Pedro Magalhães

João Martins
email: jf.martins@fct.unl.pt

António Joyce
email: antonio.joyce@lneg.pt

Luís Coelho

Nelson Tavares

Ricardo Pereira

Solar Trigeneration System Model for Off-Grid Residential Applications

Keywords: Solar Trigeneration, Cooling, PV/T, Heat Pump, Off-grid, Model, SDHW, HVAC, Autonomous Systems, Residential Sector

A solar trigeneration system for off-grid households, based on photovoltaic-thermal (PV/T) collectors, photovoltaic (PV) modules and a heat pump (HP), whose aim is to provide enough electricity, domestic hot water (DHW), heating and cooling power to meet the typical demand of an offgrid single family dwelling, is modeled to predict its performance, enable system sizing and evaluate the impact of different control and management strategies. The system integrates an autonomous photovoltaic system, a solar DHW system and a heating, ventilation and air-conditioning (HVAC) system. Thus, according to local climate data, construction elements, load profiles and storage dynamics, the model computes the system's net results using a simple supply and demand approach. Additionally, a design space methodology is used to evaluate system performance for different sizes and identify a feasible design region within which reliable and cost-effective system sizing is possible.

Introduction

Solar trigeneration systems are able to simultaneously generate electricity, heat and cooling power from solar energy. Among the solar trigeneration systems already devised, most feature absorption cycle chillers as the cooling equipment [START_REF] Al-Sulaiman | Exergy modeling of a new solar driven trigeneration system[END_REF]. However, research has shown that electric-driven refrigeration has greater economic viability than absorption refrigeration for the residential sector [START_REF] Fong | Comparative study of different solar cooling systems for buildings in subtropical city[END_REF], [START_REF] Immovilli | Solar trigeneration for residential applications, a feasible alternative to traditional micro-cogeneration and trigeneration plants[END_REF]. Additionally, absorption chillers have high temperature requirements and not all solar harnessing technologies are well suited to drive them, namely PV/T collectors, which are likely unable to provide such high temperature heat most of the year unless multiple glass covers are used, and whose PV laminate must be kept at lower temperatures to prevent damage to the laminate [START_REF] Dupeyrat | Efficient single-glazed flat plate photovoltaic-thermal hybrid collector for domestic hot water system[END_REF]. Thus, PV/T collectors are well suited to provide lower temperature heat for DHW while simultaneously providing electric power to drive cooling equipment. Among them, electric driven vapour compression (VC) refrigeration is deemed the most cost-effective for residential applications, due to among other factors, high efficiencies and a consolidated economy of scale [START_REF] Immovilli | Solar trigeneration for residential applications, a feasible alternative to traditional micro-cogeneration and trigeneration plants[END_REF]. Application of PV/T collectors has been focused in grid-connected applications, mainly because these are seen as the main market for PV/T collectors [START_REF] Zondag | Flat-plate PV-Thermal collectors and systems: A review[END_REF]. However, use of PV/T collectors in autonomous systems has been reported in crop drying and solar distillation processes though not in the residential sector.

The aim of this article is to evaluate the potential of a solar trigeneration system for the off-grid residential sector based on PV modules, PV/T collectors and a VC heat pump by following the modeling methodology described in [START_REF] Joyce | A PV/T and Heat Pump based Trigeneration System for Residential Applications[END_REF]. Additionally, a sizing methodology is used to determine which configurations are most suitable for reliable system operation.

Contribution to Value Creation

The present work is to contribute to value creation by highlighting tools and guidelines that can be used to understand and size off-grid solar trigeneration systems. Also, the methodology used in this article can be used to size a system which enables continuous operation for an off-grid dwelling, but can also be extended to other applications, which may differ in scope, scale and in the technologies used.

System Configuration

A simplified schematic of the proposed solar trigeneration system is illustrated on Fig. 1. The key components of the system are PV modules, PV/T collectors, an inverter, maximum power point tracking (MPPT) devices, a battery bank, an air-to-water vapor compression heat pump (HP) and thermal storage tanks (TST) for DHW (DHW-TST) and HVAC (HVAC-TST). Other system configurations are possible with these key components, though with different levels of complexity, parts and controls. This paper will focus on the simplest and most reliable configuration, which will serve as a background against which other options can be evaluated. In this regard, the HVAC-TST is optional and will increase initial costs, maintenance and installation space but it allows for increased flexibility, which may prove important to optimize system performance -by operating the HP during periods suitable for high efficiency operation and storing cold or hot water in the HVAC-TST for later use.

The PV modules and the PV/T collectors provide electric power to the loads, either instantaneously or via a storage element, enabling continuous system operation. The PV/T collectors also provide power to the solar DHW system through a thermal storage tank, the DHW-TST. The heat pump unit provides and extracts heat to and from the household, respectively. The system power flow is illustrated on Fig. 2.

System Model

The system model is a tool for understanding and predicting the performance of the trigeneration system as well as sizing it. A definitive model is one that not only covers the most distinctive phenomena associated with a process, but also those believed to be secondary in nature. However, certain aspects of the system performance, which are deemed to be of secondary nature, can be ignored if properly justified according to the specified objectives. Regarding the proposed trigeneration system, the authors chose to ignore the transient performance of the electric system since it is highly dependent on the installation and quality of the components rather than system sizing. On the other hand, the transient performance of solar collectors and thermal storage tanks was not ignored since their combined performance is known to be decisively influenced by transient dynamics [START_REF] Santbergen | Detailed analysis of the energy yield of systems with covered sheet-and-tube pvt collectors[END_REF].

The system model was developed according to the methodology presented in [START_REF] Joyce | A PV/T and Heat Pump based Trigeneration System for Residential Applications[END_REF] which consists on having three submodels -climate, building and trigeneration system -with various types of interactions. The system model was developed around MATLAB/SIMULINK, which integrates all system components whether or not these have been developed in MATLAB/SIMULINK -most were and a custom MATLAB/SIMULINK library was developed to accommodate them. The climate model uses input data from the SOLTERM software, a computer program which provides reference climate data for Portuguese municipalities, and the building model was mostly done using DesignBuilder, a building performance analysis software that complies with the ASHRAE 140-2004 standard as required under Portuguese legislation for Energy Efficient Buildings.

Climate Model

The climate model uses hourly reference outdoor temperatures and irradiation values on an horizontal surface to estimate other relevant climate variables, namely sky temperature and irradiation on a sloped surface, respectively. The isotropic irradiation model was used to determine the irradiation on a sloped surface, since it is known to provide the most conservative estimates.

Building Model

The thermal energy that must be provided to or extracted from the household in order to meet thermal comfort levels was estimated using DesignBuilder, which calculates these values in one hour steps according to climate data and occupancy schedules. DesignBuilder was also used to shape electric load profiles concerning lighting and domestic appliances. MATLAB/SIMULINK was used to model the remaining thermal (DHW load profiles) and electric loads (HP and DHW backup power).

Trigeneration Model

The outputs of the climate and building models are used as inputs of the trigeneration model, which acts as an energy conversion and storage model, while also containing several submodels. Among them are a PV array model, a PV/T collector array model, a TST model, a HP model, an electric battery model, various tunable controllers, a simplified steady state inverter model and cable losses estimation model. The models are arranged in a way so that the system power flow is exactly like the one displayed in Fig. 2. Brief descriptions of key component models are provided.

The inverter model, like all other components of the electric system, was developed according to a steady-state power based approach. The model uses readily available efficiency curves supplied by manufacturers, safeguarding maximum and minimum input power constraints.

The electric battery was implemented as a steady-state energy storage model as suggested by [START_REF] Arun | Sizing curve for design of isolated power systems[END_REF]. Thus, the model ignores the typical voltage-current model of batteries and instead focuses on energy storage irrespective of form while including different charging and discharging efficiencies and also self-discharge.

The HP model implemented is a steady state electric load using manufacturer supplied efficiency tables. This approach lacks the detail of more complex models but lessens the computational burden and allows users to easily evaluate different HP units because the model relies on readily available data.

The performance of PV modules was estimated using a steady state model based on the maximum power point, which decreases almost linearly with cell temperature. Hence, if the array is connected to a maximum power point tracking (MPPT) device, the model is valid and less computationally intensive than the single diode equivalent circuit model commonly used for transient rather than steady state simulations.

A single cover sheet and tube PV/T collector was modeled to determine the steady state and transient responses of the collectors using a set of one-dimensional energy balance equations, an adequate approach according to [START_REF] Santbergen | Detailed analysis of the energy yield of systems with covered sheet-and-tube pvt collectors[END_REF][9] [START_REF] Silva | Hybrid photovoltaic/thermal (PV/T) solar systems simulation with SIMULINK/MATLAB[END_REF].

The thermal storage tank model must be effectively capable of reproducing stratification phenomena for it affects the performance of solar collectors [START_REF] Santbergen | Detailed analysis of the energy yield of systems with covered sheet-and-tube pvt collectors[END_REF]. The multi-node model presented in [START_REF] Nelson | Parametric studies on thermally stratified chilled water storage systems[END_REF] was implemented due to its relative simplicity and completeness, which includes heat transfer to the surroundings, conduction from warm layers to cold layers, conduction through thermocline and thermal mixing.

Simulation

The proposed trigeneration system was simulated for a typical meteorological year (TMY) under Lisbon climate. However, the actual simulated setup is different from the one presented in Fig. 1 due to the omission of the HVAC-TST, which is optional and whose inclusion must be properly evaluated. Thus, the system is simulated without the HVAC-TST as a way to provide results against which improvementsnamely the inclusion of the HVAC-TST -can be evaluated.

Parameters

Lisbon is located at 38º42'N and 9º8'W. The climate is considered to be Subtropical-Mediterranean and temperatures range from 4ºC up to 36ºC. Annual irradiation peaks at a south facing 30º slope with the horizontal plane and is about 1600 kWh/m².

Simulations were conducted on a single family dwelling, whose construction elements are in accordance with Portuguese building codes, for four occupants with 2 floors, an attic and a total living area of 225 m². The electric and DHW load profiles were set to resemble typical daily and annual consumption levels.

The PV/T collectors used for this simulation are 1.67 m² single cover sheet and tube collectors whose thermal and electric efficiencies are displayed in Fig. 3, exhibiting maximum thermal and electric efficiencies of about 59% and 14%.

