graduate work
2.1 Mathematical model of the radar environment
The radar situation is characterized by the location and nature of radar objects (targets) in the radar coverage area, as well as the conditions environment, affecting the propagation of radar signals.
When propagating radio waves, the phenomenon of wave dispersion should be taken into account, i.e. dependence of phase velocity on signal frequency. The phenomenon of dispersion is observed due to the fact that the refractive index of the atmosphere differs from unity, i.e. the speed of electromagnetic waves in this case is slightly less than the speed of light.
Another significant effect of radio wave propagation in a real environment is the bending of the direction of propagation or wave refraction. This phenomenon can occur in a heterogeneous environment, i.e. environment with the refractive index varying from point to point /4/.
Since all these effects weakly change the characteristics of the radar signal, they can be neglected.
Any radar target or object is characterized by its location in space, motion parameters, effective reflective surface (RCS), as well as the function of ESR distribution over the surface of the object (for distributed objects).
The location of an object (target) is characterized by the position of the center of mass of this object (target) in some reference coordinate system /2/. In radar, the local spherical coordinate system is most often used, the origin of which is located at the location of the radar antenna.
In a ground-based radar, one of the axes of the coordinate system usually coincides with the northern direction of the meridian passing through the position of the radar antenna, and the location of the target C is found based on the results of measuring the slant range D, azimuth b and elevation angle c (Figure 2.1). In this case, the system is motionless relative to the earth's surface.
Figure 2.1 - Local spherical coordinates
Measuring the range to a target using radio engineering methods is based on the constancy of the speed and straightness of the propagation of radio waves, which are maintained in real conditions with fairly high accuracy. Range measurement comes down to recording the moments of emission of the probing signal and reception of the reflected signal and measuring the time interval between these two moments. Reflected pulse delay time:
where D is the distance between the radar and the target (Figure 2.1), m;
c is the speed of propagation of radio waves, m/s.
To determine the radial speed of a moving object, the Doppler effect /3/ is used, which consists in changing the frequency of observed oscillations if the source and observer move relative to each other. Therefore, the task of determining the radial velocity comes down to determining the frequency of reflected oscillations in comparison with emitted ones. The simplest and most convenient derivation of quantitative relationships for the Doppler effect for radar is based on considering the “transmission - reflection - reception” process as a single one. Let vibrations enter the antenna:
The signal reflected from a stationary target and delayed by time t3 at the receiver input will have the form:
There is a phase shift here:
as well as a constant phase shift μ μ that occurs during reflection. When moving away from the radar with a constant radial speed, the range.
where V P is the radial speed of the target (Figure 2.2), m/s.
Figure 2.2 - Radial speed of the target relative to the radar
Substituting the corresponding value from (1) into (4), we get:
The frequency of reflected oscillations, determined by the derivative of the oscillation phase μ C with respect to time, is equal to:
From here (8)
those. When the target moves away from the radar, the frequency of reflected oscillations is lower than that of emitted ones.
Magnitude
called Doppler frequency.
The power of the reflected signal at the input of the radar receiver depends on a number of factors /4/ and, above all, on the reflective properties of the target. The primary (incident) radio wave induces conduction currents (for conductors) or displacement currents (for dielectrics) on the target surface. These currents are a source of secondary radiation in different directions.
The reflective properties of targets in a radar are usually assessed by the effective scattering area (RCS) of the target S 0:
where o is the depolarization coefficient of the secondary field (0 ? o ? 1);
P OTR = S·D 0 ·П 1 - reflected signal power, W;
P 1 is the power flux density of the radar signal on a sphere of radius R in the vicinity of the point where the target is located, W/m 2 ;
D 0 - the value of the backscatter diagram (BSD) in the direction to the radar;
S - total scattering area of the target, m 2.
The RCS of a target is a coefficient expressed in square meters that takes into account the reflective properties of the target and depends on the configuration of the target, the electrical properties of its material and the ratio of target size to wavelength.
This value can be considered as a certain target area equivalent to a normal radio beam with area S0, which, isotropically dissipating all the wave power incident on it from the radar, creates at the receiving point the same power flux density as the real target. The effective scattering area does not depend on either the intensity of the emitted wave or the distance between the station and the target.
Since measuring the EPR of real objects is difficult in practice due to the complex shape of the latter, sometimes in calculations they operate with the amount of energy reflected from a radar object or the ratio of reflected energy to emitted energy.
