PWM and PWM - what is it? What is PWM Digital Pulse Width Modulation
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TwitterWith PWM, according to the sign of the analog modeling signal b(t) (Figure A), the width (pulse duration (c)) of the subcarrier changes while their amplitude and repetition rate are constant.
PWM is sometimes called long pulse modulation (CPM).
There are ONE-WAY and DOUBLE-WAY PWM.
With one-way PWM, the change in pulse width occurs only due to the shift of the pulse cutoff (PWM-1) (Figure B)
And with a double-sided cut and the front of the pulse PWM-2 (Figure D)
The most widely used is PWM-1
And we will assume that the modeling signal
changes according to the harmonic law, according to which
The pulse width is:
Where 
-pulse duration deviation
Substituting this value 
to previous
expression we obtain the spectral signal of the PWM signal.
It is most convenient to implement a PWM signal modulator on integrated circuits (ICs)
A pulse subcarrier is supplied to input 2
At input 5 – analogue modeling signal b(t)
PWM demodulator are most often low-pass filters
27. Pulse phase modulation. FI signal modulators.
With PPM, according to the law of the simulated analog signal b(t), only the temporary position of the subcarrier video pulses changes, and their amplitude and duration remain unchanged.
If you differentiate the PWM signal in time, you get positive and negative pulses.
A positive pulse corresponds to the edge of the PWM signal, and a negative pulse corresponds to its cutoff.
With one-way PWM, positive pulses are stationary, and negative pulses are shifted in proportion to the modeling signal b(t) along the time axis.
The stationary pulses can be eliminated using a full-wave rectifier with an active load, and the remaining pulses are PPM signals.
The PPM signal modulator in this case consists of a PWM modulator, to the output of which a differentiating device remote control and a half-wave rectifier OB are connected. (see picture)
The analytical expression of the PIM signal has the form:
- pulse amplitude
-function describing the envelope of the measuring pulse.
- subviation of the temporary position of the measuring pulse
- the meaning of the transmitted message at the moment of time 
The frequency spectrum of PIM signals is difficult to represent analytically
The approximate value for the amplitude of the transmitted harmonic signal in the PPM spectrum is:
Where 
- message frequency
- pulse duration
The amplitude of the transmitted signal in the PIM spectrum is very small (much less than in the PIM and PWM spectra and is a function of the modeling frequency 
, i.e. distorted).
Therefore, demodulation of PPM signals using low-pass filters is directly impossible.
They are converted into AIM or PWM signals.
28. Pulse frequency modulation. Chim signal detectors.
The detector can be made according to the circuit
Where F-channel filter; JSC-amplitude limiter; DC-diff. chain; Far East-full-wave rectifier with active load; OB- one-shot; D-detector with voltage doubling; LPF-low pass filter.
The operation of the detector is explained using timing diagrams.
After passing through the narrowband circuits of the communication channel, the PFM signal becomes similar to an analog FM signal. By the AO block it is deeply limited in amplitude on both sides so that at its output there are identical rectangular pulses of different repetition rates and durations. In the DC block, these pulses are differentiated in time, as a result of which at its output UDC (t) represents fronts and cuts. The latter are very narrow multi-polar pulses, which in the LW block are converted into unipolar ones Udv(t), thereby doubling the repetition frequency. In the OB block, identical rectangular pulses of the same duration, but of different repetition rates are formed, which are supplied to the input of block D. Schematic diagram of block D:
At the output of the circuit there is a transmitted analog signal Ud(t). In some cases, the OB block is excluded. The high stability of the parameters of this detector has led to its widespread use even for analog FM signals.
Pulse width modulation consists of changing the width (duration) of pulses following each other at a constant frequency. Pulse-width modulation (PWM) - approximation of the desired signal (multilevel or continuous) with a real binary one (with two levels - on/off), so that on average, over a period of time, their values are equal . The main regulating factor is the relative duration of the pulses or the duty cycle
,where T is the pulse repetition period. With single-ended PWM, the reference voltage is a periodic sawtooth oscillation. In this case, modulation is carried out by changing the position of only one pulse edge. For bidirectional PWM, a triangular (preferably equilateral) reference voltage is required. Double-sided PWM has higher performance than single-sided PWM, so it is used more often. If the input signal is bipolar, then the polarity and average value of the output voltage must change. In this case, two types of modulation are possible: multi-polar PWM and unipolar PWM.
