current simulation results that have been conducted at 1.6142V input amplitude voltage at 16Hz, which is equivalent to the amplitude voltage and frequency of the VREH transducer running at 10 RPM.
From the above figure, we can see that both HFVD and FWVD with similar diodes components reacted to the current that is being drawn similarly. At low current draw, the DSF01S30SL diode has the best efficiency, while the active voltage doubler and the other passive voltages have relatively low efficiency at the start. During higher current load, just before the current load is too large, the active voltage doubler outperforms the passive voltage doublers and achieves 99.24% efficiency at 2mA current load. Towards the end of the graph we can also see that the FWVD1 and HFVD1 outperformed the HFVD2 and FWVD2 even though higher efficiency was found during low load.
Figure 13. Experimental result, Efficiency vs Current drawn, at 10 RPM
Figure 13 illustrates the efficiency vs. load current obtained from the experimental results that have been performed on the VREH transducer setup running at ~10RPM. Similar to the simulated circuitry, both the HFVD and FWVD with similar diode types behaved similarly. When comparing the simulated circuits with figure 13, all passive voltage doublers behaves similarly to the simulation, but higher efficiencies can be found in the experimental study in comparison to the simulation.
However, the active voltage doubler that is being illustrated in figure 13 performed poorer efficiency-wise compared to the simulation, at around 0.01mA 56.81% efficiency can be found in the simulation, while only 23.53%
efficiency is achieved. When comparing the different intersections between the experimental analysis and the simulated results, similar intersection can be found between the different passive voltage doubler efficiencies, but the active voltage doubler intersects the passive voltage doublers later in the experimental analysis. This gives passive voltage doublers better efficiency range at small current loads in comparison to the active voltage doubler.
In the experimental study a maximum efficiency of 93.7% was achieved at 0.5mA compared to 97.77% in the simulation.
5.2 Output power measurements
Output power also plays a significant role in determining the best rectifier during different scenarios. This is why this report will focus especially on power output compared to efficiency, which will be discussed later on.
Figure 14. Simulation result, Power output vs Current drawn, at 1.6142V amplitude at frequency 16 Hz (10 RPM) (higher is better)
From figure 14, we can clearly see that the active voltage doubler provided the highest amount of output power compared to the passive voltage doublers. The second highest output power is sourced by passive voltage rectifiers that use the CTS05S40 diode compared to the DSF01S30SL rectifiers that outputted the least amount of power. From the collected data, the active voltage doubler provided a maximum output power of 1.51mW at 1mA, thus providing the largest voltage at constant current draw during high current loads.
Figure 15. Experimental result, Output power vs Current load, at 10 RPM, (higher is better) Similar trend as the simulation can be seen from the experimental results. When comparing both diagrams one can see that the power output of the real rectifiers is lower compared to the simulated version. The maximum power output is achieved by the active voltage doubler at 1mA with an output of 1.29mW compared to 1.51mW at 1mA in the simulations. Like the simulation the second highest power output is provided by HFVD1 and FWVD1, followed by FWVD2 and lastly HFVD2.
Figure 16. Experimental result, Output power vs Current load, at 10 RPM (logarithmic) (higher is better)
Figure 16 illustrates the same experimental results presented in figure 15 but using a logarithmic scale for easier comparison. From the above figure one can determine that the passive voltage doublers that use the CTS05S40 diode outperformed the DSF01S30SL diode, although the CTS05S40 diode had significantly lower power efficiency compared to rectifiers that use the DSF01S30SL diode during low loads. This phenomenon is crucial to consider, hence why this paper will discuss the difference between benchmarking the rectifiers based on efficiency or power output more in great detail in the next chapter.
5.2.1 Maximum Power
This sub-chapter will present the maximum power that can be obtained at different RPMs which have been collected from the performed simulations. See appendix B for the corresponding AC amplitude voltage and frequency for each RPM.
Figure 17. Simulation result, Maximum power vs RPM, (higher is better)
The maximum power obtained from each rectifier plays a key role in determining which rectifier will output the most power under optimal load.
From the bar graph illustrated on the above figure, one can identify that the active voltage doubler have the best power performance compared to the passive voltage doublers, especially under higher RPMs (higher input voltage and frequency).