Fig. 3. Thermal and electric efficiencies of the single cover sheet and tube PV/T collectors

The solar DHW system was simulated with 6.68 m² of PV/T collector area, a differential temperature controller with 10ºC and 2ºC thresholds for on and off modes, respectively, a specific flow rate of 10 Kg/m²h and a TST model with three vertical nodes whose properties are specified in Table 1. These values are typical and while the PV/T collector area is slightly higher than the 6 m² of collector area used in [START_REF] Santbergen | Detailed analysis of the energy yield of systems with covered sheet-and-tube pvt collectors[END_REF], [START_REF] Silva | Hybrid photovoltaic/thermal (PV/T) solar systems simulation with SIMULINK/MATLAB[END_REF], the other parameters are common in residential solar DHW systems. Regarding the HVAC system, a commercial air-to-water HP unit with adequate power rating was selected and set to produce cold water at 7ºC and hot water at 35ºC. Fan-coils were selected as the terminal HVAC units for the simulation.

The number of PV modules and the slope angle at which they are to be positioned for simulation purposes must be determined via comprehensive system sizing. Nonetheless, the parameters of the PV modules are displayed in Table 2.

Sizing

A multi-variable design space sizing methodology, similar to the one presented in [START_REF] Arun | Sizing curve for design of isolated power systems[END_REF], was used in order to size the system according to design constraints. The purpose is to understand which combinations of PV module area, slope and battery size allow system operation without loss of load (LOL) occurrence while safeguarding the condition for multi-year operation, i.e., the battery's state of charge (SOC) after one year must be higher or equal to its initial value. A straightforward strategy was used to simplify this otherwise complex problem: the total PV area is divided into groups of PV modules with different slopes. Thus, production can be shaped to match demand throughout the year. The design space -displayed in Fig. 4 as a domain of system configurations within which adequate system operation is possible -was obtained for two PV groups, one of which is composed of 20 modules sloped at 30º south, and relates battery size, slope and number of PV modules in the second group.

Fig. 4. Design space according to battery size, number of PV modules and slope angle of the 2 nd PV group: beyond the surface the system is feasible, otherwise the system is unfeasible

The domain seen in Fig. 4 is mostly shaped by low photovoltaic generation and insufficient storage capacity, namely for combinations of low PV area and battery size. The design space is also shaped by climate data and load patterns. In this particular case, peak demand occurs during the Winter months and peak solar irradiation occurs during the Summer months, thus requiring large battery sizes if power is to be continuously supplied to the household throughout the year.

The design space suggests multiple possible system sizes though additional constraints, namely cost, can help narrow down the feasible options. The battery is purportedly the most sensitive component, namely with regard to cost per kWh and lifetime. However, increasing the number of PV modules to decrease battery size also increases the battery rating, thus also increasing the cost. A simple compromise is to select the lowest possible battery size and the lowest possible array area -as seen in Fig. 5. Fig. 5. System design space according to battery size and number of PV modules at the 2 nd group for a slope angle of 60º -the plot is a horizontal slice of Fig. 4 A system comprising 20 PV modules in the first group (30º), 30 PV modules in the second group (60º) and a battery size of 192 kWh was determined as reliable and cost-effective according to the strategy outlined earlier. The battery required for the aforementioned system must have a minimum power rating of 11520 W or 240 A at 48 V, in order to be able to absorb the combined power of the PV modules and PV/T collectors under minimum temperature conditions -i.e., a conservative constraint.

Results and Analysis

The building simulation revealed that the annual thermal energy demand to reach comfort levels amounts to 4842 kWh of energy that must be provided to the household and 1552 kWh of energy that must be extracted from the household. Fig. 6 shows displays the heat transfer requirements for thermal comfort in one hour steps. Fig. 6. Thermal energy to be provided to (red) and extracted from (blue) the household According to the simulation results, the HP operates at annual average efficiencies of 4.25 in heating mode and 3.5 in cooling mode, requiring a total of 1595 kWh of electricity annually -the annual simulation results are displayed in Table 3. The solar DHW system performs well, reaching a solar thermal fraction of 65%. The PV/T collectors generated 1643 kWh of thermal energy at an average efficiency of about 15% compared to 24.3% in [START_REF] Santbergen | Detailed analysis of the energy yield of systems with covered sheet-and-tube pvt collectors[END_REF], which is best explained by the backup system used. The aspects affecting thermal performance are explained in detail in [START_REF] Joyce | A PV/T and Heat Pump based Trigeneration System for Residential Applications[END_REF].

The bulk of photovoltaic production is due to the PV modules rather than the PV/T collectors, due to lower collector areas and generally higher absorber temperature. In any event, photovoltaic production is marred by considerable waste of solar power due to the inability to charge the battery beyond its rated capacity during the Summer.

The battery size is considerably large but within standard figures with regard to the days of average consumption it can withstand without being charged, in this case about 11 days -according to [START_REF] Mulder | Electricity storage for grid-connected household dwellings with PV panels[END_REF] it should typically be between 3 and 20 days. The battery SOC after one year -87% -is considerably higher than its initial value -75% -which means the system is feasible and also that, if battery lifetime considerations are ignored, system performance is likely to improve after the first year.

Conclusions

A model of the proposed trigeneration system based on PV modules, PV/T collectors and a HP has been developed and simulated. The design space obtained for the system shows that the system is feasible though costly. This is due, in part, to the domestic load profile selected, which reflects traditional, i.e. grid-connected, load profiles. Also, the model enabled a deeper understanding of the limitations of solar technology if peak demand occurs during low irradiation months, thus suggesting the need for seasonal energy storage or an alternative energy source for Winter months. Future research will focus on improving existing models and establishing detailed cost functions to avoid waste and ensure cost-effective system sizing.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Proposed system configuration: off-grid solar trigeneration system with HVAC-TST

Table 1 .

 1 DHW-TST parameter values

	Parameter Volume (m²) Inner Surface Area (m²) Heat Loss Coefficient (W/m²K)
	Value	0.2	2	1

Table 2 .

 2 PV module parameter values under standard test conditions (STC)

	Parameter Area (m²)	P rated (W)	η module (%)	ρ (%)	P rated Temperature Coefficient (W)
	Value	1.67	230	13.78	87	-0.38

Table 3 .

 3 Annual simulation results for the proposed trigeneration system

	Production	Energy (kWh)	Demand	Energy (kWh)
	Electric Production (DC)	8228	Electric Demand (AC)	6179
	-Waste	10446	-Heating	1152
	-Ohmic Losses	111	-Cooling	443
	-PV	7966	-DHW Backup	1242
	-PV/T	485	-Lighting	1102
	Electric Production (AC)	6179	-Appliances	2240

Acknowledgments. The authors would like to thank ENERGIA PRÓPRIA S.A. and the Portuguese QREN (2007-2013) program for proposing and funding the SOL3 project (QREN reference 2010/12516).


J P M Mendes

L M Redondo

H Canacsinh

M Vieira

José O Rossi

Modelling of n-Stage Blumlein Stacked Lines for Bipolar Pulse Generation

Keywords: Blumlein line, propagation waves, reflection coefficient, transmission coefficient, voltage gain

A Blumlein line is a particular Pulse Forming Line, PFL, configuration that allows the generation of high-voltage sub-microsecond square pulses, with the same voltage amplitude as the dc charging voltage, into a matching load. By stacking n Blumlein lines one can multiply in theory by n the input dc voltage charging amplitude. In order to understand the operating behavior of this electromagnetic system and to further optimize its operation it is fundamental to theoretically model it, that is to calculate the voltage amplitudes at each circuit point and the time instant that happens. In order to do this, one needs to define the reflection and transmission coefficients where impedance discontinuity occurs. The experimental results of a fast solid-state switch, which discharges a three stage Blumlein stack, will be compared with theoretical ones.

Introduction and Contribution to Value Creation

Short duration high voltage pulses with fast rise and fall times and flat top are required for many applications such as: medical treatment, food and water sterilization and exhaust gas discharge [START_REF] Mir | Biomedical applications of electric pulses with special emphasis on antitumor electrochemotherapy[END_REF][START_REF] Barsotti | Food processing by pulsed electric fields[END_REF][START_REF] Raso | Pulse Electric Fields Technology for the Food Industry[END_REF]. A practical way of getting high voltage, almost, rectangular pulses, with width less than one microsecond, are with the help of PFL. A quick rise time switch is necessary for achieving these pulses and the most used ones in the literature for high voltage amplitudes are spark gaps [START_REF] Gupta | Design and construction of double-Blumlein HV pulse power supply[END_REF]. However, the evolution of solid-state switches in terms of voltage amplitude, rise time, internal resistance, price and size make this technology an alternative for switching stack transmission lines [START_REF] Jiang | Compact pulsed power and its industrial applications[END_REF], making this systems more compact and less expensive.

The basic operation principle of single transmission line and up to two stack Blumlein line generator have been characterized in many articles and books, such as, [START_REF] Raso | Pulse Electric Fields Technology for the Food Industry[END_REF][START_REF] Gupta | Design and construction of double-Blumlein HV pulse power supply[END_REF][START_REF] Somerville | An efficient stacked-Blumlein HV pulse generator[END_REF][START_REF] Riveletto | Characterization and realization of a 120 kV, 200 ns transmission line pulse generator[END_REF][START_REF] Smith | Transient electronics and pulsed power circuit technology[END_REF][START_REF] Verma | Design and performance analysis of transmission linebased nanosecond pulse multiplier[END_REF], for unipolar generator. In [START_REF] Mendes | Solid State Marx Modulator with Blumlein Stack for Bipolar Pulse Generation[END_REF], appear the hybrid modulator capable of delivering a high voltage bipolar pulse, Blumlein generator.

In order to understand the completely voltage wave propagation phenomena in each stage, this work derives an n th model for the reflection and transmission coefficients of a Blumlein stack intended for bipolar generation, considering a matched load. The correct theoretical modeling allows the assembling of high-voltage pulse modulators with better pulse shape characteristics, which in terms results in enhanced performance in applications areas such as medical treatment where this is critical. Theoretical time evolution of the voltage in load will be compared with experimental ones for a three stage Blumlein stacked generator.

It is expected that this technology after being completely developed may avoid the time consuming, expensive cost and painful traditional treatments, improving significantly the quality of life of deceased people.

Calculation of the Reflection and Transmission Coefficients in a Blumlein Line System

Each Blumlein line cell is composed of two identical transmission lines with characteristic impedance Z 0 , and length l, connected in series. Stacking stages in parallel allows a Blumlein generator to multiply the voltage source amplitude by the number of stages, as seen in Fig. 1

ρ τ ρ + = + - = 1 i r i r Z Z Z Z . (1) (2)
where Z r and Z i are, respectively, the impedance to the back and front, in relation to ground, of the considered line point.

