What is a demodulator? Demodulators. Block diagram of a quadrature demodulator
Demodulators And modulators are converting devices and are used to convert AM signals into analog form (demodulators) and analog signals into AM form (modulators). By their design, these devices are reversible, i.e., by swapping the input and output of such a device, you can get a modulator from a demodulator and vice versa.
Structurally, the operation of these converters is based on the use of high-speed switching devices. Mechanical relays (usually polarized), diode circuits, or circuits with transistors in key modes are used as such devices. According to the design principle, demodulators and modulators are single-wave or full-wave.
Half-wave demodulator based on a polarized relay
Let's consider the operating principle of a half-wave demodulator based on a polarized mechanical relay. The converter circuit is shown in Fig. 4.3.
Rice. 4.3.
The input amplitude-modulated voltage is supplied to the primary winding of the transformer Tr. The voltage taken from the secondary winding of the transformer is periodically supplied to the output of the demodulator in accordance with the polarity of the mains voltage supplied to the winding of the polarized relay. A polarized relay has a group of three contacts. Movable middle contact 1 closes with one of the extreme fixed (2 or 3) depending on the polarity of the mains voltage supplied to the relay winding. The demodulator uses only one fixed contact 2, which closes only with one polarity of the mains voltage on the relay winding. In Fig. Figure 4.4 shows the waveforms at the inputs and output of the demodulator.
Rice. 4.4.
Note that the polarity of the output signal depends on the phase relationship of the input and network signals. For example, in the case shown in Fig. 4.4, the coincidence of the phases of the network and input signals leads to the appearance of positive half-cycles of the input signal at the demodulator output. In the case when the phases of the network and input signals are shifted by 180° relative to each other, negative zero-cycles of the input signal appear at the output of the demodulator. This is why demodulators are sometimes called phase sensitive rectifiers(FChV).
The ripple level of the demodulator output signal is quite high, and to smooth it out, a low-pass filter is used, shown in Fig. 4.3 dotted line. This filter is a passive aperiodic (inertial) element. Typically, the role of a resistor with resistance I f performs the internal active resistance of the demodulator input signal source, reduced to the output winding of the transformer Tr, and the value of the capacitor capacitance S f is selected. This choice depends on the time constant of such a filter, which is defined as T f = I F S F. The larger this constant, the more effectively the pulsations are smoothed out.
Let us estimate the transmission coefficient of such a demodulator at a unit transmission coefficient of the input transformer. Let the amplitude of the input amplitude-modulated signal be fixed. Then
The shape of the demodulator output signal in this case is shown in Fig. 4.5, A. This signal can be represented as a sum of two components: a constant component U 0 and a variable (pulsating) component Yx(t), shown respectively in Fig. 4.5, biv.
Estimating the average value of the output signal over one period and further, taking the ratio of the average value of the output signal to the amplitude of the input AM signal, we obtain the transmission coefficient of a single-cycle demodulator:
Fourier series expansion of the variable component Y,(?), shown in Fig. 4.5, in, on period T gives the value of the amplitude of the main (first) gar-
and, Urn
Monica U ( = -.
Rice. 45. The shape of the demodulator output signal at a fixed amplitude of the AM signal at the input ( A), constant component (b) and variable component (in) of the output signal
The frequency of this harmonic is the same as the carrier frequency. All harmonics with higher numbers have decreasing amplitudes. The degree of decrease directly depends on the value of the harmonic number. In addition, the higher the harmonic number in the expansion of the variable component K,(0 at the output of the demodulator, the more it will be attenuated by a filter in the form of an inertial link. Therefore, it is necessary to try to smooth out the fundamental (first) harmonic as much as possible. All other harmonics with higher numbers will be weakened more.
Returning to the time constant of the filter at the output of the demodulator, it should be remembered that this filter increases the order of the characteristic equation of the open-loop system and can lead to a deterioration in the quality of the closed-loop system and even to its loss of stability if the increase is excessive. T f. In practice, when choosing the filter time constant, they strive to satisfy the inequality
where ср is the cutoff frequency of the open-loop system.
The last inequality guarantees an additional phase shift at the cutoff frequency of the open-loop system, not exceeding -5°.
The main disadvantages of demodulators and modulators based on mechanical relays are their relatively low reliability and limited operating frequency, not exceeding 1 kHz. In order to eliminate these shortcomings, such converters are built using semiconductor diodes or using transistors in key modes. Diode circuits are less common because they require careful selection of diodes and ballast resistors to balance the circuits in the absence of an input signal. For these reasons, we will not dwell on them. If necessary, you can refer to the relevant literature.
Study of optimal coherent
PURPOSE OF THE WORK
Studying the principle of operation of demodulators. Operation of the demodulator in conditions of interference. Studying the influence of threshold on error probability in AM.
1.CODING AND MODULATION
In modern systems for transmitting discrete messages, it is customary to distinguish between two groups of relatively independent devices: codecs and modems. Codec are called devices that convert a message into a code (encoder) and a code into a message (decoder), and modem- devices that convert code into a signal (modulator) and signal into code (demodulator).
When transmitting a continuous message a(t) it is first converted into a primary electrical signal b(t), and then like; Typically, a signal is generated using a modulator s(t), which is sent to the communication line. Accepted swing x(t) undergoes inverse transformations, as a result of which the primary signal is isolated b(t). Using it, the message is then reconstructed with varying accuracy. a(t).