If the radar object is distributed, i.e. consists of many independent emitters, then to find the EPR, one of two reflection models is used. In both models, the target is represented as a set of n point elements, among which there is no dominant reflector (first model), or there is one dominant reflector (second model), which gives a stable reflected signal.
In the technical radar literature /2, 4/ on radar, a generalized Swerling model is used with a distribution of the form:
where is the average EPR value, m 2.
This expression corresponds to a 2 distribution with 2k degrees of freedom, where k determines the complexity of the target reflection model. For k = 1, we obtain a model with an exponential EPR distribution, and for k = 2, we obtain a model of a target in the form of a large reflector that changes orientation in space within small limits, or a set of equal reflectors plus the largest one.
The law of distribution of amplitudes of the reflected signal is reduced to the generalized Rayleigh law /4/:
where E is the amplitude of the reflected signal, V;
E 0 - amplitude of the reflected signal from the dominant emitter, V;
y 2 - dispersion of orthogonal amplitude components, V 2;
I 0 - modified Bessel function of the first kind of zero order:
In the case of a group emitter consisting of n point emitters, the EPR distribution diagram along azimuths has a very complex lobe structure, depending on the relative position of the reflecting elements and the relative distances between them. Therefore, group targets, depending on their angular position relative to the line of sight, can give significant fluctuations in the power of the reflected signals. These oscillations occur relative to an average level proportional to the average EPR value for incoherent addition. Simultaneously with fluctuations in the power of the reflected signal, random changes in its delay time and angle of arrival are observed.
For moving distributed targets, the phenomenon of interference of secondary radiation oscillations from different points arises, which is based on a change in the relative position of the target's point reflectors. The Doppler effect is a consequence this effect. To describe the phenomenon, a backscatter diagram (BSD) is used, which characterizes the dependence of the amplitude of the reflected signal on the direction /2/.
In addition, when targets are irradiated, the phenomenon of depolarization of the probing signal occurs, i.e. the polarization of the reflected and incident waves do not coincide. For real purposes, fluctuating polarization takes place, i.e. all elements of the polarization matrix /1/ are random and it is necessary to use the matrix of numerical characteristics of these random variables.
In a statistical approach to the analysis of radar objects, a correlation function or a correlation matrix /8/ is used to describe the functions of the latter, which characterize the change in the parameters of the object over time. The disadvantage of this model is the complexity of calculations due to the need to use statistical methods and the complexity of organizing the input of initial parameters.
Based on the above, to describe a radar object, it is necessary to know its position in space, its extent in range and azimuth (for distributed objects), the EPR and its distribution model, the model of object motion or the law of change in the Doppler frequency increment of the reflected signal, the number of point emitters (for group emitters).
An algorithm that heuristically constructs an optimal graph for a decentralized search problem
In our approach, we want to understand what optimal structures look like. Also analyze the growth pattern of the objective function. Additionally, I wonder if it is possible to perform the search faster...
Graphical solution of linear programming problems
A mathematical model is a mathematical representation of reality. Mathematical modeling is the process of constructing and studying mathematical models. All natural and social sciences that use mathematical apparatus...
The problem of minimizing the cost of moving vehicles
Measuring beam deflection in MathCAD
We calculate the support reaction: We study the influence of given forces and distributed loads on the bending moment of the sections: We build diagrams of the transverse force Q and the bending moment M: 2...
Simulation model for assessing and predicting submarine search efficiency
1. Pobn:=Nobn/N - basic formula. Probability of detection pl; 2. Nobn:=Nobn+1, if (t=tk3) or (t=tk4) - accumulation of detected pl; 3. tk3:=t-ln(Random)/Y2, if (t=tk1) and (tk2>tk1) - calculation of the moment of detection of the submarine by means of KPUG without evasion; 4. tk4:=t-ln(Random)/Y3...
Modeling the operation of a bibliographic system
It is necessary to determine the average queue length to the terminal, the probability of failure and computer load factors. Let's define the variables and equations of the mathematical model: Kzag.1, Kzag...
Simulation of the operation of a telephone call point
Let's define the variables and equations of the mathematical model. In this case: l1,2 - the intensity of receipt of applications for regular and urgent negotiations; m - channel productivity; c is the reduced intensity; model equations:...