Blumlein Stack

One Blumlein stage comprises two identical transmission lines connected in series, as shown in Fig. 1

( ) ( ) 2 1 4 2 2 2 0 0 0 0 0 0 0 0 = = + + - + = Z Z Z Z Z Z Z Z b ρ . ( 3
= = + + + + + + - + = = = + + + + - + + + = Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z b b ρ ρ . (4) (5)
Three Blumlein stages comprise six identical transmission lines connected, as in Fig. 1 c), where regions a and c are the as in Fig. 1 a). Then for region b, the reflection coefficient ρ b are, respectively, for the three stages,

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 6
= = + + + + + + + + + + - + = = = + + + + + + + + - + + + = = = + + + + + + - + + + + + = Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z b b b ρ ρ ρ . ( 6
) (7) (8)
The n stages Blumlein system is composed by 2n identical transmission lines connected in agreement with Fig. 2 circuit.

Influence of Other Stages

In order to account for the influence of the voltage waves in each stage, one must explicit the reflection and transmission coefficients calculated in the last section with the contribution for the reflected and transmitted voltage in each stage.

In regions a and c there aren't any influence of other stages because region a, it was considered that the voltage source internal resistance is null, and in region c, each transmission line is independent of each other, thus this study is center in region b. Hence, considering a two Blumlein stack, as in Fig. 1

= = + = + = b b τ ρ ρ . ( 10
)
In addition, a transmitted wave in the first stage takes into account that, ( )

2 1 4 2 4 1 7 4 7 7 2 1 1 = =       - - = - - = b b ρ τ τ . ( 11
)
A transmitted wave in the second stage takes into account that,

= = + = + = b b τ τ τ . ( 12
)
Considering a three Blumlein stack, as in Fig. 1 c), a reflected voltage wave in the first stage takes into account that, ( )

2 1 6 3 6 1 6 3 6 5 3 2 1 1 = =       - - = - - = b b b ρ ρ ρ ρ . ( 13
)
A reflected wave in the second stage takes into account that,

= = + + = + + = b b b τ τ ρ ρ . ( 15
)
In addition, a transmitted wave in the first stage takes into account that, ( )

= =       + - - = + - - = b b b ρ ρ τ τ . 2 1 6 3 6 1 6 3 11 6 11 11 3 2 1 1
A transmitted wave in the second stage takes into account that, ( )

= =       - - + = - - + = b b b ρ τ τ τ . ( 17
)
And a transmitted wave in the third stage takes into account that

= = + + = + + = b b b τ τ τ τ . (18)
Consequently, for n stages the reflected waves take into account that,

N n x even is x if x n odd is x if x n n x bx x x x b n x n x bx x x bx n x ∈ ∀        = - + + - - = = - + + - = ∑ ∑ ∑ ∑ - - - - , 2 1 1 1 1 2 4 2 1 1 1 2 4 1 1 1 1 1 1 ρ τ ρ ρ τ ρ . (19) ( ) ( ) ( ) ( )
Also, for n stages the transmitted waves take into account that, ( )

( ) ( ) N n x even is x if x n odd is x if x n n x x b x x bx n x n x bx x x bx n x ∈ ∀        = - + + - = =       - - + - = ∑ ∑ ∑ ∑ + + + + + , 2 1 1 1 2 4 2 1 1 1 2 4 1 1 1 1 1 1 1 ρ τ τ ρ τ τ . ( 20
)

Theoretical Results versus Experimental Results

Considering a three stage Blumlein system, the theoretical results, presented in Fig. 3.1 thru Fig. 6, show the time diagram of the voltage propagation waves in each line, for simplicity it was assumed the odd transmission lines as active line and the even transmission lines as passive line, in agreement with Fig. 1 c), as in [START_REF] Rossi | Design and Construction of a 150kV/300A/1us Blumlein Pulser[END_REF], for the coefficients determined in the last section. For validate the theoretical model, a experimental Blumlein generator prototype with three stages (Fig. 1 c)) was assembled, using URM43 coaxial cable, characteristic impedance of 50 Ω, with 5 m of length per line, speed of propagation 66% of the light speed, and transition time 25 ns in each transmission line. A fast MOSFET DE475-102N21A, with rise and fall times below 10 ns, was used to charge and discharge the stack.

In agreement of Fig. 1.c), Fig. 7 and Fig. 8 show the results of the positive and negative output pulse V L , after charging the system with V=1 kV amplitude during a long time (> 150 µs) and afterward discharged in a matched load. Comparing the results of the theoretical model with the experimental ones, it is observed that an approximately 50 ns bipolar pulse is generated with 3 kV. However, the model doesn't consider the experimental losses and devices nonlinearities.

Conclusions

A mathematical model of Blumlein stack generator was derived, considering the reflection and transmission coefficients, for an n th stages system. The experimental results of a three stages 1 kV prototype were compared with the theoretical for the 3 kV bipolar output voltage produced into a matched load. Good agreement was reach, however because the real system parameters and losses it will be interesting in the future to try to model also the real line characteristics.

Fig. 1 .

 1 Fig. 1. Blumlein system with a) one; b) two and c) three stages. The voltage waves injected in each line propagate in a medium characterized by impedance, ε µ = Z, with transition time t 0 , along one section of line,

.

  a). There are three characteristic impedance regions where discontinuity occurs: a, b and c. In each there are reflected and transmitted voltage waves. Considering a voltage V injected in Line 1, and the internal resistance of the source null, as in a short-circuit, then in region a the reflection coefficient ρ a and transmission coefficient τ a are, respectively, For region b, the reflection coefficient ρ b , is:

  )For region c, the open circuit end of the line, the reflection coefficient ρ c and transmission coefficient τ c are, respectively, stages comprise four identical transmission lines connected, as in Fig.1 b), where regions a and c are the as in Fig.1 a). Then for region b, the reflection coefficient ρ b are, respectively, for the two stages, (

Fig. 2 .

 2 Fig. 2. Blumlein system with n stages

  b), a reflected voltage wave in the first stage takes into account that,

  the reflected wave in the third stage takes into account that,

Fig. 3 .

 3 Fig. 3. Propagation voltage waves and load voltage between 0<t<δ.

Fig. 4 .

 4 Fig. 4. Propagation voltage waves and load voltage between δ=t<2δ.

Fig. 5 .

 5 Fig. 5. Propagation voltage waves and load voltage between 2δ=t<3δ.

Fig. 6 .

 6 Fig. 6. Propagation voltage waves and load voltage between 3δ=t>3δ.

Fig. 7 .

 7 Fig. 7. Experimental positive pulse, V L , 1kV/div and input charging voltage V, 200V/div, both width 50 ns/div.

Fig. 8 .

 8 Fig. 8. Experimental negative pulse, V L , 1kV/div and input charging voltage V, 200V/div, both width 50 ns/div.

This work was supported by the Portuguese National Strategic Reference Framework, QREN, under project 1600/A2P2/2008. CH1=VL CH2=V CH2=V CH1=VL


H Canacsinh

J F Silva

S Pinto

L M Redondo

J Santana

Solid-State Bipolar Marx Converter with Output Transformer and Energy Recovery

Keywords: Bipolar high-voltage pulses, solid-state switches, high-voltage transformer, Marx converter topology, Energy recovery

The purpose of this paper is to present and discuss a general HV topology of the solid-state Marx modulator, for unipolar or bipolar generation connected with a step-up transformer to increase the output voltage applied to a resistive load. Due to the use of an output transformer, discussion about the reset of the transformer is made to guarantee zero average voltage applied to the primary. It is also discussed the transformer magnetizing energy recovering back to the energy storage capacitors. Simulation results for a circuit that generates 100 kV pulses using 1000 V semiconductors are presented and discussed regarding the voltage and current stress on the semiconductors and result obtained.

Introduction

Industries such as food sterilization and wastewater processing have demonstrated an increased interest in high-voltage pulses over the last years. Experience has shown that in most of these cases the use of bipolar pulses results in an improved process performance and in enhanced final products, compared to the obtained with the use of unipolar positive or negative pulses. This represents an additional value to the industrial method and has contributed strongly to the development of efficiency and flexibility of the bipolar high-voltage modulators [START_REF] Gaudreau | Pulsed Power systems for Food and Wastewater processing[END_REF][START_REF] Keith | Distributed Magnetic Coupling Synchronizes a Staked 25-kV Mosfet Switch[END_REF].

Considering the techniques that are based on solid-state technology, a frequent method to generate high-voltage bipolar pulses includes the use of two d-c power supplies with series switches, for the positive and negative voltage, which implies the use of series stacks of semiconductors to hold-off the voltage [START_REF] Gaudreau | Pulsed Power systems for Food and Wastewater processing[END_REF][START_REF] Wang | A 12 kV solid state high voltage pulse generator for a bench top PEF machine[END_REF]. Also, solid-state multilevel converters have been proposed to generate high-voltage bipolar pulses [START_REF] Petkovsek | Multilevel bipolar high voltage pulse source -Interlock dead time reduction[END_REF].

The circuit used to obtain high-voltage pulses either unipolar or bipolar is based on the Marx modulator concept. Recent technological upgrading done in the mature Marx unipolar generator concept led to the intensive use of semiconductor switches contributing to a performance increase of the original circuit [START_REF] Cassel | A Solid State High Voltage Pulse Modulator which is Compact and without oil or pulse transformer, Power Modulator Conf[END_REF][START_REF] Redondo | All Silicon Marx-bank topology for high-voltage, high-frequency rectangular pulses[END_REF][START_REF] Kim | High voltage pulse power supply using Marx generator & solid-state switches[END_REF]. A generalized solid-state Marx modulator with one low power supply and able to deliver repetitive unipolar or bipolar high-voltage output pulses was presented by [START_REF] Redondo | Generalized Solid-State Marx Modulator Topology[END_REF], shown in Fig. 1.

Hybrid topologies were attained with the combination of Marx generator with a step-up pulsed transformer [START_REF] Redondo | Solid-state Marx Generator Design with an Energy Recovery Reset Circuit for Output Transformer Association[END_REF]. This approach decreases the number of needed solidstate switches, reduces the turns ratio of the transformer and provides galvanic isolation to the load.

In this work, simulated results and analysis is made regarding the connection of a pulse transformer to the Fig. 1 topology to further increase the pulse amplitude. The reset of the transformer is discussed to improve the circuit performance.