The general principles of modulation are assumed to be known. Let us briefly dwell on the features of discrete modulation.
With discrete modulation, the encoded message A, which is a sequence of code symbols-( b i ), is converted into a sequence of elements (messages) of the signal ( s i). In a particular case, discrete modulation is reduced to the effect of code symbols on the carrier f(t).
Through modulation, one of the carrier parameters changes according to a law determined by the code. In direct transmission, the carrier can be a direct current, the changing parameters of which are the magnitude and direction of the current. Typically, alternating current (harmonic oscillation) is used as a carrier, as in continuous modulation. In this case, it is possible to obtain amplitude (AM), frequency (FM) and phase (PM) modulations. Discrete modulation is often called manipulation, and the device that performs discrete modulation (discrete modulator) is called a manipulator or signal generator.
In Fig.1. The signal forms in binary code for various types of manipulation are given. With AM, symbol 1 corresponds to the transmission of a carrier oscillation during time T (send), symbol 0 - absence of oscillation (pause). In FM, the transmission of a carrier wave with a frequency f 1 corresponds to symbol 1, and the transmission of vibrations with a frequency f O corresponds to 0. With binary PM, the carrier phase changes by 180 0 with each transition from 1 to 0 and from 0 to
In practice, the system of relative phase modulation (RPM) has found application. Unlike PM, with OFM the phase of signals is counted not from some standard, but from the phase of the previous element of the signal. In the binary case, symbol 0 is transmitted by a sinusoid segment with the initial phase of the previous signal element, and symbol 1 by the same segment with an initial phase that differs from the initial phase of the previous signal element by . In OFM, transmission begins with the sending of one element that does not carry information, which serves as a reference signal for comparing the phase of the subsequent element.
2. DEMODULATION AND DECODING
Reconstruction of the transmitted message at the receiver is usually carried out in the following sequence. First produced demodulation signal. In systems for transmitting continuous messages, as a result of demodulation, the primary signal representing the transmitted message is restored.
In discrete message transmission systems, as a result demodulation the sequence of signal elements is converted into a sequence of code symbols, after which this sequence is converted into a sequence of message elements. This transformation is called decoding.
That part of the receiving device that analyzes the incoming signal and makes a decision about the transmitted message is called decisive scheme.
In discrete message transmission systems, the decision circuit usually consists of two parts: first - demodulator and the second - decoder
The input of the demodulator from the output of the communication channel receives a signal distorted by additive and multiplicative noise. At the output of the demodulator, a discrete signal is generated, i.e., a sequence of code symbols. Typically, a certain segment (element) of a continuous signal is converted by the modem into one code symbol (element-by-element reception). If this code symbol always coincided with the transmitted one (received at the input of the modulator), then the communication would be error-free. But as is already known, interference makes it impossible to reconstruct the transmitted code symbol from the received signal with absolute certainty.
Each demodulator is mathematically described by a law according to which a continuous signal received at its input is converted into a code symbol. This law is called decision rule or decision scheme. Demodulators with different decision rules will, generally speaking, produce different decisions, some of which will be correct and others incorrect.
We will assume that the properties of the message source and encoder are known. In addition, the modulator is known, i.e. it is specified which implementation of the signal element corresponds to a particular code symbol, and the mathematical model of the continuous channel is also specified. It is necessary to determine what the demodulator (decision rule) should be in order to ensure optimal (i.e., the best possible) reception quality.
This problem was first posed and solved (for a Gaussian channel) in 1946 by the outstanding Soviet scientist V.A. Kotelnikov. In this setting, quality was assessed by the probability of correctly receiving the symbol. The maximum of this probability
for a given type of modulation V.A. Kotelnikov called , and the demodulator providing this maximum is ideal receiver. From this definition it follows that in no real demodulator the probability of correctly receiving a symbol can be greater than in an ideal receiver.
At first glance, the principle of assessing the quality of reception by the probability of correctly receiving a symbol seems quite natural and even the only possible one. It will be shown below that this is not always the case and that there are other quality criteria that are applicable in certain particular cases.
3. RECEIVING SIGNALS AS A STATISTICAL PROBLEM
Typically, the transmission method (coding and modulation method) is given and it is necessary to determine the noise immunity that various reception methods provide. Which of the possible methods of administration is optimal? These issues are the subject of consideration of the theory of noise immunity, the basis for which was developed by Academician V. A. Kotelnikov.
The noise immunity of a communication system is the ability of the system to distinguish (restore) signals with a given reliability.
The task of determining the noise immunity of the entire system as a whole is very complex. Therefore, the noise immunity of individual parts of the system is often determined: a receiver for a given transmission method, a coding system or modulation system for a given reception method, etc.
The maximum achievable noise immunity is called, according to Kotelnikov, potential noise immunity. Comparing the potential and actual noise immunity of a device allows us to assess the quality of a real device and find yet unused reserves. Knowing, for example, the potential noise immunity of a receiver, one can judge how close the actual noise immunity of existing reception methods is to it and how advisable their further improvement is for a given transmission method.
Information about the potential noise immunity of the receiver for various transmission methods makes it possible to compare these transmission methods with each other and indicate which of them are the most advanced in this regard.
