Separation of signals. Frequency division multiplexing
If we consider the simplest network, consisting of two points A and B, between which N digital channels are organized (it is not specified here how), then the independent transmission of signals through these channels is possible if these channels divided between themselves. The following ways of dividing channels between two points are possible:
Space division, using different transmission media to organize channels;
Time division (time division), which carries out the transmission of digital signals at different time intervals in different channels;
Code division, in which division occurs by applying specific code values for each signal;
Wavelength division, in which digital signals are transmitted over digital channels organized at different wavelengths in an optical cable;
Mode separation when organizing a channel on various types of electromagnetic waves (modes) of hollow waveguides and optical cables;
Polarization separation of an electromagnetic wave of hollow waveguides and an optical cable.
In all cases, the separation of channels between two nodes does not imply the presence of a single medium for the propagation of an electromagnetic signal. To transmit signals in one propagation medium, channels separated by one or another criterion (except for spatial) are grouped using the combining (multiplexing) operation, forming a digital transmission system (DSP).
In digital switching systems (DSC), this combination and division of signals is most often done using time division multiplexing. Time multiplexing is currently an important component not only of the DSP, but also of the DSC, and plays a decisive role especially at the junction of these systems. In telephony, time division multiplexing is defined as a tool for distributing (splitting and combining) telephone channels in time when transmitted over a single physical communication line. In this case, one of the types of pulse modulation is used. Each pulse corresponds to a signal from one of the channels; signals from different channels are transmitted sequentially.
The principle of temporal combining of signals is shown in Fig. 1.8, which depicts a rotating commutator TO(center), alternately connecting to the outputs of the channel sequence. The switch is connected to the output of channel 1 at the time t, to the output of channel 2 at the moment of time t 2, to the output of channel N at the moment of time t N, after which the process is repeated. The resulting output signal will consist of a sequence of signals from different channels, offset from each other by time At.
Separation of signals on the receiving side will be similar: the rotating switch is alternately connected to the channels, transmitting the first signal to channel 1, the second to channel 2, etc. Obviously, the operation of the switches on the receiving and transmitting sides must be synchronized in a certain way, so that the signals arriving along the line are directed to the necessary channels. In fig. 1.9 shows the timing diagrams for the case of combining three channels through which amplitude - pulse modulated signals are transmitted.
As mentioned above, DSPs use PCM signals, which are digital code sequences consisting of several bits.
Temporary unification several PCM signals is a combination of code sequences coming from different sources for joint transmission over a common line, in which the line at a time is provided for the transmission of only one of the received code sequences.
Temporal combining of PCM signals is characterized by a number of parameters. Cycle temporal combining is a set of consecutive time intervals allocated for the transmission of PCM signals from different sources. In the time-combining cycle, each PCM signal is assigned a specific time interval, the position of which can be determined unambiguously. Since usually each signal corresponds to its own transmission channel, such a time interval allotted for the transmission of one channel is called timeslot(CI). There are two types of cycle - basic, whose duration is equal to the sampling period of the signal, and supercycle - a repeating sequence of successive main cycles, in which the position of each of them is uniquely determined.
Rice. 1.8. Circular interpretation of time division multiplexing
Rice. 1.9. Temporary unification
When constructing PCM equipment, use is made of homogeneous temporary association PCM signals, at which the bit rates of the code words of the combined PCM signals are the same. This makes it possible to produce group association PCM signals and build on the basis of this hierarchical systems for the transmission of PCM signals.
L EK C I Z No. 16
Theme:
Discipline lecture text:"Theory of electrical communication"
Kaliningrad 2013
Lecture text No. 27
by discipline:"Theory of electrical communication"
"Frequency, time and phase separation of signals"
Introduction
The most expensive element of a communication system is the communication line. In transmission systems, the common medium can be coaxial, balanced or optical cables, overhead communication cables or radio links. It becomes necessary to seal the physical circuits by simultaneously transmitting information from several terminal communication means. Compaction of the communication line is carried out by means of compression equipment, which, together with the transmission medium, forms multi-channel transmission system.