Contribution to Value Creation

The connection of a high-voltage pulsed transformer to a solid-state bipolar Marx modulator in order to further increase the voltage in a load is an innovation. If the semiconductor switches are triggered the right way it is possible to reset the transformer core between pulses, recovering this energy to the main capacitors, and at the same time decreasing the reset voltage on the transformer secondary. This will be useful to food sterilization and wastewater processing cutting costs and creating higher quality products.

Circuit Topology

Fig. 2 presents the circuit of Fig. 1 connected to a set-up pulse transformer, aiming the increase by N 2 /N 1 of the pulse voltage amplitude applied by the solid-sate bipolar Marx generator into a resistive load.

The Marx topology in Fig. 2 circuit, explained in detail in [START_REF] Redondo | Generalized Solid-State Marx Modulator Topology[END_REF], can be described shortly as a circuit that generates bipolar high-voltage pulses by connecting in series a set of capacitors into a load, previously charged in parallel from a relatively low voltage dc power supply, U dc . During the charging mode switches T dc , D dc , D hi , T gi , D fi and T ei are turned on. During this period, the on-state of the switches T ei and D fi , guarantees that voltage, v 0 applied to the primary of the transformer is nearly zero volts.

The pulse mode operation can be divided in negative and positive pulses. To apply negative pulse into the load, T bi and T ci are switched on, being all the remaining switches off. During this period capacitors C i (except capacitor C 1 ) are connected in series applying a voltage, for n stages,

dc p nU v - = (1)
to the transformer primary, considering all capacitor charged with U dc , and a voltage

1 2 0 N N nU v dc - = (2)
applied to the load. During this period, primary current i p is equal to

' 0 i i i m p + = ( 3
)
where i m is the magnetizing current of the transformer. Considering a linear equivalent circuit with magnetizing inductance L m , it is

m p p m L t v i = (4)
where t p is the pulse period and L m the magnetizing inductance of the transformer, and i' 0 is the secondary current reduced to the primary,

T dc U dc r dc Source module Solid-state module 1 D dc T a1 T c1 T b1 T d1 T e1 D f1 T g1 D h1 C 1 C 2 T an T cn T bn T dn T en D fn T gn D hn C n+1 Solid-state module n Load + v P - + v S - + v 0 - N 1 :N 2
N N i i = (5)
being the load current given by

0 0 R v i o = (6)
for a resistive load R 0 .

After the negative pulse, the transformer core must be reset with and opposite voltage such that the volt-seconds product is equal to the negative pulse period voltssecond. Normally, this is achieved using auxiliary dissipative circuits where freewheeling diodes are used for speediness. The circuit presented in Fig. 2 has natural paths with diodes that accomplished this task, which consists of the IGBTs anti-parallel diodes. Moreover, these paths include the main C i capacitors whereas the reset circuit is non dissipative, besides the normal losses in the parasitic resistances of the components. Hence, after the negative pulse the magnetizing current of the transformer has a path set by freewheeling diodes D ci and D bi and capacitors C i (except capacitor C 1 ), as shown in Fig. 3.

In this case, during the reset time, the transformer magnetizing energy is recovered back to the energy storage capacitors C i (except capacitor C 1 ), and the transformer primary is subject to an opposite polarity voltage with same magnitude of the applied pulse, which is further amplified by N 2 /N 1 and applied to the load. This means that two equal amplitude pulses are successively applied to the load with opposite polarity, which is normally not desirable.

Afterwards, when the magnetizing current goes to zero the diodes go off and the reset period is over.

In order to have a lower reset voltage, it is possible to set another path for the magnetizing current to flow after the negative pulse. For example, this path can be set by freewheeling diodes D d1 , D a1 , D hi (except D h1 ) and T gi (except T g1 ) and capacitor C n+1 , as shown in Fig. 4. Meaning that is possible to choose just one capacitor to receive the magnetizing energy. For the positive pulse condition the analysis is similar, being the positive pulse obtained by switching on IGBTs T ai and T di , being all the remaining switches off. During this period, capacitors C i (except capacitor C n+1 ) are connected in series.

The natural path to reset the transformer magnetizing energy, after the positive pulse, is set through the freewheeling diodes D di and D ai and capacitors C i (C n+1 is not used), as shown in Fig. 5.

Again, in reset this condition, the transformer magnetizing energy is recovered back to the energy storage capacitors C i (except C n+1 ), and load withstands an opposite polarity voltage with same magnitude of the applied pulse. An alternative way is to use freewheeling diodes D dn , D an , D fi (except D fn ) and T ei (except T en ) and capacitor C n-1 , as shown in Fig. 6.

Solid-state module 1 D c1 D b1 T gn D hn C n+1 Solid-state module n Load - v P + - v S + - v 0 + N 1 :N 2

Simulation Results

In order to validate the described concept described in the last section, a simulation circuit was designed using SIMULINK/MATLAB software, containing 10 stages Marx generator operating with U dc =1000 V, C i = 1 µF, and a 1:10 step up transformer, AMCC -1000, from POWERLITE Inductor Cores, with parameters presented in Table 1, capable of receiving a 10 kV pulse in the primary and delivering a 100 kV pulse in the secondary. The simulated operating condition were set to 1% duty cycle with 1 kHz repetition rate and 120 µs reset time, into a 100 kΩ resistive load. Fig. 7 shows the simulated waveform for primary voltage, v p , and a primary winding pulse current, i p , into the 100 kΩ resistive load, using all the freewheeling diodes to reset the core with the total voltage. It is shown in Fig. 7 that, in this situation, during the reset period (necessary to guaranty an equal volt-second balance), an opposite polarity voltage is applied into a load with the same magnitude of the pulse. This situation is not wanted as explained above. If the condition now is set to just one capacitor being used for reset, then the results are obtained in Fig. 8. The difference in the areas of the pulse and reset period are due to energy dissipated. It can be clearly observed the two current components of the primary currents described in (3).

Observing Fig. 8b), the slope of the magnetizing current decreases from its maximum value to zero during the reset of the transformer. As described above, this current is redirected to the capacitors, recovering the magnetizing energy. Fig. 8c) shows the voltage in the secondary of the transformer.

The amplitude of the reset voltage in Fig. 8 is nearly the voltage of the power supply, 1000 V, so the reset time is longer than in Fig. 7. 4 and6; horizontal scale 0.1 (ms/div): a) primary voltage, v p , 2 (kV/div); b) primary current, i p , (5A/div); c) secondary voltage, v 0 , 20 (kV/div).

Conclusions

A hybrid integrated solid-state bipolar Marx generator circuit was presented, which associates the advantage of the intensive use of power semiconductor switches to increase the performance of the classical Marx circuit and the advantage of the topology being capable to connect an output transformer to further increase the output voltage. The Marx type bipolar topology used has the ability of recovering the transformer magnetizing energy, during the pulse off-state, back to the energy storage capacitors.

Simulation results showed 10 stages Marx circuit using 1 kV per stage, operating with 1 kHz repetition rate and 1% duty cycle, with a 1:10 step-up, giving 100 kV bipolar pulses at the load and resetting the transformer with U dc after each pulse, recovering the energy to one main capacitor.

Fig. 1 .

 1 Fig. 1. General HV topology of the n stages solid-state Marx modulator, for unipolar or bipolar generation.

Fig. 2 .

 2 Fig. 2. Circuit of the Fig. 1 connected to a step-up transformer.

2 Fig. 3 .

 23 Fig. 3. Transformer reset operation mode of the circuit of Fig. 2, after negative pulse, set by freewheeling diodes D ci and D bi and capacitors C i (but capacitor C 1 ).

Fig. 4 . 2 Fig. 5 .

 425 Fig. 4. Transformer reset operation mode of the circuit of Fig. 2, after negative pulse, set by freewheeling diodes D d1 , D a1 , D hi (except D h1 ) and T gi (except T g1 ) and capacitor C n+1 , for a lower reset voltage.

2 Fig. 6 .

 26 Fig. 6. Transformer reset operation mode of the circuit of Fig. 2, after positive pulse, set by freewheeling diodes D dn , D an , D fi (except D fn ) and T ei (except T en ) and capacitor C n-1 , for a lower reset voltage.

Fig. 7 .Fig. 8 .

 78 Simulation results for the circuit of Figure2with transformer reset as shown in Figures3 and 5; horizontal scale 0.1 (ms/div), primary: a) voltage, v p , 2 (kV/div); b) current, i p , (5A/div). Simulation results for the circuit of Figure2with transformer reset as shown in Figures

Table 1 .

 1 Calculated 1:10 step-up transformer parameters.

	N 1	43 turns	R 1	275 mΩ
	N 2	430 turns	R 2	28 Ω
	L m	20 mH	V 1	10 kV
	L 1	398 µH	V 2	100 kV
	L 2


H Canacsinh

J F Silva

S Pinto

L M Redondo

Solid-State Bipolar Marx Generator with Voltage Droop Compensation

Keywords: Bipolar high-voltage pulses, Solid-state switches, Voltage droop compensation, Marx converter topology, PWM control

This paper addresses the voltage droop compensation associated with long pulses generated by solid-stated based high-voltage Marx topologies. In particular a novel design scheme for voltage droop compensation in solid-state based bipolar Marx generators, using low-cost circuitry design and control, is described. The compensation consists of adding one auxiliary PWM stage to the existing Marx stages, without changing the modularity and topology of the circuit, which controls the output voltage and a LC filter that smoothes the voltage droop in both the positive and negative output pulses. Simulation results are presented for 5 stages Marx circuit using 1 kV per stage, with 1 kHz repetition rate and 10% duty cycle.

Introduction

The Marx generator topology is often used to produce both unipolar or bipolar highvoltage rectangular pulses into different types of industrial and research applications [START_REF] Gaudreau | Pulsed Power systems for Food and Wastewater processing[END_REF][START_REF] Keith | Distributed Magnetic Coupling Synchronizes a Staked 25-kV Mosfet Switch[END_REF]. This circuit produces high-voltage pulses by switching in series a set of capacitors into a load. The capacitors are previously charged in parallel by a relatively low voltage dc power supply. The Marx generator has gained popularity by the intense utilization of semiconductors [START_REF] Cassel | A Solid State High Voltage Pulse Modulator which is Compact and without oil or pulse transformer[END_REF][START_REF] Redondo | Generalized Solid-State Marx Modulator Topology[END_REF]. The use of solid-state switches enables high flexibility for changing the pulse parameters, low losses and high operation frequency, at the same time it allows for different load conditions.