Model of the information system of the supply department of the enterprise LLC "Biscuit"
When analyzing and synthesizing any systems, the task arises of constructing a model that describes the functioning of the system in the language of mathematics, i.e. mathematical model...
Processing text information in the Delphi environment
Texts based on a certain alphabet will be considered as information to be encrypted and decrypted. These terms mean the following...
Development of a program that calculates a definite integral using the trapezoidal method for the integrand
Runge-Kutta method of 4th order of accuracy Displacement from point to point does not occur immediately, but through intermediate points. In practice, the most widely used method is the 4th order of accuracy...
Sorting by counting method
Counting sort is a sorting algorithm that uses a range of numbers in the array (list) being sorted to count the matching elements...
2.2 Mathematical model of radar
As already noted in paragraph 1.1, the main radar modules are the antenna unit, together with the antenna switch, transmitter and receiver. A large class of various devices can be used as a terminal device, differing in the way they display information and not affecting the received radar signals, so this class of devices is not considered.
2.2.1 Mathematical model of the antenna
One of the main characteristics of the antenna is its directional pattern (DDP) /5/, which characterizes the dependence of the radiated power on the direction (Figure 2.3).
Figure 2.3 – Antenna power pattern
The antenna radiation pattern in the azimuth-range plane at a constant elevation angle with a uniform field distribution across the aperture is expressed by the function:
(14)
The angle β for uniform motion of the antenna in a circle can be found using the formula:
(15)
where ω is the angular speed of rotation of the antenna, rad/s.
Let's consider the shape of the reflected signal in a 360-degree radar. As the antenna rotates, the amplitude of the probing pulses irradiating the target changes in accordance with the radiation pattern. Thus, the probing signal irradiating the target turns out to be modulated and described by a function of time
where s P (t) – radio pulses of the transmitter.
Let us assume that the target practically does not change the duration of the reflected pulses, and that the movement of the target during the irradiation time can be neglected. Then the reflected signal is characterized by the function:
where k is a constant coefficient.
For a single-antenna radar, in which the antenna radiation pattern during reception is described by the same function F E (t) as during transmission, the signal at the receiver input is written in the form:
Because the antenna rotation speed is relatively low and the beam displacement during the delay time is much less than the width of the radiation pattern, then F E (t)≈F E (t – t W). In addition, a function characterizing the power radiation pattern:
(19)
where β is the angle measured in one direction from the maximum to the target azimuth, degrees;
Θ 0.5 – width of the radiation pattern at half power, measured in both directions from the maximum (Figure 2.3), degrees.
Taking into account the above, (17) can be represented as:
those. The pulses at the receiver input are modulated in amplitude in accordance with the power directional pattern of the antenna.
The target azimuth is determined by the parameters of the angle-code converter sensor (Figure 2.4).
Figure 2.4 – Scheme for connecting the angle-code converter sensor
When the antenna rotates, the signals from the photo emitter are recorded by the photo receiver after the signals pass through holes in the plate located on the axis of the antenna. Signals from the photodetector are transmitted to the counter, which generates pulses called MAI pulses (short azimuth intervals). The angle of rotation of the antenna, and, consequently, the azimuth of the received radar signal is determined by the MAI pulses. The number of MAI coincides with the meter's conversion factor and determines the accuracy with which azimuth is measured.
Based on the above, the antenna module is characterized by the following parameters: the shape of the radiation pattern and its width, the antenna gain, the number of MAIs.
2.2.2 Mathematical model of the transmitting device
The transmitting device can be characterized by the radiation power, the number and type of probing signals and the law of their arrangement.
The radar range in the case of optimal signal processing and a given spectral noise density depends on the energy of the probing signal, regardless of its shape /5/. Considering that the maximum power of electronic devices and antenna-feeder devices is limited, an increase in range is inevitably associated with an increase in pulse duration, i.e. with a decrease in potential range resolution.
Complex or power-intensive signals resolve conflicting demands for increased detection range and resolution. Detection range increases when using high energy signals. An increase in energy is possible by increasing either the power or the duration of the signal. The power in a radar is limited from above by the capabilities of the radio frequency generator and especially by the electrical strength of the feed lines connecting this generator to the antenna. Therefore, it is easier to increase the signal energy by increasing the signal duration. However, long duration signals do not have good range resolution. Complex signals with a large base can resolve these contradictions /7/. Currently, frequency-modulated (FM) signals are widely used as one of the types of complex signals.