1. Task formulation
In this course work, a pulse-width modulator with the following parameters is developed:
Table 1. Contents of the task
2. Development of a functional diagram of the device
Let's consider the functional diagram and operating principle of the device. |
Figure 1 – Functional diagram
A rectangular pulse generator is needed to generate pulses on the next block - CLAY.
Based on the task, we determine that the reference voltage should be “triangles”. At the output of GLIN we have triangular pulses, which are the same reference voltage supplied to the comparator.
A comparator is a device whose negative input is supplied with a reference signal in the form of triangles, and the positive input is supplied with a modulated continuous analog signal.
According to the instructions, the modulated signal is a sinusoid with a frequency of 200 Hz.
Also, according to the instructions, the amplitude of the output signals should be 10V. The required amplitude is provided by an electronic key.
3. Function blocks
3.1 Square pulse generator
A quartz oscillator is a generator of oscillations synthesized by a quartz resonator that is part of the generator. Typically has a low power output.
External stress on a quartz plate causes its deformation. And this, in turn, leads to the appearance of charges on the surface of quartz (piezoelectric effect). As a result, mechanical vibrations of the quartz plate are accompanied by synchronous vibrations of the electric charge on its surface and vice versa.
To ensure communication between the resonator and the rest of the circuit elements, electrodes are applied directly to the quartz, or a quartz plate is placed between the plates of the capacitor.
We use the Pierce Generator. The circuit uses a minimum of components: one digital inverter, one resistor, two capacitors, and a quartz crystal that acts as a highly selective filter element.
A generator with an RC frequency-setting circuit, its operating principle is based on the process of charging and discharging capacitor C through resistor R. Through this resistor, the OOS is carried out with direct current, and through the capacitor-POS with alternating current.
The second inverter in the generator circuit is designed to reduce the duration of the fronts of the generated rectangular oscillation. This is necessary to reduce the influence of the subsequent circuit on the stability of the master oscillator oscillations, as well as for more reliable operation of the frequency divider digital counters.
Figure 2 – Block 1. Rectangular voltage generator
Frequency divider circuit to the desired frequency. To implement the divider, you will need a 561IE16 microcircuit.
3.2 Voltage ramp generator
This block is a triangular voltage generator. Currently, generators with a low nonlinearity coefficient (ε<0,0) и слабым влиянием нагрузки на форму выходного напряжения создаются с использованием операционных усилителей.
In particular, generators based on an integrator controlled by a rectangular input voltage pulse are common. The elements of the circuit are a power supply, charging resistor R 6, capacitor C3 and discharge transistor VT1. The output voltage of the generator is the voltage across the capacitor, amplified by the operational amplifier. The op-amp is covered by negative (R 5 and R 9) and positive (resistor R 10) feedback.
Figure 3 – CLAY
The generator works as follows. At the moment when field-effect transistor VT1 is closed, capacitor C3 is charged through resistors R10 and R7. As soon as we apply a pulse to VT1, the capacitor of this field-effect transistor discharges.
3.3 Comparator
This block is a comparator, the essence of which is to compare two incoming signals and obtain pulses of different durations at the output. A reference signal is supplied to the negative input, i.e. "triangular pulses", and on the positive - the modulated continuous analog signal itself. The pulse frequency corresponds to the frequency of the triangular pulses. That part of the period in which the input signal is above the reference signal is one at the output, and below it is zero.
Figure 4 - Comparator
3.4 Electronic key
To obtain output pulses of the required amplitude, we use transistor VT2 and the “NAND” element DD5. Resistor R13 limits the current to the base input of the transistor. Resistor R15 is a load.
Figure 5 – Electronic key circuit
4. Calculation part and selection of circuit elements
4.1 Calculation of the pulse generator
Figure 6 shows a generator consisting of an active element - an inverter - and a passive element - a quartz resonator.
Figure 6 – Crystal oscillator
Instead of one inverter, you can install any odd number of inverters.