However, the capacitor type discharge into the load is limited by the ratio of the energy stored in the main capacitors and the energy delivered during the pulse into the load, which depends directly on the pulse duration. If the energy delivered to the pulse is in the order of the energy stored in the main capacitors the pulse shape has no longer a rectangular shape and the capacitor voltage decay, or droop, is increasingly evident. In fact, applications that use long pulses may have a significant voltage droop by the end of the pulse. Circumventing this problem is possible by increasing the stored energy if larger capacitance is used, but this technique increases the size and cost of the circuit.

Another approach is to build an auxiliary voltage compensation circuit. Several authors have come up with different solutions in unipolar Marx type circuits [START_REF] Cassel | Pulsed Voltage Droop Compensation for Solid State Marx Modulator[END_REF][START_REF] Boris | Optimal Design of Two-Winding Inductor Bouncer Circuit[END_REF][START_REF] Tang | A Vernier Regulator for ILC Marx Droop Compensation[END_REF][START_REF] Pfeffer | A Long Pulse Modulator for Reduced Size and Cost[END_REF], using auxiliary resonant circuits that are charged during the charging mode of the main capacitors and deliver further energy during the pulse period when the voltage droop sets. These circuits can either be connected as an independent stage or associated in each Marx stage. However, this issue has not yet been studied in bipolar type generators, where sequences of positive and negative pulses are generated neither a PWM closed loop solution was presented.

This paper presents the first results of a novel design scheme for voltage droop compensation in solid-state based bipolar Marx generators, adding one independent auxiliary modulator stage to the existing Marx stages that performs closed loop PWM generation, without changing the modularity and topology of the circuit. The closed loop PWM generation controls the output voltage and a LC filter smoothes the voltage droop in both the positive and negative output pulses. Simulation results are presented for 5 stages Marx circuit using 1 kV per stage, with 1 kHz repetition rate and 10% duty cycle, into a resistive load.

Contribution to Value Creation

A closed loop PWM technique is used to generate a voltage that is superimposed to the pulse voltage generated from a solid-state Marx bipolar topology in order to compensate the voltage droop of the signal during long pulse applications. An output LC filter is added at the load stage in order to smooth the voltage. This auxiliary circuit is assembled in an extra Marx stage, without compromising the operation of the other Marx stages and satisfying the same properties in terms of maximum voltage hold-off by the semiconductors.

This novel droop voltage compensation method operates during both positive and negative pulses in a bipolar topology and will contribute to value creation by reducing costs of bipolar pulse high voltage generators which in turn can be used for example in food and sterilization industry, as well in research, enhancing economic activity and creating jobs. The simplified circuit topology which delivers either repetitive unipolar or bipolar high-voltage output pulses into a load, including the voltage droop compensation and an output filter, is presented in Fig. 2. This circuit comprises the source module, which includes the power supply U dc and switches T dc and D dc for charging and to avoid source U dc taking part in the pulse process and resistance r dc , which represents the equivalent resistance of source module branch.

Circuit Topology

All circuit stages are equal, consisting of 6 IGTBs (with anti-parallel diodes) T ai , T bi , T ci , T di , T ei and T gi , and diodes D fi and D hi , where the subscript i∈{1, 2, …, n, n+1, aux}, and two energy storing capacitors C i . Thus, for n semiconductor stages the circuit has (n+1) capacitors, meaning that each stage needs two capacitors for producing negative and/or positive pulses, one of the capacitors being shared between two stages. The auxiliary module differs only in the triggering control system. This module includes capacitor C aux for negative pulsing and C n+1 for positive, the last being shared with n+1 stage. Fig. 2 shows an auxiliary module, the solid-state switch voltage droop compensation module. In order to not compromise the modularity concept of the Marx modulator, this module differs only from the triggering control system, consisting in IGBTs (with anti-parallel diodes) T a_aux , T b_aux , T c_aux , T d_aux , T e_aux and T g_aux , and diodes D f_aux and D h_aux , and one energy storing capacitor C aux .

Circuit Operation

Fig. 2 circuit presents several operating modes depending on the semiconductor switching sequence and the required output into the load (i.e. unipolar or bipolar).

Consider first the charging of capacitors C i , from the dc charging power supply, U dc . It consist in turning on switches T dc , D dc , D hi , T gi , D fi as shown in Fig. 3.

For semiconductor and power supply protection, during the initial charging transient, the power supply voltage amplitude is slowly raised or its output current limited to a safe value.

The on-state of T ei and D fi switches during the capacitors C i charging period guarantees that voltage v 0 applied to the load is nearly constant, being negligible in comparison to the pulse output voltage.

For negative pulse mode, switches T bi and T ci are on (except T b_aux and T c_aux ), all the remaining being off, as shown in Fig. 4. When droop compensation is functioning, the auxiliary stage is short circuited through T d_aux anti-parallel diode and T c_aux on. During this period, capacitors C i (except capacitor C 1 and C aux when compensation is not working), are connected in series and the voltage applied to the load is, nearly,

dc nU v - ≈ 0 (1)
assuming all capacitors charged to U dc . For positive pulse mode, switches T ai and T di are on (except T a_aux and T d_aux ) and all the remaining are off, as shown in Fig. 5. When droop compensation is not operating, this stage is short circuited through the T c_aux anti-parallel diode and T d_aux on. During this period capacitors C i (except capacitor C n+1 that is used in this mode for voltage droop compensation) are connected in series and the voltage applied to the load is, ideally,

dc nU v + ≈ 0 (2)
assuming all capacitors charged to U dc .

The time interval between the negative and positive pulses, called the relaxation time, can be adjusted. This time, between the negative and positive pulse, is, usually, long enough to allow re-charging the C i capacitors. This is useful for high load currents. Otherwise the negative and positive pulse amplitude will not be equal due to the voltage droop.

i 0 T c1 T b1 C 2 T cn T bn C n+1

Voltage Droop Compensation and Filtering

The voltage mode hysteresis controller system that generates the switching function for the voltage droop compensation module, shown in Fig. 6, integrates the difference between the output voltage and the input reference voltage with an active integrator,

( ) 0 1 0 = - ∫ dt v v T ref (3)
which generates a saw tooth shaped carrier that feeds a hysteretic comparator, generating the switching function to control the switches T a_aux or T b_aux of the voltage droop compensation module, with a much higher frequency than the operating Marx repetition rate.

In negative pulse mode operation, the output voltage without compensation is generated as seen in Fig. 4. When output pulse voltage amplitude starts decreasing from its initial value, the hysteresis controller starts to reduce the error between the output voltage and the input reference voltage by modulating the switch T b_aux which connects the capacitor C aux in series with the Marx modulators capacitors as can been seen in Fig. 4 (dashed line).

Positive pulse without compensation is applied into a load as seen in Fig. 5. When output pulse voltage starts decreasing, the hysteretic control module switch on T a_aux in order to reduce the error between the output voltage and the input reference voltage, which connects the capacitor C n+1 in series with the Marx modulators capacitors as can been seen in Fig. 5

(dashed line).

Compensation results in a PWM voltage output waveform, superimposed to the normal pulse voltage shape, which needs to be smoothed. An LC filter was dimensioned, taking into account the frequency of the modulation. Once the frequency of the controller, w, is 100 kHz, the cut off frequency of the filter, w c , has to be lower, so it was considered 50 kHz.

The output filter parameters, L and C, was calculated based on, where ξ = 0,85 and R 0 = 1 kΩ is the resistive load. The LC output filter must be designed for the total output voltage.

Simulation Results

The circuit of Fig. 1, with 5 stages and voltage droop compensation stage, was simulated in SIMULINK, MATLAB software. The simulated circuit was operated with V dc =1000 V, applying bipolar pulses with 10% duty cycle with 1 kHz repetition rate, into a 1 kΩ resistive load, producing 5 kV/ 5A pulses. Fig. 7a) shows the simulated waveform for the bipolar output voltage into a resistive load, without any compensation, a bipolar voltage pulse, v 0 , 100 µs pulse width for each negative and positive pulse, and 100 µs relaxation time. It can be seen that the output voltage shape is not rectangular, showing a 500 V voltage droop by the end of the pulse.

Fig. 8 shows the simulated waveform for the bipolar output voltage into a resistive load, with voltage droop compensation but without any filter. It can be seen the modulation mode by Fig. 6 controller, during pulse mode operation. Fig. 7b) shows the simulated waveform of Fig. 8a), filtered by the output LC filter, with less than 5 V ripple. The pulse waveform improvement is confirmed by the, almost, flat pulses obtained in comparison with Fig. 7a). Simulation results show that the voltage droop module labouring as pulse width modulation, and the output filter, compensates and smoothes the voltage droop of the pulse shape when the circuit operates with a 5 stages Marx circuit using 1 kV per stage, with 1 kHz repetition rate and 10% duty cycle.

Conclusions

Fig. 1 Fig. 2 .Fig. 1 .

 121 Fig.1shows the conceptual block diagram of the bipolar solid-state Marx modulator with voltage droop compensation. The first block is the trigger system of the Marx modulator which accepts as entries the type of pulse, unipolar or bipolar pulse repetition rate and duty cycle of the pulse. It also has the voltage mode hysteresis controller that compares the output voltage and the input reference voltage to generate the switching function for the voltage droop compensation module. The second block is the Marx modulator shown in Fig.2, comprising the voltage droop compensation module. The last two blocks are the output filter to smooth the output voltage and the resistive load.

Fig. 3 .

 3 Fig. 3. Charging mode operation of the general HV topology of the n stages solid-state Marx modulator, for unipolar or bipolar generation.

Fig. 5 .

 5 Fig. 5. Positive pulse mode operation of the general HV topology of the n stages solid-state Marx modulator, for unipolar or bipolar generation.

Fig. 4 .

 4 Fig. 4. Negative pulse mode operation of the general HV topology of the n stages solid-state Marx modulator, for unipolar or bipolar generation.

Fig. 6 .

 6 Fig. 6. Diagram of the voltage mode hysteric controller system.

AFig. 7 .Fig. 8 .

 78 new design scheme for voltage droop compensation in solid-state based bipolar Marx generators was proposed for high-voltage repetitive pulsed power applications. An independent auxiliary modulation stage was added to the existing Marx stages, without changing the modularity and topology of the circuit, which compensates the output voltage plus an output filter to smooth the voltage in both the positive and a) b) Simulation output voltage result, v 0 , a) without compensation; b) with compensation; vertical scale 2 (kV/div) and horizontal scale 0.1 (ms/div). negative output pulses. As explained above the circuit keeps the voltage modularity of the Marx generator topology. a) b) Simulation output voltage result, v 0 , with compensation, a) bipolar pulse; b) zoom of the compensation during positive pulse; vertical scale 2 (kV/div) and horizontal scale 0.1 (ms/div).