The entire set of FM signals can be described using the formula:
(21)
where T is the pulse duration, s;
t – time, function argument, varies within , c;
b k – coefficients of signal phase series expansion;
f 0 – signal carrier frequency, Hz.
Indeed, with n = 1 we obtain a linearly frequency-modulated (chirp) signal, whose coefficient b 0 - the signal base - can be found as:
(22)
where Δf is the frequency deviation of the chirp signal, Hz.
If we take n = 1 and frequency deviation Δf = 0 Hz, we obtain a MONO signal or video pulse with a rectangular envelope, which is also widely used in radar for detecting targets at short distances.
Another way to increase the signal energy while maintaining a short pulse duration is to use bursts of pulses, i.e. a series of pulses separated by interpulse intervals is considered as a single signal. In this case, the signal energy is calculated as the sum of the energies of all pulses /7/.
The P-15 (P-15MN) radar station of the decimeter wave range was intended to detect targets flying at medium, low and extremely low altitudes. Entered service in 1955. It was used as part of radar posts of radio engineering units and as a reconnaissance and target designation station for anti-aircraft missile units.
The P-15 station was mounted on one vehicle along with the antenna system and was deployed into a combat position in 10 minutes. The power supply unit was transported in a trailer.
Model from ZZ MODELL, the base vehicle ZIL-157 was supplied (most likely) from ICM and is made of plastic, in my opinion, not bad at all. There was no particular hassle during assembly. Kung resin station. During the assembly process, it was necessary to tinker with the fit of the rear wall (where the double doors are). The jacks are also made of resin and are quite fragile; one broke. The antenna-feeder system is made of photo-etched material.
The model was painted with Tamia Color acrylic paints, and the whole thing was blown over with Humbrol matte varnish. 
From the modifications to the model presented to you, I decided to do the following:
- tool boxes located under the rear wall of the kung on both sides;
- the second fuel tank of the car (there is only one included with the model for some reason unknown to me);
- rear license plate mount;
- waveguide on the upper antenna feed;
- the bottom step to the ladder on the rear side wall of the kung.
I didn’t lift it high on jacks, because... According to the instructions - still Soviet - it is enough only for the wheels of the suspended equipment to turn if it is located on a hard surface. There is also such a thing as to preserve rubber in the summer, the wheels are painted white. Although in my practice I have seen painted wheels a couple of times.
Of the shortcomings I noticed in the assembly diagram, I noticed one little thing. In the circuit, the feed holders of the upper and lower antennas are attached in the same way - with tubes to which the radio frequency cable is attached downwards. Although in a real station, on the lower antenna, it is mounted in reverse (see photo). I noticed this thing by accident when trying to imitate a radio frequency cable, when everything was already assembled. The lower waveguide part of the lower photo-etched antenna is also not made accurately - it does not correspond to the original, it had to be corrected.
As for the degree of correspondence of the entire model to the original, I was quite satisfied with it. Although there is some work to be done.
Designing modern military radar systems is no easy task. But the use of the latest modeling tools and techniques allows us to resolve many of the difficulties of the development process.
HONGLEI CHEN, SOFTWARE ENGINEER, RICK GENTILE, PRODUCT MANAGER MATHWORKS
The development of radar systems is a complex, multi-domain task. With the rise of phased array antenna (PAA) technology, engineers have access to new capabilities such as electronic beam steering and spatial signal processing. But new opportunities have led to the complication of systems as a whole. In addition, an increase in the number of interference sources, “filling” the radio frequency spectrum with their radiation, coupled with an ever-decreasing effective scattering surface (RCS) of targets, creates new difficulties in achieving the required performance indicators of radar systems.
A convenient dynamic simulation environment can become a decisive factor in optimizing the radar development process and help reduce the risks that inevitably arise during design. complex systems working in difficult conditions. Simulation of multi-domain radar systems will help make the right decisions during the development process, and will also allow you to detect design errors at the earliest stages. For example, using the model, you can evaluate the radar’s ability to detect targets with small RCS, or test signal processing algorithms in conditions of noise and interference. At later stages, the same models can be used to demonstrate the need for modification to an existing system and demonstrate the benefit of such modification before purchasing or manufacturing any additional components. In addition, the model can predict the behavior of the system in the event of failure of one or more components.
