Duty cycle of clock

Duty cycle: Duty cycle of a clock is defined as the fraction of a period of clock during which the clock is in active state. Duty cycle of a clock is normally expressed as a percentage. For instance, figure below shows a clock having an active state of '1' stays low for 2 ns during its period of 10 ns. It is, therefore, said to have a duty cycle of 20%.


How duty cycle impacts timing: Duty cycle of clock plays a big role in timing closure of designs. We need to consider following factors related to duty cycle variation while timing:

  • Half cycle timing paths: If there are both positive and negative edge-triggered flip-flops in the design, duty cycle of the clock matters a lot. For instance, if we have a clock of 100 MHz with 20% duty cycle; For a timing path from positive edge-triggered flip-flop to negative edge-triggered flip-flop, we get only 2 ns for setup timing for positive-to-negative path and 8 ns for negative-to-positive path as compared to 10 ns for a full cycle path. However, if the same clock had duty cycle of 50%, we would have got 5 ns for the same half cycle timng path.

  • Minimum pulse width requirements: At high frequencies, duty cycle matters a lot. For instance, every sequential element has requirement of minimum pulse width that should reach it (read this). If the duty cycle of the clock is not close to 50%, we are limited in providing high frequency even if we are capable of meeting timing at even higher frequencies. Let us take an example. If the minimum pulse width requirement of a flip-flop is 500 ps, then with 50% duty cycle clock, we can use a clock of 1 GHz (1 ns clock period). But if we use a clock of duty cycle of 20%, we cannot use a clock greater than 400 MHz.
With the above things in mind, it makes sense to use a clock with duty cycle as close to 50%. However, in many scenarios, it may not be feasible to do so. So, one needs to decide the priorities; i.e., architecture complexities vs timing complexities. Generating a divided clock of 50% duty cycle is not always possible and there are a few complexities involved in architecture. For instance, clock waveform synchronization between the clocks if there are multiple dividers. Also, for odd division factors like divide_by_3 etc., we need more complex divider circuitry than what may be required for divide_by_2 or divide_by_4 etc.

Which type of jitter matters for timing slack calculation?

In the post Clock jitter, we learnt about the basics of clock jitter. We also learned about different types of clock jitter. Now, the question arises as to what type of clock jitter is useful for calculation of timing slack, both setup and hold slacks. We will gradually try to build understanding for the same.

If we look into the equation of setup slack for a positive edge-triggered flip-flop to another positive edge-triggered flip-flop, we see that setup slack depends upon "clock period". Now, if look closely, we will find that the clock period that we are talking about is actually distance between two clock edges. The larger the distance between the clock edges, greater will be the clock period. Hence, more positive will be setup slack.



 Now, period jitter represents the absolute deviation of clock period from its ideal clock period. So, the jitter we should be looking for is maximum value of "peak-to-peak period jitter". Peak-to-peak period jitter can either increase or decrease clock period. But, we need to take the effect of jitter to decrease clock period. This is because we have to take the worst case of clock period to have most pessimistic setup slack value. And the worst clock period will occur when peak-to-peak jitter is maximum.

So, we can say that for setup slack calculation,
Clock period (actual) = Clock period (ideal) - peak-to-peak jitter (maximum)


What will happen to clock jitter if I divide down the clock?

As we have discussed above, due to clock jitter, for setup calculation, we will assume that peak-to-peak period jitter has caused edge 2 to come closer to edge 1, thereby reducing actual clock period by that margin. Similarly, edge 3 can come closer to edge 2. So, ideally, if we look at DIV_2 clock, the possible jitter here should be 2 times the jitter of SOURCE_CLOCK. Similarly, a DIV_4 clock is expected to have 4 times the jitter and a DIV_8 clock is expected to have 8 times the jitter. And so on..

Now comes the tricky part. As per the definition of long term jitter, nth edge of clock cannot have a jitter more than long term jitter. So, if I say that a PLL has a long term jitter spec of 6 times that of maximum peak-to-peak period jitter, then a DIV_8 clock will have peak-to-peak jitter equal to 6 times the peak-to-peak period jitter of SOURCE_CLOCK. Even a DIV_16 clock will have same maximum jitter.