Andrei Blinov

Dmitri Vinnikov

On Implementation Possibilities of High-Voltage IGBTs in Resonant Converters

Keywords: resonant converter, half bridge, power losses

The conventional hard switching half-bridge topology used as a rolling stock auxiliary power supply unit has limited switching frequency due to high power losses in semiconductors. The study analyses LLC and LCC topologies in attempt to improve the performance of the converter and presents a simulation of the operation and an estimation of power losses.

Introduction

Along with the development of 6.5 kV IGBT modules, complex applications managed by series connection of numerous lower voltage semiconductors could be simplified by replacing them with a single 6.5 kV module, which would enable simple and reliable two-level half-bridge (HB) voltage-source inverter (VSI) topologies to be implemented for the rolling stock auxiliary power units.

This research focuses on an experimental half-bridge converter recently developed at Tallinn University of Technology. This converter is based on two Infineon 200 A 6.5 kV IGBT modules (FZ200R65KF1). Investigations have shown that the experimental converter is capable of providing required performance within the whole range of rolling stock supply voltage of 2.2…4.0 kV and a wide power range -10…50 kW [START_REF] Jalakas | Development of 50-kW Isolated DC/DC Converter with High-Voltage IGBTs, Compatibility in Power Electronics[END_REF]. The converter consists of primary and secondary parts galvanically isolated by the high frequency transformer. The primary part is a square-wave twolevel half-bridge PWM inverter and the secondary part consists of a full-bridge rectifier and an LC filter. Such converters (Fig. 1a) are very simple in control and protection, have reduced component count and provide good reliability.

Main concerns of this topology relate to parasitic oscillations after IGBT turn-off (Fig. 1b) [START_REF] Blinov | Switch-Off Behaviour of 6.5 kV IGBT Modules in Two-Level Voltage Source Inverter[END_REF], high power losses in semiconductors due to hard switching and consequently, limited switching frequency (around 2 kHz) because of thermal issues. This imposes increased requirements on the passive components of the converter and associated cooling system. As a result this leads to increased price and reduced power density of the converter. Several ways exist of how to improve the switching process of semiconductor switches in the HB inverters, which can be classified as asymmetrical, auxiliary switch, and resonant converters [START_REF] Aydemir | Operation principles of a switched capacitor snubber circuit suggested for half-bridge DC-DC converters[END_REF].

This however, requires increased number of components including controlled switches. Due to increased complexity the reliability is expected to be decreasing. Investigations of 6.5 kV IGBTs operating in resonant topologies report significant increase in efficiency [START_REF] Lindenmuller | Characterization of a 6.5 kV / 500A IGBT module in a series resonant converter[END_REF][START_REF] Weigel | High voltage IGBTs in medium frequency traction power supply[END_REF], however, the transistors were operating in both zero voltage switching (ZVS) and quasi-zero current switching (ZCS) mode. This mode of operation is hard to achieve with wide input voltage and load variations. The following investigation focuses on the HB resonant converters based on two 6.5 kV IGBT modules that require minimum modifications to the hardswitched topology.

T T 1 > 1 > 1 > 1 > 1 > 1 > 1 > 1 > 2 > 2 > 2 > 2 > 2 > 2 > 2 > 2 > (a) (b)

Contribution to Value Creation

Modern high-voltage power electronic applications relate to several fields, such as industrial electrical drives and traction as well as equipment for power generation, transmission and distribution. There are trade-offs between size, complexity, reliability, cost and many other parameters of the system. Evaluation of these factors is critical to achieve an optimum valuable design. This is often impossible without taking into account the most innovative technology achievements or without applying the available solutions to particular needs. This article investigates the ways of optimisation of the experimental converter in an attempt to create a more valuable and innovative system.

Resonant Converter Types

Resonant converters are an attractive alternative to traditional hard-switched ones because of reduced switching losses and the EMI due to the sinusoidal behaviour of the resonant circuit. Such converters (Fig. 2) could operate at high frequencies to reduce the size of their reactive components. These converters generally feature the second or the third order resonant tank circuit, i.e. the storage tank consists of two or three energy storage elements [START_REF] Batarseh | Steady state analysis and performance characteristics of the LLC-type parallel resonant converter[END_REF]. Resonant tanks can be divided into three groups as Fig. 2. Generalised resonant converter topology and different resonant tanks. series (Fig. 2a), parallel (Fig. 2b) and series-parallel. In turn, converters with seriesparallel resonant tanks could be classified as LCC, and LLC (Figs. 2c and2d, respectively). In resonant converters regulation of output parameters is performed by varying the IGBT switching frequency around the resonance frequency of the converter [START_REF] Aydemir | Operation principles of a switched capacitor snubber circuit suggested for half-bridge DC-DC converters[END_REF].

A major advantage of a series-resonant converter is that the current in the power devices decreases with a decrease in the load, leading to higher efficiency. However, there are difficulties in regulating the output voltage at light load operation [START_REF] Yang | LLC resonant converter for front end DC/DC conversion[END_REF][START_REF] Cavalcante | High Output Voltage Series-Parallel Resonant DC-DC Converter for Medical X-Ray Imaging Applications[END_REF]. Since the studied converter must operate with wide load variations, this topology is not considered suitable. In contrast to the series-resonant converter, the parallelresonant converter can regulate the output voltage at no load by running at a frequency above resonance. On the other hand, such converters have higher device current that is relatively independent of the load. This leads to high conduction losses in semiconductor and reactive components, decreasing the efficiency, especially at light loads.

LLC Resonant Converter

LLC resonant converters introduce several advantages over other resonant converters. These converters require a relatively narrow variation of switching frequency to control the output voltage; can operate with a wide load range and ZVS could be achieved over the entire operating range. Moreover, the transformer leakage and magnetizing inductances can be utilised as the resonant elements of the power stage and, thus, reduce the overall part count. In addition, the series resonant capacitor also provides DC blocking, favourable for an isolation transformer in the half-bridge configuration. The LLC converter has two resonant frequencies: L r and C r determine the higher resonant frequency, while lower resonant frequency is determined by C r and the series inductance of L p and L r . The characteristics of the converter are dependent on the L r /L p inductor ratio. As L r is reduced, the lower frequency needed at low voltage input decreases. In this case variations in the switching frequency within the operating range are increased, resulting in a complicated passive component design. On the other hand, larger L r will make the IGBT turn-off current higher, which increases switching losses. Two resonant frequencies, f r1(LLC) and f r2(LLC) are defined as follows [START_REF] Lin | Implementation of a series resonant converter with series-parallel connection[END_REF]:

Gain Gain (a) (b)
r (LLC) r C L f ⋅ ⋅ = π 2 1 1 , (1)
r p r (LLC) r C L L f ⋅ + ⋅ = ) ( 2 1 2 π . ( 2
)
Since the load independent point (higher resonant frequency) is in the ZVS region (Fig. 3a), the converter could be designed to operate around this point [START_REF] Cavalcante | High Output Voltage Series-Parallel Resonant DC-DC Converter for Medical X-Ray Imaging Applications[END_REF][START_REF]LLC resonant half-bridge converter design guideline[END_REF]. High efficiency is achievable by applying lossless capacitive snubbers across the inverter transistors.

The LLC converter does not require an LC output filter used in traditional hardswitching HB converter. Only the capacitor filter can be used, leading to a simpler and lighter secondary part. The required capacitance value is estimated by

Load(min) sw(min) out f R f U C ⋅ ⋅ ∆ ⋅ = 4 1 , (3)
where ∆U out is the output voltage ripple, f sw(min) is the minimum switching frequency, and R Load(min) is the minimum equivalent load resistance.

LCC Resonant Converter

The series-parallel converter, also referred to as an LCC converter, aims at combining the advantages of the series and the parallel converters, at the same time reducing or eliminating their disadvantages. Similarly to the LLC, the LCC converter does not require an LC output filter used in a traditional hard-switching HB converter. The transformer leakage inductance can be utilised as the resonant element L r .

The low resonant frequency is determined by a series resonant tank L r and C r while the high resonant frequency is determined by L r and an equivalent capacitance of C r and C p in series. Two resonant frequencies, f r1(LCC) and f r2(LCC) are defined as follows [START_REF] Steigerwald | A Comparison of Half-bridge resonant converter topologies[END_REF] r r

(LCC) r C L f ⋅ ⋅ = π 2 1 1 , (4)
.

2 1 2 r p r p r (LCC) r C C C C L f + ⋅ ⋅ ⋅ = π (5)
The behaviour is dependent on the C r /C p ratio. As C p is reduced, the converter resembles a series converter and the upper frequency needed at light loads increases. On the other hand, with an increased C p the converter resembles a parallel converter and the circulating current no longer decreases with the load [START_REF] Batarseh | Steady state analysis and performance characteristics of the LLC-type parallel resonant converter[END_REF].

Unlike in the case of the LLC converter, the load independent point (lower resonant frequency) is in the ZCS region, while in the ZVS region (the higher resonant frequency) the converter is more sensitive to changes in the load (Fig. 3b). Only the operation above the upper resonance will be considered in the following as it is more desirable from the practical point of view since the ZVS is provided for the IGBTs, allowing the use of capacitive snubbers to reduce turn-off losses.

Simulation Results and Loss Comparison

Design of resonant components is always a compromise between load power range, operating frequency, input voltage range, circulating energy in the resonant circuit etc.

From the efficiency point of view the LLC converter is best to be operated at the resonant frequency f r1(LLC) . In this case the both circulating energy in the resonant network as well as the switching losses are low. Since this operating point is only achievable for one given U in and load power, the LLC resonant converter is usually designed around f r1(LLC) for a full load and maximum U in . With an increase in the load or a decrease in the input voltage, the switching frequency is decreased to keep the output voltage regulated.

Similarly, the LCC converter is usually designed around f r2(LCC) for a full load and minimum U in . The step-by-step analysis and design methods of LLC and LLC converters were presented in a range of publications [START_REF] Batarseh | Steady state analysis and performance characteristics of the LLC-type parallel resonant converter[END_REF][START_REF] Yang | LLC resonant converter for front end DC/DC conversion[END_REF][START_REF] Cavalcante | High Output Voltage Series-Parallel Resonant DC-DC Converter for Medical X-Ray Imaging Applications[END_REF][START_REF]LLC resonant half-bridge converter design guideline[END_REF][START_REF] Steigerwald | A Comparison of Half-bridge resonant converter topologies[END_REF][START_REF] Jung | Theoretical analysis and optimal design of LLC resonant converter, Power Electronics and Applications[END_REF] and are beyond the scope of this paper.

