# Signal Parameters

Last Modification: February 4 2013

For complex waveforms, it's often inadequately to specify only the effective or average value. Sometimes there are limits on parameters such as ringing, overshoot and rise and fall times, and must also be specified.

## Defining parameters.

Figure 1 shows a not ideal square wave with the definitions in the time and amplitude domain.
On the right side of the square wave the corresponding histogram is shown. This histogam shows how often a certain value appears. The histogram consists of a number of containers (bins) that the amplitude levels represents. From the voltage that is analysed samples are taken with a regular time interval. The value of the sample is measured and the counter of the corresponding bin is increased. The two "bins" that have the highest values are defined as the top and base.

Below are some common definitions for a square wave shaped voltage. (Where voltage is read, it can also be replaced by current.)

• Base (line): The lower of the most common levels.
• Top (line): The higher of the most common levels.
• Base line offset: The base line level in relation to the reference (for example 0 V).
• Amplitude: The difference between the base and top.
• pkpk (peak to peak): The difference between the highest and lowest occurring levels.
• Minimum: The lowest occurring value in relation to the reference (for example 0 V).
• Maximum: The highest occurring value in relation to the reference (for example 0 V).
• Rise time: The time to rise between two specified values. The specified values are the 10% en 90% levels between base en top. The specification 20% and 80% is also used.
• Fall time: The time to fall between two specified values. The specified values are the 90% en 10% levels between base en top. The specification 80% and 20% is also used.
• Width: The time between the 50% levels of the rising and falling edge.
• Period: The time of a single period. Defined as the time between the pass of the 50% levels of the rising edge.
• Frequency: The number of periods per second.
• (Sag of) droop: The drop (of rise) of the horizontal parts of a square wave.
• Overshoot: The shoot through of the voltage above the top line after the rising edge. Defined as the highest level of the rising edge above the top line. Or the shoot through of the falling edge below the base line. In that case specified as the lowest level of the falling edge in relation to the base line.
• Preshoot: Voltage peak prior the rising or falling edges. The value is in relation of the base or top line.
• Ringing: A damped oscillation after the rising or falling edge. Defined as the peak to peak value of the oscillation.
• Settling time: The time needed to damp the ringing till a predefined amplitude of the start value.

The above definitions can also be applied to other waveforms.

### Amplitude

The term amplitude, which is used in measuring and monitoring, differs from the official definition as used in maths and physics: The amplitude is the maximum value of a harmonic vibration relative to its resting state.

Manufacturers of measuring instruments use most often the peak to peak value of a signal as the definition of the amplitude; The value of the output of function generators is identified as: "Amplitude ... Vpkpk." The term amplitude is also used in general to indicate a quantity: "Amplitude accuracy:... %."

In practice, the official definition is of little importance because pure harmonic waveforms are very rare. In this article the general definition is used: The peak to peak value of a clean signal.

### Histogram

A number of measuring instruments, such as digital oscilloscopes, uses the histogram to determinate the base and top. The amplitude is the difference between the top and base level. Caution should be taken, not all signals has an easy identifiable base and top as shown below.

## Noise influence

The graph on the right shows a clean sinewave (red) and a sinewave with noise (blue) with the related histograms in corresponding colours.
The histogram shows that the clean sinewave has the most common values on the minimum and maximum levels. The histogram has a sharp boundary at the ends. The two peaks in the histogram correspond to the peaks of the sinewave.
The sinus with noise has less sharp boundaries in the histogram. Also, it is noticeable that the peaks in the histogram are slightly shifted towards the center.
The histograms show evidently that a signal with noise measures a smaller amplitude compared with the signal without noise. This situation can be avoided by removing the noise prior the measuring by using a low-pass filter. The real amplitude is equal for both (with and without noise) signals.

## Incomplete references

The following example shows a full wave rectified sine. The histogram shows now only a single peak. The top level is well defined, but the base can not recognised due to the absence of a lower peak in the histogram. A good instrument will therefore use other methods to find the base and top.
The figure shows also that by doing a full wave rectifying a signal is created that has twice the number of periods. The measured frequency has doubled.

## Flat histogram

As a final example, a saw tooth or triangle waveform. With this shape, all voltages are equally common. The histogram is therefor completely flat. Again, a good instrument will choose a different method to define the top and base. Often, the base and top will be made equal to the edges of the histogram. This has the disadvantage that the top and base are not well defined if a signal is noisy. The best practice is to remove the noise before the signal is measured.

A note about the definitions in the time domain: The rise and fall times are exactly defined. The instrument will do the measurement between the 10...90% or 20...80% boundaries. The measured time will therefore be smaller.

### What is measured?

The examples above shows already that measured values depend on the measurement method and signal conditions. Check always the method the instrument uses.

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