System Simulation:System Simulation in Communication System Design.

System Simulation in Communication System Design

Introduction

Telecommunication systems are characterized frequently by a large complexity and variety of their subsystems and components. The different analysis and simulation tasks are just as varied [13.38], [13.45]. Some examples are shown in table 13.2, arranged in accordance with the degree of abstraction of their description. The design tasks reach from the specification engineering of global communication networks down to microelectronic implementations of analog and digital circuits.

For simulation purposes at first it must be distinguished between system and circuit design. At the circuit level we have to differentiate addition- ally between logic and electrical level, or, corresponding to the type of signals, between digital and analog. Very efficient simulation tools are available for these individual design tasks. Without any completeness or a valuation, some of them are mentioned:

• COMNET III, Op Net and BONES for the simulation of communication nets;

• SDT (with the modeling language SDL) for very abstract descriptions of hardware/software systems;

• Matlab/Simulink, Math Cad for signal processing algorithms (described as formulas);

• COSSAP and CoCentric System Studio [13.69], SPW [13.15], Matlab/Simulink, DSPStation [13.51], TESLA and Ptolemy [13.12] for a block-oriented system simulation (the formulas are transferred partly into block diagrams and partly into textual equations);

• SpectreRF [13.15], [13.43] for analog systems and circuits (particularly in the high frequency domain);

• ADS [13.1] for circuit and system simulation, for analog as well as digital signal processing;

• SWITCAP, SCAP, and TUSCA for switched capacitor circuits.

The traditional simulation at gate and transistor circuit level is executed with the simulators mentioned in the previous sections, thus, e.g.:

• VERILOG, Leapfrog, LSIM and VSS for digital system and gate simulation;

• SPICE, ELDO, SABER, SPECTRE and MDS for analog circuits.

Additionally, mixed-signal simulators are increasingly used, above all if they have HDLs for behavioral modeling.

Even in the design of complex communication systems, a global view over more than one abstraction level is necessary and all design phases (from concept to implementation) have to be included in the design methodology. But there are different deficiencies:

• During the transition from the system to the circuit design, the description methods and languages, models and tools (e.g., the simulators) must usually be changed, therefore, a common system and circuit design is hardly possible.

• The simultaneous development of hardware and software (HW/SW co-design) as well as the inclusion of already existing real hardware (e.g., DSPs or FPGAs) into the simulation of the whole system or its emulation is not sufficiently supported.

Improved possibilities for HW/SW co-simulation will be offered by the new description languages SystemC and SystemC-AMS [13.84], [13.85], 13.86].

It is an aim of the software providers to reduce the gap between system and circuit design. Examples are particularly the simulation systems SPECTRE-RF and ADS, which already support

circuit and system simulation of communication systems. This is realized by multi-level simulation and compatible model libraries at both levels. If there is, e.g., a subsystem ‘mixer’, then there exist an abstract system-level model ‘mixer’ as well as a corresponding low-level model in form of a transistor circuit. Both models realize the behavior of a mixer but with different accuracy and simulation time. The parameters of the system model ‘mixer’ can be gained by simulation of the transistor circuit almost automatically. In the simulation of a system both models can be exchanged with each other.

In the following two typical simulation tasks in communication engineering are to be regarded more in detail: the bit-true simulation of digital signal processing algorithms and the mixed-signal simulation based on simulator coupling.

Simulation of Signal Processing Algorithms

A simple signal processing system is a digital filter. The transfer function of a FIR filter of 3rd order is:

x(k) is the input signal of the filter at the time point k; x(k−1), x(k−2) and x(k−3) are the earlier input signal values delayed by 1, 2, or 3 clock cycles, respectively, y(k) is the output signal, and the filter coefficients are C0 to C3. Such an algorithm can be simulated easily with any tool (e.g., Matlab or a self-written C program). Signal values and coefficients are usually defined as floating-point numbers of high accuracy (for the sake of comfort or to examine the filter function only basically). But the final technical implementation will usually come with a fixed-point or an integer arithmetic to reduce the hardware costs or the computing time, or both. These different number representations may have large influences on the filter characteristic and should be examined by simulation care- fully.

Bit-true simulation means that the variables and operators in the algorithms are regarded exactly in the same way, as they will be used later in the circuit implementation. The bit-true simulation is prepared and realized by:

• the definition of the fixed-point, integer or floating-point number format;

• the number of bits to be used for each signal;

• the sign handling (e.g., a one’s or two’s complement representation);

• in connection with the operators: the number format of intermediate results and perhaps, followed by a rounding procedure;

• the overflow handling and other error handling mechanisms in case of arithmetic problems.