At 5 RPM active voltage doublers does not show significant improvement over the traditional passive voltage doublers. The active voltage doubler outputted a maximum power of 0.23mW compared to the passive voltage doubler FWVD1 that outputted a power of 0.22mW. At 15 RPM significant improvement can be seen on the active voltage doubler in comparison to the passive voltage doubler, 3.635mW was obtained from the ACVD1 while the HFVD1 only outputted 3.191mW which is an improvement of 0.444mW over the passive voltage doubler.
At higher RPMs (20 RPM), the active voltage doubler outputted a maximum power of 6.28mW in comparison to only 5.33mW from the HFVD1.
It is important to note that the results obtained from the active voltage doubler does not include the comparator power usage, thus the power difference between the passive and active voltage doubler should indicate the margins of which how much power the comparators can use before the active voltage doubler is not worthwhile.
5.2.2 Impedance matching
Figure 18. Figure illustrates the output power at a range of frequencies at 0.125mA load (10RPM) (higher is better)
Beside of collecting results of the different rectifiers at different current loads, simulations have also been done under range of frequencies in order to determine the performance of the circuitries at different input frequencies.
Figure 18 illustrates the results collected for the different rectifiers in a range of frequencies. At the start we can see that FWVDs have highest power output in comparison to the other circuitries, which at 10 Hz starts to separate into two distinct trends where each trend has its own common diode. The rectifiers that uses the CTS05S40 diode achieved the highest output power during 10Hz.
When comparing the different passive rectifiers one can identify that the maximum power of all passive voltage doublers is obtained at around 10Hz, this is the frequency at which all passive voltage doublers performed the best, likewise similar behavior can be seen on the active voltage doubler near the 1- 15Hz range.
The underlying reason for why this behavior is manifested depend on the circuitry matching, when frequency increases the complex source impedance of the source increases (inductor) while the complex source load deceases
(capacitor), when both source impedance and load impedance (conjugate) are equal the whole rectifier is matched with the transducer, thus enabling us to transfer the maximum power.
From equation 12 in the theory chapter, 2𝜋𝑓𝐿 = 1
2𝜋∗𝑓∗𝐶𝑡𝑜𝑡 → 𝑓2 = 1
4𝜋2∗𝐶𝑡𝑜𝑡∗𝐿 (13)
𝑓2 = 1
4𝜋2∗200𝑢𝐹∗632𝑚𝐻 → 𝑓 = √ 1
4𝜋2∗200𝑢𝐹∗632𝑚𝐻 ≈ 14 𝐻𝑧 (14)
This means that the maximum output power is achieved at around 14 Hz which is similar to the obtained simulation results for the passive voltage doublers.
At higher frequencies, the active voltage doubler start to deviate from the common pattern of the rest of the passive rectifiers and starts to increase its output power drastically, this behavior is related to the MOSFET dynamic characteristics which changes its properties at different frequencies. One can assume that the increase of the output power of the active voltage doubler is related to the drain and source capacitance which changes depending on the frequency, which at 100Hz seems to match with the inductor impedance giving us maximum power.
In general, FWVD1 seems to have the best output power while the active voltage doubler provided the highest instantaneous output power at around 100Hz, according to the simulation.
5.3 Power quality
In this section we will discuss the power quality of the different rectifiers and how the choice of components can affect the power output of these circuitries From the equation obtained for the half-wave voltage doubler (equation 7) we can conclude that higher current load leads to bigger ripples which affects the power quality that is being delivered. For full-wave voltage doublers no equations can be found that illustrate the relationship between ripple and current draw. Thus, this paper will aim to provide some measurements on ripple and raise time, in order to evaluate the presented theories.
5.3.1 Ripple measurements
Figure 19. Figure illustrates the Ripple voltage at different current loads (10RPM) (logarithmic) (lower is better)
From figure 19, we can see that the ripple voltage is actually exponential rather than being linear as shown earlier. Which means that the referenced equation, equation 7 is actually incorrect according to the simulations (in this case). In the simulations we can see that the ripple voltage is lower in passive voltage doublers that utilize the DSF01S30SL diode, while passive voltage doublers that use the CTS05S40 diode have higher starting ripple under small current load. However, at higher currents all passive voltage doublers seem to merge into a common trend.