What will happen to clock jitter for a multicycle path?
Similar to the case of divided down version of clock, a multicycle path also involves other than consecutive edges. So, similar concepts will apply here. So, a multicycle path for setup of 2 will have a jitter of 2 times the peak-to-peak jitter of SOURCE_CLOCK, etc.

Also read:

Clock jitter

Clock jitter: By definition, clock jitter is the deviation of a clock edge from its ideal position in time. Simply speaking, it is the inability of a clock source to produce a clock with clean edges. As the clock edge can arrive within a range, the difference between two successive clock edges will determine the instantaneous period for that cycle. So, clock jitter is of importance while talking about timing analysis. There are many causes of jitter including PLL loop noise, power supply ripples, thermal noise, crosstalk between signals etc. Let us elaborate the concept of clock jitter with the help of an example:

A clock source (say PLL) is supposed to provide a clock of frequency 10 MHz, amounting to a clock period of 100 ns. If it was an ideal clock source, the successive rising edges would come at 0 ns, 100 ns, 200 ns, 300 ns and so on. However, since, the PLL is a non-ideal clock source, it will have some uncertainty in producing edges. It may produce edges at 0 ns, 99.9 ns, 201 ns etc. Or we can say that the clock edge may come at any time between (<ideal_time>+- jitter); i.e. 0, between 99-101 ns, between 199-201 ns etc (1 ns is jitter). However, counting over a number of cycles, average period will come out to be ~100 ns.

Figure 1 below shows the generic diagram for clock jitter:



Please note that the uncertainty in clock edge can be for both positive as well as negative edges (above example showed only for positive edges). So, there are both full cycle and half cycle jitters. By convention, clock jitter implies full cycle clock jitter.


Types of clock jitter: Clock jitter can be measured in many forms depending upon the type of application. Clock jitter can be categorized into cycle-to-cycle, period jitter and long term jitter.
  • Cycle to cycle jitter: By definition, cycle-to-cycle jitter signifies the change in clock period accross two consecutive cycles. For instance, it will be difference in periods for 1st and 2nd cycles, difference in periods for 10th and 11th cycles etc. It has nothing to do with frequency variation over time. For instance, in figure below, the clock has drifted in frequency (from period = 10 ns to period = 1 ns), still maintaining a cycle-to-cycle jitter of 0.1 ns. In other words, if t2 and t1 are successive clock periods, then cycle_to_cycle_jitter = (t2 - t1).

  • Period jitter: It is defined as the "deviation of any clock period with respect to its mean period". In other words, it is the difference between the ideal clock period and the actual clock period. Period jitter can be specified as either RMS period jitter or peak-to-peak period jitter.
    • Peak-to-peak period jitter: It is defined as the jitter value measuring the difference between two consecutive edges of clock. For instance, if the ideal period of the clock was 20 ns, then for clock shown above,
      • for first cycle, peak-to-peak period jitter = (20 - 20) = 0 ns
      • for second cycle, peak-to-peak period jitter = (20 - 19.9) = 0.1 ns
      • for last cyle, peak-to-peak period jitter = (20 - 1) = 19 ns
    • RMS period jitter: RMS period jitter is simply the root-mean-square of all the peak-to-peak period jitters available.

  • Long term jitter: Long term jitter is the deviation of the clock edge from its ideal position. For instance, for a clock with period 20 ns, ideally, clock edges should arrive at 20 ns, 40 ns and so on. So, if 10th edge comes at 201 ns, we will say that the long term jitter for 10th edge is 1 ns. Similarly, 1000th edge will have a long term jitter of 0.5 ns if it arrives at 20000.5 ns.

Let us try to understand the difference between all the three kinds of jitter with the help of an illustrative example waveform below:


Reference:
* Understanding SYSCLK jitter

Also read:

Post your query

Hi Friends

Please feel free to post your queries as comments. We will try our level best to answer these. You can also write to us at myblogvlsiuniverse@gmail.com.

Can jitter in clock effect setup and hold violations?

First of all, we need to understand what is meant by jitter. In most simplistic language, jitter is the uncertainty of a clock source in production of clock edges. For example, if we say that there is a 100 MHz clock source. Ideally, it should produce a clock edge at 0 ns, 10 ns, 20 ns... So, if we say that there was a clock edge at time t = 30 ns, we should get the next clock edge at t = 40 ns. But this is hardly so; due to the uncertainty of getting a clock edge, we might get the next edge between 39.9 ns to 40.1 ns. So, we say that 0.1 ns is the jitter in the period of the clock. In reality, the definition of jitter is more complex. But, for our scope, this understanding is sufficient.

