# Metastability (electronics)

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Metastability in electronics is the ability of a digital electronics system to persist for an unbounded time in an unstable equilibrium or metastable state. [1] In digital logic circuits, a digital signal is required to be within certain voltage or current limits to represent a '0' or '1' logic level for correct circuit operation; if the signal is within a forbidden intermediate range it may cause faulty behavior in logic gates the signal is applied to. In metastable states, the circuit may be unable to settle into a stable '0' or '1' logic level within the time required for proper circuit operation. As a result, the circuit can act in unpredictable ways, and may lead to a system failure, sometimes referred to as a "glitch". [2] Metastability is an instance of the Buridan's ass paradox.

## Contents

Metastable states are inherent features of asynchronous digital systems, and of systems with more than one independent clock domain. In self-timed asynchronous systems, arbiters are designed to allow the system to proceed only after the metastability has resolved, so the metastability is a normal condition, not an error condition. [3] In synchronous systems with asynchronous inputs, synchronizers are designed to make the probability of a synchronization failure acceptably small. [4] Metastable states are avoidable in fully synchronous systems when the input setup and hold time requirements on flip-flops are satisfied.

## Example

A simple example of metastability can be found in an SR NOR latch, when both Set and Reset inputs are true (R=1 and S=1) and then both transition to false (R=0 and S=0) at about the same time. Both outputs Q and Q are initially held at 0 by the simultaneous Set and Reset inputs. After both Set and Reset inputs change to false, the flip-flop will (eventually) end up in one of two stable states, one of Q and Q true and the other false. The final state will depend on which of R or S returns to zero first, chronologically, but if both transition at about the same time, the resulting metastability, with intermediate or oscillatory output levels, can take arbitrarily long to resolve to a stable state.

## Arbiters

In electronics, an arbiter is a circuit designed to determine which of several signals arrive first. Arbiters are used in asynchronous circuits to order computational activities for shared resources to prevent concurrent incorrect operations. Arbiters are used on the inputs of fully synchronous systems, and also between clock domains, as synchronizers for input signals. Although they can minimize the occurrence of metastability to very low probabilities, all arbiters nevertheless have metastable states, which are unavoidable at the boundaries of regions of the input state space resulting in different outputs. [5]

## Synchronous circuits

Synchronous circuit design techniques make digital circuits that are resistant to the failure modes that can be caused by metastability. A clock domain is defined as a group of flip-flops with a common clock. Such architectures can form a circuit guaranteed free of metastability (below a certain maximum clock frequency, above which first metastability, then outright failure occur), assuming a low-skew common clock. However, even then, if the system has a dependence on any continuous inputs then these are likely to be vulnerable to metastable states. [6]

When synchronous design techniques are used, protection against metastable events causing systems failures need only be provided when transferring data between different clock domains or from an unclocked region into the synchronous system. This protection can often take the form of a series of delay flip-flops which delay the data stream long enough for metastability failures to occur at a negligible rate.

## Failure modes

Although metastability is well understood and architectural techniques to control it are known, it persists as a failure mode in equipment.

Serious computer and digital hardware bugs caused by metastability have a fascinating social history. Many engineers have refused to believe that a bistable device can enter into a state that is neither true nor false and has a positive probability that it will remain indefinite for any given period of time, albeit with exponentially decreasing probability over time. [7] [8] [9] [10] [11] However, metastability is an inevitable result of any attempt to map a continuous domain to a discrete one. At the boundaries in the continuous domain between regions which map to different discrete outputs, points arbitrarily close together in the continuous domain map to different outputs, making a decision as to which output to select a difficult and potentially lengthy process. [12] If the inputs to an arbiter or flip-flop arrive almost simultaneously, the circuit most likely will traverse a point of metastability. Metastability remains poorly understood in some circles, and various engineers have proposed their own circuits said to solve or filter out the metastability; typically these circuits simply shift the occurrence of metastability from one place to another. [13] Chips using multiple clock sources are often tested with tester clocks that have fixed phase relationships, not the independent clocks drifting past each other that will be experienced during operation. This usually explicitly prevents the metastable failure mode that will occur in the field from being seen or reported. Proper testing for metastability often employs clocks of slightly different frequencies and ensuring correct circuit operation.

## Related Research Articles

In digital logic and computing, a counter is a device which stores the number of times a particular event or process has occurred, often in relationship to a clock. The most common type is a sequential digital logic circuit with an input line called the clock and multiple output lines. The values on the output lines represent a number in the binary or BCD number system. Each pulse applied to the clock input increments or decrements the number in the counter.

Digital electronics, digital technology or digital (electronic) circuits are electronics that operate on digital signals. In contrast, analog circuits manipulate analog signals whose performance is more subject to manufacturing tolerance, signal attenuation and noise. Digital techniques are helpful because it is much easier to get an electronic device to switch into one of a number of known states than to accurately reproduce a continuous range of values.

In digital circuit theory, sequential logic is a type of logic circuit whose output depends not only on the present value of its input signals but on the sequence of past inputs, the input history as well. This is in contrast to combinational logic, whose output is a function of only the present input. That is, sequential logic has state (memory) while combinational logic does not.

In electronics and especially synchronous digital circuits, a clock signal is a particular type of signal that oscillates between a high and a low state and is used like a metronome to coordinate actions of digital circuits.

In digital circuits, a runt pulse is a narrow pulse that, due to non-zero rise and fall times of the signal, does not reach a valid high or low level. A runt pulse may occur when switching between asynchronous clocks; or as the result of a race condition in which a signal takes two separate paths through a circuit, which may have different delays, and is then recombined to form a glitch; or when the output of a flip-flop becomes metastable.

