# 1 - Operating Points for Logic, Analog and Mixed Signal Circuits   The Operating Point issue is relevant for any design: pure logic, pure analog, or mixed signal. Operating points can be defined in two ways: Any experienced PCB developer knows he must set his board so that it ends-up in a unique initial “Rest State” when the power is on: it stays put. Selecting the most convenient Rest State is daily practice for PCB developers! The immediate impact is on testability, then on the cost of usage of the industrial tester… IC designers look at such initialization through Virtual Testing, as the “Operating Points” of their simulator: finding all operating points gives them precious information on the topology of their design, on its robustness, and may give them precious clues on how to speed-up actual simulation from then on…   An Operating Point is defined by the value of each node voltage and state of each device for which the circuit is "stable": it is crucial to determine initial conditions for a meaningful simulation or test. Several Operating Points can be found in an analog or mixed signal circuit much like the various summits and troughs on a mountain range: The designer can modify his circuit to eliminate Operating Points unsuitable for efficiency of simulation or test Five heuristics and one algorithm (power-up) are implemented in SMASH to identify operation points   A case study: the better the simulator, the more realistic Operating Points! Operating Point “B” is metastable, i.e. a small stimulus in transient mode moves the circuit out of this state SMASH in default mode proceeds through a complete search with all its heuristics and algorithms, and gives the first viable result it finds; but for the expert designer, SMASH makes all search processes controllable and gives choice of the most adequate Operating Point.   Why multiple operating points?   The operating point are like the summits and the troughs of a mountain range The troughs are stable operating points, that is to say the circuit goes back to this point upon a small stimulus The summits are metastable (limit unstable) operating points, that is no say the circuit goes away from this point upon a small stimulus Mathematically, the operating point is defined by the values of the node voltages for which the Kirchhoff low is verified: the sum of the currents is equal to zero for each node of the circuit. Physically, it means that each electron comes from a known place and goes to a known place. Example of a circuit with several operating points: the Memory Point 3 possible operating points: 2 stable, 1 metastable     As proof of existence of multiple Operating Points, as well as metastable ones, logic simulators VHDL and VERILOG start by initializing all signals with value "X". Example of a circuit with only a metastable operating point: the Ring Oscillatore This unique operating point is metastable. That is normal for an oscillator!   < SMASH Differentiators

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