slewrate

Slew rate of bilevel waveform

Syntax

s = slewrate(x)

s = slewrate(x,Fs)

s = slewrate(x,t)

[s,lt,ut] = slewrate(___)

[s,lt,ut,ll,ul] = slewrate(___)

s = slewrate(___,Name,Value)

slewrate(___)

Description

s = slewrate(x) returns the slew rate for all transitions found in the bilevel waveform x. To determine the transitions, the slewrate function estimates the state levels of the input waveform by a histogram method and identifies all regions that cross the upper-state boundary of the low state and the lower-state boundary of the high state.

s = slewrate(x,Fs) specifies the sample rate Fs.

s = slewrate(x,t) specifies the sample instants t.

[s,lt,ut] = slewrate(___) returns the time instants when the waveform crosses the lower-percent reference level lt and upper-percent reference level ut. If you do not specify lower- and upper-percent reference levels, the levels default to 10% and 90%, respectively. You can specify an input combination from any of the previous syntaxes.

[s,lt,ut,ll,ul] = slewrate(___) returns the waveform values that correspond to the lower-reference levels ll and upper-reference levels ul.

s = slewrate(___,Name,Value) returns the slew rate for all transitions with additional options specified by one or more Name,Value arguments.

slewrate(___) plots the bilevel waveform and darkens the regions of each transition where the slew rate is computed. The plot marks the lower- and upper-reference level crossings and associated reference levels. The plot also indicates the state levels and associated lower and upper tolerances.

Examples

Slew Rate For One-Transition Waveform

Use slewrate with no output arguments to plot the slew rate information for a step waveform sampled at 4 MHz.

Load the transitionex.mat file and compute the slew rate. Annotate the slew rate in a plot of the waveform.

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

slewrate(x,t)

ans = 
1.0310e+07

Slew Rates for Three-Transition Waveform

Create a bilevel waveform with three transitions, two positive and one negative. The sample rate is 4 MHz. Obtain the slew rates for the three transitions.

load('transitionex.mat','x')
fs = 4e6;

y = [x;fliplr(x)];
t = (0:length(y)-1)/4e6;

S = slewrate(y,t)

S = 3×1
107 ×

    1.0310
   -0.9320
    1.0310

Annotate the result on a plot of the waveform.

slewrate(y,t);

Lower and Upper Transition Times

Return the lower- and upper-transition times for a three-transition waveform sampled at 4 MHz.

load('transitionex.mat','x')
fs = 4e6;

y = [x;fliplr(x)];
t = (0:length(y)-1)/fs;

[~,LT,UT] = slewrate(y,t)

LT = 3×1
10-4 ×

    0.0504
    0.0998
    0.1504

UT = 3×1
10-4 ×

    0.0521
    0.0978
    0.1521

Repeat using the sample rate instead of the time vector.

[~,LT,UT] = slewrate(y,fs)

LT = 3×1
10-4 ×

    0.0504
    0.0998
    0.1504

UT = 3×1
10-4 ×

    0.0521
    0.0978
    0.1521

Annotate the result on a plot of the waveform.

slewrate(y,fs);

Lower and Upper Reference Levels

Return the waveform values corresponding to the lower- and upper-reference levels for a three-transition waveform sampled at 4 MHz. Compute these values for 10% and 90%, the default levels.

load("transitionex.mat","x")
fs = 4e6;

y = [x;fliplr(x)];
t = (0:length(y)-1)/fs;

[~,~,~,LL,UL] = slewrate(y,t)

LL = 
0.2212

UL = 
2.0564

Repeat the calculation for 20% and 80%. Annotate the result on a plot of the waveform

slewrate(y,t,PercentReferenceLevels=[20 80]);

Input Arguments

x — Bilevel waveform

real-valued vector

Bilevel waveform, specified as a real-valued vector. If the input waveform does not have at least one transition, the function returns an empty matrix. The first time instant in x corresponds to t=0.

Fs — Sample rate

positive real scalar

Sample rate, specified as a positive real scalar in hertz.

t — Sample instants

vector

Sample instants, specified as a vector. The length of t must equal the length of the input bilevel waveform x. The sample instants correspond to the indices of the input vector.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: s = slewrate(x,t,Tolerance=5)

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: s = slewrate(x,t,'Tolerance',5)

PercentReferenceLevels — Percent reference levels

[10,90] (default) | 1-by-2 real-valued vector

Percent reference levels, specified as a 1-by-2 real-valued vector. For more information, see Percent Reference Levels.

StateLevels — Low- and high-state levels

1-by-2 real-valued vector

Low- and high-state levels, specified as a 1-by-2 real-valued vector. The first element is the low-state level and the second element is the high-state level. If you do not specify StateLevels, the function estimates the state levels from the input waveform using the histogram method.

Tolerance — Tolerance levels

2 (default) | scalar

Tolerance levels (lower and upper state boundaries), specified as a scalar and expressed as a percentage. 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. For more information, see State-Level Tolerances.

Output Arguments

s — Slew rate

vector

Slew rate, returned as a vector. A positive slew rate indicates that the upper-percent reference level occurs later than the lower-percent reference level. A negative slew rate indicates that the upper-percent reference level occurs before the lower-percent reference level. The slew rate is the slope of the line connecting the 10% and 90% reference levels.

lt — Time instants when input signal crosses lower percent reference level

vector

Time instants when the input signal crosses the lower percent reference level, returned as a vector.

ut — Time instants when input signal crosses upper percent reference level

vector

Time instants when the input signal crosses the upper-percent reference level, returned as a vector.

ll — Waveform values at lower reference level

vector

Waveform values at the lower-percent reference level, returned as a vector.

ul — Waveform values at upper reference level

vector

Waveform values at the upper-percent reference level, returned as a vector.

More About

Percent Reference Levels

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

$$S_1+\frac{U}{100}(S_2-S_1).$$

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

$$S_1+\frac{L}{100}(S_2-S_1).$$

Slew Rate

The slew rate is the slope of a line connecting the upper- and lower-percent reference levels. Let t_L denote the time instant when the waveform crosses the lower reference level and t_U denote the time instant when the waveform crosses the upper percent reference level. Using the definitions for the upper and lower percent reference levels given in Percent Reference Levels, the slew rate is

$$\frac{S_1+\frac{U}{100}(S_2-S_1)-\{S_1+\frac{L}{100}(S_2-S_1)\}}{t_U-t_L}=\frac{U-L}{100}\frac{S_2-S_1}{t_U-t_L}.$$

When t_L occurs earlier than t_U, the slew rate is positive. When t_U occurs earlier than t_L, the slew rate is negative.

State-Level Tolerances

You can specify lower- and upper-state boundaries for each state level. Define the boundaries 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, specify the scalar as a small number such as 2/100 or 3/100. In general, the $$\alpha \%$$ region for the low state is defined as

$$S_1\pm \frac{\alpha }{100}(S_2-S_1),$$

where $$S_1$$ is the low-state level and $$S_2$$ is the high-state level. Replace the first term in the equation with $$S_2$$ to obtain the $$\alpha \%$$ tolerance region for the high state.

This figure shows lower and upper 5% state boundaries (tolerance regions) for a positive-polarity bi-level waveform. The thick dashed lines indicate the estimated state levels.

References

[1] IEEE^® Standard on Transitions, Pulses, and Related Waveforms, IEEE Standard 181, 2003.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2012a