Types of simple periodic signals

ANALOG AND DIGITAL SIGNALS.

Analog electrical signals- signals that change in time continuously and can take any value in a certain range of voltages, currents, frequencies or other characteristics (metrics). The analog nature is natural for many physical processes and signals - sound, movement, temperature changes, etc. Therefore, the metrics of these physical processes / signals are conveniently (and naturally) converted into analog electrical signals for the purpose of their further conversion by electronic circuits. For example, a temperature of 25.256 degrees Celsius can be encoded as a voltage of 2.5256 V. The biggest problems with analog signals are:
- their sensitivity to interference, leading to distortion of values ​​(for example, in the above example, a 0.1V interference will lead to a temperature error of 1 degree Celsius);
- high errors of cascade processing electronic circuits(amplification, integration, etc.) associated with the complexity / impossibility of manufacturing electronic components (resistors, capacitors, transistors, microcircuits) with parameters (resistance, capacitance, transmission coefficients, etc.) of high and ultra-high accuracy (up to thousandths percent) and stability in the range of temperatures, pressures, etc.

Discrete electrical signals- signals for which only values ​​from a predetermined limited set are allowed. The values ​​are indicated with a margin of error. For example, a discrete electrical signal has three allowable voltages: 0V, 5V and 10V, with a tolerance of ± 1V. Physical processes and signals can be discrete. For example, the state of the control key (on / off - 2 values) or the sensor of the set gear in the car's gearbox (the number of discrete values ​​is equal to the number of gears) or pulses in the elementary particle detector (yes / no). The use of discrete signals has an important advantage - the admissibility of setting the value with some significant error, which sharply increases the noise immunity and reduces the requirements for the accuracy of the parameters of the electronic stages.

Digital electrical signals- this is usually the name for those discrete signals that have only two valid states. Status data (for example, voltage levels 0V and 5V) are encoded by two digits - "0" and "1". These digits are equivalent to the valid values ​​of the digits of the binary representation of numbers (binary digit -binary digits or bit), as well as the valid values ​​of variables in logic algebra (Boolean algebra) - "True" (TRUE or "1") and "False" (FALSE or " 0 "), which allows these numbers to be encoded as digital electrical signals. With the help of the simplest transistor stages operating in the simplest - key mode (on / off), it is possible to implement the basic functions of the algebra of logic (logical (Boolean) functions) and, their (logical functions) through, the basic mathematical functions (addition, subtraction, multiplication , division) for numbers in binary notation. There are various storage (memory) schemes for bi-level (digital) values. Two-tier digital signal easy to transmit over long distances with significant interference (for example, "1" - voltage = 10 ± 5V, "0" - voltage = 1.5 ± 1.5V), and not only by electrical wires, but also via other types of channels, for example, via fiber-optic cable ("light" on / off).

There are elements with different methods of electrical coding of binary information;
potential,
pulse,
impulse potential.
With a potential coding method with positive logic, a high potential is taken as one ("1"), and a low potential as zero ("O"). The signal remains unchanged for a period of at least one repetition period of the synchronization signals (Fig. 1, a).
In pulse coding of binary information, most often "1" corresponds to a pulse in phase with the synchronization signal, and "O" - the absence of a pulse; the value of the signal in the pause between the synchronization signals is not considered (Fig. 1, b).
One of the varieties of the pulse method is dynamic coding of signals, when a sequence of pulses between two synchronization pulses corresponds to unity, and their absence corresponds to zero (Fig. 1, c).

Rice. 1. Methods of representation of binary information, with potential a), with impulse b) and with impulse-potential c) coding methods

All these properties made it possible to put digital signals in the basis of modern computing devices, in particular, microprocessors, and in the basis of data storage and transmission systems.