In the absence of interference to each received signal X corresponds to a well-defined signal s. In the presence of interference, this one-to-one correspondence is broken. Interference, affecting the transmitted signal, introduces uncertainty regarding which of the possible messages was transmitted and the received signal X Only with some probability can one judge that a particular signal s was transmitted. This uncertainty is described a posteriori probability distribution P(s/x).
If the statistical properties of the signal are known s and interference w(t), then you can create a receiver that, based on signal analysis X will find the posterior distribution P(s|x). Then, based on the type of this distribution, a decision is made about which of the possible messages was transmitted. The decision is made by the operator or the receiver itself according to a rule that is determined by a given criterion.
The task is to reproduce the transmitted message in the best possible way in terms of the selected criterion. Such a receiver is called optimal, and its noise immunity will be maximum for a given transmission method.
Despite the random nature of the signals X, in most cases it is possible to identify many of the most probable signals (x i ), i=1,2...m, corresponding to the transmission of some signal s i. The probability that the transmitted signal is received correctly is equal to Р(х i/s i), and the probability that it is accepted incorrectly is equal to 1- Р(х i | s i) = . Conditional probability Р(х j |s i) depends on the method of signal generation, on the interference present in the channel, and on the selected decision circuit of the receiver. The total probability of erroneous reception of a signal element will obviously be equal to:
Where P(s i)- a priori probabilities of transmitted signals.
4. CRITERIA FOR OPTIMAL SIGNAL RECEPTION
In order to determine which of the decision schemes is optimal, it is necessary first of all to establish in what sense optimality is understood. The choice of optimality criterion is not universal; it depends on the task at hand and the operating conditions of the system.
Let the sum of signal and noise arrive at the receiver input x(t) =s k (t)+w(t), Where s k (t)- the signal to which the code symbol corresponds and k , w(t)- additive noise with a known distribution law. Signal s k at the reception location is random with a priori distribution P(s k). Based on fluctuation analysis x(t) the receiver plays the signal s i. If there is interference, this reproduction may not be completely accurate. Based on the received signal implementation, the receiver calculates the posterior distribution Р(s i /х), containing all the information that can be extracted from the received signal implementation x(t). Now it is necessary to establish a criterion by which the receiver will output based on the posterior distribution P(s i /x) decision regarding the transmitted signal s k.
When transmitting discrete messages, the Kotelnikov criterion is widely used ( ideal observer criterion). According to this criterion, a decision is made that the signal has been transmitted s i , for which the posterior probability Р(s i /х) has the greatest
value, i.e. the signal is registered s i if the inequalities are satisfied
P (s i /x) > P (s j /x), j i. (1)
When using such a criterion, the total probability of an erroneous decision is P0 will be minimal. Indeed, if on signal X a decision is made that a signal has been transmitted s i , then, obviously, the probability of a correct decision will be equal to Р(s i /х),
and the probability of error is 1 - P(s i /x). It follows that the maximum posterior probability Р(s i /х) corresponds to the minimum total probability of error
Where Р(s i)- a priori probabilities of transmitted signals.
Based on Bayes' formula
P(s i /x)= .
Then inequality (1) can be written in another form
P(s i) р(х/s i.) >P(s j) р(х/s j)(2)
Function p(x/s) often called likelihood function. The greater the value of this function for a given signal implementation X, the more plausible it is that the signal was transmitted s. The relation included in inequality (3)
called likelihood ratio. Using this concept, the solution rule (3), corresponding to the Kotelnikov criterion, can be written in the form
If the transmitted signals are equally probable P(s i) =Р(s j) = , then this decision rule takes a simpler
Thus, the ideal observer criterion comes down to comparing likelihood ratios (5). This criterion is more general and is called the maximum likelihood criterion.
Consider a binary system in which messages are transmitted using two signals s1(t) And s2(t), corresponding to two code symbols a 1 And a 2. The decision is made based on the result of processing the received oscillation x(t) threshold method: registered s 1, If X<х 0 , And s 2, If x x 0, Where x 0- some threshold level X. There may be two types of errors here: reproduced s 1 when it was transmitted s 2, And s 2 when it was transmitted s 1. The conditional probabilities of these errors (transition probabilities) will be equal to:
The values of these integrals can be calculated as the corresponding areas limited by the density plot of the conditional probability distribution (Fig. 2). Probabilities of errors of the first and second types, respectively:
P I =P(s 2)P(s 1 |s 2) = P 2 P 12,
P II =P(s 1)P(s 2 |s 1) = P 1 P 21.
The total probability of error in this case
P 0 = P I + P II = P 2 P 12 + P 1 P 21.
Let P 1 = P 2, Then
P 0 = .
It is easy to verify that in this case the minimum P 0 takes place when P 12 = P 21, i.e., when choosing a threshold in accordance with Fig. 2. For such a threshold P 0 =P 12 =P 21. In Fig.2. meaning P0 determined by the shaded area. For any other threshold value, the value P 0 there will be more.
Despite its naturalness and simplicity, the Kotelnikov criterion has disadvantages. The first is that in order to construct a decision circuit, as follows from relation (2), it is necessary to know the a priori probabilities of transmitting various code symbols. The second disadvantage of this criterion is that all errors are considered equally undesirable (have the same weight). In some cases, this assumption is not correct. For example, when transmitting numbers, an error in the first significant digits is more dangerous than an error in the last digits. Missing a command or a false alarm in different alarm systems can have different consequences.
