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# risetime

Rise time of positive-going bilevel waveform transitions

## Syntax

R = risetime(X)
R = risetime(X,FS)
R = risetime(X,T)
[R,LT,UT] = risetime(...)
[R,LT,UT,LL,UL] = risetime(...)
[...] = risetime(...,Name,Value)
risetime(...)

## Description

R = risetime(X) returns a vector, R, containing the time each transition of the input bilevel waveform, X, takes to cross from the 10% to 90% reference levels. To determine the transitions, risetime estimates the state levels of the input waveform by a histogram method. risetime identifies 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. Because risetime uses interpolation, R may contain values that do not correspond to sampling instants of the bilevel waveform, X.

R = risetime(X,FS) specifies the sampling frequency in hertz. The sampling frequency determines the sample instants corresponding to the elements in X. The first sample instant in X corresponds to t=0. Because risetime uses interpolation, R may contain values that do not correspond to sampling instants of the bilevel waveform, X.

R = risetime(X,T) specifies the sample instants, T, as a vector with the same number of elements as X.

[R,LT,UT] = risetime(...) returns vectors, LT and UT, whose elements correspond to the time instants where X crosses the lower- and upper-percent reference levels.

[R,LT,UT,LL,UL] = risetime(...) returns the levels, LL and UL, that correspond to the lower- and upper-percent reference levels.

[...] = risetime(...,Name,Value) returns the rise times with additional options specified by one or more Name,Value pair arguments.

risetime(...) plots the signal and darkens the regions of each transition where rise time is computed. The plot marks the lower and upper crossings and the associated reference levels. The state levels and the corresponding associated lower- and upper-state boundaries are also plotted.

## Input Arguments

 X Bilevel waveform. X is a real-valued row or column vector. FS Sample rate in hertz. T Vector of sample instants. The length of T must equal the length of the bilevel waveform, X.

### Name-Value Pair Arguments

 'PercentReferenceLevels' Reference levels as a percentage of the waveform amplitude. The low-state level is defined to be 0 percent. The high-state level is defined to be 100 percent. The value of 'PercentReferenceLevels' is a two-element real row vector whose elements correspond to the lower and upper percent reference levels. Default: [10 90] 'StateLevels' Low- and high-state levels. Specifies the levels to use for the low- and high-state levels as a 2-element real row vector. The first element is the low-state level. The second element is the high-state level. 'Tolerance' Tolerance levels (lower- and upper-state boundaries) expressed as a percentage. See State-Level Tolerances. Default: 2

## Output Arguments

 R Rise times. R is a vector containing the duration of each positive-going transition. If you specify the sampling rate, FS, or the sampling instants, T, rise times are in seconds. If you do not specify a sampling rate, or sampling instants, rise times are in samples. LT Instants when positive-going transition crosses the lower-reference level. By default, the lower reference level is the 10% reference level. The upper reference level is the 90% reference level. You can change the default reference levels by specifying the 'PercentReferenceLevels' name-value pair. UT Instants when positive-going transition crosses the upper-reference level. By default, the lower reference level is the 10% reference level. The upper reference level is the 90% reference level. You can change the default reference levels by specifying the 'PercentReferenceLevels' name-value pair. LL Lower reference level in waveform amplitude units.LL is a vector containing the waveform value corresponding to the lower reference level in each positive-going transition. By default, the lower reference level is the 10% reference level. You can change the default reference levels by specifying the 'PercentReferenceLevels' name-value pair. UL Upper reference level in waveform amplitude units. LL is a vector containing the waveform value corresponding to the upper reference level in each positive-going transition. By default, the upper reference level is the 90% reference level. You can change the default reference levels by specifying the 'PercentReferenceLevels' name-value pair.

## Examples

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### Rise Time in a Bilevel Waveform

Determine the rise time in samples for a 2.3 V clock waveform.

Load the 2.3 V clock data. Determine the rise time in samples. Use the default [10 90] percent reference levels.

```load('transitionex.mat','x');
R = risetime(x);```

The rise time is less than 1, indicating that the transition occurred in a fraction of a sample.

### Rise Time with 20% and 80% Reference Levels

Determine the rise time in a 2.3 V clock waveform sampled at 4 MHz. Compute the rise time using the 20% and 80% reference levels.

Load the 2.3 V clock data with sampling instants. Plot the waveform.

```load('transitionex.mat','x','t');
plot(t,x);```

Determine the rise time using the 20% and 80% reference levels.

`R = risetime(x,'PercentReferenceLevels',[20 80]);`

### Rise Time, Reference-Level Instants, and Reference Levels

Determine the rise time, reference-level instants, and reference levels in a 2.3 V clock waveform sampled at 4 MHz.

Load the 2.3 V clock waveform along with the sampling instants.

`load('transitionex.mat','x','t');`

Determine the rise time, reference-level instants, and reference levels.

`[R,LT,UT,LL,UL] = risetime(x,t);`

Plot the waveform in microseconds with the lower- and upper-reference levels and reference-level instants. Show that the rise time is the difference between the upper- and lower-reference level instants.

```plot(t.*1e6,x);
xlabel('microseconds'); ylabel('Volts');
hold on; grid on;
plot(LT.*1e6,LL,'ro','markerfacecolor',[1 0 0]);
plot(UT.*1e6,UL,'ro','markerfacecolor',[1 0 0]);
fprintf('Rise time is %1.4f microseconds.\n',(UT-LT)*1e6)```

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### Positive-Going Transition

A positive-going transition in a bilevel waveform is a transition from the low-state level to the high-state level. A positive-polarity (positive-going) pulse has a terminating state more positive than the originating state. If the waveform is differentiable in the neighborhood of the transition, an equivalent definition is a transition with a positive first derivative. The following figure shows a positive-going transition.

In the preceding figure, the amplitude values of the waveform do not appear because a positive-going transition does not depend on the actual waveform values. A positive-going transition is defined by the direction of the transition.

### Percent Reference Levels

If S1 is the low state, S2 is the high state, and U is the upper-percent reference level. The waveform value corresponding to the upper percent reference level is

If L is the lower-percent reference level, the waveform value corresponding to the lower percent reference level is

### State-Level Tolerances

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 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 α% tolerance region for the low state is defined as

where S1 is the low-state level and S2 is the high-state level. Replace the first term in the equation with S2 to obtain the α% 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.

## References

[1] IEEE® Standard on Transitions, Pulses, and Related Waveforms, IEEE Standard 181, 2003, pp. 15–17.