LOGICAL STATES

Voltage is usually used to encode the values ​​of logical variables or binary digits (bits). Current, frequency and other signal characteristics are also used, but only in special cases - mainly when transferring data or as a convenient option for interfacing electrical cascades.
Allowable voltage levels according to their values ​​are conventionally called HIGH and LOW. As mentioned above, the level corresponds not to one, but to a range of voltage values: for example, 2.5.5V - High level, 0.1 V - LOW level, but for convenience, indicate only the "nominal" (usually extreme) level, for example, 5V and 0V. It should be understood that the LOW level is understood to be the low voltage value, and not the complete absence of a signal, since such a variant may occur when the line is broken.
The two indicated voltage levels can be associated with a pair of logical values ​​(logical states, binary digits).
If the HIGH voltage level of the digital signal corresponds to the value "1" or "TRUE", and the LOW voltage level corresponds to the value "0" or "FALSE", then this method of encoding a logical variable is called POSITIVE (POSITIVE) LOGIC.
IF the HIGH voltage level of the digital signal corresponds to the value "0" or "FALSE", and the LOW voltage level corresponds to the value "1" or "TRUE", then this method of encoding a logical variable is called NEGATIVE (NEGATIVE) LOGIC.
The type of logic (POSITIVE or NEGATIVE) is not only a characteristic of the digital signal itself, but also a characteristic of a digital element (block, circuit) that processes a given signal based on this method of encoding it. For example, the element of the popular logic chip SN7408 is fully referred to in the documentation as "two-input AND gate with positive signal coding." If you use negative coding, then the function of this element will change to "OR".
Modern element base and circuitry as a whole are focused on positive (positive) logic. However, in some cases, negative (negative) logic may be a more convenient way to encode digital or logical values. For example, the circuitry for detecting a key press on a keyboard is often structured in such a way that a HIGH level is generated when the button is not pressed, and a LOW level when a button is pressed. That is, if you encode the fact of pressing the button as "TRUE" and a LOW signal level is generated, then we get negative (negative) coding. Often the convenience of negative logic for signals of digital elements is determined by the peculiarities of the internal circuitry of these elements.
In order not to get confused with which elements in the circuit use positive coding and which ones are negative, it is agreed that all elements in the circuit use one type of signal coding (for example, positive), and if a signal with negative coding, it is converted from / to positive by inverting. Such inverted signals are indicated on the diagrams by a line above the signal name (the sign of the boolean operation "negation"), and the input or output of the element on which the signal is inverted (often this is an imaginary inversion - the circuit uses a directly negatively encoded signal inside itself), is indicated by a circle.

Notes:
1) Due to the greater natural perception (the principle "more corresponds to more") and the prevalence of positive logic in schematic slang, they often call the HIGH voltage level - "1", and the LOW voltage level - "0". Thus, in the case of using negative logic, confusion can arise: speaking of "one on the signal line" means a HIGH voltage level, which actually corresponds to the logical value "0".
2) The terms "positive" logic and "positive" logic, as well as "negative" and "negative" logic are equivalent and are found in various combinations in the literature. The original source is the English words "positive" and "negative". There is also a variant of "direct" - "inverse" logic (it is understood that a signal with negative logic ("inverse") can be obtained by inverting a signal with positive logic ("direct").

DIGITAL SIGNAL PARAMETERS

The parameters of real digital signals, the most important for circuit design, are:
- Voltage range for logic "0" and "1", for outputs of logic elements / circuits and for inputs of digital elements / circuits;
- Load capacity (fanout ratio) of digital circuit outputs - fanout;
- Duration of state switching - time of signal state measurement from LOW to HIGH and vice versa (transition from logical "0" to "1" and vice versa) - transition time;
- Time delay of a digital signal when "passing" through a logic gate / circuit - propagation delay.

Voltage ranges for logical "0" and "1".

Another feature / problem is the use of digital microcircuits with different supply voltages. The fact is that when the supply voltage of the microcircuits changes, the high and low voltage levels also change (see the figure below). At the moment, in digital technology, the most common supply voltages are 5V, 3.3V, 2.5V, 1.8V. The need to reduce the supply voltage is caused by many reasons, the main of which are a decrease in consumed and released power, an increase in the speed of circuits, a decrease in the physical size of transistors on a chip of integrated circuits.

Rice. 2. Voltage levels of digital signals for microcircuits with different supply voltages

It can be seen that the levels of circuits with different power supplies are not compatible with each other. Moreover, they often have to be used together in one scheme. For example, the power supply of the microprocessor can be 5V, and the power supply of the microcircuits connected to it can be 3.3V. And analogs with a different power supply are not produced! In this case, add special stages / microcircuits for converting voltage levels of digital signals. Sometimes these stages are built into microprocessors. Sometimes it is possible to achieve partial level compatibility, for example, a 3.3V microcircuit can be connected to it input signals with voltage up to 5V with correct recognition of HIGH and LOW levels. Reverse connection may not be allowed, for example, outputs "3.3V" to inputs "5V".
It should be noted that since any sharing of circuits with different voltage levels is a potential source of errors and often the reason for the complexity of the circuit, then, unnecessarily, they try not to make mixed circuits.