Therefore, in the general case, when choosing an optimal reception criterion, it is necessary to take into account the losses incurred by the message recipient in the event of various types of errors. These losses can be expressed by certain weighting coefficients assigned to each of the erroneous decisions. The optimal decision scheme will be one that provides minimum average risk. The minimum risk criterion belongs to the class of so-called Bayesian criteria.
The Neyman-Pearson criterion is widely used in radar. When choosing this criterion, it is taken into account, firstly, that a false alarm and missing a target are not equivalent in their consequences, and, secondly, that the a priori probability of the transmitted signal is unknown.
5. OPTIMAL RECEPTION OF DISCRETE SIGNALS
The source of discrete messages is characterized by a set of possible message elements u 1 , u 2 ,..., u m the probabilities of the appearance of these elements at the output of the source Р(u 1), Р(u 2),..., Р(u m). In the transmitting device, the message is converted into a signal in such a way that each element of the message corresponds to a specific signal. Let us denote these signals by s 1, s 2 ..., s m and their probabilities of appearance at the output of transmitters (a priori probabilities) respectively through P(s 1), P(s 2),..., P(s m). Obviously, the prior probabilities of signals P(s i) equal to prior probabilities Р(u i) relevant messages P(s i) =P(u i). During transmission, interference is applied to the signal. Let this interference have a uniform power spectrum with intensity .
Then the input signal can be represented as the sum of the transmitted signal s i (t) and interference w(t):
x(1) = s i (t) + w(t) ,(i =1, 2,..., m).
In the case when the prior probabilities of the signals are the same P(s 1)=P(s 2)=...=P(s m) = , Kotelnikov's criterion takes the form:
It follows that with equiprobable signals, the optimal receiver reproduces the message corresponding to the transmitted signal that has the smallest standard deviation from the received signal.
Inequality (9) can be written in another form by opening the brackets:
For signals whose energies are the same, this is an inequality for all i j takes a simpler form:
In this case, the optimal reception condition can be formulated as follows. If all possible signals are equally probable and have the same energy, the optimal receiver reproduces the message corresponding to the transmitted signal whose cross-correlation with the received signal is maximum.
Thus, when E 2 = E 1, the Kotelnikov receiver, which implements operating conditions (10), is correlational (coherent) (Fig. 3).
Rice. 3. Correlation receiver Fig.4. Receiver with matched filters.
Optimal reception can also be implemented in a circuit with matched linear filters (Fig. 5), the impulse responses of which should be
g i =cs i (T - t), where c is a constant coefficient.
The considered optimal receiver circuits are of the type coherent, they take into account not only the amplitude, but also the phase of the high-frequency signal. Note that in the circuits of optimal receivers there are no filters at the input, which are always present in real receivers. This means that the optimal receiver for fluctuation interference does not require filtering at the input. Its noise immunity, as we will see later, does not depend on the receiver bandwidth.
6. PROBABILITY OF ERROR IN COHERENT RECEPTION
BINARY SIGNALS
Let us determine the probability of error in the binary signal transmission system when received at the optimal receiver. This probability will obviously be the minimum possible and will characterize the potential noise immunity for a given transmission method.
If the transmitted signals s 1 And s 2 equally probable P 1 = P 2 = 0.5, then the total probability of error P0 with optimal reception of binary signals s 1 (t) and s 2 (t) will be equal to:
P 0 = , (11)
Where Ф()=- probability integral, .
From the above formula it follows that the probability of error P 0, which determines the potential noise immunity, depends on the value - the ratio of the specific energy of the signal difference to the noise intensity N 0. The larger this ratio, the greater the potential noise immunity.
Thus, with equally probable signals, the probability of error is completely determined by the value . The value of this quantity depends on the spectral density of interference N 0 and transmitted signals s1(t) And s2(t).
For systems with an active pause, in which the signals have the same energy, the expression for 2 can be written as follows:
where is the cross-correlation coefficient between signals, and is the ratio of signal energy to specific interference power.
The error probability for such systems is determined by the formula
It follows that when = - 1 , i.e. s 1 (t) = - s 2 (t), the system provides the greatest potential noise immunity. This is a system with opposite signals. For her = 2q 0 . A practical implementation of a system with opposing signals is a phase shift keying system.
It is convenient to compare various systems for transmitting discrete messages using a parameter representing the reduced ratio of signal to noise at the output of the optimal receiver for a given transmission method.
In general, a radiotelegraph signal can be written
s i (t) =А i (t)cos(), 0
Where are the oscillation parameters? A i, , take on certain values depending on the type of manipulation.
For amplitude keying A 1 (t)=A 0 , A 2 =0 ,
For frequency shift keying A 1 (t)=A 2 (t)=A 0 ,. With optimal choice of frequency spacing()2, where k- an integer and , we get
For phase shift keying A 1 (t) =A 2 (t) =A 0,
A comparison of the obtained formulas shows that of all binary signal transmission systems, the system with phase shift keying provides the greatest potential noise immunity. Compared to the FM, it allows you to get a two-fold, and compared to AM, a four-fold increase in power.
In communication systems, a signal is usually made up of a sequence of simple signals. Thus, in telegraphy, each letter corresponds to a code combination consisting of five elementary parcels. More complex combinations are also possible. If the elementary signals that make up the code combination are independent, then the probability of erroneous reception of the code combination is determined by the following formula:
P ok = 1 - (1 - P 0) n,
where P 0 is the probability of an elementary signal error, n is the number of elementary signals in the code combination (code value).
