TECHNICAL FIELD

The present disclosure relates to techniques for determining and applying an aging model for rechargeable batteries and to corresponding devices.

BACKGROUND

Rechargeable batteries are subject to aging, and such aging may depend on time and on usage of the rechargeable battery, e.g., a number of charging cycles. Due to aging, performance of the rechargeable battery may degrade. For example, the ca pacity of the rechargeable battery may decrease due to aging.

However, the aging of battery cells is a complex process. As a result, the aging pro cess is typically described by semi-empirical models which require carefully designed experiments and time-costly experiments. Examples of such semi-empirical aging models are for example described in “Development of a lifetime prediction model for lithium-ion batteries based on extended accelerated aging text data” by M. Ecker et al. , Journal of Power Sources 215 (2012) 248-257, and in “From Accelerated Aging Tests to a Lifetime Prediction Model: Analyzing Lithium-Ion Batteries” by J. Schmalstieg et al., EVS27 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium, Barcelona, Spain, November 17-20, 2013.

SUMMARY

Accordingly, there is a need for techniques which allow for efficiently and accurately determining an aging model for rechargeable batteries.

In view of the above need, the present disclosure provides a method according to claim 1 , a method according to claim 10, and a device according to claim 18. The de pendent claims define further embodiments.

According to an embodiment, a method is provided. The method may be used for learning a parametric aging model. According to the method, impedance data of at least one battery cell are collected. Further, parameters of an aging model function describing aging of the at least one battery cell are determined. Further, a transfer function is determined which relates the impedance data to the parameters of the ag ing model function.

According to an embodiment, the aging model function is a function of an age varia ble. The age variable may correspond to a calendar age of the battery cell or to a number of charging cycles performed on the battery cell. The parameters of the ag ing model function may include a coefficient parameter and an exponent parameter. The aging model function may multiply the age variable, raised to the power of the exponent parameter, by the coefficient parameter.

The parameters of the aging model function may each depend on at least one state variable. The impedance data may then be collected for different values of the at least one state variable over an aging cycle of the at least one battery cell. The at least one state variable may comprises one or more of: temperature, state of charge, cell current, and depth of discharge. In some scenarios, the impedance data may be collected over an accelerated aging cycle of the at least one battery cell.

The parameters of the aging model function may be determined based on analytical model. In addition or as an alternative, the parameters of the aging model function may be determined based on machine learning.

According to an embodiment, a further method is provided. The method may be used assessing an aging state of a battery cell. According to the method, impedance data of a battery cell are measured. Further, a transfer function is acquired. The transfer function relates impedance data to parameters of an aging model function describing aging of the battery cell. The transfer function may for example be acquired based on the above-described method or from a database. Based on the measured impedance data and the transfer function, the parameters of the aging model function are deter mined. Based on the aging model function and the determined parameters, an aging state of the battery cell is determined.

In the above embodiments, the aging model function may be a function of an age variable. The age variable may correspond to a calendar age of the battery cell or to a number of charging cycles performed on the battery cell. The parameters of the ag ing model function may include a coefficient parameter and an exponent parameter. The aging model function may multiply the age variable, raised to the power of the exponent parameter, by the coefficient parameter.

The parameters of the aging model function may each depend on at least one state variable. The impedance data may then be collected for different values of the at least one state variable over an aging cycle of the at least one battery cell. The at least one state variable may comprises one or more of: temperature, state of charge, cell current, and depth of discharge. In some scenarios, the impedance data may be collected over an accelerated aging cycle of the at least one battery cell.

The parameters of the aging model function may be determined based on analytical model. In addition or as an alternative, the parameters of the aging model function may be determined based on machine learning.

In the above embodiments, the transfer function may comprise at least one n-th order complex polynomial, with n being equal to or larger than 2. The order n may depend on how the coefficient parameter and/or the exponent parameter depend on the state variable(s) and/or on the impedance data. For example, a higher order n may allow for better describing more complex dependencies. The transfer function can be cal culated in the time domain or in the frequency domain.