From probe pulses to detections
Let's try to highlight several aspects of how the model can help with estimating system parameters. Figure 1 shows a multi-domain system model created in Simulink. The model contains blocks of the radar system responsible for the generation, reception, transmission and spatial processing of signals. Mathematical descriptions of targets and propagation environments are also included in the system model.
Figure 1. Multi-domain radar model.
This is a model of an X-band radar that allows you to detect targets with low RCS values (<0.5 м 2). Требуемая дальность в данном примере – 35 км с разрешением по дальности 5 метров. Каждый из блоков, показанных на Рис. 1, может быть с лёгкостью описан на языке MATLAB или настроен в соответствии с выбранной конфигурацией системы. Например, такие параметры, как тип сигнала, требуемая мощность передатчика или коэффициент усиления антенны могут быть явно установлены в каждом из блоков.
Development of probing pulses
Once we have determined the range and velocity resolution parameters, as well as the minimum and maximum coverage range of our radar, we can interactively select the modulating pulse parameters to suit the system requirements. Figure 2 shows the configuration of the probe pulse parameters that are set interactively. The resulting “signal characteristics” are highlighted with a frame, and we can verify that they satisfy the system requirements. Figure 3 shows the response of the corresponding matched filter.
Figure 2. Modulating pulse.
Figure 3. Corresponding matched filter.
For such radar systems, we try to minimize the transmitter power, and therefore reduce the cost. Despite the power limitation, we are faced with the task of detecting targets with small RCS. This can be achieved by using antenna arrays with high gain in the system.
Development of antenna arrays
We can interactively design and analyze lattice parameters, including geometry, spacing of elements, relative positions of elements, and weighting functions. An example is shown in Figure 4 - a rectangular lattice of 36x36 equally spaced elements. The beam generated by such gratings can be deflected both in azimuth and elevation. Figure 5 shows the radiation pattern of the designed antenna. An array of this size for X-band radars can be easily installed on many platforms, including mobile ones.
Latest update of the description by the manufacturer 21.09.2018
Filterable list
Active substance:
ATX
Pharmacological group
Nosological classification (ICD-10)
3D images
Compound
| Film-coated tablets | 1 table |
| active substances: | |
| ethinylestradiol | 0.03 mg |
| drospirenone | 3 mg |
| excipients (core): lactose monohydrate - 43.37 mg (the amount of lactose monohydrate may vary depending on the purity of the active substance substance); corn starch - 12.8 mg; pregelatinized starch - 15.4 mg; povidone-K25 - 3.4 mg; croscarmellose sodium - 1.6 mg; magnesium stearate - 0.4 mg | |
| Excipients (shell): Opadry yellow 03B38204 (hypromellose 6cP - 62.5%, titanium dioxide - 29.5%, macrogol 400 - 6.25%, yellow iron oxide dye - 1.75%) - 2 mg |
pharmachologic effect
pharmachologic effect- contraceptive, estrogen-gestagenic.Directions for use and doses
Inside. The tablets should be taken in the order indicated on the package, at approximately the same time every day, with a small amount of water.
You should take 1 tablet. continuously for 21 days. Taking the tablets from the next package begins after a 7-day break, during which menstrual-like bleeding (withdrawal bleeding) is usually observed. As a rule, it begins on the 2-3rd day after taking the last pill and may not end until you start taking pills from a new package.
Start taking MODELL ® PRO. If you have not taken any hormonal contraceptives in the previous month, the use of MODELL ® PRO should begin on the 1st day of the menstrual cycle (i.e., on the 1st day of menstrual bleeding). It is possible to start taking it on the 2-5th day of the menstrual cycle, but in this case it is recommended to additionally use a barrier method of contraception during the first 7 days of taking the tablets from the first package.
Switching from other COCs, vaginal ring or contraceptive patch. It is preferable to start taking MODELL PRO the day after taking the last tablet from the previous package, but in no case later than the next day after the usual 7-day break. Taking MODELL ® PRO should begin on the day the vaginal ring or patch is removed, but no later than the day when a new ring is to be inserted or a new patch is applied.
Switching from contraceptives containing only gestagens (mini-pills, injectable forms, implant or IUD with controlled release of gestagen). You can switch from a mini-pill to taking MODELL ® PRO on any day (without a break), from an implant or IUD - on the day of their removal, from an injectable contraceptive - on the day when the next injection is due. In all cases, it is necessary to use an additional barrier method of contraception during the first 7 days of taking the pills.