Let us consider a simple timing path from a positive edge-triggered flip-flop to a positive edge-triggered flip-flop.


Now, let us come to our discussion. First, let us discuss the effect of clock jitter on setup slack.

Effect of clock jitter on setup slack for single cycle paths: From our knowledge of STA basics, setup check formed, in this case, will be from edge 1 -> edge 3. Now, if we know that edge 1 arrived at 20 ns, then edge 3 may arrive at any time (20 ns + CLOCK_PERIOD + jitter) and (20 ns + CLOCK_PERIOD - jitter). So, to cover worst case timing scenario, we need to time as per (20 ns + CLOCK_PERIOD - jitter). So, effectively, we will get (CLOCK_PERIOD - jitter) as effective clock period.

In other words, jitter in clock period makes the setup timing more tight. Or it decreases setup slack for single cycle timing paths.


Effect of clock jitter on hold slack for single cycle paths: Going on the same grounds as setup slack, hold check will be from edge 1 -> edge 1 only. And we know with certainty that edge 1 will leave the source at 20 ns only. So, hold slack should not get bothered by the amount of jitter present at the clock source for single cycle timing paths.

Now, you understand the basics of  how jitter affects setup and hold slacks. We can state as below:

If the check being formed involves two different edges of same polarity (for instance, different rising edges), then, jitter in clock period will affect setup slack. Otherwise, it will not.

Now, can you guess the effect of jitter on setup and hold slacks for zero cycle timing paths?

Also, what will be the amount of pessimism needed to be taken into account for setup and hold slacks' calculations if the timing path is a multi-cycle path taking 2 cycles for setup and zero cycle for hold?

Also read:



Recovery and removal checks

Recovery and removal checks are associated with deassertion of asynchronous reset. The assertion of reset causes the output to get reset and deassertion transfers the control of output to clock signal; i.e., deassertion of reset does not change the output as we discussed in post synchronous and asynchronous resets. However, to ensure that the design comes out of reset in deterministic cycle and to avoid metastability, there must be a region around arrival of clock edge within which reset must not be deasserted. This is similar to setup and hold timing checks, the difference being that:
Setup and hold checks are associated with synchronous data signals for a flop and are applied to both rise and fall transitions of data. Recovery and removal checks, on the other hand, are for asynchronous reset transitioning from active state to inactive state only (deassertion of reset).
To properly understand what recovery and removal checks are, we need to understand what asynchronous reset assertion and deassertion does.

Asynchronous reset assertion: In a flip-flop, assertion of reset causes the output to go to its reset value (which is normally "0"). The assertion of reset is an asynchronous event and is not impacted by the state of clock. Figure 1 below depicts the assertion of reset. As it can be seen, Output asynchronously goes to "0" as an effect of reset going to its active state "1".


Asynchronous reset deassertion: The deassertion of asynchronous reset causes the output to get out of the impact of reset and behave like a normal flip-flop. When the reset gets deasserted, its output remains to be "0" until the clock edge. When the clock edge arrives, the value at the input of the flop propagates to the output. Figure 2 below depicts the same. However, the position of reset deassertion with respect to clock edge matters here as is the case with setup and hold checks. If the reset toggles in the vicinity of clock edge, the flip-flop may go metastable. This is avoided by defining recovery and removal checks for reset deassertion. For the sake of simplicity, we can say that recovery and removal checks are setup and hold checks for reset deassertion.



Reset recovery check: Recovery check ensures that the deasserted reset signal allows the clock signal to take control of the output at the desired clock edge. For this, reset signal must be stable at least "recovery time" before the active clock edge. Recovery time is the minimum time required between the deassertion of reset signal and arrival of clock edge. This can be modelled similarly as a setup check with the difference of it being a single sided synchronous check only.

Reset removal check: Removal check ensures that the deasserted reset signal does not get captured on the clock edge at which it is launched by reset synchronizer. For this, reset signal must be stable at lease "removal time" after the active clock edge. Removal time is the minimum time required after the arrival of clock edge for which reset must not be deasserted at the flop's reset pin. This can be modelled similarly as a hold check with the difference of it being a single sisded synchronous check only.