According to a further embodiment, a device is provided. The device is configured to perform a method according to any one of the above embodiments. Accordingly, such device may be configured to collect impedance data of at least one battery cell, determine parameters of an aging model function describing aging of the at least one battery cell, and determine a transfer function relating the impedance data to the pa rameters of the aging model function. Alternatively or in addition, such device may be configured to measure impedance data of a battery cell, acquire a transfer function relating impedance data to parameters of an aging model function describing aging of the battery cell, based on the measured impedance data and the transfer function, determine the parameters of the aging model function, and based on the aging model function and the determined parameters, determine an aging state of the battery cell. The device may comprise at least one processor and a memory containing program code executable by the processor. Execution of the program code may cause the de vice to perform the steps of a method according to any of the above embodiments. In particular, execution of the program code may cause the device to collect impedance data of at least one battery cell, determine parameters of an aging model function de scribing aging of the at least one battery cell, and determine a transfer function relat ing the impedance data to the parameters of the aging model function. Alternatively or in addition, execution of the program code may cause the device to measure im pedance data of a battery cell, acquire a transfer function relating impedance data to parameters of an aging model function describing aging of the battery cell, based on the measured impedance data and the transfer function, determine the parameters of the aging model function, and based on the aging model function and the determined parameters, determine an aging state of the battery cell.

According to a further embodiment, a computer program or computer program prod uct is provided, e.g., in the form of a computer readable storage medium. The com puter program or computer program product comprises program code executable by at least one processor of a device. Execution of the program code may cause the de vice to perform the steps of a method according to any of the above embodiments. In particular, execution of the program code may cause the device to collect impedance data of at least one battery cell, determine parameters of an aging model function de scribing aging of the at least one battery cell, and determine a transfer function relat ing the impedance data to the parameters of the aging model function. Alternatively or in addition, execution of the program code may cause the device to measure im pedance data of a battery cell, acquire a transfer function relating impedance data to parameters of an aging model function describing aging of the battery cell, based on the measured impedance data and the transfer function, determine the parameters of the aging model function, and based on the aging model function and the determined parameters, determine an aging state of the battery cell.

Details of the above embodiments and further embodiments will be apparent from the following detailed description.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 schematically illustrates an example of a usage scenario of a rechargeable battery.

FIG. 2 schematically illustrates an example of a system for battery aging assessment according to an embodiment. FIG. 3A illustrates a graphical representation of an exemplary aging model function of a battery cell.

FIG. 3B illustrates a graphical representation of exemplary impedance data of a bat tery cell.

FIG. 4A shows a block diagram for schematically illustrating determination of a trans fer function in accordance with an embodiment.

FIG. 4B shows a block diagram for schematically illustrating usage of the transfer function for determining an aging state of a battery cell.

FIG. 5 shows a flowchart for schematically illustrating a method according to an em bodiment.

FIG. 6 shows a flowchart for schematically illustrating a further method according to an embodiment.

FIG. 7 schematically illustrates structures of a processor-based device according to an embodiment.

DETAILED DESCRIPTION

In the following, embodiments of the present disclosure will be described in more de tail with reference to the accompanying drawings. It is noted that the illustrated em bodiments constitute examples of implementing the principles underlying the present disclosure and have the purpose of conveying an understanding of these principles and functionalities which may be used for implementing these principles. It is noted that connections or couplings between components illustrated in the figures may cor respond to direct or indirect signal connections. Further, such connection may corre spond to a wire-based connection, to a wireless connection, or to a combination of a wire-based and wireless connection. Functional elements illustrated in the drawings or explained in the text may be implemented by hardware, software, or a combination of hardware and software.

The concepts illustrated herein aim at efficiently and accurately describing aging of battery cells by means of a mathematical aging model function. The aging model function depends on an age variable. The age variable may for example correspond to calendar time, e.g., counted in terms of hours or days. Alternatively, the age varia ble may correspond to a number of charging cycles of the battery cell. In view of the fact that in practical use battery cells are typically not fully discharged and often not fully charged, the charging cycles may for example be counted in terms of charging cycles in which the battery cell is discharged below a first threshold and then charged above a second threshold. In some scenarios, the age variable could also be based on a combination of calendar age and charging cycles. For example, the age variable could correspond to an effective age determined based on a weighted sum of the cal endar age and the number of charging cycles. In the following, the age variable will be denoted as t. The age function may be represented as:

SOH = l - a^ , (1 ) where SOH denotes a state of health value, t is the age variable, and a and z are pa rameters of the aging model function. Here, the parameter a corresponds to a multi plicative coefficient and is thus also denoted as a coefficient parameter. The parame ter z is an exponent applied to the age variable t and is thus also denoted as expo nent parameter. The illustrated concepts take into account that the parameters and a and z depend on operational conditions and may thus also vary between battery cells of identical design and over lifetime of the same battery cell. More specifically, the il lustrated concepts involve determining a transfer function which relates the parame ters and a and z to impendance data collected from battery cells. In particular, the transfer function may translate between a functional dependency of the parameters a and z on the operational conditions and a functional dependency of the parameters a and z on the impedance data.