It is not of principal importance whether the im- plementation of the algorithms takes place later

• as software on a digital signal processor (DSP) or

• as hardware, consisting of arithmetic-logical units (ALUs), registers, and gate logic.

The simulation models for both kinds of signal processing mechanisms must be adaptable to it.

For this task simulators like COSSAP, SPW, and also Matlab (especially in connection with the Communication Toolbox) can be used. In fig.

13.4 a COSSAP representation is shown, where the formula was interpreted as a block diagram. This diagram was sketched with the schematic entry tool of the simulator. The three applied block types correspond to the operators in the filter function and may be found in the COSSAP model library:

• DELAYB: Signal delay with one clock cycle;

• MULTC_FXP: Multiplication of a signal value by a constant;

• ADD_FXP: Addition of two signals.

These models realize a fixed-point arithmetic in which the word length, the number of the integer digits, as well as rounding procedures and overflow handling can be determined. In this way numerical effects can be examined. For the simulation of the whole filter additional models are necessary which deliver or convert the test signals and output the results. In the example the elements DIRAC_GEN (pulse generator), R2FXP and FXP2R (converter between real and fixed- point signals) and DMPNR_AC (graphical output) are used. They also belong to the library of the simulator.

The efficiency of a system simulator is particularly determined by the efficiency of the simulation method and by the content and quality of its model libraries, too. Frequently the design task consists of the realization of a certain subsystem or module. To verify its design the interfaces to the entire system also have to be considered. In the ideal case these interfaces and the rest of the system can be described completely with sufficient accuracy by simulator models, so that a complete test environment for the module can be created with reasonable effort.

SPW [13.15] and COSSAP [13.69] are system simulators with very large model libraries specialized in communication technology. SPW contains, e.g., models for:

• basic mathematical operations (addition, mult plication, division) for fixed- or floating-point numbers;

• digital filters (high-pass, low-pass and band pass filters with Butterworth, Bessel, or other characteristics);

• adaptive filters (LMS and RLS algorithm);

• modulators and demodulators (e.g., PSK, QAM,GMSK, FM);

• coder and decoder (e.g., BCH, convolutional, Reed-Solomon, Viterbi);

• signal generators (e.g., white noise, sine waves,

modulated carrier, unit impulse);

• result output and post-processing (FFT, eye and scatter diagram display in the signal calculator).

Similar models are also offered by COSSAP and the Communication Toolbox of Matlab/Simulink [13.50]. In each case there are very extensive libraries with some hundreds of models. Beyond that the simulator providers offer more and more model libraries which are adapted exactly to a certain communication standard. They must usually be bought optionally. With SPW are, e.g., libraries for GSM, ADSL and Wideband CDMA.

The simulation efficiency is also influenced by the simulation algorithms. SPW and Matlab operate like logic simulators for clocked systems: in each clock cycle the input signals of the blocks are used for the calculation of their output signals which may be used in the next clock cycle. In COSSAP another simulation principle is implemented, which will be presented briefly. COSSAP operates as a data driven simulator. The sys- tem model consists of interconnected blocks (fig. 13.4) for which behavioral models exist in the library. At each block the interconnection terminals are uniquely partitioned into inputs and outputs. The individual blocks operate autonomously in the sense that they always calculate the maximally possible number of output data according to the number of input signal values actually available. The output signal values are then passed to the successor blocks. There is no global view on the system and no supervisor algorithm, no explicit clock pulses and not even a time. Instead, each block operates if as many data as necessary are available at its input. The user must interpret the data sequences in a time frame. This sounds some- what complicated, but it leads to a very fast simulation (particularly in systems without feedback loops or with large delays in feedback loops). The relations between the input and output signals are described as C procedures in a COSSAP typical way. For the bit-true simulation, many operators are pre-defined as blocks and do not have to be programmed by the user.

Occasionally the designers of digital circuits do not have access to one of the specialized communication engineering simulators mentioned above. One reason could be the prices which are quite high, corresponding to the large power of these simulators. Then the use of logic simulators re- mains as an alternative, but these logic simulators must be extended by libraries for signal processing components. The mathematical signal processing algorithms must be formulated in the modeling language of the simulator (or in its graphical input mode as block diagrams). In [13.25] such a library for VHDL simulators is described. It contains the following model classes (comparable to a subset of the larger libraries in COSSAP and SPW):

• amplifiers;

• generators: function tables for deterministic time functions, random bit sequences;

• converters: A/D, D/A, sample-and-hold elements; pulse-shaping elements: GAUSS, cos**2;

• coder/decoder: binary, ternary, trellis; scrambler/de-scrambler;

• modulators/demodulators: FSK, ASK/PSK, QAM; AM, PM, FM;

• filters: digital (FIR, IIR) and analog; adaptive filters;

• communication channels with and without random disturbances.