For the active voltage doubler, the ripple remains constant throughout the different current loads which makes it rather very stable, compared to passive voltage doublers at high current draw.
Figure 20. Figure illustrates the Ripple voltage at different current loads at 10 RPM (logarithmic) (lower is better)
Because the mechanical VREH setup contains variations, significant noise was generated in the output voltage measurements. Therefore, the voltage samples obtained from the experimental analysis had to be filtered to only include the output rectifier ripples and not the variations caused by the input voltage.
This was done by filtering the data obtained from the measurements using a bandpass filter in the range of 14-18Hz for the half-wave voltage doublers and a bandpass filter at a range of 30-34Hz for both the full-wave voltage doublers and the active doublers. Note that the passband frequency range is specified using the ripple frequency, which is the same as the input frequency for half- wave and double the input frequency for the full wave (including ACVD).
Figure 20 illustrates the ripples from the experimental measurement.
Compared to the simulations, full-wave, and half-wave voltage doublers do not follow the same trend at high current withdraw. Instead, we find that full- wave voltage doublers have lower ripples at low and high current loads.
Furthermore, we can find that active voltage doublers have a stable, steady ripple independent of the current load, similar to the simulation.
In conclusion we can say that FWVD2 had the smallest ripples under low to mid current loads, which is verified by both the simulations and the experimental study. When it comes to higher currents, active voltage doubler had the best performance.
5.3.2 Rise time measurements
Rise time plays an important aspect when it comes to power quality, quick power delivery is important for fast sensor measuring systems.
Figure 21. Figure illustrates the rise time at different frequencies at 10 RPM using 100uF capacitors (logarithmic) (lower is better)
From the above figure we can see that full-wave voltage doublers performed the best when it comes to rise time under a range of frequencies, second, we get the active voltage doublers and lastly the half-wave voltage doublers. It is good to note that figure 21 is logarithmic, thus the ripple time decay is exponential.
The half-wave voltage doubler have the least ripple at around 10hz which is the same as were the maximum power output is achieved.
Figure 22. Figure illustrates the rise time at different capacitance at 10 RPM (x-axis is logarithmic) (lower is better)
The above figure illustrates the rise time using different capacitance values at 10 RPM.
Using high capacitance values, we can see that the rise time increases significantly for the half-wave voltage doubler compared to the full-wave voltage doublers, the cause of this behavior is due to the nature of the half-wave voltage doublers which only operates at half a cycle.
For best power quality a balance between ripple and rise time needs to be considered when choosing the capacitor values. Higher capacitance improves the ripple due to the filtering effect but increases in turn the rise time due to the additional charging time required.
5.4 Active voltage doublers
In this sub-section we will talk about the different active voltage doublers that was evaluated and the assumptions on why the active voltage doubler with the large MOSFETs did not rectify the AC voltage properly.
Figure 23. Figure illustrates the output voltage of ACVD2 using an oscilloscope (10Hz, 1Vpp)
Figure 23 illustrates the output voltages of the active voltage doubler that uses the larger MOSFET die size, also known as power MOSFETs. From the oscilloscope, we can see that the positive (yellow) and negative (green) output voltages of the rectifier did not rectify the voltage; therefore, no measurements were done as a result.
The reason why the circuitry exhibits this behavior is not known, but some assumptions can be made in accordance with the presented theory. From the first look, we can see that switching of the AC voltage is happening, but no capacitor is charging. One might think that the capacitors were not connected properly, but this has been checked, and the capacitors were indeed working correctly.
This leads to the assumption that the MOSFET is not switching fast enough due to the bigger gate capacitance of the power MOSFETs, which require larger currents to the gate for faster gate capacitance charge and discharge. This explains the large current drain measured in the external voltage source, which was used to power the comparators. The current drain was about ~100uA at
0.5mA load for the active voltage doubler that uses the big MOSFETs compared to only ~2-3uA for the rectifier with the small MOSFET pair (ACVD1).