Figure 7 – Equivalent equivalent circuit
The equivalent circuit of a quartz resonator is shown in Figure 7.
The Pierce generator is one of the most popular circuits. It is the basis of almost all generators on one valve. Quartz behaves like a large inductance since it is connected in parallel. The role of load on the output of the resonator is played by capacitors C1 and C2. Capacitors C1 and C2 play the role of load capacitance of the quartz resonator.
We choose a quartz resonator as a resonator: KX-49 whose nominal frequency is 2.4576 MHz. Table 2 shows the parameters of the quartz resonator.
Table 2 KX-49 parameters
| With L | R 1 | C 0 | F |
| 30pF | 200 Ohm | 7pF | 2.4576 MHz |
Resistor R1 is designed to automatically start the generator when the power is turned on. The same element determines the gain of the inverter, and the greater this gain is, the more rectangular oscillations will be formed at its output, and this, in turn, will lead to a decrease in the current consumed by the quartz oscillator. Let's choose the value of resistor R1 equal to 1Mohm.
Resistor R2 increases the impedance of the circuit so that, together with capacitor C2, increases the phase shift. This is necessary so that the generator operates at the desired frequency, and not at a higher one. The resistor also isolates the inverter output from the resonator circuit and thereby maintains a rectangular pulse shape. The resistor value should be approximately equal to the load impedance Z L, which can be calculated using the given formula:
Pulses with a frequency of f = 2.4576 MHz are supplied to the counter IE16, from Q7 of the counter output we receive pulses with a frequency of f/ 256 = 9.6 kHz.
4.2 Calculation of a linear voltage generator
The circuit in Figure 5 is selected as a linearly varying voltage generator.
The GLIN under consideration is made on the basis of a voltage integrator (DD2, RC circuit, power supply U1), controlled by a square pulse generator and power supply U1. When the transistor is turned off, an uncontrolled (initial) drain current flows through it. When the transistor is open, the current through the transistor must be determined by the value of the load resistance and the supply voltage.
The pulse width modulation (PWM) method is one of the most effective in terms of improving the quality of the output voltage of the AU. The main idea of the method is that the output voltage curve is formed in the form of a series of high-frequency pulses, the duration of which varies (modulates) according to a certain law, in most cases sinusoidal. The pulse repetition rate is called the carrier (or clock) frequency, and the frequency with which the pulse duration changes is called the modulation frequency. Since the carrier frequency is usually significantly higher than the modulation frequency, harmonics that are multiples of the carrier frequency and are present in the output voltage spectrum are relatively easily suppressed using an appropriate filter.
Currently, quite a few types of PWM are known, classified according to various criteria. For example, based on the type of output voltage pulses, modulation is distinguished between unipolar and bipolar. The simplest example of bipolar modulation is the processes implemented in a single-phase half-bridge inverter circuit (Fig. 4.9). The control pulses supplied to the bases of the power transistors, as shown in Figure 4.9(b), are formed by comparing the modulating, low-frequency voltage with a sawtooth reference voltage, the frequency of which is the carrier frequency.
Let us assume that the control system is organized in such a way that if the instantaneous value of the reference voltage is greater than the value of the modulating voltage, then transistor VT2 is turned on and a pulse of positive polarity is formed at the load, as shown in Figure 4.9(c). Accordingly, if the reference voltage becomes less than the modulating voltage, then transistor VT2 turns off and transistor VT1 turns on, which leads to a change in the polarity of the voltage across the load. With the active-inductive nature of the load, the polarity of the output voltage changes due to the inclusion of a reverse diode VD1, through which the load current is closed, supported by the inductive emf L.
When the modulating voltage changes, the duration of the positive and negative output voltage pulses changes; accordingly, the average voltage value over the period of the carrier frequency changes.
The combination of these average values of the output voltage forms a smooth component, the shape of which is determined by the modulating signal. The main disadvantage of bipolar modulation is the large amplitude of the first harmonic of the carrier frequency.
With unipolar modulation, as shown in Figure 4.10, in the output voltage curve during one half-wave of the modulating signal, pulses of only one polarity are formed, and instead of voltage pulses of the opposite polarity, an interval with zero voltage (zero shelf) is formed. In this case, when the duration of the voltage pulses changes, the duration of the zero shelf changes accordingly so that the period of the carrier frequency remains constant.