Blocks for the mathematical basic functions:

• ADD, SUB, MUL, DIV;

• ABS, INV, SQR, SQRT, POW;

• EXP, EXP2, EXP10; LN, LD, LG;

• SIN, COS, TAN, ASIN, ACOS, ATAN; SINH,COSH, TANH;

• FALT, SUM, DIFF (Basic algorithms of signal processing);

• D_TO_FIX, D_TO_FL, Conversion functions

(conversion of digital signals into fixed-point and floating-point numbers).

The models of the basic mathematical functions are supplied both as blocks, which can be inserted into a circuit, and as C functions, which the user can include into own behavioral models. Block models are delivered for operations with floating- point numbers and parameterizeable fixed-point numbers, C functions only for parameterizeable fixed-point numbers. Similar libraries are also of- fered as part of commercial design systems (e.g., in the Communication Toolbox of Matlab/Simulink, in the Telecom Libraries of Mentor Graphics for

the mixed-signal simulator ELDO, and of Analogy for the mixed-signal simulator Saber), but they are not programmed in VHDL. The use of such models for communication systems in connection with general-purpose VHDL simulators is not only a ‘less than ideal solution’ if no better simulators are available. It also offers the advantage that the signal processing algorithms can be simulated together with the digital system parts – a very important aspect within an overall system simulation!

The bit-true simulation was used in the design of an echo canceller for a telephone system [13.42]. The main problem of a full-duplex transfer over a two-wire line is the cross modulation of the transmitted signal on the received signal in the hybrid four-wire terminating circuit. In fig. 13.5 the communication system with two transceivers (A and B) and a channel is shown.

The non-ideal impedance matching between the hybrid four-wire terminating circuit and the trans- mission line is the reason that a part (the ‘echo’) of the transmitted signal of station A is fed back into its own receiver. The echo canceller estimates the echo to be expected and then it may be subtracted from the received signal of the station B. Because the echo canceller in each device must be adapted to the concrete circuit and transmission line, an adaptive filter is used. In the adaptation phase of the echo canceller the transmitted signal of the station B is equal to zero, therefore it is sufficient in the following to consider only one transceiver (subsystem A in the fig. 13.5). For estimating the echo different methods of adaptive digital signal processing are available, which differ according to the implementation effort and their numerical accuracy. The resulting accuracy depends both on the applied algorithm and on the number type and word length chosen for the arithmetic processing unit in the target hardware (DSP, ALU and gate logic). These hardware resources define the limit frequency of the communication system. All these effects can be determined by the bit-true system simulation.

For the verification of the echo canceller a simplified system model (fig. 13.6) is used. The echo arising in the hybrid four-wire terminating circuit is modeled by a transversal filter. A transversal filter structure was also chosen for the echo canceller and the filter coefficients cN are determined according to the signum algorithm. The stimulus signal values x(k) were assumed to be white Gaussian noise. The results of the system simulation (fig. 13.7) show the influence of the fixed-point arithmetic on the behavior of the echo canceller. With a favorably selected number format (a) one can obtain a well-compensated echo. After a transient time of approximately 15 ms the filter has been adapted sufficiently well to the interface transceiver channel. With improper parameter se- lection (b) overflow effects impair the function of the echo canceller.

Frequently the signal processing algorithms which are to be implemented are formulated in such a way that they can be simulated completely by system simulators like COSSAP and SPW. That is the case whenever

• the hardware operates clocked;

• the Z-transform is used to transform signals

and filter characteristics between time and frequency domain; or

• there is an approximate transformation of ordinary differential equations into difference equations (to be solved by the system simulator).

That is, however, not the case if the nonlinear behavior of transistors and the pulse distortions on transmission lines have to be analyzed very exactly since these effects influence the system performance substantially. Figure 13.8 shows symbolically a communication system for which multi- level, mixed-signal modeling and simulation are necessary to verify the correctness of the system.

It should be possible to carry out a mixed-signal simulation with PSpice (or comparable simulators) as described in chapter 12. But these simulators are focused on transistor circuits with analog and digital functionality. Most communication systems contain very large circuits to realize the signal processing and it is not possible to simulate these circuits at transistor level. Higher level mod- els for system simulation are necessary. On the other hand, it is not possible to simulate transistor circuits with Spice-like accuracy in COSSAP, Co- Centric System Studio, or SPW. Different methods are under investigation to realize a true multi- level mixed-signal simulation of communication systems.