Buridan's ass is an illustration of a paradox in philosophy in the conception of free will. It refers to a hypothetical situation wherein a donkey that is equally hungry and thirsty is placed precisely midway between a stack of hay and a pail of water. Since the paradox assumes the ass will always go to whichever is closer, it dies of both hunger and thirst since it cannot make any rational decision between the hay and water. A common variant of the paradox substitutes two identical piles of hay for the hay and water; the ass, unable to choose between the two, dies of hunger.

Source-Synchronous clocking refers to a technique used for timing symbols on a digital interface. Specifically, it refers to the technique of having the transmitting device send a clock signal along with the data signals. The timing of the unidirectional data signals is referenced to the clock sourced by the same device that generates those signals, and not to a global clock. Compared to other digital clocking topologies like system-synchronous clocks, where a global clock source is fed to all devices in the system, a source-synchronous clock topology can attain far higher speeds.

The term synchronizer may refer to:

A synchronous circuit is a digital circuit in which the changes in the state of memory elements are synchronized by a clock signal. In a sequential digital logic circuit, data is stored in memory devices called flip-flops or latches. The output of a flip-flop is constant until a pulse is applied to its "clock" input, upon which the input of the flip-flop is latched into its output. In a synchronous logic circuit, an electronic oscillator called the clock generates a string of pulses, the "clock signal". This clock signal is applied to every storage element, so in an ideal synchronous circuit, every change in the logical levels of its storage components is simultaneous. Ideally, the input to each storage element has reached its final value before the next clock occurs, so the behaviour of the whole circuit can be predicted exactly. Practically, some delay is required for each logical operation, resulting in a maximum speed at which each synchronous system can run.

An asynchronous circuit, or self-timed circuit, is a sequential digital logic circuit which is not governed by a clock circuit or global clock signal. Instead it often uses signals that indicate completion of instructions and operations, specified by simple data transfer protocols. This type of circuit is contrasted with synchronous circuits, in which changes to the signal values in the circuit are triggered by repetitive pulses called a clock signal. Most digital devices today use synchronous circuits. However asynchronous circuits have the potential to be faster, and may also have advantages in lower power consumption, lower electromagnetic interference, and better modularity in large systems. Asynchronous circuits are an active area of research in digital logic design.

The Muller C-element is a small digital block widely used in design of asynchronous circuits and systems. It has been specified formally in 1955 by David E. Muller and first used in ILLIAC II computer. In terms of the theory of lattices, the C-element is a semimodular distributive circuit, whose operation in time is described by a Hasse diagram. The C-element is closely related to the rendezvous and join elements, where an input is not allowed to change twice in succession. In some cases, when relations between delays are known, the C-element can be realized as a sum-of-product (SOP) circuit ,. Earlier techniques for implementing the C-element include Schmidt trigger, Eccles-Jordan flip-flop and last moving point flip-flop.

Static timing analysis (STA) is a simulation method of computing the expected timing of a digital circuit without requiring a simulation of the full circuit.

In integrated circuit design, dynamic logic is a design methodology in combinatory logic circuits, particularly those implemented in MOS technology. It is distinguished from the so-called static logic by exploiting temporary storage of information in stray and gate capacitances. It was popular in the 1970s and has seen a recent resurgence in the design of high speed digital electronics, particularly computer CPUs. Dynamic logic circuits are usually faster than static counterparts, and require less surface area, but are more difficult to design. Dynamic logic has a higher toggle rate than static logic but the capacitative loads being toggled are smaller so the overall power consumption of dynamic logic may be higher or lower depending on various tradeoffs. When referring to a particular logic family, the dynamic adjective usually suffices to distinguish the design methodology, e.g. dynamic CMOS or dynamic SOI design.

In digital electronic design a clock domain crossing (CDC), or simply clock crossing, is the traversal of a signal in a synchronous digital circuit from one clock domain into another. If a signal does not assert long enough and is not registered, it may appear asynchronous on the incoming clock boundary.

A frequency divider, also called a clock divider or scaler or prescaler, is a circuit that takes an input signal of a frequency, , and generates an output signal of a frequency:

Timing closure is the process by which a logic design consisting of primitive elements such as combinatorial logic gates and sequential logic gates is modified to meet its timing requirements. Unlike in a computer program where there is no explicit delay to perform a calculation, logic circuits have intrinsic and well defined delays to propagate inputs to outputs. In simple cases, the user can compute the path delay between elements manually. If the design is more than a dozen or so elements this is impractical. For example, the time delay along a path from the output of a D-Flip Flop, through combinatorial logic gates, then into the next D-Flip Flop input must satisfy the time period between synchronizing clock pulses to the two flip flops. When the delay through the elements is greater than the clock cycle time, the elements are said to be on the critical path. The circuit will not function when the path delay exceeds the clock cycle delay so modifying the circuit to remove the timing failure is an important part of the logic design engineer's task.

A digital signal is a signal that is being used to represent data as a sequence of discrete values; at any given time it can only take on one of a finite number of values. This contrasts with an analog signal, which represents continuous values; at any given time it represents a real number within a continuous range of values.

In electronics, a flip-flop is a circuit that has two stable states and can be used to store state information – a bistable multivibrator. The circuit can be made to change state by signals applied to one or more control inputs and will have one or two outputs. It is the basic storage element in sequential logic. Flip-flops and latches are fundamental building blocks of digital electronics systems used in computers, communications, and many other types of systems.

Low Power flip-flops are flip-flops that are designed for low-power electronics, such as smartphones and notebooks. A flip-flop, or latch, is a circuit that has two stable states and can be used to store state information.

## References

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