Multichannel transmission system(MRP) is a set of technical means that provide simultaneous and independent transmission of two or more signals over one physical circuit or communication line.
In multichannel telecommunications, frequency division multiplexing (FDM) and time division multiplexing (TDM) are used. Code division multiplexing is used in mobile radio communication systems.
With FDC, a certain spectrum (band) of frequencies is assigned to each communication channel. With TDM, pulse trains of very short pulses are transmitted to the communication line, containing information about the primary signals and shifted relative to each other in time.
MRPs with RDC are analog, and MRPs with RDC are digital systems.
For these purposes, multiple access and compaction systems are being created. It is these systems that underlie modern communication.
Frequency division of signals
The functional diagram of the simplest multichannel communication system with frequency separation of channels is shown in Fig. 1
In foreign sources, the term Frequency Division Multiply Access (FDMA) is used to denote the principle of frequency division of channels (FDMA).
First, in accordance with the transmitted messages, the primary (individual) signals having energy spectra,, ..., modulate the subcarriers of each channel. This operation is performed by modulators,, ..., channel transmitters. The spectra of the channel signals obtained at the output of the frequency filters,, ..., occupy respectively the frequency bands,, ...,, which in the general case may differ in width from the spectra of the messages,, ...,. With wideband modulation types, for example, FM, the spectrum width 
, i.e. in general . For simplicity, we will assume that AM-SSB is used (as is customary in analog SP with FDCs), i.e. and .
Let us trace the main stages of signal formation, as well as the change in these signals in the process of transmission (Fig. 2).
We will assume that the spectra of individual signals are finite. Then it is possible to select the subcarriers w K so that the bands, ..., do not overlap in pairs. Under this condition, the signals; 
mutually orthogonal.
Then the spectra,, ..., are summed up and their totality is fed to the group modulator (). Here, the spectrum is transferred by means of the carrier frequency oscillation to the frequency range allocated for the transmission of this group of channels, i.e. the baseband signal is converted to a linear signal. In this case, any type of modulation can be used.
At the receiving end, the linear signal is fed to the group demodulator (receiver P), which converts the spectrum of the linear signal into the spectrum of the group signal. The spectrum of the baseband signal is then again divided by means of frequency filters,, ..., into separate bands corresponding to the individual channels. Finally, the channel demodulators D convert the signal spectra into message spectra for the recipients.
From the explanations given, it is easy to understand the meaning of the frequency division method. Since any real communication line has a limited bandwidth, then in multichannel transmission, a certain part of the total bandwidth is allocated to each individual channel.
On the receiving side, signals of all channels act simultaneously, differing in the position of their frequency spectra on the frequency scale. To separate such signals without mutual interference, the receiving devices must contain frequency filters. Each of the filters must pass without attenuation only those frequencies that belong to the signal of this channel; the frequency of signals of all other channels must be suppressed by the filter.
In practice, this is not feasible. The result is mutual interference between channels. They arise both due to the incomplete concentration of the signal energy of the k-th channel within a given frequency band, and due to the imperfection of real band-pass filters. In real conditions, it is also necessary to take into account mutual interference of nonlinear origin, for example, due to the nonlinearity of the characteristics of the group channel.
To reduce the crosstalk to an acceptable level, it is necessary to introduce guard frequency intervals (Fig. 3).
So, for example, in modern multichannel telephone communication systems, each telephone channel is allocated a kHz frequency band, although the frequency spectrum of transmitted audio signals is limited by a band from
The functional diagram of the simplest multichannel communication system with frequency division of channels is shown in Figure 6.2.
Figure 6.2 - Functional diagram of a multichannel communication system with frequency
channel separation
In foreign sources, the term is used to denote the principle of frequency division of channels (FDM) Frequency Division Multiply Access(FDMA).