Figure 24. Figure illustrates the output voltage of ACVD1 using an oscilloscope (10Hz, 1Vpp)
In comparison to ACVD2, we can see that rectification is achieved when smaller MOSFETs are used. The yellow signal represents the positive DC voltage obtained from the active voltage doubler, while the green signal represents the negative output of the voltage doubler with some ripples. As earlier mentioned, the comparator's current draw in the ACVD1 setup was about 2-3uA, which is remarkably similar to the current draw that was observed in study [8]. Note that in the power/efficiency calculations, the comparator's power usage was not taken into account.
6. Conclusion and Discussion
In this chapter we will conclude and discuss the results obtained from the different measurements both from the simulations and the experimental studies.
6.1 Conclusion
6.1.1 Conclusion - Power and efficiency
Output power and efficiency are two essential aspects to consider when choosing different rectifiers for energy harvesting systems. Therefore, in this sub-chapter, we will discuss the obtained results from the collected measurements.
According to the results compiled from the performed experimental analysis, we can determine that HFVD2 and FWVD2 had the highest observed efficiency at relatively low current loads (0.01mA-0.1mA). However, during high current loads (>0.25mA), the maximum efficiency was demonstrated by the ACVD1 with an efficiency of 93.7% at 0.5mA, meanwhile the FWVD2 demonstrated an efficiency of 95.8% at 0.01mA.
From the observed measurements, we can see that even though the HFVD2 and FWVD2 had better efficiency performance in both the simulation and experimental analysis. Experimental data shows that rectifiers that utilized the CTS05S40 diode (HFVD1 and FWVD1) outputted more power during low loads than the other passive rectifiers. This begs the question of whether efficiency is indeed a good indicator of a rectifier's performance or not.
Ultimately, the output power is what counts in an energy harvesting system, which is the actual energy generated. Therefore, this thesis will draw its conclusion based on power output, rather than efficiency, like many other authors/works.
Experimental power measurements show that at high current loads (1mA), ACVD1 and FWVD1 outputted the highest power. When comparing the results with simulations performed on various RPMs (at optimum loads), we can see that similar behavior is exhibited at 10 RPM, but the active voltage doubler performed significantly better at higher RPMs compared to the passive voltage doublers. With the small power margins between active voltage doubler and passive voltage doublers during low RPMs, one should take care when choosing the comparators, which can be a determining factor between the choice of active voltage doubler or passive voltage doublers.
Impedance matching of the rectifiers is also a principal factor to consider when designing such rectifiers. With the presented simulation results, one can determine that different frequencies largely affect the performance of the rectifiers due to the nature of reactive circuitries. Therefore, one should aim to optimize the rectifiers by determining the frequency range the rectifier will operate in and adjust the capacitance values accordingly. Furthermore, one should also attempt to use a DC-DC converter in order to run the rectifiers in their optimal load points, which will also affect their performance.
It is good to keep in mind that ACVDs need additional power in order to start the comparators, which can be supplied using external power supply like a battery or by using a self-starting topology which requires even more research and good comparator design to accomplish. In comparison to ACVDs, passive voltage doublers does not need extra circuitries therefore they are easier to realize in practical implementations. As seen from the experimental study bigger MOSFETs (also known as power MOSFETs) are harder to maintain in comparison to smaller MOSFETs, this is due to the large gate capacitance, which makes switching rather slow, therefore even though bigger MOSFETs have lower on-resistance, smaller once are more preferred due to the fast switching which is critical in active rectification.
In summary, when taking into account the possible comparator power usage, this report will conclude that ACVD are recommended at high RPM (>10RPM) while passive voltage doublers (especially FWVD1) are recommended at lower RPMs when it comes to output power. If comparator power is negligible ACVDs are more recommended than passive voltage doublers.
6.1.2 Conclusion - Power quality
The quality of power that is being delivered to a sensor system is essential for optimal performance. Therefore, in this section, we will briefly summarize the conclusions that we can draw regarding the power quality of the different rectifiers.
When it comes to ripple measurements, we can conclude that FWVDs have the lowest ripple compared to the HFVDs. FWVDs have double the ripple frequency as the input frequency, which gives the FWVDs advantage over HFVDs. The increase in the ripple frequency allows for easier filtering due to the isolated ripples.