The values of the resonant tank components of both converters are selected so that their switching frequency range is similar and relatively narrow (3…4 kHz) and the isolation transformer turns ratio is the same. The main parameters of the analysed converters are listed in Table 1. The input voltage and load power range as well as the output voltage values are the same as for the hard-switched converter. Both converters are able to operate with ZVS within desired conditions. The simulated waveforms and4b, respectively. Simulations show that the turn-off current of IGBT as well as peak current of the rectifier diodes is essentially higher in the LCC converter (Fig. 5). The estimated inverter IGBT power loss in the studied solutions is presented in Fig. 6. The simulations of LLC and LCC converters include the IGBT loss reduction during the turn-off with the snubber capacitors. Since reductions in the IGBT turn-off power loss by help of capacitive snubbers have been reported to be lower than expected due to increased current tail duration and could vary between different IGBTs, the approximate average reduction of 50% [START_REF] Naayagi | Investigating the effect of snubber capacitor on high power IGBT turn-off[END_REF][START_REF] Fujii | Characterization and Comparison of High Blocking Voltage IGBTs and IEGTs Under Hard-and Soft-Switching Conditions[END_REF][START_REF] Song | Switching characteristics of NPT-and PT-IGBTs under zero-voltage switching conditions[END_REF][START_REF] Petterteig | IGBT turn-off losses for hard switching and with capacitive snubbers[END_REF] is considered in this paper. It should be mentioned that in real converters, the power losses could be distinctly higher than the simulated values due to additional power dissipation of passive components and the output rectifier. Despite operating with higher switching frequency than the hard-switched converter, the resonant LLC converter is able to provide essential (up to 57%) reduction of inverter losses. On the contrary, the power losses of the LCC converter are higher, especially at higher input voltages. This situation could be improved by adjusting C r /C p ratio. As a downside, the operation frequency range will increase.

Conclusions

Implementation of resonant converters instead of the hard switching half-bridge topologies seems to be an attractive way of improving the efficiency of the power converter. Both LLC and LCC converters can deliver low noise and ZVS of the inverter switches over the whole range of operation conditions. From the two, the LCC converter design requires additional adjustments in order to reduce switching losses. This will result in a wider regulation frequency range, making design more challenging. On the contrary, the LLC converter performance seems advantageous due to lower power losses with a similar regulation frequency range. On the other hand, the additional complexity of the topology, its control and protection as well as possible reduction in robustness reliability may not overcome the advantages it brings. The further research will focus on investigations of HB topology with phaseshifted synchronous rectifier, which seems an advantageous alternative since it does not require any modifications in the inverter part.

Fig. 1 .

 1 Fig. 1. Hard-switched high-voltage half-bridge converter topology (a) and measured IGBT voltage and current waveforms (b).

Fig. 3 .

 3 Fig. 3. Generalised voltage gain vs. normalised frequency at different loads for LLC converter (a) and LCC converter (b).

  r

Fig. 4 .

 4 Fig. 4. Main simulation waveforms of LLC (a) and LCC (b) converters (U in =3000V, P out =30kW).of LLC and LCC converters operating at nominal conditions are shown in Figs.4a and 4b, respectively. Simulations show that the turn-off current of IGBT as well as peak current of the rectifier diodes is essentially higher in the LCC converter (Fig.5). The estimated inverter IGBT power loss in the studied solutions is presented in Fig.6. The simulations of LLC and LCC converters include the IGBT loss reduction during the turn-off with the snubber capacitors. Since reductions in the IGBT turn-off power loss by help of capacitive snubbers have been reported to be lower than expected due to increased current tail duration and could vary between different IGBTs, the approximate average reduction of 50%[START_REF] Naayagi | Investigating the effect of snubber capacitor on high power IGBT turn-off[END_REF][START_REF] Fujii | Characterization and Comparison of High Blocking Voltage IGBTs and IEGTs Under Hard-and Soft-Switching Conditions[END_REF][START_REF] Song | Switching characteristics of NPT-and PT-IGBTs under zero-voltage switching conditions[END_REF][START_REF] Petterteig | IGBT turn-off losses for hard switching and with capacitive snubbers[END_REF] is considered in this paper. It should be mentioned that in real converters, the power losses could be distinctly higher than the simulated values due to additional power dissipation of passive components and the output rectifier.Despite operating with higher switching frequency than the hard-switched converter, the resonant LLC converter is able to provide essential (up to 57%) reduction of inverter losses. On the contrary, the power losses of the LCC converter are higher, especially at higher input voltages. This situation could be improved by adjusting C r /C p ratio. As a downside, the operation frequency range will increase.

Fig. 5 .

 5 Fig. 5. IGBT turn-off current vs. load power of the considered converters (U in =3000 V).

Fig. 6 .

 6 Fig. 6. Single IGBT module power loss estimation vs. output power at different input voltages in hard-switched (a), LLC (b) and LCC (c) converters.

Table 1 .

 1 Main parameters of the compared converters.

	Converter	Switching frequency (fsw, kHz)	Transformer turns ratio (Ns/Np)	Cr (µF)	Cp (µF)	Lr (mH)	Lp (mH)	Lf (mH)	Cf (mF)
	Hard-switched	2	0.4	-	-	-	-	5	0.74
	LLC	2.9…3.9	0.17	1.2	-	1.32	2.64	-	2.4
	LCC	3.0…3.9	0.17	2.2	1.8	2.87	-	-	2.4

Acknowledgement. This research work has been supported by Estonian Ministry of Education and Research (Project SF0140016s11), Estonian Science Foundation (Grant ETF8020) and Estonian Archimedes Foundation (project -"Doctoral School of Energy and Geotechnology II").


Manuela A Vieira

Alessandro Fantoni

Paula Louro

Adolfo S Garção

Photonics Active Filters Based on SiC Multilayer Structures: A Two Stage Active Circuit

Keywords: Amorphous Si/SiC photodiodes, photonic, optoelectronic, demultiplexer devices, optical filters

Characteristics of tunable wavelength filters based on a-SiC:H multilayered stacked cells are studied both theoretically and experimentally. Results show that the light-activated photonic device combines the demultiplexing operation with the simultaneous photodetection and self amplification of an optical signal. The sensor is a bias wavelength currentcontrolled device that make use of changes in the wavelength of the background to control the power delivered to the load, acting a photonic active filter. Its gain depends on the background wavelength that controls the electrical field profile across the device.

Introduction

There has been much research on semiconductor devices as elements for optical communication when a band or frequency needs to be filtered from a wider range of mixed signals [START_REF] Louro | Optical readout in pinpi'n and pini'p imagers: a comparison[END_REF]. Active filter circuits can be designed. Amorphous silicon carbon tandem structures, through an adequate engineering design of the multiple layers' thickness, absorption coefficient and dark conductivities can accomplish this function [START_REF] Louro | Optical readout in pinpi'n and pini'p imagers: a comparison[END_REF]. Here the manipulation of the magnitude is achieved by changing the wavelength (color channels) of the modulated lights and its frequency under appropriated wavelength backgrounds [START_REF] Vieira | Light-activated amplification in Si-C tandem devices: A capacitive active filter model[END_REF] and can be described in terms of a wavelength controlled photo-capacitance.

Combined tunable converters based on SiC multilayer photonics active filters are analyzed and optimized for a fine tuning of a specific wavelength. The operation combines the properties of active high-pass and low-pass filter sections into a capacitive active band-pass filter. A capacitive active band-pass filter model supports the experimental data. A numerical optoelectronic simulation gives insight into the physics of the device.

Contribution to

Systems that transmit, receive, and/or process intelligence require some form of modulation, which is the deliberate distortion o (data) upon it, in a manner that allows the subsequent recovery of the information. By providing a complex illumination of the device combining radiations with different and complementary penetration depths it is possibl the device.

A combined RGB wavelength router/switch optical network can increase the connectivity of an optical system in visible range using automatically reconfigurable circuit-switching solutions and reduce the numb wavelength division switches required by conventional multi architecture It provides a low optoelectronic interconnection technologies and architectures accor suitability of adoption in optical cross connects (OXCs), switches and routers. conception of new devices based on new materials for optically switchable on SiC multilayer photonic structures in the visible spectrum is a demand in the an increased potential for value creation

Experimental

The active device is n)/ITO double heterostructure produced by PECVD. Deposition conditions are described elsewhere [START_REF] Vieira | Bias sensitive multispectral structures for imaging applications[END_REF] The thickness (200 nm) and the absorption coefficient of the front photodiode (based on a-SiC:H) are optimized for short wavelength wavelength transmittance, and the thickness of the back one (1000 nm) adjusted to achieve full absorption in the intermediate wavelength region and high collection in the long wavelength spectral section. As a result, b optical filters confining, respectively, the short and the long wavelength optical carriers, while the intermediate ones are absorbed across both. configuration is depicted.

The device operates within the visible range the wave square modulated light (external regulation of frequency and intensity) supplied by a red (R: 626 nm; 51 blue (B: 470 nm; 115 µ illumination (background) was superimposed brought in LEDS driven at a constant M. A. Vieira et al.

Contribution to Value Creation

Systems that transmit, receive, and/or process intelligence require some form of modulation, which is the deliberate distortion of a carrier to impress intelligence (data) upon it, in a manner that allows the subsequent recovery of the information. By providing a complex illumination of the device combining radiations with different and complementary penetration depths it is possible to control the spectral response of A combined RGB wavelength router/switch optical network can increase the connectivity of an optical system in visible range using automatically reconfigurable switching solutions and reduce the number of signal demultiplexers and wavelength division switches required by conventional multi-stage switching node It provides a low-cost solution to many aspects of optical and optoelectronic interconnection technologies and architectures according to their suitability of adoption in optical cross connects (OXCs), switches and routers. conception of new devices based on new materials for optically switchable on SiC multilayer photonic structures in the visible spectrum is a demand in the direction of an increased potential for value creation.

Experimental Details

is a glass/ITO/a-SiC:H (p-i-n)/ a-SiC:H(-p) /Si:H(-i)/SiC:H ( double heterostructure produced by PECVD. Deposition conditions are 3].

Fig.1. Device configuration

The thickness (200 nm) and the absorption coefficient of the front photodiode SiC:H) are optimized for short wavelength collection and long wavelength transmittance, and the thickness of the back one (1000 nm) adjusted to achieve full absorption in the intermediate wavelength region and high collection in the long wavelength spectral section. As a result, both front and back diodes act as optical filters confining, respectively, the short and the long wavelength optical carriers, while the intermediate ones are absorbed across both. In Fig. 1 the device configuration is depicted.