First, in accordance with the transmitted messages, the primary (individual) signals having energy spectra G 1 (w), G 2 (w), ..., G N(w) modulate subcarriers w K of each channel. This operation is performed by modulators M 1 , M 2 , ..., M N channel transmitters. Obtained at the output of frequency filters F 1 , F 2 , ..., Ф N spectra g K ( w) of the channel signals occupy, respectively, the frequency bands D w 1, D w 2, ..., D w N, which in the general case may differ in width from the message spectra W 1 , W 2 , ..., W N.
Let's trace the main stages of the formation of signals, as well as the change in these signals in the process of transmission (Figure 6.9).
Signal spectra g 1 (w), g 2 (w),..., g N(w) are summed up (S) and their totality g(w) is fed to the group modulator ( M). Here the spectrum g(w) using the carrier frequency oscillation w 0 is transferred to the frequency range allocated for the transmission of this channel group, i.e. group signal s(t) is converted to a linear signal s L ( t). In this case, any type of modulation can be used.
At the receiving end, the linear signal goes to the group demodulator (receiver NS), which converts the spectrum of the line signal to the spectrum of the baseband signal g¢ (w). The baseband spectrum is then filtered using frequency filters F 1 , F 2 ,...,Ф N splits again into separate stripes Dw K corresponding to individual channels. Finally, channel demodulators D transform signal spectra g K (w) to message spectra G ¢ K (w) intended for recipients.
Figure 6.3 - Conversion of spectra in a frequency division multiplexing system
The meaning of the frequency method of channel separation is as follows: a real communication line has a limited bandwidth, and in multichannel transmission, a certain part of the total bandwidth is allocated to each individual channel.
On the receiving side, signals of all channels act simultaneously, differing in the position of their frequency spectra on the frequency scale. To separate such signals without mutual interference, the receiving devices must contain frequency filters. Each of the filters F K must pass without attenuation only those frequencies wÎDw K that belong to the signal of this channel; the frequency of signals of all other channels must be suppressed by the filter.
To reduce the crosstalk to an acceptable level, guard frequency intervals D w PROTECTION (Figure 6.4).
Figure 6.4 - Spectrum of the group signal with guard intervals
In modern multichannel telephone systems, each telephone channel is allocated a frequency band of 4 kHz, although the frequency spectrum of transmitted audio signals is limited to a band from 300 to 3400 Hz, i.e. the spectrum width is 3.1 kHz. Between the frequency bands of adjacent channels, intervals of 0.9 kHz are provided, designed to reduce the level of mutual interference when filtering signals. This means that in multichannel communication systems with frequency division signals, only about 80% of the bandwidth of the communication line is effectively used.
When transmitting signals from several sources of messages, it becomes necessary to separate these signals so that on the receiving side it is possible to determine to which source of messages each signal belongs and send it to its receiver. A similar problem occurs when transmitting the elements of the code signal. In telemechanics, three main methods are used to separate signals or their elements: conductive (circuit), time and frequency.
At conductive separation for each message (or code signal element) an independent electrical communication circuit is assigned. Independent and parallel transmission of messages can be carried out on each electrical circuit. Consider a conductive separation system that uses polar current indicators to transmit messages (Figure 2.9). The sending of signals from each source of messages is carried out by two-position keys, depending on the position of which one or another direction of direct current is set in the line wires. The receivers are polarized electromagnetic relays. The transmission of information from each source of messages is carried out through its own wire, the return wire is common for all channels. The extremely uneconomical use of communication lines practically excludes the use of this separation method in telemechanics for communication line lengths exceeding 3-5 km. Really conductive signal separation is used in remotely controlled systems.
Rice. 2.9. Conductive signal separation circuit
At time division(compaction) of signals, each of the message sources is alternately provided with a communication line: for the time interval t1, the signal of the first source is transmitted, during the time interval t2 for the second, etc. (in Fig.2.10, a transmission from five sources is shown). It follows from this figure that with time division, the signal from each source occupies its own time interval, which is not occupied by the signal from another source. The time it takes to transmit signals from all sources is called a cycle.