Load capacity (branching ratio at the outlet)

The load capacity of a digital circuit output shows how many digital circuit inputs can be connected to a given output without overloading the output stages and without distorting the digital signal levels for the inputs. The load capacity depends on and is set for a pair of "output-input" types. For example, for an output of type X, the number of connected inputs of type Y and the number of connected inputs of type Z are set, etc. The loading capacity may differ for the HIGH and LOW levels, but usually only one is indicated, the lower value.
Typical load capacity is 20 inputs of the same type as the output. If inputs of another type are connected to an output of one type, the ratio changes.
The following are the negative consequences of overloading the outputs:
- The LOW level output voltage may exceed Iv.O.max. and LOW level will be defined as HIGH;
- The HIGH level output voltage may be lower than IvhL.min. and the HIGH level will be defined as LOW;
- The time of level change from LOW to HIGH and vice versa exceeds the value allowed by the specification of this circuit;
- The propagation delay of the signal through the circuit exceeds the value allowed by the specification of this circuit;
- Overheating of circuit elements due to increased heat generation due to overload. As a result, a change in circuit parameters (voltage levels, load capacities, performance parameters) or physical damage to overheated elements may occur.

Duration of state switching

Rice. 3. Ideal (a) and real (b, c) switching of digital outputs

Transition delay is a negative factor in the functioning of digital circuits and, along with signal propagation delay, significantly complicates their design. The main reasons for this:
- finding the output in an undefined state leads to the possibility of incorrect operation of the input, moreover, multiple;
- desynchronization in the operation of elements / parts of digital circuits;
- increased power consumption while in an indeterminate state.

Signal propagation delay.

The propagation delay through the element (propagation delay, tp) is the time between the edge (edge) of the digital signal at the input of the element and the edge (input edge) of the signal at the output of the element caused by it. The propagation delay is caused by the response time of the transistor switches inside the element. She will be more than more quantity such keys along the signal propagation path inside the element, i.e. the number of successive stages. Propagation delay can be different for the output slope from LOW to HIGH (tpLH) and for the slope from HIGH to LOW (tpHL).

1 year

The purpose of the story is to show what is the essence of the concept of "signal", what common signals exist and what common characteristics they have.

What is a signal? To this question, even a small child will say that this is "such a thing with the help of which you can communicate something." For example, using a mirror and the sun, signals can be transmitted over a line-of-sight distance. On ships, signals were once transmitted using semaphore flags. Specially trained signalmen were engaged in this. Thus, with the help of such flags, information was transmitted. Here's how to convey the word "signal":

There are many signals in nature. In fact, anything can be a signal: a note left on the table, some sound - can serve as a signal to start a certain action.

Okay, with such signals everything is clear, so I will turn to electrical signals, which in nature are no less than any others. But at least they can be somehow conventionally divided into groups: triangular, sinusoidal, rectangular, sawtooth, single impulse, etc. All of these signals are named for the way they look when plotted on a chart.

The signals can be used as a metronome for counting beats (as a timing signal), for timing, as control pulses, for controlling motors or for testing equipment and transmitting information.

Characteristics of el. signals

In a sense, an electrical signal is a graph that reflects the change in voltage or current over time. What in Russian means: if you take a pencil and mark the time on the X-axis, and the voltage or current on the Y-axis, and mark the corresponding voltage values ​​at specific times with dots, then the final image will show the waveform:

There are a lot of electrical signals, but they can be divided into two large groups:

• Unidirectional
• Bidirectional

Those. in unidirectional current flows in one direction (or does not flow at all), and in bidirectional current is variable and flows either "there", then "here".

All signals, regardless of type, have the following characteristics:

• Period - the time interval after which the signal begins to repeat itself. Most often denoted by T
• Frequency - indicates how many times the signal will be repeated in 1 second. Measured in hertz. For example 1Hz = 1 repetition per second. Frequency is the inverse of the period (ƒ = 1 / T)
• Amplitude - measured in volts or amperes (depending on which signal: current or voltage). Amplitude refers to the "strength" of the signal. How far the signal graph deviates from the X-axis.

Types of signals

Sinusoid

I think that presenting a function whose graph in the picture above makes no sense is well known to you. sin (x). Its period is 360 o or 2pi radians (2pi radians = 360 o).