A first approach is the development of more accurate component and subsystem models qualified for system simulators. This is increasingly supported by software implemented in widely used CAD systems. Cadence offered sophisticated models with many parameters (so-called ‘k- models’) for the simulator SPW. These models describe the dynamic linear and the static nonlinear behavior of analog subsystems (usually transistor circuits) very precisely [13.31]. But the parameter adjustment of the models is very complicated and a complex task which has to be supported by special software (‘model generators’, see fig. 13.9). This generator software needs as input those signals which are calculated for the nonlinear transistor circuits with an analog circuit simulator (here SpectreRF). With the system simulator SPW the whole system performance can be calculated at higher abstraction level with reduced accuracy but with a very high simulation speed.

An alternative approach is the use of analog simulators for transistor circuits, which were extended by more abstract system models for digital signal processing tasks, as specified above. This joint simulation at circuit and system level (multi-level simulation) was applied in the design of an ADR satellite broadcasting receiver (ASTRA Digital Radio) [13.11]. With this method the application

of COSSAP or SPW could be avoided which can- not simulate transistor circuits with such a SPICE- like accuracy as was needed in the design tasks. Figure 13.10 shows the block diagram of the entire receiver.

The influence of the properties of the FM de- modulator (which was, therefore, modeled as a transistor circuit) on the bit error rate (BER) of the disturbed data transmission has to be investigated. For the simplification of the modeling and for saving computing time, MUSICAM coding and the error protection in the digital channels were not considered in the model. A binary pseudo-random sequence was used to determine the bit error rate of the ADR transmission. Figure 13.11 shows the model of the entire ADR system and the different sampling rates.

For a pure system simulation the simulation of the high frequency circuit parts (from the FM modulator to the FM demodulator) can be carried out in the baseband. Instead of the frequency-modulated carrier of 489.5 MHz, the magnitude and phase of the FM signal are transmitted as a complex signal (with ‘carrier frequency equal to 0 Hz’). In this way the very short sampling time (0.5 ns) of this signal can be avoided in the simulation and the simulation could be accelerated drastically.

A baseband modeling of the RF module is not possible in the favored multi-level simulation, since the FM demodulator processes directly the

frequency-modulated signal, i.e., the modulated carrier in the passband. In order to reduce the computing time, nevertheless the system was modeled as a multi-rate system. The signals in the system are divided into three classes according to their typical frequencies. In the same way the system is partitioned into subsystems with appropriate sampling rates. Intersection points are determined by the modulators and demodulators which realize the transition to other frequency ranges and thus to other sampling rates. Figure 13.11 shows the model of the entire ADR system modeled according to these considerations.

To determine the influence of the FM demodulator on the system performance, a transistor circuit model has been inserted into the system model. Figure 13.12 shows an implementation version of the FM demodulator. By the joint simulation of the transistor circuit with the other, more abstract, modeled subsystems the influence of circuit parameters on the bit error rate can be  determined. The evaluation of the transmission performance results, e.g., from the inspection of ‘scatter diagrams’ or ‘constellation diagrams’ (fig. 13.13). For the QPSK transmission method which had to be examined, the received signal values are represented as points in quadrant fields. In an ideal data communication without distortion, exactly one point is located in each quadrant, so that a unique decision on the received signal value is possible. In the case of a disturbed signal transmission, ‘clouds’ are displayed in the scatter diagram. A doubtfree detection of the signal values is possible if these clouds are clearly separated from each other. In fig. 13.13 it is shown that the characteristics of the disturbed signal transmission are very similar with all three selected modeling accuracies. So it is allowed to choose the most simple kind of modeling related to the smallest simulation time and still sufficient accuracy.

The large computing times may not be kept secret, however. A realistic determination of the bit error rates requires the transmission of at least 105 bits for each ADR channel and thus a simulation of approximately 40 ms real time. Thus about 8 · 1010 simulation steps would have to be executed because of the high clock rate of the FM transmission. This is also not possible with the multi-rate modeling in reasonable simulation times. After further model modifications finally the following computing times were measured:

• pure system simulation with the analog simulator: 1 hour 15 minutes;

• multi-level simulation: 45 hours.

This illustrates why the application of a multi- level mixed-signal simulation for such complex functionalities can be recommended only if the required accuracy cannot be gained by other kinds of system verification.

If both ways

• new and highly accurate models for a system simulator;

• extension of a circuit simulator by models at system level

are not possible (simulation and modeling software may not be available, transistor circuits may not be simulated sufficiently accurately at system level, there is a large part of digital control logic, ... ), simulator coupling has to be considered.

Simulator Coupling

For the realization of the multi-level simulation (see fig. 13.8) simulator couplings were developed (fig. 13.14). Hereby the most appropriate simulator can be used for each subsystem (at algorithmic, logic, or transistor level). For the correct interaction of the simulators a special coupling software is necessary. It

• synchronizes the cooperation of the simulators (e.g., it must be awaited on the slowest simulator);

• executes the necessary data conversion (e.g., between real variables at the electrical level, Boolean variables for modeling the digital gate circuits, integer or fixed-point variables at the algorithmic level); and

• organizes the data transfer between the simulators, which can also reside on different computers in a local or global network.