After an abortion in the first trimester of pregnancy, you can start taking the drug immediately - on the day of the abortion. If this condition is met, the woman does not need additional methods of contraception.
After childbirth or abortion in the second trimester of pregnancy. It is recommended to start taking the drug on the 21-28th day after childbirth (in the absence of breastfeeding) or abortion in the second trimester of pregnancy.
If use is started later, it is necessary to use an additional barrier method of contraception during the first 7 days of taking the pills. If sexual contact has taken place, then before starting to take the drug MODELL ® PRO, you should exclude pregnancy or wait until your first menstruation.
Taking missed pills. If the delay in taking the drug is less than 12 hours, contraceptive protection is not reduced.
You should take the tablet as soon as possible, and take the next tablet at the usual time. If the delay in taking the drug is more than 12 hours, contraceptive protection may be reduced. The more pills are missed and the closer the missed pill is to the 7-day break in taking pills, the greater the likelihood of pregnancy. In this case, you can be guided by the following two basic rules:
The drug should never be interrupted for more than 7 days;
To achieve adequate suppression of the hypothalamic-pituitary-ovarian axis, 7 days of continuous tablet use are required. Accordingly, if the delay in taking the pills is more than 12 hours (the interval from the moment of taking the last pill is more than 36 hours), the woman should follow the recommendations given below.
The first week of using the drug. The last missed pill should be taken as soon as possible, as soon as the woman remembers (even if this means taking two pills at the same time). The next tablet is taken at the usual time. Additionally, you should use a barrier method of contraception (such as a condom) for the next 7 days. If sexual intercourse took place during the week before missing the pill, the possibility of pregnancy must be taken into account.
Second week of using the drug. The last missed pill should be taken as soon as possible, as soon as the woman remembers (even if this means taking two pills at the same time). The next tablet is taken at the usual time. Provided that the woman has taken the pills correctly for the 7 days preceding the first missed pill, there is no need to use additional contraceptive measures.
Otherwise, or if you miss two or more tablets, you must additionally use barrier methods of contraception (for example, a condom) for 7 days.
Third week of using the drug. The risk of pregnancy increases due to the upcoming break in taking the pills. You should strictly adhere to one of the following two options. However, if during the 7 days preceding the first missed pill, all pills were taken correctly, there is no need to use additional contraceptive methods. Otherwise, you must use the first of the following regimens and additionally use a barrier method of contraception (for example, a condom) for 7 days.
1. It is necessary to take the last missed pill as soon as possible, as soon as the woman remembers it (even if this means taking two pills at the same time). The next tablets are taken at the usual time until the tablets in the current pack run out. The next pack should be started immediately without interruption.
Withdrawal bleeding is unlikely until the second pack is finished, but spotting and breakthrough bleeding may occur while taking the tablets.
2. You can also stop taking tablets from the current package, thus starting a 7-day break (including the day you missed tablets), and then start taking tablets from a new package. If a woman misses taking pills and then does not have withdrawal bleeding during the break, pregnancy must be ruled out.
Recommendations in case of gastrointestinal disorders. In case of severe gastrointestinal disorders (vomiting, diarrhea), absorption may be incomplete, so additional methods of contraception should be used. If vomiting occurs within 3-4 hours after taking the tablet, you should follow the recommendations for skipping tablets. If a woman does not want to change her usual dosing schedule and move her menstrual cycle to another day of the week, an additional tablet should be taken from a different package.
Changing the day of the start of the menstrual cycle. In order to delay the onset of menstruation, it is necessary to continue taking tablets from the new MODELL ® PRO package without a 7-day break. Tablets from the new package can be taken for as long as necessary, incl. until the packaging runs out. While taking the drug from the second package, spotting from the vagina or breakthrough uterine bleeding are possible. You should resume regular use of MODELL ® PRO from the next package after the usual 7-day break. In order to postpone the onset of menstruation to another day of the week, a woman should shorten the next break in taking pills by the desired number of days. The shorter the interval, the higher the risk that she will not have withdrawal bleeding and will subsequently experience spotting and breakthrough bleeding while taking the second pack (just as if she would like to delay the onset of menstruation).
Additional information for special categories of patients
Use in children. The effectiveness and safety of the drug as a contraceptive have been studied in women of reproductive age. It is assumed that the effectiveness and safety of the drug in post-pubertal age up to 18 years are similar to those in women after 18 years. The use of the drug before menarche is not indicated.