The device operates within the visible range using as input color channels (data) the wave square modulated light (external regulation of frequency and intensity) supplied by a red (R: 626 nm; 51 µW/cm 2 ), a green (G: 524 nm; 73 µW/cm blue (B: 470 nm; 115 µW/cm 2 ) LED. Additionally, steady state red, green and blue illumination (background) was superimposed brought in LEDS driven at a constant Systems that transmit, receive, and/or process intelligence require some form of f a carrier to impress intelligence (data) upon it, in a manner that allows the subsequent recovery of the information. By providing a complex illumination of the device combining radiations with different e to control the spectral response of A combined RGB wavelength router/switch optical network can increase the connectivity of an optical system in visible range using automatically reconfigurable er of signal demultiplexers and stage switching node cost solution to many aspects of optical and ding to their suitability of adoption in optical cross connects (OXCs), switches and routers. So, the conception of new devices based on new materials for optically switchable on SiC direction of i)/SiC:H (double heterostructure produced by PECVD. Deposition conditions are

The thickness (200 nm) and the absorption coefficient of the front photodiode collection and long wavelength transmittance, and the thickness of the back one (1000 nm) adjusted to achieve full absorption in the intermediate wavelength region and high collection in ck diodes act as optical filters confining, respectively, the short and the long wavelength optical 1 the device using as input color channels (data) the wave square modulated light (external regulation of frequency and intensity) W/cm 2 ) and a te red, green and blue illumination (background) was superimposed brought in LEDS driven at a constant current value (R: 290 µW/cm 2 , G: 150 µW/cm 2 , B: 390 µW/cm 2 ). Light was always impinging from the glass side.

Transfer Function Characteristics

The transfer function magnitude (or gain) at each wavelength allows us to determine how well the optical filter can distinguish between signals at different wavelengths. In Fig. 2, the spectral photocurrent at 250 Hz, is displayed under red, green and blue background irradiations (color symbols) and without it (black symbols). For comparison the normalized spectral photocurrent for the front, p-i'-n, and the back, pi-n, photodiodes (lines) are superimposed. In Fig. 3 the gain, defined as the ratio between the spectral photocurrents, under red (α R ), green (α G ) and blue (α B ) steady state illumination and without it (no background) are plotted at 250 Hz (lines) and 3500 Hz (symbols). Data shows that each diode, separately, presents the typical response of single p-i-n cells with intrinsic layers based on a-SiC:H or a-Si:H materials, respectively. The front diode, based on a-SiC:H heterostructure, cuts the wavelengths higher than 550 nm while the back one, based on a-Si:H, rejects the ones lower than 500 nm. The overall device presents a high spectral sensitivity in-between. Under red irradiation, the photocurrent is strongly enhanced at short wavelengths and disappears for wavelengths higher than 550 nm, acting as a short-pass filter. Under blue irradiation the devices behaves as a long-pass filter for wavelengths higher than 550 nm, blocking the shorter wavelengths. Under green irradiation the spectral response depends on the frequency. At 250 Hz the spectral sensitivity is strongly reduced while at 3500 Hz the device behaves as a band-stop active filter that screens out the medium wavelength range (green) enhancing only the photocurrent for wavelengths outside of that range. So, by changing the wavelength of the background the front and back diode sensitivities can be tuned.

Fig. 4 shows the spectral gain as a function of the frequency under red (α R ), green (α G ) and blue (α B ) backgrounds at 624 nm (α R , red channel), at 526 nm (α G , green channel) and at 470 nm (α B , blue channel). Under red and green irradiations two frequency regimes can be considered. One, for frequencies lower than 2000 Hz, were either under red and green backgrounds the green and the red channel gains are very low (<<1) and the blue gain is strongly enhanced (>>1) under red background or reduced (<1) under green irradiations. The other regime, for frequencies higher than 2000 Hz, the gain increases with the frequency, gradually under red and quickly under green steady state Under blue, the gain increases slowly with the frequency being higher than one for the red and green channels and lower for the blue one. Consequently, under red irradiation (Fig. 4a) the transfer function has extra gain at short wavelengths (blue channel), than at longer wavelengths acting as a short-pass filter whatever the frequency. Under green background (Fig. 4b), the manipulation of amplitude is achieved by changing the frequency of the modulated lights. At high frequencies the device is a band-stop active filter that works to screen out wavelengths that are within a certain range (green channel), giving easy passage only all wavelengths below (blue channel) and above (red channel). In the low frequency regime all the amplitudes are quenched. Under blue steady state optical bias (Fig. 4c) the device behaves as a longpass active filter that transmits and enhances the long wavelength photons (red and green channels) while blocking the shorter wavelengths (blue channel).

Numerical Simulation

In order to understand the light filtering properties of the device, under different electrical and optical bias conditions, a simulation program ASCA-2D [START_REF] Fantoni | Simulation of hydrogenated amorphous and microcrystalline silicon optoelectronic devices[END_REF] was used having as input parameters the experimental data. Under negative applied voltage, in Fig. 5a, it is reported the electric field profile under different wavelengths backgrounds of the optical bias. In Fig. 5b, under red background, the three red, green and blue channels were added and the electrical field profile displayed.

Results show that the balance between the electrical field adjustments due to the non uniform absorption throughout the structure depends on the generation/recombination profiles at each background wavelength. The shallow penetration of the blue photons into the front diode, the deep penetration of the red photons exclusively into the back diode or the decay of the green absorption across both controls the sensor behavior. The external background interferes mainly with the less absorbing cell (the front under red, the back under blue and with both under green irradiations) [5]. Both the front and the back diodes are optically and electrically in series. Under steady state irradiation, to sustain the current across the device, the current at the less absorbing diode has to be adjusted through an increase of the electrical field and thus it becomes reverse biased (Fig. 5a). The superposition of a color channel will affect locally this field. Under red background (Fig. 5b), the blue channel increases the field intensity in the front diode and even reverse it at the internal interface increasing carrier collection. The red and the green channels change the field in an opposite way.

Frequency dependence of the device responsivity can be explained in terms of different induced background photo capacitances due to the transient charge accumulation (free and trapped) created in the top diode region. The photocapacitance can be assumed to be a measure of the density of photogenerated carriers in the space charge region. Fig. 6 shows the internal space charge profile within the complete device under different light wavelength. Charge accumulation is mainly localized at the internal interface between the two diodes. Under blue and red background light the charge accumulation is maximized for the complementary wavelength while under green background there is no marked difference between the space charge accumulation caused by the three signals and the background itself. This charge accumulation corresponds to a photo capacitance behavior of the internal recombination junction. Depending on the imposed background the different channel wavelengths produce a different displacement of the space charge distribution. This effect produces a background dependence of the device frequency response, allowing frequency filtering, or even the definition of an oscillatory frequency resonance. Combined with the series and parallel resistance of the diodes will result in the explicit definition of cut off frequencies for a frequency capacitive filters activated by the light background (Fig. 4).

A Two Stage Active Circuit

An optoelectronic model supported by the complete dynamical large signal Ebers-Moll model was developed [START_REF] Vieira | Bias sensitive multispectral structures for imaging applications[END_REF] and is displayed in Fig. 7. The electrical model can be divided into two parallel sections (Fig. 7a): a short-pass filter (front phototransitor, Q 1 ) and a long-pass filter (back phototransistor, Q 2 ) sections. (Fig. 7b). The charge stored in the space-charge layers is modeled by the capacitor C 1 and C 2 . R 1 and R 2 model the dynamical resistances of the internal and back junctions under different dc bias conditions (Fig. 5c). The operation is based upon the following principle: the flow of current through the resistor connecting the two transistor bases, R 1 , is proportional to the difference in the voltages across both capacitors (charge storage buckets). To allow independent blue, red and green channels transmission and to take into account the wavelength background effect four square-wave current sources with different intensities are used; two of them, α 1 I B and α 2 I R , with different frequencies to simulate the input blue and red channels and the other two, α 1 I Gpi'n and α 2 I Gpin , with the same frequency but different intensities, to simulate the green channel due to its asymmetrical absorption across both front and back phototransistors. When the device is negatively biased, the base-emitter junction of both transistors are inversely polarized and conceived as phototransistors, taking, so, advantage of the amplifier action of adjacent collector junctions which are polarized directly. This results in a current gain proportional to the ratio between both collector currents. The amplifying elements, α 1 and α 2 , control the spatial variation of the photocurrent and so of the photo capacitance of both front and back phototransistors and can provide gain if needed or attenuate unwanted wavelengths (<1) while amplifying (>1) desired ones. The values and the strategic placement of the resistors determine the basic shape of the output signals.

i(OFF) R 1 =1KΩ R 2 =5kΩ V=-8V i(ON) α 1 =0.19 α 2 =1.7 α 3 =0.42 α 4 =0.42
To validate the model, in intensities were multiplied by the on/off ratio between the input channels with and without optical bias (Fig. 3). A good agreement between experimental and simulated data was achieved. Under red background the expected optical amplification in the low wavelength range is observed due to the effect of the active multiple-feedback filter when the back diode is light triggered. The device behaves like an optoelectronic controlled transmission system that stores, amplifies and transports the minority carriers generated by the current pulses, through the capacitors C 1 and C 2. Depending on its wavelength, the optical bias changes the photo capacitance and so the voltages across one or both capacitors. The amplitude of the ac current sources is affected by an α factor that takes into account the enhancement or quenching of the channels due to the steady state irradiation.

Fig. 2 .Fig. 3 .

 23 Photocurrent (nA)

Fig. 4 .

 4 Fig. 4. Spectral gain as a function of the frequency at 624 nm (red channel), at 526 nm (green channel) and at 470 nm (blue channel) under red (αR), green (αG) and blue (αB) backgrounds. a) short-pass filter , b) band-stop filter, c) long-pass filter

Fig. 5 .

 5 Fig. 5. Electric field profiles within the p-i'-n/p-i-n tandem structure. a) under different wavelengths backgrounds (λ R,G,B ) and without it, b) red background (λ R ) and different color channels (λ chR, λ chG, λ chB )

Fig. 6 .

 6 Fig. 6. Internal space charge profile within the device under different light wavelength. Results are shown under reverse bias and for different background illumination

Fig. 7 .

 7 Photocurrent (µA)

  Fig. 7d, experimental (solid lines) and the simulated (symbols) waveform under negative bias and red background is shown. The bit sequences to drive the channels are shown in the top of the Fig.. The current sources are also displayed (dash lines). To simulate the red background, current sources