Digital Waveform Detailed Explanation

A digital waveform is a graphical representation of the logic level versus time. Usually, we call a waveform with only two discrete values ​​a pulse waveform. In this respect, the pulse waveform is consistent with the digital waveform, except that the digital waveform is represented by the logic level, while the pulse waveform is represented by the voltage value.
Similar to the definition of analog waveforms, digital waveforms can also be divided into periodic and non-periodic. Figure 1.1.4 shows these two types of digital waveforms:

Periodic digital waveforms are also described by period T or frequency f; and the frequency of pulse waveforms is often called pulse repetition rate PRR--Pulse Repetition Rate .
Pulse waveform parameters:
Pulse width: _tw represents the duration of the pulse action;
Duty cycle: q represents the percentage of pulse width _tw in the entire period T, and is often expressed by the following formula:
Duty cycle is an important parameter, and its definition also applies to digital waveforms.
Figure 1.1.5 shows two digital waveforms and their periods, frequencies, pulse widths, and duty cycles:

Example 1.1.1 Suppose the high level of the periodic digital waveform lasts for 6ms and the low level lasts for 10ms
. What is the duty cycle q?

Solution: According to the given high level duration, tw ₌ 6ms, and the sum of the high level and low level duration is the period T

So T = 6ms + 10ms = 16ms

So far, the digital waveforms we have discussed are all ideal waveforms. However, in actual digital systems, the rise and fall of digital waveforms take a period of time, that is, the waveform has a rise time t _r and a fall time t _f . The definition of
rise time t _r is: the time from 10% to 90% of the pulse amplitude; the definition of fall time t _f is just the opposite: the time from 90% to 10% of the pulse amplitude. The typical values ​​of t _r and t _f are about a few nanoseconds (ns), depending on different types of devices and circuits.
The definition of pulse width is the time span between two time points before and after when the pulse amplitude is 50%. The non-ideal pulse is shown in Figure 1.1.6:

Example 1.1.2 Draw a pulse waveform. Suppose its duty cycle is 50%, pulse width tw ₌ 100ns, rise time _tr = 10ns, and fall time tf ₌ 20ns.

Solution: According to the question, the pulse waveform can be drawn as follows:

Figure 1.1.7 Waveform of Example 1.1.2

Generally speaking, the rise or fall time of a waveform is much shorter than the duration of a high level or a low level. The purpose of drawing a waveform is mainly to understand the time that a high or low level experiences. Therefore, in an ideal waveform, there are only high and low levels, and the rise and fall time are ignored
. The digital waveform used in this course will use an ideal waveform.
Of course, in reality, no matter how straight the rising and falling edges of the waveforms are from the oscilloscope, t _r and t _f cannot be zero. However, in digital circuits, we only need to pay attention to the high and low logic levels. Therefore, when drawing a waveform, we only need to draw the time that the high and low levels experience, and there is no need to draw the rising and falling edges.

(a)

(b)

Figure 1.1.8 Binary bit pattern represented by logical 1 and 0
(a) Symmetrical square wave (b) Binary data

The figure above is a binary bit graph, in which the minimum time occupied by 1 or 1 is called the bit time
, that is, the time occupied by 1 bit of data. We call the number of bits transmitted per second the data rate or the bit rate .
Example 1.1.3 A communication system transmits 1.544 megabits of data per second. Find the time per bit of data.

Solution: According to the question, we only need to count down 1.544M to get the time for each bit of data:

For example, for a 22-bit binary bitmap as shown in Figure 1.1.8b, if the time taken by each bit of data is 648ns, then the 22 bits take up a total of 14256ns, or 14.256 microseconds, and the data rate is 1.544 megabits.
When designing digital integrated circuits, sometimes in order to analyze the logical relationship between various signals
, it is necessary to arrange multiple digital waveforms together in time to indicate the time relationship between them. We call such a relationship diagram a timing diagram .
Each waveform in the timing diagram is called a time signal. Timing diagrams are widely used in the design of digital integrated circuits. When designing digital application circuits such as memory and microprocessors, timing diagrams must be attached to facilitate the analysis, application and design of digital systems.
Figure 1.1.9 is an example of a timing diagram:

Figure 1.1.9 Digital timing diagram

In the figure, CP is a clock pulse signal, which is used as a time reference signal in the system. It is generally generated by a quartz crystal oscillator. As shown in the figure, the waveform is a symmetrical square wave. The specific functions of each waveform in the figure will be introduced in later courses.