It should be noted that the probability of error in the cases considered above is completely determined by the ratio of the signal energy to the spectral density of the interference and does not depend on the signal shape. In general, when the interference spectrum is different from uniform, the probability of error can be reduced by changing the signal spectrum, i.e., its shape.
TEST QUESTIONS
1. What is the purpose of a demodulator in a digital communication system? What is its main difference from an analog system demodulator?
2. What is the dot product of signals? How is it used in the demodulator algorithm?
3. Is it possible to use matched filters in an optimal demodulator?
4. What is the “ideal observer criterion”?
5. What is the “maximum likelihood rule”?
6. How is the threshold of the solver selected? What happens if you change it?
7. What is the decision-making algorithm in RU?
8. Explain the purpose of each demodulator block.
11. Optimal demodulator algorithm and its functional diagram for FM.
12. Explain the difference in noise immunity of communication systems with different types of modulation.
13. Explain the oscillograms obtained at different control points of the demodulator (for one of the types of modulation).
LITERATURE
1. Zyuko A.G., Klovsky D.D., Nazarov M.V., Fink L.M. Signal transmission theory. M.: Radio and communication, 1986.
2. Zyuko A.G., Klovsky D.D., Korzhik V.I., Nazarov M.V. Theory of electrical communication. M.: Radio and communication, 1998.
3. Baskakov S.I. Radio engineering circuits and signals. M.: Higher School, 1985.
4. Gonorovsky I.S. Radio engineering circuits and signals. M.: Soviet radio, 1977.
BRIEF CHARACTERISTICS OF THE CIRCUITS AND SIGNALS STUDYED
The work uses a universal stand with a replaceable unit "MODULATOR - DEMODULATOR", the functional diagram of which is shown in Fig. 20.1.
The source of the digital signal is ENCODER-1, which produces a periodic sequence of five symbols. Using toggle switches, you can set any five-element code combination, which is indicated by a line of five LED indicators with the inscription “TRANSMITTED”. In the MODULATOR block, modulation (manipulation) of binary symbols of “high-frequency” oscillations in amplitude, frequency or phase occurs, depending on the position of the “MODULATION TYPE” switch - AM, FM, FM or OPM. When the switch is in the “zero” position, the modulator output is connected to its input (no modulation).
The communication CHANNEL is a signal adder from the modulator output and noise, the generator of which (GN) is located in the SIGNAL SOURCES block. The internal quasi-white noise generator, simulating the noise of a communication channel, operates in the same frequency band in which the spectra of modulated signals are located (12-28 kHz).
The DEMODULATOR is made according to a coherent circuit with two branches; switching of modulation types is common with the modulator. Therefore, the reference signals s 0 and s 1 and the threshold voltages at the control points of the stand change automatically when the type of modulation is changed.
The signs (X) on the functional diagram indicate analog signal multipliers made on specialized ICs. The integrator blocks are made using operational amplifiers. Electronic switches (not shown in the diagram) discharge the integrator capacitors before the start of each symbol.
Adders (å) are designed to introduce threshold voltage values depending on the energy of the reference signals s 1 and s 0.
The "RU" block - a decisive device - is a comparator, that is, a device that compares the voltages at the outputs of the adders. The “solution” itself, i.e. a "0" or "1" signal is applied to the demodulator output at the moment before the end of each symbol and is stored until the next "decision" is made. The moments of making a “decision” and the subsequent discharge of capacitors in the integrators are set by a special logic circuit that controls the electronic switches.
To demodulate signals from the PSKM, blocks (not shown in the diagram) are added to the PM demodulator circuit, which compare the previous and subsequent decisions of the PM demodulator, which makes it possible to draw a conclusion about the phase jump (or lack thereof) in the received symbol. If there is such a jump, a “1” signal is sent to the demodulator output; otherwise, a “0” signal. The replaceable block contains a toggle switch that switches the initial phase (j) of the reference oscillation (0 or p) - only for PM and OFM. For normal operation of the demodulator, the toggle switch must be in the zero position.
With amplitude keying, it is possible to manually set the threshold in order to study its effect on the probability of error in symbol reception. The error probability is assessed in a PC by counting the number of errors during a certain analysis time. The error signals themselves (in a symbol or “letter”) are generated in a special block of the stand (“ERROR CONTROL”) located below the DAC block. For visual monitoring of errors, the stand has LED indicators.
The measuring instruments used are a two-channel oscilloscope, a built-in voltmeter and a PC operating in error counting mode.
HOMEWORK
1.Study the main sections of the topic using lecture notes and literature:
pp. 159¸174, 181¸191; With. 165¸192.
LABORATORY TASK
1. Observe waveforms of signals at various points in the demodulator circuit in the absence of noise in the channel.
2. Observe the appearance of errors in the operation of the demodulator in the presence of noise in the channel. Estimate the error probability for AM and FM at a fixed signal-to-noise ratio.