And if you divide to divide 1 sec by the period T, then you will find out how many periods are indicated in 1 sec, or, in other words, how often the period repeats. That is, you will determine the frequency of the signal! By the way, it is indicated in hertz. 1 Hz = 1 sec / 1 rep per sec

Frequency and period are opposite to each other. The longer the period, the lower the frequency and vice versa. The relationship between frequency and period is expressed by simple ratios:

Signals that resemble rectangles in shape are called "rectangular signals". They can be conventionally divided into just rectangular signals and meanders. A square wave is a square wave with equal pulse and pause durations. And if we add up the duration of the pause and the pulse, we get the period of the meander.

A regular square wave signal differs from a square wave in that it has different pulse and pause durations (no pulse). See the picture below - she speaks better than a thousand words.

By the way, there are two more terms for square-wave signals that you should know. They are inverse to each other (like period and frequency). it fabledness and fill factor. The load factor (S) is equal to the ratio of the period to the pulse duration and vice versa for coeff. filling.

Thus, a square wave is a rectangular signal with a duty cycle of 2. Since its period is twice the pulse duration.

S - duty cycle, D - duty cycle, T - pulse period, - pulse duration.

By the way, the graphs above show ideal square wave signals. In life, they look slightly different, since in no device can the signal change absolutely instantly from 0 to some value and back down to zero.

If you go up the mountain, and then immediately go down and record the change in the height of our position on the graph, we will get a triangular signal. A crude comparison, but true. In triangular signals, the voltage (current) first increases and then immediately begins to decrease. And for a classic triangular signal, the rise time is equal to the decay time (and is equal to half the period).

If the rise time of such a signal is less or more than the decay time, then such signals are already called sawtooth. And about them below.

Sawtooth signal

As I wrote above, an unbalanced triangle waveform is called a sawtooth waveform. All these names are conditional and are needed just for convenience.

Material carriers of information are signals of various physical nature. In a narrow sense, signals are called oscillations of electric current, voltage, electromagnetic waves, mechanical oscillations of some elastic medium. Information signals are formed by changing certain parameters of the carrier according to a certain law. Thus, an information signal can be any physical process, the parameters of which are capable of changing depending on the transmitted information. This process of changing the parameters of the carrier is usually called modulation, and the parameters themselves information... Unlike a message, receiving a signal after it has been generated is optional.

When a signal passes through a physical medium, various destabilizing factors act on it, as a result of which noise and interference of a very different nature arise (Fig. 12.4). When registering a signal, the main task is to isolate the useful component from the total signal and to maximize the suppression of noise and interference.

Rice. 12.3.

To analyze, investigate and process signals, you must use mathematical model signal, which is mathematical description signal. The word "model" comes from the Latin modelium, which means: measure, way, image. The purpose of the model is that it displays only the most important features of the signal and allows one to abstract from its physical nature and the material form of the carrier. As a rule, the signal description is given functional dependence its values ​​on the independent variable, for example, s (t).

The simplest signals are one-dimensional signals, i.e. signal value depends on one parameter (for example, sound signals). An example of a one-dimensional signal in Figures 12.3, 12.4.

In general, signals are multidimensional functions of spatial, temporal, and other coordinates. An example is the intensity of a computer image p (x, y) (Figure 12.5).

According to the form of representation, signals are of two types - analog and digital (discrete)(fig.12.6). Analog signal is defined for any value of the independent parameter, that is, it is a continuous function of a continuous argument. Sources of analog signals, as a rule, are physical processes and phenomena that are continuous in their development (dynamics of changes in the values ​​of certain properties) in time, in space or in any other independent variable, while the recorded signal is similar (analogous) to the process that generates it.

The fundamental analog signal is the sine wave (Figure 12.7). In general, a sinusoidal signal can be represented as follows:

A sinusoidal signal can be defined by three parameters: maximum amplitude, frequency and phase. Maximum amplitude is the maximum value or intensity of a signal over time; the maximum amplitude is measured, usually in volts. Frequency is the rate at which signals are repeated (in periods per second, or hertz). The equivalent parameter is the signal period T, which is the time over which the signal repeats; hence, . Phase is a measure of the relative time offset within an individual signal period.