Figure below shows reset de-assertion as a complete picture and summarises what we have discussed in this post.



Next read: Reset basics

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Synchronous and asynchronous resets

In the post reset basics, we discussed the need of having reset and the strategies used by designers related to reset. One of the decisions that designers need to finalize is to choose synchronous vs asynchronous reset strategy. Each of these reset strategies is capable of achieving the purpose of a reset. A design may also have a mixed approach in which a part of the device is driven by synchronous reset and another part has an asynchronous approach to reset. In this post, we will be discussing the pros and cons of each.
  • Synchronous reset: If the reset affects the state of the design only on the active edge of the clock, we term it as a synchronous reset signal. A synchronous reset is fed into the D fanin cone of a flip-flop. Figure 1 below shows a sample design with synchronous reset.

Generally, the reset signal must be closest to the target flip-flop in order to have least number of gates. If the reset of above figure is restructured, one AND gate must be converted to two AND gates to have the reset propagated to the target flip-flop in all situations. But this kind of data path results in increased data path for other critical functional paths. So, synthesis tool needs to take intelligent decision of gate count vs critical signals' timing.
Synchronous reset generation results in smaller flip-flops, but the combinational gate count grows as reset must be applied through combinational logic only.
We can afford to have glitches in reset signal as long as it is meeting setup and hold timing. Therefore, if reset signal is generated by a set of internal logic conditions, synchronous reset is the only goto as there will be glitches formed upon mingling of different conditions. 
Reset pulse must be big enough to get captured at the active clock edge target registers. For example, if the register gets launched on a clock of period 5 ns and is targetted for a flip clop receiving a clock of period 20 ns, there is a chance of getting the reset pulse not getting captured. So, there will be a requirement of a pulse stretcher circuit.
There are further complexities when clock gating is implemented to save power. If the clock is gated, you cannot force the design into reset state. Only asynchronous reset can work in that scenario. 
  • Asynchronous reset: If the reset affects the state of the design asynchronously; i.e., whether or not clock is running, then the design is said to have asynchronous reset.
For designs with asynchronous reset, datapath is independent of reset signal. So, logic levels in datapath are less. This means that we can achieve higher frequency using asynchronous resets.
The design can be reset even when clock is gated. Also, no work arounds are needed during synthesis as in case of synchronous resets.
An asynchronous reset signal needs to be glitch free. Even a small glitch on reset signal can reset the design.
For a flip-flop with asynchronous reset, assertion of reset resets the flip-flop asynchronously. Deassertion of reset leaves the output of flip-flop unchanged. The state of flip-flop will change only on arrival of next clock pulse. There can be two scenarios:
  1. Clock is gated during deassertion of reset: In this case, we can safely deassert the reset and ungate the clock some time after deassertion.
  2. Clock is running during deassertion of reset: In this case, we need to take care of the recovery/removal timing of deassertion of reset. The deassertion of reset must be synchronous with respect to clock. Reset synchronizers are needed to synchronize the deassertion of reset signal.

Figure below shows the timing waveform for assertion and deassertion of asynchronous reset. As we can see, the assertion of reset causes the output to go to '0', whereas deassertion waits for the clock edge to arrive and cause the output to change. 

Also read:


VLSI - 3

So continuing on the previous post of two current sources in series, this example is important when you analyze lot of circuits.

Lets assume you simulate with ideal current sources

Case 1 : When top current source > lower current source

Since, they are ideal current sources, it happens that they will sink or source that much current ir respective of the voltage across the sources, so it implies that currents may be unequal in single wire and the node potential in between increases.

The reason it increases is that top current source pumps in current but the down source only sinks lesser current, hence forth the rest of the current will charge up the cap at the node and hence forth increases the node potential.

Case 2 : When top current source < lower current source

Since, they are ideal current sources, it happens that they will sink or source that much current ir respective of the voltage across the sources, so it implies that currents may be unequal in single wire and the node potential in between decreases.

The reason it increases is that top current source pumps in lesser current but the down source only sinks higher current, hence forth the rest of the current will be provided by the cap at the node and hence forth decreases the node potential.

Interested studentts should find time in simulating the circuit by replacing the current sources with NMOS and PMOS and understand what will happen.

This is an important step in understanding CMFB.