In the illustrated concepts, it can be utilized that the impedance of the battery cell im plicitly reflects various information on the physical parameters of the battery cell, in cluding the evolution of such physical parameters. For example, the thickness of electrodes is typically related to the diffusion resistance, the electrolyte correlates with the ohmic resistivity, the surface coating, and calendering and electrolyte addi tives are related to charge throughput reaction, all of which typically have characteris tic effects on the impedance observed on the battery cell.

FIG. 1 schematically illustrates a typical usage scenario of a rechargeable battery 10. The rechargeable battery 10 may for example correspond to a Lithium-ion battery. However, it is noted that the illustrated concepts could also be applied to other types of rechargeable batteries. In the illustrated example, the rechargeable battery 10 drives equipment 20. The equipment 20 could for example be an electric motor, e.g., of a battery-electric vehicle or of a hybrid vehicle. In more generic terms, the equip ment 20 may be considered as an electric load driven by the rechargeable battery 10.

The rechargeable battery 10 includes a number of battery cells 12. Various numbers and designs of the battery cells 12 may be used. Depending on the design of the re chargeable battery 10, some of the battery cells 12 may be connected in series and/or some of the battery cells 12 may be connected in parallel. The battery cells 12 store electric energy to be supplied by the rechargeable battery 10.

As further illustrated, a management system (MS) 14 is coupled to the rechargeable battery 10. Although the rechargeable battery 10 and the management system 14 are illustrated as separate components, it is noted that at least some functionalities of the management system 14 could also be integrated in the rechargeable battery 10. The management system 14 may be implemented based on software executed by one or more processors. Alternatively or in addition, the management system 14 could be implemented based on an ASIC (Application Specific Integrated Circuit) and/or based on an FPGA (Field Programmable Gated Array). Communication between the re chargeable battery 10 and the management system 14 may for example be based on a bus system.

As further illustrated, a communication interface (IF) 16 is coupled to the manage ment system 14. Although the rechargeable battery 10 and the communication inter face 16 are illustrated as separate components, it is noted that at least some func tionalities of the communication interface 16 could also be integrated in the recharge able battery 10. In particular, both the management system 14 and the communica tion interface 16 could be part of the rechargeable battery 10. The communication in terface 16 may be used for making various data concerning operation or status of the rechargeable battery 10 externally available. Such data may for example be collected by measurements on the battery cells 12. Such data measured on the battery cells 12 may also include impedance data obtained by measuring the impedance Z of the battery cell 12, e.g., based on a response to a current pulse applied to the battery cell 12. Further, the data measured on the battery cells 12 may also include temperature, in the following denoted as T, state of charge, in the following denoted as SOC, cell current, in the following denoted as /, and depth of discharge, in the following de noted as DOD.

FIG. 2 illustrates a system which may be used for assessment of battery aging in ac cordance with the illustrated concepts. In particular, FIG. 2 illustrates a measurement system 100 and a plurality of rechargeable batteries 10 coupled to the measurement system 100. The rechargeable batteries 10 may each have a configuration as illus trated in FIG. 1 , and the coupling between the measurement system 100 and the re chargeable batteries 10 may be based on the above-mentioned communication inter face 16. It is noted that the rechargeable batteries 10 may typically be of the same or similar type, e.g., be based on the same design. The plurality of rechargeable batter ies may thus form a statistical ensemble for which it can be assumed that information evaluated from the data provided by a particular rechargeable battery 10 are also ap plicable to other rechargeable batteries 10 of the ensemble 10. In the illustrated con cepts, the measurement system 100 may in particular collect data form the recharge able batteries 10 which include the impedance data, temperature T, state of charge, cell current /, and depth of discharge DOD. The data may be collected over an accel erated aging cycle of the rechargeable batteries 10, thereby expediting collecting data which reflect aging of the rechargeable batteries 10 over a regular lifetime. The data collected by the measurement system 100 and/or information evaluated by the measurement system 100 based on the collected data may be stored in a database (DB) 110 coupled to the measurement system.

