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74                      4 MODELLING IN HARDWARE DESCRIPTION LANGUAGES


                        END LOOP;
                  WAIT UNTIL rising_edge(clk);              -- Wait for rising edge
                  q <= res;                        -- Signal assignment for output
                END PROCESS;
               END behaviour2;
               Hardware description 4.7  Behavioural description of a multiplier on the basis of moving
               and adding


               Digital signal assignment

               Up until now we have based our description of a signal assignment upon an intu-
               itive understanding, which in some cases can be deceptive. This can be clarified by
               looking at a simple inverter gate. The function of the inverter is quickly described.
               However, in some cases this does not achieve the desired result. The inverter may
               have a delay time of 100 picoseconds. If a pulse of one picosecond occurs at its
               input then we would assume in the first approximation that this pulse would be
               observed in the opposite polarity at the output 100 picoseconds later. However, this
               is not physically correct because the pulse is much too short to effect a change
               at the output. Before this has moved to a significant degree, the cause has disap-
               peared again. In order to bring about this ‘inert’ behaviour it is necessary for each
               signal assignment to evaluate the right-hand side correctly and to draw up a list of
               current and future events. If necessary, the future events may have to be deleted
               again before they are realised. This is also the case, for example, if the right-hand
               side always produces an assignment with the same value, so that a formal assign-
               ment yields no new information for the signal. In this case we can postpone the
               assignment, so that no events without information content are produced. This task
               and others are undertaken by the so-called signal driver.


               4.5.4    Analogue modelling

               Introduction

               We can differentiate between three classical applications of analogue modelling,
               see Vachoux and Berge [406]. Firstly, and self-evidently, it is implemented when
               the system under investigation consists wholly or partially of analogue compo-
               nents. But even when looking at digital systems, the consideration of an analogue
               environment of the circuit may still be necessary. Finally, analogue effects, such
               as signal delays or coupling capacitances, often cannot be disregarded especially
               for digital high-speed circuits.
                 Again, the extremely different levels of abstraction can be represented. Thus, on
               the purely behavioural level we can provide models based upon transfer functions
               or differential equations. At a lower level of abstraction, so-called macromodels are
               often used, which may represent the standard blocks of analogue circuit design, e.g.
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