Different operating system services can be used for the software coupling: files, sockets, pipes, TCP/IP, . . . up to pvm (parallel virtual machine) or Internet based communication tools.

Only for some simulators is such a coupling software offered commercially (e.g., for Saber- Verilog, Spectre-Verilog, COSSAP-VSS). An experienced programmer often can develop this coupling software, but the principal suitability of the involved simulators must be presupposed Mostly this is given if a C interface for modeling new elements exists for the simulator. This interface can be used frequently for simulator coupling too. In this way also was the coupling shown in fig. 13.14 implemented [13.26]. It is a border case of simulator coupling if additional autonomous simulation algorithms are included into a communication system simulator (e.g., COSSAP) as subroutines [13.61].

An example will demonstrate the application of simulator coupling. In fig. 13.15 the block diagram of a SLICOFI circuit (Subscriber Line Interface Circuit with CODEC Filter – an Infineon product) is shown. It is the link between analog telephone signals on a two-wire line and the PCM transmission in digital nets. Special modeling problems are:

• analog modeling of the high voltage section of the SLIC (voltage peaks up to 160 V are to be processed);

• high clock rate in the digital filter part SICOFI (over-sampling);

• multi-rate circuits (decimation and interpolation filters);

• word length effects in the digital signal processing (some DSPs realize filter functionality);

• transient simulation, AC and DC analysis have to be carried out.

Figure 13.16 shows a part of the simulation model for transient simulation and the behavior in the frequency domain (AC simulation). A separate simulation of the individual subsystems does not enable a complete verification, since thereby, e.g., the permanent adaptation of some digital filters to the analog voltage-current relations on the trans- mission lines can not be simulated. By the application of the three coupled simulators COSSAP, Saber, and (alternatively) Leapfrog or Verilog (seefig. 13.14) even those effects can be simulated  which can be explained only by the interaction of the subsystems. The computing time was in the range of some hours and resulted particularly from the analog simulation at transistor level, necessary for handling non-linear transistors and linear trans- mission line effects.

Similarly large computing times result frequently from the coupling of analog and digital simulators to realize a mixed-signal system simulation. It is hoped that the new VHDL-AMS and Verilog-

AMS simulators can reduce these computing time problems, since they will probably consist of a closer union of highly efficient analog and digital simulators. Their performance could be better than a self-programmed coupling via C interfaces and a resulting large communication overhead.

System Simulation in Microsystems Technology Requirements to the Simulation Microsystems technology and the design of micro- electro-mechanical systems (MEMS) are emerging engineering disciplines which increasingly win importance for electronic engineers also [13.27], [13.28], [13.57]. Airbag sensors in automobiles, which are connected with other sensors and control units by field buses, represent just one (but typical) example. Sensors and actuators in automatic control systems and in medicine (example:

the implanted insulin pump) are mostly combined with electronic signal processing, partly also with wireless data transmission. The functional principles of micro-mechanical sensors and actuators are closely connected with electrical phenomena, e.g., for determining the mechanical deflection by capacitance measurement and for controlling the position of a mechanical component by applied voltages. Because of

• the participation of electrical phenomena;

• the production of many classes of MEMS with micro-electronic technologies (e.g., the standard CMOS fabrication process);

• the efficiency of EDA tools in computer-aided design of complex and also heterogeneous systems;

it is worthwhile examining the applicability of system simulation approaches, established in electronics, also in microsystems engineering.

At a first glance the modeling strategy adapted best to the MEMS design problems is a description as spatially distributed systems. Bending beams, membranes and plates, pipes, or electrical fields between moving electrodes are characterized by their geometrical dimensions. They can be described mathematically by partial differential equations (PDEs) which are to be solved numerically by discretization in space and time. Simulation with the methods of the FEM (Finite Element Method) [13.14], [Z-T94], the FDM (Finite Difference Method), the BEM (Boundary Element Method) and others is very accurate but needs also extremely long computing time. After discretization tens or hundreds of thousands of equations or ordinary differential equations (ODE) must be solved.

Widely used FEM simulators with large application areas are ANSYS [13.4], COSMOS/M, MSC/NASTRAN, CAPA, ABAQUS, ALGOR, INERTIA and RASNA.

