The "waveform" of a signal is a graphical representation of a wave, showing a physical quantity in relation to time. A periodic wave whose quantity changes sinusoidally with respect to time is called a "sine wave," a waveform in which the amplitude transitions from a steady state (the gradient changes by a specified value), lasts for a finite time, and returns to the original state is called a "pulse," a pulse train in which the pulse is rectangular and repeats periodically is called a "square wave," and a pulse with a steep change and short duration is called an "impulse."
In measuring instruments, waveforms are input as voltage signals, and generally, the amplitude of the waveform is displayed relative to a "reference level" of 0V.
Sine wave (AC waveform)
Vp: Peak value
Vpp: Peak-to-peak value
Vr: RMS value = Vp / √2
T: Repeating period (s)
f: Repetition frequency = 1 / T (Hz)
pulse
The magnitude of an AC waveform is expressed as follows: the "peak value," which is the maximum positive or negative value of the waveform within a specified time; the "peak-peak value," which is the difference between the positive and negative peak values; the "average value," which is the average of the absolute values of instantaneous AC values over one period; and the "effective value," which is expressed as the DC value at which the power consumed by the same resistance is the same.
For a sine wave, the peak value Vp, RMS value Vr, and peak-to-peak value Vpp have the following relationships:
Vr = √2Vp (√2: represents the square root of 2)
Vpp = 2Vp
AC waveform
<Average values>
The mean value is the average of the absolute values of instantaneous AC values over one period. If the instantaneous AC value is a(t), then the mean value can be calculated using the following formula.
1/𝑇 ∫129_0^𝑇▒|𝛼(𝑡)|ⅆ𝑡
Here, T is the period of the alternating current.
<Effective value>
The magnitude of an alternating current (AC) is expressed as the DC value at which the power consumed by the same resistance is the same. This value is equal to the square root of the average of the squares of the instantaneous AC values over one period. If the instantaneous AC value is denoted by , its RMS value can be calculated using the following formula.
Here, T is the period of the alternating current.
Furthermore, to represent the point in time at which a particular phenomenon occurs, it is expressed using "point in time," which indicates a single point on the time axis representing the flow of time; "duration," which is the time from the beginning to the end of a certain phenomenon; "period" ("repetition time"), which is the time of one cycle of a repeating waveform; "frequency," which is the reciprocal of this period; "delay time," which is the time from a certain point in time; and "phase," which is the period time expressed in terms of electrical angles, with the delay time being 360 degrees.
In the case of a square wave, its magnitude is expressed as follows: the steady state is called the "baseline" (low level), the transition width is called the "pulse amplitude" (high level), the duration of the pulse is called the "pulse width," the repetition frequency in the pulse train is called the "pulse repetition frequency," the ratio of the pulse width to one period is called the "pulse occupancy," or the ratio of the low level to the high level is called the "duty cycle."
When the baseline of a waveform differs from a reference level, the waveform is said to be offset, and its magnitude is expressed as the amplitude of the baseline relative to the reference level.
square wave
Depending on the transmission conditions of the pulse signal, strains such as "preshoot," which occurs just before the transition and swings in the opposite direction; "spikes," which are pulse-like strains that are sufficiently short compared to the pulse width; "ringing," which is a damped, oscillating strain; and "tilt," which is a strain where high-level and low-level signals that should be horizontal become tilted, may occur.
Distorted waveform
Now, pulse counter measuring instruments such as tachometers have a circuit in the signal input section that has a function to reshape distorted waveforms into clean waveforms.
Normally, the signal is converted into a pulse, which, depending on the magnitude of the input, is converted into two different states: high level and low level. The input voltage that marks the boundary between these high and low levels is called the "threshold" (also known as the threshold voltage).
In AC-coupled circuits, the threshold voltage is generally 0V (zero-crossing).
Some DC coupling systems allow you to adjust the threshold setting using a volume control called the level (also known as the trigger level). There is a dead zone where the system will not operate if the signal amplitude is too small.
The specifications in catalogs and other documentation include information on the types of signal waveforms that can be operated, their amplitude, and frequency range. Make sure to input a signal that matches the instrument's specifications.
(Excerpt from the email newsletter issued on August 23, 2002)