Most analog signals in nature are more complex in shape. Periodic, that is, repeating at a certain time interval, arbitrary waveforms, can be represented as a sum harmonic vibrations using the Fourier transform. By applying the Fourier transform, i.e. By adding together a sufficient number of sinusoidal signals with appropriate amplitudes, frequencies and phases, an electromagnetic signal of any shape can be obtained. Likewise, any signal is considered as a collection of periodic analog (sinusoidal) signals with different amplitudes, frequencies and phases.

The digital signal can be expressed as follows:

The set of spectral components of the signal forms it spectrum... The amplitude of each spectral component characterizes the energy of the corresponding harmonic of the fundamental frequency of the signal. The higher the rate of change of the signal, the more high-frequency harmonics in its spectrum. The difference between the maximum and minimum frequency in the signal spectrum is called signal spectrum width.

In accordance with a change in the amplitude of an analog signal, its power or energy changes, proportional to the square of the amplitude. Depending on the signal measurement time, a distinction is made between average and instantaneous power... The decimal logarithm of the ratio of the maximum instantaneous signal power to the minimum is called dynamic range signal.

The sign of the protected signal, which allows it to be detected and recognized among other signals, is called unmasking... Signal attributes describe the parameters of fields and electrical signals generated by the protected object: power, frequency, signal type, spectrum width, etc.

Analog signal described by a set of parameters that are its features. These include the parameters we discussed earlier:

• frequency and frequency range;
• amplitude (and power) of the signal;
• signal phase;
• signal duration;
• type of modulation;
• signal spectrum width;
• dynamic range of the signal.

The unmasking features of signals include the time of their appearance, depending on which signals are divided into regular (the recipient knows the time of appearance) and random (the time of occurrence is not known).

The type of information contained in the signal changes its unmasking features. For example, a standard speech signal transmitted over telephone line, has a spectrum width of 300-3400 Hz, audio - 16-20000 Hz, television - 6-8 MHz, etc.

For discrete signals, the amplitude has a finite, predetermined set of values. The most common signal used, in particular, in computers, is a binary signal. The binary signal has two amplitude levels: low and high.

A discrete signal is generally characterized by the following parameters: amplitude, power, pulse duration, period, signal spectrum width, pulse duty cycle (the ratio of the period to the duration of one pulse).

A binary periodic signal is characterized by the following parameters:

When discrete signals pass through the wires, their spectrum changes due to various influencing factors from the outside and the properties of the transmission medium. As a result, their shape is distorted and the steepness of the pulses decreases, which reduces the distance of their transmission.

3. Signals. Types of signals and their parameters

Characteristics of various signals

All signals can be subdivided into periodic and non-periodic.

A periodic signal is a signal whose values ​​are repeated at regular intervals, called a signal repetition period, or simply period... For non-periodic signal this condition is not met.

The simplest periodic signal is a harmonic oscillation.

where S, w - amplitude and angular frequency of vibration.

Another example of a periodic signal is the sequence rectangular pulses(fig. 3.2, a). What do you think this pulse train consists of? It turns out from sinusoids. Take a look at fig. 3.2. As the initial sinusoid, we choose one for which the oscillation period coincides with the period T rectangular pulses (Fig. 3.2, b)

, (3.1)

where is the amplitude of the sinusoid, and.

Oscillation (3.2.) Of a given frequency and amplitude can be represented in the form of a graph: mark the value on the frequency axis and draw a vertical line with a height equal to the signal amplitude (see Fig. 3.2, b).

The next sinusoid has an oscillation frequency 3 times higher, and an amplitude 3 times lower.

The sum of these two sinusoids still has little resemblance to rectangular pulses (Fig. 3.2, v). But if we add to them sinusoids with oscillation frequencies of 5, 7, 9, 11, etc. times larger, but with amplitudes of 5, 7, 9, 11, etc. times smaller, then the sum of all these fluctuations:

Rice. 3.2. Periodic sequence of rectangular pulses (a) and the formation of its signal (b – e)

where, will not be so much different from rectangular pulses (Fig. 3.2, G and d). Thus, the degree of "squareness" of the pulses is determined by how many sinusoids with ever higher oscillation frequencies we will add up.

It may seem that the representation of rectangular impulses in the form of a set of sinusoids is nothing more than a mathematical device and has nothing to do with reality. However, it is not. Radio engineers are very familiar with devices (they are called spectrum analyzers) that allow you to isolate each sinusoid entering a complex signal.