Other simulators are specialized in magnetic field calculations (e.g., MAFIA) or fluidic simulation (FLOTRAN). In the microsystems technology the interaction of effects in different physical domains (mechanics, electronics, optics, fluidics, ...) very often has to be investigated. Many FEM simulators cannot handle such complex systems or need unacceptable large computing time. For the simulation of such complex systems basically two ways exist, which are sketched in fig. 13.17.

An important method is the simplification of the descriptions at the ‘lower’ levels by abstraction and thus the transition to ‘higher’ levels by suitable modeling. Also the transformation of models at the same abstraction level from one physical domain into another belongs to this method. Thus, e.g., mechanical networks can be transformed into electrical networks and then analyzed with a circuit simulator. The model of the entire system can be simulated with a network simulator if all subsystems can be treated in this way.

Continuous-time and continuous-value processes dominate in micro-system engineering. Therefore,

• analog simulators such as Matlab/Simulink and MatrixX (for systems, which can be described by block diagrams); and

• circuit simulators such as Spice, Saber or ELDO (using analogy relations between the different physical domains)

are frequently used as system simulators. Also simulators from the mechatronics and mechanics domain:

ADAMS, DYMOLA-MBSDYM, MEDYNA, NEWEUL, ITI-SIM [13.36], SIMPLORER [13.64], . . .

can be applied, but they are not very common in the EDA world and therefore not considered any further here.

The other method is simulator coupling, once again. It can be recommended whenever the modeling task is too complex or leads to inaccurate results. Sometimes it is just the completely different physical domains of the subsystems and the experiences of the designers in handling special simulators which let the simulator coupling appear as the most obvious form of an interdisciplinary mode of operation.

Modeling for MEMS Design

The goal is the description of the phenomena in such a way that the multi-domain problems can be analyzed with only one simulator (the simulator coupling as an alternative is regarded in the next paragraph). Figure 13.18 gives an overview of modeling methods used at present or are investigated in research projects in the micro- system engineering [13.59], [13.60], [13.62], [13.63], [13.64], [13.78], [13.81].

Two of these methods are to be presented here in more detail:

• modeling with generalized Kirchhoffian net-works;

• model export from FEM simulators and order reduction.

The assumption that the ordinary differential equations describing a microsystem are easy to formulate, and then simulators for general continuous systems (Matlab/Simulink, MatrixX...) can be used, is unfortunately often not fulfilled. The reason for this is that these systems are usually conservative systems. Therefore the use of net- work models (section 13.1.2) emphasizes itself.

Modeling with Generalized Networks

The key to the understanding of network applications as models of non-electrical systems (not only for microsystems technology, but, e.g., also for mechatronics), may be found in the concepts of ‘through quantity’, ‘across quantity’, and ‘generalized Kirchhoff laws’.

By networks we understand such systems in electronics which consist of elements (one-ports, multi-poles) and connections. Voltages and cur- rents are assigned to the terminals of the elements and to the connections. Conservation laws apply to the voltages and currents, i.e., Kirchhoff’s mesh and node law (or current and voltage law):

• Kirchhoff’s voltage law, KVL: The sum of all voltage drops over the elements in a closed mesh is zero;

• Kirchhoff’s current law, KCL: The sum of all currents flowing into a node is zero.

This concept can be extended to conservative non- electrical systems. The following generalizations are necessary:

Instead of currents, flow quantities are considered (e.g., strength in mechanics, flow rate in fluidics). A flow quantity is measured at one place, therefore it is also called a 1-point quantity or a through quantity.

Instead of voltages, difference quantities are considered (e.g., displacements in mechanics, pressure differences in fluidic systems). A difference quantity is always measured between two points, therefore it is also called a 2-point quantity or an across quantity.

For the introduced flow and difference quantities the generalized mesh and node laws apply in the non-electrical systems too. These conservation laws are well known from physics, e.g., from New- ton’s mechanics, and can be brought into the form of Kirchhoff’s law.

The relations between flow quantities and difference quantities at an element are determined by the model equations of the element (network-element relations).

Flow and difference quantities at the terminals of the elements and on the connections between the elements can be multi-dimensional (e.g., forces and moments in three-dimensional space).

In fig. 13.19 these concepts are summarized. Since electrical networks belong to generalized networks too, simulators for electrical circuits can be used very effectively for the analysis of non-electrical systems. In table 13.3 the most important one-port elements in generalized networks are represented. In the treatment of coupled phenomena, addition- ally the interactions between different physical domains are to be modeled. Transformers and gyrators are used for the transformation between

the domains. The relationships between the net- works in different physical domains are also called analogy relations (table 13.3). The application of the concept of generalized networks for the simulation of non-electrical systems has a long and successful tradition and is therefore promising success for micro-system engineering [13.28], [13.40], [13.46], [13.58], [13.73], [13.83].