Figure 2.10. Explanation of time division of signals
a) separation of channels on the time axis.
c) implementation of the synchronization method using the network
To implement the temporary method, the transmitting and receiving nodes of telemechanics devices are alternately connected to the communication line using in-phase switching devices (distributors), which are currently performed on contactless elements. For clarity, Fig. 2.10, b shows a telemechanics system with time division of signals, in which contact distributors are used - step finders (SHI). When transmitting information, the polar qualities of the current are used. Messages from each source are determined by the position of the control keys; polarized ones are used as decoding devices on the receiving side. During one cycle of valve operation, messages from all sources of information are transmitted sequentially in time. Time division devices can operate in a cyclic or sporadic. In the cyclic mode, the systems operate continuously, in sporadic mode, information is transmitted as it accumulates or is needed, the rest of the time the distributors are in their initial state and do not switch channels.
The main condition for reliable and accurate signal separation is strict in-phase distribution of the valves. To do this, in cyclic systems, three main methods of synchronization are used: a common network, cyclic and step-by-step.
When synchronizing with a shared network (Fig. 2.10, c) the power supply of the valve drives (PR) is carried out from the general electrical network of 50 Hz, called the synchronous power supply. The network of one power system is often used as such a source. This method can be used with relatively short (up to 20 km) communication lines (LAN). In these lines, due to changes in the loads connected to the power system, in time it is possible to disrupt the in-phase power supply and, therefore, the in-phase operation of the distributors.
During cyclic synchronization, the valve drives located on the transmitting and receiving side are connected to special control pulse generators tuned to the same frequency. However, even with precise mutual tuning of the generators, the valve position misalignment will accumulate over time. To eliminate the mismatch, once per cycle, the valves are forced into phase by setting them to their initial position.
With step synchronization, a pulse generator is used on the transmitting side, which switches both valves. At each step of the valves, it is necessary to transmit special synchronizing pulses.
In the sporadic operation of the telemechanical system, start-stop synchronization is used, which can be considered a modification of the cyclic one.
At frequency division(compaction) each source of messages is allocated a certain frequency band: the first source is the frequency band ∆F 1, the second is ∆F 2, etc. (Figure 2.11, a). The frequency bands used for the transmission of different messages do not overlap. In this case, signals from all sources of messages are transmitted over the communication line simultaneously. In fig. 2.11, b shows a block diagram of a frequency division system for transmitting binary signals. The message from each source is transmitted along the line by sinusoidal signals of a certain frequency f created by the generators G. The absence of sending oscillations of the corresponding frequency means 0, the sending of oscillations - 1. The oscillations are summed up in the communication line. The separation of parcels from the sources of messages is carried out on the receiving side by bandpass filters PF ", the outputs of which are connected through rectifiers B to the executive relays P.
Figure 2.11. Explanations for the frequency method of signal separation
a) the location of the channels on the frequency axis
b) functional diagram of the system
Literature
1. Strygin V.V. "Fundamentals of Automation and Computer Engineering". M. High School. 1977 year
2. Gritsevsky P.M. and others. "Fundamentals of automation, pulse and computer technology." M. Radio and communication. 1987 year
3. Chekvaskin A.N. and others. "Fundamentals of Automation". M. Energy. 1977 year
4. Gordin V.S. and others. "Fundamentals of Aviation Automation". M. Oboronizd. 1972 year
5. Askerko V.S. and others. "Fundamentals of Aviation Automation". M. Oboronizd. 1972 year
6. Shishmarev V. Yu. "Typical elements of automatic control systems." 4th edition M .: Publishing Center "Academy", 2009.
7. Kelim. Yu. M. Typical elements of automatic control systems. M.: FORUM: INFRA-M, 2002.
1. Topic 1.1. Basic concepts of automation ………………………………….… 3
2. Topic 1.2. Measuring transducers (sensors) ……………………… 9
3. Topic 1.3. Electrical relays ……………………………………………… ..28
4. Topic 1.4. Magnetic amplifiers …………………………………………… ..32
5. Topic 1.5. Typical dynamic links of automation systems …………… .... 39
6. Topic 1.6. Stability and quality of the automatic system …………… ..43
7. Topic 2.1. Systems for remote transmission of angular movements on alternating current ……………………………………………………….… ..48
8. Topic 2.2. Tracking AC systems ……………………………………………………………………………………… ..... 51
9. Topic 2.3. Telemechanical systems of automatic control and monitoring ………………………………………………………………………… .53
Separation of signals - ensuring the independent transmission and reception of many signals on the same communication line or in the same frequency band, in which the signals retain their properties and do not distort each other.