3. Obtain the dependence of the probability of errors in AM on the threshold voltage.
METHODOLOGICAL INSTRUCTIONS
1. Operation of the demodulator in conditions without interference.
1.1. Assemble the measurement scheme according to Fig. 20.2. Using the ENCODER toggle switches - 1, enter any binary combination of 5 elements. Set the “THRESHOLD AM” control knob to the extreme left position. In this case, the regulator is turned off and the threshold is set automatically when changing the type of modulation. Set the DEMODULATOR reference oscillation phasing switch to the “0 0” position. Connect the output of the noise generator (NG) in the SIGNAL SOURCES block to the n(t) input of the communication CHANNEL. The noise generator output potentiometer is in the extreme left position (no noise voltage). Connect the external synchronization input of the oscilloscope to socket C2 in the SOURCES block, and switch the vertical beam deflection amplifiers to open input mode (to pass through the constant components of the processes under study).
1.2. Use the button to switch modulation types to set option “0”, corresponding to the signal at the MODULATOR input. Having taken an oscillogram of this signal and, without changing the sweep mode of the oscilloscope, select one of the types of modulation (AM). Draw oscillograms at the control points of the demodulator:
· at the demodulator input;
· at the outputs of multipliers (on the same scale along the vertical axis);
· at the outputs of integrators (also on the same scale);
· at the output of the demodulator.
On all obtained oscillograms, mark the position of the time axis (i.e., the position of the zero signal level). To do this, you can fix the position of the scan line when closing the input terminals of the oscilloscope.
1.3. Repeat step 1.2 for another type of manipulation (FM).
2. Operation of the demodulator in conditions of interference.
2.1. Set the MODULATION TYPE switch to FM. Connect one of the inputs of the two-beam oscilloscope to the input of the modulator, and the second to the output of the demodulator. Obtain still waveforms of these signals.
2.2. By gradually increasing the noise level (using the GS potentiometer), rare “glitches” appear on the output oscillogram or on the input ACCEPTED display.
2.3. Using an oscilloscope, measure the established signal-to-noise ratio. To do this, by sequentially disconnecting the noise source, measure the signal range at the demodulator input (in divisions on the screen) - 2a - (i.e., double the amplitude of the signal), and by disconnecting the signal source from the channel input and restoring the noise signal, measure the noise range (also in divisions) - 6s. Enter the found ratio a/s into Table 20.1.
2.4. Use the “Modulation type” switch to set AM, FM, and FM sequentially, observing the frequency of errors from the flashes of the “ERROR” LED or from the oscillogram of the demodulator output signal. Include the observation results in the report.
2.5. Without changing the noise level in the channel, measure the probability of a demodulator error in receiving a symbol for a finite analysis time (i.e., an estimate of the error probability). To do this, put the PC into error probability measurement mode (see APPENDIX) and set the analysis time to 10-30 s. Starting with FM (and then FM and AM), determine the number of errors during the analysis and estimate the probability of error. Enter the obtained data into the table. 20.1.
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3.1. Set the MODULATION TYPE switch to AM. Set the noise generator output potentiometer to minimum. Using an oscilloscope connected to the output of the lower integrator, measure the vertical peak-to-peak voltage swing in volts - U max.
3.2. Prepare table 20.2, provide in it at least 5 values of the threshold U pores.
Table 20.2 Estimation of error probability depending on the threshold (for AM)
3.3. Use the “THRESHOLD AM” potentiometer to set the threshold value U max /2 (measuring the voltage “E 1 /2” at the demodulator control point using a direct voltage voltmeter). Increase the noise level in the channel until rare failures occur. Without changing the noise level, measure the error probability estimate for this threshold (U max /2), and then for all other values of U pores. Draw a graph of the dependence P osh = j (U pore).
The report must contain:
1. Functional diagram of measurements.
2. Oscillograms, tables and graphs for all measurement points.
3. Conclusions on points 2.4 and 3.3.
In general, a phase-shift keyed signal demodulator is a PD, one input of which receives a modulated signal, and the other receives a signal from a reference oscillation source. To detect a signal with four phase values, two PDs are required, to which the input signal arrives with the same phase, and the signals from the reference oscillation source are phase shifted by 90° relative to each other. When demodulating signals with a PPM, it is necessary to compare the phases of the received signal in two adjacent clock time intervals.
Due to the high modulation speed, demodulators of PPM signals have a number of features. Demodulation is carried out on the IF, and it is necessary to create a path with a bandwidth of 500-1000 MHz.
The demodulator of OFM-4 signals transmitted at a speed of 200 Mbit/s uses a PD circuit with 3 dB QNO, consisting of two directional couplers with distributed communication (8.34 dB each). This circuit uses only two diodes. It has good impedance characteristics and high sensitivity. To improve matching, four diodes can be used here.
If demodulation is carried out at an intermediate frequency, then automatic frequency control can be applied (ACH) local oscillator The figure shows the block diagram of the receiver. The input signal together with the local oscillator signal ( Get.) goes to the step-down mixer (Cm.), and after amplification in the amplifier - to the input of the signal demodulator (Dmd) and AFC detector (Det. AHR). The demodulator is a PD in which the signal from the delay line, delayed by the duration of the clock interval, is used as a reference oscillation. Intermediate frequency F IF exactly five times the clock speed F T, Therefore, the AFC detector circuit is similar to the demodulator circuit, but the delay is carried out by the value of the clock interval plus p/2. Signals from the regeneration device and the AFC detector enter the AFC circuit and form a local oscillator control signal at its output, which rearranges it so that it constantly maintains F IF =5F T.