The applicability of the network concept is not only based on the use of formal analogy relations, because, e.g., the elements in the different physical domains are described by ordinary differential equations of similar structure. Above all it bases on the fundamental physical principles of

• the hierarchical decomposability of a system into components (or, more general, into subsystems);

• the description of the ‘terminal behavior’ of the components (in a special form as in electrical four-pole theory, well-known to electrical engineers); and

• the validity of conservation laws for the flow quantities and the across quantities at the inter- faces between the components.

Here also a relation is to be seen with object- oriented modeling [13.16].

Particularly important in microsystems engineer- ing is another modeling step which leads from spatially distributed systems to networks with spatially concentrated elements. Mathematically this spatial discretization corresponds to the transition from partial differential equations (PDE) to ordinary differential equations (ODE). A further discretization in the time domain by the designer is not necessary, since the generated ordinary differential equations can be solved in the time domain most effectively by analog simulators. The steps for the construction of a network model are:

1. Partitioning of the whole system into sub- systems (or components) which can be simpler modeled;

2. Field quantities are ‘concentrated’ on quantities which are assigned to the connections be- tween the subsystems and their terminals: re- placement of the electrical field strength by an electrical voltage, ...;

3. Definition of the terminals of the subsystems or components (interface definition);

4. Modeling of the terminal behavior of the sub- systems (by behavioral or structural models); spring k , mass m, damping d

5. Use of the subsystem models as components in a superior network which corresponds to the whole system.

In fig. 13.20 a typical mechanical microsystem component – a bending beam – is shown together with a network model for one segment of the bending beam [13.46]. Actually this segment should be infinitesimally small, but by the spatial discretization it has a finite length Δx. Experience shows that a rough partition into 4 or 8 of these segments is most often completely sufficient for the accuracy desired in system simulation [13.53].

But in the design of more complicated MEMS it is often very difficult to model them by such simple networks. Then it is more favorable to describe

the mathematical relations for a subsystem with a behavioral model [13.54], [13.62]. With the aid of the above-mentioned modeling languages it is then possible to use these models in appropriate simulators. This procedure is described for a mi- crosystem with a relatively complicated structure, a translational acceleration sensor, in fig. 13.21 [13.53], [13.70].

For the whole system a network model is constructed which consists of models for the homogeneous bending beams and the connections between them (fig. 13.22). Since both translational and rotational forces and moments, respectively, in the three-dimensional space are to be examined, multi- poles with the according number of terminals have to be defined. Their terminal quantities are used in the behavioral models. These equations are too large to be discussed here in detail. They correspond, however, exactly to the mathematical equations used in the text books of mechanics for the description of bending beams and other basic components. Therefore only the interface and a simple mathematical model of a bending beam of length L in the form of a matrix equation are shown. From such network elements the main network is assembled as the model of the whole system. In contrast to the simple structural model in fig. 13.20, in which only the translation in x-

direction and the rotation around the z-axis are considered, translation and rotation in all three directions in space are included here.

Model Export

The way just described is directly plausible, but it has also its difficulties. The formulation of the mathematical relations for the modeling of the basic components is everything but simple, even if these equations are to be found in the literature. The formulas are usually only given for simple geometrically homogeneous structures. More complicated structures may be simulated numerically by solving the partial differential equations. FEM simulators have complicated algorithms (meshing algorithms) in order to set up the describing equations also for inhomogeneous structures . There- fore another modeling approach consists of us- ing these simulator-internal equations and exporting them to set up externally a behavioral model [13.32]. But the number of equations used in these models are too large to be used directly in system simulation where many of these components have to be considered simultaneously. A substantial simplification of the equations by order reduction (i.e., the reduction of the number of equations and variables) is necessary to achieve short computing times. The price is the effort for model reduction and a reduced simulation accuracy which is,

however, sufficient for system simulation [13.81], [13.82]. In fig. 13.23 this way is sketched.

Order reduction is a sophisticated mathematical problem, therefore algorithms and programs for it are still in the research stage. So it is very impor- tant to note that at least for special, but particularly important, classes of problems some of today’s FEM simulators support the automatic generation of behavioral models by the export of a reduced set of internal equations. E.g., the FEM simulator ANSYS has a ‘sub-structuring mode’ to export equations from ANSYS, already reduced with the Guyan algorithm [13.4]. Figure 13.24 shows a detail of a very inhomogeneous mechanical microsystem. A model for the static deformation in the x, y and z directions and the dynamic behavior  under the effect of an external force Fe has to be formulated.