FIG: 3A illustrates an exemplary course of the aging model function. As can be seen, the state of health value SOH decreases as the age variable t increases. The charac teristic course of the aging model function may be attributed to functional dependen cies of the parameters a and z on the operating parameters of the considered battery cell 12, in particular a functional dependency on temperature T, state of charge, cell current /, and depth of discharge DOD. These functional dependencies may be ex pressed as: a = f (SOC, T, DOD, /) , and (2) z = g(SOC, T,DOD,I) . (3) These functional dependencies may be determined based on various known semi- emprical method, e.g., as described in “Development of a lifetime prediction model for lithium-ion batteries based on extended accelerated aging text data” by M. Ecker et al., Journal of Power Sources 215 (2012) 248-257, or in “From Accelerated Aging Tests to a Lifetime Prediction Model: Analyzing Lithium-Ion Batteries” by J. Schmalstieg et al., EVS27 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium, Barcelona, Spain, November 17-20, 2013. The determination of the functional dependencies may be based on the data which the measurement system 100 collects from the battery cells 10, e.g., as described in connection with Fig. 2.

The determination of the functional dependencies may be based on an analytical model of the battery cells 12, on machine learning (ML), or on a combination of an analytical model and machine learning.

FIG. 3B shows exemplary impedance data measured on the battery cells 12. More specifically, FIG. 3B illustrates the impedance Z in the complex plane. As can be seen, the impedance Z shows characteristics which reflect different operational con ditions of the battery cell 12, in the graphical representation of FIG. 3B denoted by re gions A, B, C, and D. The region A corresponds to the battery cell 12 operating under conditions of conductance and skin effect. The region B corresponds to the battery cell 12 operating under conditions of SEI (Solid Electrolyte Interface) growth. The re gion C corresponds to the battery cell 12 operating under conditions of charge trans fer. The region C corresponds to the battery cell 12 operating under conditions of dif fuse double layer formation. The region E corresponds to the battery cell 12 operat ing under conditions of mass transport. These contributions to the measured imped ance Z are in the following denoted as Z _ohm (corresponding to region A), Z _SEI (corre sponding to region B), Z _CT (corresponding to region C), Z _DL (corresponding to region D), and Z _ML (corresponding to region E). It is however noted that other contributions to the measured impedance could be considered as well.

Based on the data collected from the battery cells, also functional dependencies of the parameters a and z on the measured impedance data may be determined. These functional dependencies may be expressed as: ^{a =} f'(Z _ohm ,Z _SEI Z _CT ,Z _DL ,Z _ML ) _> ^an d (4) For the parameter a, the transfer function can thus be determined as:

For the parameter z, the transfer function can thus be determined as: g'( ^z ohm’ ^Z SEI, ^z CT’ ^Z DL’ ^Z ML ) g(SOC,T,DOD,I ) (7)

Flere, it is noted that H _a and H _z may be regarded as components of a multi-dimen sional transfer function for both parameters a and z. The transfer function compo nents H _a and H _z may each be determined as an n-th order complex polynom. The or der n may depend on the functional dependencies of the parameters a and z. The calculation of the transfer function components may for example be based on an opti mization algorithm which balances complexity of the transfer function against accu racy of translating between on the one hand the functional dependencies /, and g and, on the other hand, the functional dependencies and g'. The transfer function components H _a and H _z may each be calculated in time domain or in frequency do main. The transfer function may be stored in terms of a set of complex coefficients. For example, the measurement system 100 may store the transfer function in the da tabase 110.

FIG. 4A shows a block diagram which schematically illustrates the above-described functionalities for determining the transfer function. The functionalities illustrated in FIG. 4A may be provided by the measurement system.