With phase separation, several signals are transmitted at one frequency in the form of radio pulses with different initial phases. For this, relative or phase-difference keying is used (conventional phase modulation is used less often). Currently, communication equipment has been implemented that allows simultaneous transmission of signals from two and three channels on one carrier frequency. Thus, several channels for transmitting binary signals are created in one frequency channel.
In fig. 11.3, a vector diagram of double phase shift keying (DPSK) is shown,
providing transmission of two channels at one frequency. In the first phase channel, zero (a pulse of negative polarity) is transmitted by currents with a phase of 180 °, and one (a pulse of positive polarity) is transmitted by currents with a phase of 0 °. In the second phase channel, currents with phases 270 and 90 °, respectively, are used, i.e. the signals of the second channel move by 90 ° with respect to the signals of the first channel.
Suppose that it is necessary to transmit code combinations 011 in the first channel (Fig. 11.3, c) and 101 in the second (Fig. 11.3, d) on one frequency by the DMF method. The phase shift keying process for the first channel is shown by solid lines, and for the second - by dashed lines (Fig. 11.3.6, e)). Thus, each codeword corresponds to its own sinusoidal voltage. These sinusoidal oscillations are added and the total sinusoidal oscillation of the same frequency is sent to the communication line, which
indicated by a dash-dotted line in Fig. 11.3, e. It is also shown here that in the interval 0 - t1
zero on the first channel and one on the second channel are transmitted, which corresponds to
transfer of vector A with a phase angle of 135 °. In the interval t1 - t2, the transmission of one through the first channel and zero through the second corresponds to a vector B with an angle of 315 °. and in the interval t2 - t3 - vector C with an angle of 45 °, since units are transmitted through the first and second channels.
The block diagram of the device for implementing DMF is shown in Fig. 11.4. The carrier generator H has a phase-shifting device FSU for obtaining a phase shift of the sinusoidal oscillation by 90 ° in the second channel. Phase modulators
FM1 and FM2 manipulate in accordance with Fig. 11.3, e), and the adder Σ adds sinusoidal oscillations. At the reception after the amplifier
The separation of both channels is carried out in phase detectors - demodulators FDM1 and FDM2, to which the reference carrier voltage is supplied from the Gonne generator,
in phase with the voltage of that channel. For example, when applying from
amplifier of the total sinusoidal voltage (vector A in Fig.11.3, b) on
a positive voltage will be allocated to the demodulator of the first FDM1 channel,
corresponding to the phase 0 ° (reception of the unit on the first channel), since the phase of the reference
carrier frequency coincides with the phase of the first channel. Vector A can be decomposed into two
components: Af = 0 and Af = 90. In FDM1, the signal component Af = 0 interacts with
the reference voltage supplied to this channel, and the Af component will be suppressed
(the voltage of the second channel signal at the FDM1 output will not appear, since the vector
the reference frequency is perpendicular to the phase of the voltage vector of the second channel and
the product of these vectors will be equal to zero. At the same time, in FDM2, the arrival of
the total sinusoidal voltage (vector A) will create a positive voltage corresponding to the 90 ° phase (receiving one in the second channel),
since the phase of the reference frequency is 90 ° shifted from the reference frequency of the first
channel, coincides with the phase of the second channel. The voltage of the signal of the first channel to the output
FDM2 will not arrive, since the reference frequency vector in this channel is perpendicular
voltage vector of the first channel and the product of these vectors will be equal to zero.
The transmission of two messages on the same frequency can be carried out in a similar way at
relative phase shift keying (DPM). Thus, using DFM or
DOFM allows you to double the bandwidth of the communication channel. It is also possible
transmission of three messages on one frequency using three times the relative