CARRIER RESTORATION SCHEME AND ITS PARAMETERS
The absence of a carrier frequency component in the spectrum of the OFM signal requires its restoration in the receiver to carry out coherent detection. Among the known carrier restoration schemes in high-speed DSPs of the microwave range, the most widely used is the remodulation scheme (sometimes the names are used: a scheme with a remodulator, with an inverse or restoration modulator). The figure shows a block diagram of a demodulator, in which coherent detection of the OFM-4 signal is carried out, and a circuit with remodulation and a phase locking loop is used as a VNA. The input signal from the amplifier is fed to a four-position phase detector (4-PD) and through a delay line
L31 on 4-FMD, the two digital inputs of which are supplied with detected signals with a 4PD output. The PD of the PLL ring receives signals from the restored carrier and from the control voltage generator (VCO) through the delay line L32 and from the 4-PMd output. The VCO control signal is generated by the PD and the filter of the PLL ring. This circuit contains a minimum of elements that determine the delay time of the PLL ring; its operation does not depend on clock frequency synchronization.
SOME APPLICATIONS OF OPM MODULATORS AND DEMODULATORS
To increase the volume of transmitted information while maintaining a constant modulation speed, it is proposed to use a 16-level amplitude-phase modulation signal. The signal modulator consists of two 4-PSM units, which receive digital signals, two for each, and a signal from the carrier generator. The modulated signals are summed, and the optimal case for detection is when one of the summed signals is 6 dB less than the other. The result is a 16-level AFM signal, the signal space for which is shown in the figure. During detection, inverse operations are carried out, which can be implemented in a demodulator using EHF with secondary modulation. The figure shows a block diagram of such a demodulator. The input signal arrives “and the first four-position phase detector (4-PD1) together with the reference oscillation of the restored carrier from the VCO, at the output of the regeneration device we obtain two sequences transmitted with greater amplitude. These same sequences, simultaneously with the signal from the VCO, are sent to the 4-FMD, which performs modulation a second time. Using the signal from the 4-PDM and the PLL ring input at the PD output, a VCO control signal is generated, and when subtracted, a signal is supplied to 4-PD2 along with the reference oscillation signal and forms two other transmitted sequences at its outputs.
An analysis of the literature shows a tendency towards the development of high-speed digital communication systems in the microwave range with various types of carrier phase modulation. The development of the millimeter and quasi-millimeter wave range places high demands on the design of devices that perform high-speed modulation and demodulation of the signal phase. The following main design directions can be distinguished:
– carrier phase modulation of the millimeter and quasi-millimeter wave ranges at speeds up to 250 Mbit/s using p-i-n-diodes;
– signal phase modulation in the range of 1-2 GHz at speeds up to 400 Mbit/s using DBS;
– the use of similar modulation methods when transmitting information using the OFM method in the CRRL with an intermediate frequency of 140 MHz;
– use in the design of MPL elements manufactured using thin-film technology;
– coherent detection of a wideband phase-modulated signal in the range of 1-2 GHz, including cases when the spectra of the input and detected signals are located close to each other;
– creation of a carrier recovery circuit that, with a wide acquisition band, has a large signal-to-noise ratio of the recovered carrier and a small steady-state phase error;
– the use of modulation types that allow increasing the volume of transmitted information in one radio channel and improving signal detection characteristics.
DIGITAL RSP DEMODULATOR
The demodulator is the most complex node of the digital RSP, determining the quality indicators of the transmission path as a whole.
When demodulating systems with OPM, both coherent and incoherent methods are used.
Optimal algorithm(Figure a)
a matched filter SF with a transfer function complexly conjugate to the spectral density of the signal S(t) or a correlator is used containing a reference oscillation generator Гк, a multiplier and an integrator with reset at the moment t 0 =T(Figure b)). The construction of these circuits poses significant difficulties due to obtaining a coherent reference voltage. In real circuits (Figure 18 c)) in which the reference voltage is obtained using a VKN coherent carrier restoration circuit, and instead of an ideal integrator with reset, a low-pass filter with a bandwidth of 1.2 V C is used (V C is the frequency numerically equal to the transmission speed). A binary signal regenerator is used as a decisive device, which includes circuits for isolating the clock signal. The decision about whether a 0 or 1 signal is received is made in the middle To th impulse.
COHERENT CARRIER RESTORATION SCHEME
The main schemes are:
A circuit for multiplying the PM signal in accordance with the system multiplicity to remove modulation.
Costas circuit containing a tunable reference carrier signal generator controlled by an error signal obtained by comparing the input and output digital polynomials of the regenerator.
Siforov coherent carrier recovery scheme. A variation of the Costas circuit is a demodulator in which the signal of the control oscillator of the reference carrier is modulated by the signals of the regenerators, and the error signal is determined by comparing the input and restoration ones.
The OFM-2 signal is squared and compared in the PD loop of the PLL with the IF generator signal by the VCO control voltage, the frequency of which is also multiplied by two.
Reverse modulation scheme. The manipulated signal S(t) is received at the input of the IF modulator MD, and the sequence where is the reverse symbol generated at the output of the FD at the baseband input. The IF signal restored in this way is sent to the PD of the PLL system, where it is compared with the VCO signal.
In low-speed systems, simple autocorrelation reception of signals with OPM is sometimes used. An IF signal delayed by the duration of the PM clock signal is used as a reference oscillator signal.
The block diagram of the autocorrelation demodulator OFM-2 is shown in the figure.