Block 410 is responsible for learning the parameters of the aging model function from first measurement data M1. In particular, block 410 is configured to learn the functional dependencies of the parameters a and z on the temperature T, state of charge SOC, cell current /, and depth of discharge DOD as observed over an aging cycle of the battery cells 12, typically over aging cycles of multiple battery cells 12 of an ensemble. Further, block 410 is configured to learn the functional dependencies of the parameters a and z on the impedance data as observed over an aging cycle of the battery cells 12, typically over aging cycles of multiple battery cells 12 of an ensemble. Block 410 provides the learnt parameters, in particular the learnt functional dependencies to block 420. Block 420 is responsible for determining the transfer function from the learnt functional dependencies. For this purpose, block 420 may for example apply relations (6) and (7). Block 420 outputs the learn transfer function, e.g., in terms of a set of complex coefficients. The transfer function may be stored for later use when assessing the ag ing state of a certain battery cell 12.

FIG. 4B shows a block diagram which schematically illustrates functionalities for ap plying the transfer function when assessing the aging state of a certain battery cell 12. The functionalities illustrated in FIG. 4B may be provided by a management sys tem of a rechargeable battery 10, such as the above-mentioned management system 14. Alternatively, the functionalities illustrated in FIG. 4B may be provided by a dedi cated testing tool.

Block 430 is responsible for determining the parameters of the aging model function using measurement data M2 and the previously learnt transfer function. The measure ment data include impedance data measured on the battery cell 12 to be assessed. By applying the inverse transfer function to the functional dependency of the parame ters a and z on the measured impedance data, block 430 can reconstruct the functional dependency of the parameters a and z on measured state variables S, in particular on temperature T, state of charge SOC, cell current /, and depth of discharge DOD. Block 430 outputs the reconstructed parameters to block 440.

Block 440 is responsible for applying the aging model function based on the recon structed parameters. In particular, block 440 is configured to receive measured state variables and to apply the functional dependency on temperature T, state of charge SOC, cell current /, and depth of discharge DOD, as reconstructed based on the trans fer function, to calculate values of the parameters a and z which correspond to the measured state variables S. As a result, the current aging state of the battery cell 12 can be assessed in an efficient manner, using measured impedance data and the cur rently measured state variables S.

FIG. 5 shows a flowchart for schematically illustrating a method which can be used for implementing the above concepts. The method of FIG. 5 could for example be performed by a measurement system, such as the above-mentioned measurement system 100. At step 510, impedance data are collected. The impedance data may be collected for different values of the at least one state variable over an aging cycle of the at least one battery cell. The at least one state variable may include one or more of: tempera ture, state of charge, cell current, and depth of discharge, as observed over the aging cycle of the battery cell.

At step 520, parameters of an aging model function are determined. The aging model function describes aging of the at least one battery cell. The aging model function may for example be expressed as explained in connection with relation (1 ). Accord ingly, the aging model function may be a function of an age variable, the parameters of the aging model function may include a coefficient parameter and an exponent pa rameter, and the aging model function may multiply the age variable, raised to the power of the exponent parameter, by the coefficient parameter. The age variable may correspond to a calendar age of the battery cell or to a number of charging cy cles performed on the battery cell. The parameters of the aging model may each de pend on at least one state variable, and the at least one state variable may include one or more of: temperature, state of charge, cell current, and depth of discharge of the battery cell. The impedance data collected at step 510 may correspond to differ ent values of the at least one state variable on which the parameters depend.

The parameters of the aging model function may be determined based on an analyti cal model and/or based on machine learning.

More specifically, step 520 may involve determining a functional dependency of the parameters on the at least one state variable and determining a functional depend ency of the parameters on the impedance data.

At step 530, a transfer function is determined which relates the impedance data to the parameters of the aging model function. The transfer function may include at least one n-th order complex polynomial, with n being equal to or larger than 2. The transfer function may then be stored, e.g., in a database. The transfer function may in particular be determined to translate between a functional dependency of the param eters on the at least one state variable and a functional dependency of the parame ters on the impedance data. FIG. 6 shows a flowchart for schematically illustrating a method which can be used for implementing the above concepts. The method of FIG. 6 could for example be performed by a management system of a rechargeable battery, such as the above- mentioned management system 14 or by a testing tool for rechargeable batteries.

At step 610, impedance data are measured. The impedance data may be measured for different values of the at least one state variable. The at least one state variable may include one or more of: temperature, state of charge, cell current, and depth of discharge, as observed on the battery cell. The impedance data may for example be measured by a management system of a rechargeable battery, e.g., using one or more internal sensors of the rechargeable battery. Alternatively, the impedance data could also be measured using external sensors, e.g., of a testing tool.

