Settling time for bilevel waveform
S = settlingtime(X,D)
S = settlingtime(X,FS,D)
S = settlingtime(X,T,D)
[S,SLEV,SINST] = settlingtime(...)
[S,SLEV,SINST] = settlingtime(...,Name,Value)
S = settlingtime(
S, from the mid-reference level instant
to the time instant each transition enters and remains within a 2%
tolerance region of the final state over the duration,
a positive scalar. Because
interpolation to determine the mid-reference level instant,
contain values that do not correspond to sampling instants. The length
S is equal to the number of detected transitions
in the input signal,
X. If for any transition,
the level of the waveform does not remain within the lower and upper
tolerance boundaries, the requested duration is not present, or an
intervening transition is detected,
the corresponding element in
See Settle Seek Duration for cases
settlingtime returns a
To determine the transitions,
the state levels of the input waveform by a histogram method.
all regions that cross the upper-state boundary of the low state and
the lower-state boundary of the high state. The low-state and high-state
boundaries are expressed as the state level plus or minus a multiple
of the difference between the state levels. See State-Level Tolerances.
specifies the sample rate for the bilevel waveform,
S = settlingtime(
X in hertz. The
first sample instant in
X is equal to t = 0. Because
settlingtime uses interpolation to
determine the mid-reference level instant,
S may contain values
that do not correspond to sampling instants.
settlingtime(...) plots the signal and
darkens the regions of each transition where settling time is computed.
The plot marks the location of the settling time of each transition,
the mid-crossings, and the associated reference levels. The plot also
displays the state levels with the corresponding lower and upper tolerance
Sample rate in hertz.
Vector of sample instants. The length of
Mid-reference level as a percentage of the waveform amplitude. See Mid-Reference Level.
Low and high-state levels.
Tolerance levels (lower and upper state boundaries) expressed as a percentage. See State-Level Tolerances.
The time from the mid-reference level instant to the time instant
each transition enters and remains within a 2% tolerance region of
the final state over duration,
Waveform values at the settling points.
Time instants of the settling points.
Determine the settling point and corresponding waveform value for a bilevel waveform. Specify a settle-seek duration of 10 seconds.
load('transitionex.mat', 'x') [s,slev,sinst] = settlingtime(x,10);
Plot the waveform and annotate the settling point.
ans = 1.8901
Determine the settling points for a three-transition bilevel waveform. The data are sampled at 4 MHz. Specify a settle-seek duration of one microsecond.
load('transitionex.mat','x') y = [x; fliplr(x)]; fs = 4e6; t = 0:1/fs:(length(y)*1/fs)-1/fs; [s,slev,sinst] = settlingtime(y,fs,1e-6);
Plot the waveform and annotate the settling points.
ans = 3×1 10-6 × 0.4725 0.1181 0.4725
The settling time is the time after the mid-reference level instant when the signal crosses into and remains in the 2%-tolerance region around the state level. The settling time is illustrated in the following figure. The low- and high-state levels are the dashed black lines. The 2% tolerances above and below the state levels are shown by the red dashed lines and the settling time is indicated by the yellow circle.
The mid-reference level in a bilevel waveform with low-state level, S_1, and high- state level, S_2, is
Let y50% denote the mid reference level.
Let t50%- and t50%+ denote the two consecutive sampling instants corresponding to the waveform values nearest in value to y50%.
Let y50%- and y50%+ denote the waveform values at t50%- and t50%+.
The mid-reference level instant is
Each state level can have associated lower- and upper-state boundaries. These state boundaries are defined as the state level plus or minus a scalar multiple of the difference between the high state and the low state. To provide a useful tolerance region, the scalar is typically a small number such as 2/100 or 3/100. In general, the region for the low state is defined as
where is the low-state level and is the high-state level. Replace the first term in the equation with to obtain the tolerance region for the high state.
The following figure illustrates lower and upper 2% state boundaries (tolerance regions) for a positive-polarity bilevel waveform. The red dashed lines indicate the estimated state levels.
The settle seek duration defines the interval of time after
the mid-reference level instant that
for a settling point. If
settlingtime does not
find a settling point within the settle seek duration,
the settling time. The following figure illustrates a settle seek
duration of 10 samples.
settlingtime may fail to find a settling
point in the specified settle seek duration if any one of the following
The last waveform value in the settle seek interval is not within the upper- and lower-state boundaries determined by the specified tolerance. The following figure illustrates this condition for a settle seek duration of 8 samples and a 2% tolerance region.
In the preceding figure, you see that the last sample in the settle seek interval exceeds the upper state boundary. In this example, reducing or increasing the settle seek duration can result in a valid settling time.
There is an insufficient number of waveform samples for the specified settle seek duration. The following figure illustrates this condition for a settle seek duration of 20 samples. The settle seek duration extends beyond the final sample of the waveform.
An intervening transition is detected before the end of the specified settle seek duration. The following figure illustrates this condition for a settle seek duration of 22 samples. An intervening transition is detected before the end of the 22–sample settle seek duration.
 IEEE® Standard on Transitions, Pulses, and Related Waveforms, IEEE Standard 181, 2003, pp. 23–24.