Previously, we examined signals with phase and frequency modulation PM and FM; in this article we will examine the issues of separating the information component from a bandpass radio signal during angular modulation. It is assumed that the reader is familiar with the operating principle of a quadrature local oscillator.Let there be an input bandpass signal with phase modulation:
| (1) |
Where is the amplitude of the input signal, is the carrier frequency of the signal, is the phase deviation of the PM signal (phase modulation index), and is the modulating signal that must be extracted from . It is assumed that the modulating signal does not exceed unity in magnitude.
Using a quadrature local oscillator, we select the phase envelope of the signal, as shown in Figure 1.
Figure 1: Complex envelope extraction using quadrature local oscillator
After multiplying the original signal by quadrature components we obtain:
From expression (3) we can express:
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(4) |
Thus, we were able to demodulate the PM signal and isolate the original modulating signal. In this case, it is necessary to pay attention to the following points. Firstly, the above expressions imply coherent reception of the PM signal, i.e. absence of frequency and phase mismatch between the carrier frequency and the frequency of the quadrature local oscillator, and secondly, it is assumed that the arctangent is calculated within radians (arctangent 2 function). If the condition of coherent reception is not ensured, then there is a frequency mismatch and a random phase shift of the received PM signal relative to the initial phase of the local oscillator. Thus, (2) can be rewritten as:
| (7) |
Thus, incoherent reception results in the addition of a linear component proportional to the frequency detuning plus a random initial phase to the demodulated signal. In this case, the second effect begins to appear, which is the periodicity of the arctangent. If the linear term exceeds in modulus , then, due to the periodicity of the arctangent, the output will be a “saw” as shown in Figure 2. To eliminate the periodicity, arctangent unwrap functions (unwrap functions) are used.
Figure 2: Effect of arctangent periodicity
Thus, coherent processing is required to receive the PM signal, otherwise the demodulated signal may be distorted. In practice, analog PM modulation is not widely used due to these disadvantages. However, digital phase modulation, when the modulating signal is digital, has found enormous application. With digital phase modulation, the modulating signal consists of rectangular pulses and the phase changes abruptly and phase shift key PSK is obtained, but this will be discussed in more detail in the following sections. We will return to frequency modulation. With FM frequency modulation, the original modulating signal is integrated:
Having differentiated the phase envelope, we obtain the instantaneous frequency:
| (10) |
Please note that after taking the derivative, the frequency mismatch only affects the DC component of the demodulated signal, which usually does not carry information and can be eliminated using a high-pass filter. However, before differentiation, an arctangent with “undesirable periodicity” remained. Let's get rid of it by calculating the derivative of the arctangent in expression (10) as the derivative of a complex function:
The normalized original modulating signal is shown in Figure 4. The original modulating signal performed frequency and phase modulation of the signal at a carrier frequency of 25 kHz with a frequency deviation for FM modulation equal to 2 kHz and a PM phase deviation equal to 7.
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Figure 5 shows the output of the phase detector when demodulating a PM signal. It can be seen that at the arctangent output there are obvious phase overloads caused by phase periodicity. The disclosure of the arctangent periodicity, with the corresponding normalizations of the PM and FM demodulators when accurately tuning the local oscillator frequency to the carrier frequency of the FM and PM signal are shown in Figure 6. It is clearly seen that when accurately tuning the local oscillator frequency, the signal at the output of the FM demodulator completely repeats the original modulating signal, and on The output of the PM demodulator is shifted by a DC component proportional to the random initial phase. The signal at the output of the PM and FM demodulators with a local oscillator frequency detuning of 100 (in the case of a PM signal) and 500 Hz (for an FM signal), respectively, are shown in Figure 7. It can be noted that the frequency detuning of an FM signal shifts only the DC component at the output of the FM demodulator, while at the output of the PM demodulator a linear term is added with a proportionality coefficient depending on the frequency detuning of the local oscillator.
Let us now consider the issue of disclosing the periodicity of the arctangent. For this, unwrap algorithms are used, of which there are several options. The first option is to detect phase jumps at the arctangent output close to radians. The operating principle of this algorithm is shown in Figure 8.
Due to noise and signal sampling. In this case, there is a possibility of missing a phase jump and generating an incorrect signal.
The second option for revealing the periodicity of the arctangent is as follows. The PM signal is demodulated using an FM demodulator in accordance with (11) using the structure shown in Figure 3. As a result, an instantaneous frequency is obtained equal to the derivative of the phase. After this, the phase is integrated and restored without using the arctangent (see Figure 9).
Figure 9: Arctangent periodicity disclosure using an FM demodulator
This method is not acceptable in the case of digital modulation, since the frequency demodulator does not store information about the initial phase; in addition, as a result of integration, a random integration constant is added to the output signal.
Another, perhaps the best way to reveal the periodicity of the arctangent, which has found widespread use in digital systems with phase shift keying, is to prevent the phase from increasing more (i.e., preventing the periodicity of the arctangent) through the use of phase-locked loop tracking circuits, discussed in detail in this article.
Thus, we considered the issues of constructing PM and FM demodulators. They showed that for a PM signal, the frequency detuning of the local oscillator leads to a linear term at the output of the PM demodulator, and in the case of an FM signal, with frequency detuning, only the constant component at the output of the demodulator changes. Unwrap algorithms for revealing the periodicity of the arctangent are presented.