At step 620, a transfer function is acquired, e.g., from a database. The transfer func tion relates the impedance data to parameters of an aging model function.

The aging model function describes aging of the battery cell. The aging model func tion may for example be expressed as explained in connection with relation (1 ). Ac cordingly, the aging model function may be a function of an age variable, the param eters of the aging model function may include a coefficient parameter and an expo nent parameter, and the aging model function may multiply the age variable, raised to the power of the exponent parameter, by the coefficient parameter. The age varia ble may correspond to a calendar age of the battery cell or to a number of charging cycles performed on the battery cell. The parameters of the aging model may each depend on at least one state variable, and the at least one state variable may include one or more of: temperature, state of charge, cell current, and depth of discharge of the battery cell.

The transfer function may include at least one n-th order complex polynomial, with n being equal to or larger than 2. The transfer function may in particular be determined to translate between a functional dependency of the parameters on the at least one state variable and a functional dependency of the parameters on the impedance data.

At step 630, parameters of the aging model function are determined based on the im pedance data measured at step 610 and based on the transfer function acquired at step 620. As mentioned above, the parameters of the aging model function may each depend on at least one state variable. Step 630 may then further involve that the pa rameters of the aging model function are further determined based on measuring the at least one state variable.

At step 640, an aging state of the battery cell is determined based on the aging model function and the parameters determined at step 630. For example, the aging state may be determined in terms of a state of health value.

FIG. 7 schematically illustrates structures of a device 70 which may be used for im plementing the illustrated concepts. The device 70 may for example be used for im plementing the measurement system 100, or for implementing a part of the measure ment system 100. Further, the device 70 could be used for implementing compo nents associated with a rechargeable battery 10, such as the above-mentioned man agement system 14 and communication interface 16. Further, the device 70 could be used for implementing a testing tool for rechargeable batteries, or a part of such test ing tool.

As illustrated, the device 70 includes one or more processors 71 and a memory 72 coupled to the processor(s) 71 . The memory 72 may include a Read-Only-Memory (ROM), e.g., a flash ROM, a Random Access Memory (RAM), e.g., a Dynamic RAM (DRAM) or Static RAM (SRAM), a mass storage, e.g., a hard disk or solid state disk, or the like. As illustrated, the memory 72 may include software 73 and/or firmware 74. The memory 72 may include suitably configured program code to be executed by the processor(s) 71 so as to implement the above-described functionalities for as sessing the aging state of battery cells. For example, when executed by the proces sors), the program code could cause the device 70 to perform the method of FIG. 5 and/or the method of FIG. 6. As further illustrated, the device 71 may include a com munication interface 75, e.g., to be used for output or input of various data. The pro cessors) 71 , the memory 72, and the interface 75 could be coupled by one or more internal bus systems of the device 70. In some scenarios, the teachings of the pre sent disclosure may also be implemented in the form of a computer program for im plementing functionalities of the device 70, e.g., in the form of a physical medium storing the program code and/or other data to be stored in the memory 72 or by mak ing the program code available for download or by streaming. As mentioned above, such program code could cause the device 70 to perform the method of FIG. 5 and/or the method of FIG. 6.

As can be seen from the above, the illustrated concepts allow for efficiently and pre cisely assessing the aging state of battery cells. As compared to conventional aging tests, the impedance of the battery cell can be measured quicker and based on an ensemble of fewer battery cells. The impedance can be measured time and/or in fre quency domain, using various kinds of existing sensors and measurement setups. Once the transfer function has been determined for a certain type of battery cell, the transfer function and impedance data measured on an unknown battery cell of the same type can be used to quickly and efficiently assess the aging state of the battery cell.

It is to be understood that the examples and embodiments as explained above are merely illustrative and susceptible to various modifications. For example, the illus trated concepts may be applied in connection with various kinds of rechargeable bat- tery technology, without limitation to Lithium-ion batteries. Further, the concepts may be implemented in various kinds of devices. Moreover, it is to be understood that the above concepts may be implemented by using correspondingly designed software to be executed by one or more processors of an existing device or apparatus, or by us ing dedicated device hardware. Further, it should be noted that the illustrated devices may each be implemented as a single device or as a system of multiple interacting devices or modules.