It is hardly possible to set up an analytic model by hand. It would remain – as described above – a cumbersome partition into many small homogeneous segments and joining them to an overall network model, compare fig. 13.22. With the aid of the order reduction in ANSYS a simple model for system simulation can be generated automatically. The matrices noticed in fig. 13.22 are calculated in ANSYS and exported after order reduction. For example, a simplified set of equations with 69 lines and columns is produced:

This model of a mechanical component can be used now, e.g., together with the model of an electrical subsystem for the simulation of the electro- mechanical microsystem (MEMS) with a VHDL- AMS simulator. It contains, however, only numerical parameters which may be calculated within ANSYS. In the case of modifications of the mechanical dimensions or of the material parameters the generation of this VHDL-AMS model has to be repeated.

Simulator Coupling for Microsystems Engineering

From the examples of the previous sections it is recognizable that the modeling for one simulator is possible, but often not quite easy. Therefore the second possibility for simulation of heterogeneous systems, the coupling of simulators, will be demonstrated by typical examples also for microsystems engineering.

In fig. 13.25 an electro-mechanical acceleration sensor is shown, whose seismic mass (‘proof mass’) suspended by both sides moves between the two plates under the influence of acceleration forces [13.17], [13.23]. The capacitances between the mass moved and the two electrodes are measured with a special circuit. Their changes are a measure for the displacements and thus for the acceleration forces. Additionally, the sensor is controlled, i.e., depending on the displacement of the movable mass a voltage is applied between the mass and the electrodes in order to bring the mass back into the central position. It is also shown in the picture what effect the control has on the behavior of the sensor after the appearance of a stepwise rising and then remaining constant acceleration force:

• large overshooting without control;

• substantially reduced overshooting and achieving the initial position with control.

The calculations of these heterogeneous microsystems (in which particularly the mechanical- electrostatic interactions are to be analyzed and considered especially during the automatic controller design) can be realized very well by coupling a FEM simulator (e.g., ANSYS) to a circuit simulator (e.g., Saber). Figure 13.26 shows the block diagram with the data interfaces between the two subsystems where the data exchange between the two simulators takes place. Both simulators calculate the new output signals as a reaction of their input signals. The simulators operate in parallel and have to be synchronized for data exchange. Particularly for mechatronics systems and microsystems, couplings of commercially available simulators have been developed increasingly in the last years [13.36], [13.64].

As a result of the continually decreasing dimensions of integrated circuits the electrical-thermal interactions have to be considered. On the one hand, the energy dissipation and temperature of electronic elements depend on their currents and voltages; on the other hand, elements’ currents and voltages are influenced vice versa by their individual temperatures (particularly in the junctions of bipolar transistors). Additionally, very often it is not enough just to calculate the thermal- electrical behavior only at one time point but rather also the dependences on the real input signals or several typical operating points must be simulated. From this point of view integrated circuits appear as typical heterogeneous dynamical systems with coupled effects in different physical domains.

In fig. 13.27 a part of an electronic circuit is shown which can be simulated, e.g., with Saber. There is also shown the thermal chip model, which can be calculated, e.g., with the FEM simulator ANSYS. The common simulation is realized by a simulator coupling [13.74]. The simulators exchange at each time point the energy dissipation and the temperature of those elements which are particularly power consuming and temperature-sensitive, respectively. The temperature distribution on the chip at one time point as well as the temporal changing of the temperature at two transistors are shown in fig. 13.28.

The advantages and disadvantages may be summarized (similarly as already stated in section 13.2 for communication systems):

For each subsystem the simulator can be selected which fits optimally to the physical domain (mechanical, thermal, magnetic, electronic) and the chosen abstraction level (PDE, ODE, discrete models, ... ). Model libraries, input language, simulation algorithms, coupling capabilities with other simulators, and visualization of the results are to be considered in choosing the ‘best’ simulator. Thereby the modeling effort is reduced considerably in many situations. The modeling for higher abstraction levels, based on experiences and FEM simulations, may take days, weeks or yet longer if no model generator is available. This effort can be dropped if a FEM simulator can be used for the subsystem modeled at PDE level.

Also disadvantages stand against these advantages. Up to today only a few simulators could be coupled without any additional implementation effort of the user. The simulation times are mostly considerably higher than in simulations with only one simulator, and coupling software needs more computing time. On the other hand, the frequently used FEM simulators need substantially larger computing times, anyway, because of their more detailed models.

Apart from these technical advantages further ad- vantages can arise which are related to license conditions and the very high purchase costs of simulators. Coupling of simulators may be realized not just on one processor or in a local processor grid. It is today’s state of the art to connect computers by the use of world-wide networks. Thus, e.g., in research projects the coupling of circuit simulators in Dresden with FEM simulators located in Chemnitz in Germany and in Linz in Austria via the Internet was implemented. Also the cooperation of simulators and optimization programs via the Internet has been already realized [13.68].