Unipolar modulation can be implemented in a single-phase bridge circuit AIN, provided that one pair of power transistors, for example, VT1 and VT4, switches with the frequency of the modulation signal, at moments, etc., and the second pair of transistors switches with the carrier frequency. The duration of the control pulses is formed in the same way as in the previous case, as a result of comparing the reference voltage and the modulating signal. The formation of a pulse at the output of the inverter, for example, of positive polarity, is ensured by simultaneously turning on transistors VT1 and VT2. Since transistor VT2 switches at a high frequency, when it is turned off, transistor VT1 remains on, which leads to the closure of the load current stored in the inductance through transistor VT1 and diode VD3. In this case, the voltage at the inverter output is equal to the sum of the voltage drops across the transistor and diode, i.e. close to zero. Similarly, a zero shelf is created when a negative half-wave of a smooth component is formed: when transistor VT3 is turned off, the load current is closed through transistor VT4 and diode VD2. Thus, the polarity of the smooth component of the output voltage is determined by switching on transistors VT1 or VT4, and the high-frequency filling and, accordingly, the shape of the smooth component is determined by switching transistors VT2 or VT3.
The main advantage of unipolar modulation, compared to bipolar modulation, is the reduction in the amplitudes of high-frequency harmonics.
It should be noted that unipolar modulation is not possible in some circuits, such as single-phase half-bridge. In this case, to implement unipolar modulation it is necessary to use more complex circuits, for example, the circuit shown in Figure 4.7.
Based on the method of forming the duration of high-frequency pulses, several types of pulse-width modulation are distinguished, the most common of which are PWM of the first and second types. With pulse-width modulation of the first kind (PWM-1), the duration of the generated pulse is proportional to the values of the modulating signal, selected at certain, predetermined moments in time. The principle of forming pulse duration with PWM-1 is illustrated in Fig. 4.11(a).
The principle of forming pulse duration with PWM-2 is shown in Fig. 4.11(b). In this case, the pulse duration is determined by the value of the modulating signal at the end of the pulse.
Based on the method of changing the duration, one-way and two-way modulation are distinguished. For example, in Fig. 4.9 shows one-
third-party modulation, since when the modulating signal changes, the moment at which only the trailing edge of the pulse is generated changes. Accordingly, in Fig. Figure 4.10 shows an example of two-way modulation.
The ratio of the carrier frequency to the frequency of the modulating signal is called the carrier frequency multiple. The multiplicity can be either an integer or a fraction, and in the general case the multiplicity can also be an irrational fraction. The multiplicity significantly affects the spectral composition of the output voltage, and with fractional-rational multiplicities, harmonics with a frequency lower than the frequency of the modulating signal appear in the spectrum of the output voltage. Such harmonics are called subharmonics, and their amplitudes increase as the carrier frequency factor decreases, which can lead to disruption of the normal operation of the inverter. To suppress subharmonics, the carrier frequency multiplicity should be increased, but this inevitably increases switching losses in the inverter's power devices.
The useful component of the output voltage is determined by the shape of the smooth component, which in turn depends on the shape of the modulating signal or, as it is commonly called, on the modulation law. Currently, modulation according to the sinusoidal, trapezoidal or rectangular law is most often used. In particular, the method of pulse-width control at the carrier frequency discussed above is nothing more than the use of PWM according to the rectangular law.
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3.2. Algebraic stability criteria
One of the first criteria for durability was identified by Professor J. A. Vishnegradsky and given by him in his works “On Direct-Acting Regulators” and “On Indirect-Acting Regulators.” The criterion is formulated for processes described by third-order differential equations, the characteristic equation of which is reduced to the form: .
Figure 3.4 - Diagram that defines the area of stability of systems described by 3rd order equations. (Vishnegradsky diagram)
If we introduce the notation and, then according to Vishnegradsky, in order for the system to be stable it is necessary that, or. In Figure 3.4, the hyperbola ΧΥ =1 is plotted in the coordinates X and Υ, which gives the stability limit of the system. The line between the resistance areas is usually hatched, so that the resistance areas can be seen from the hatching without further explanation.
On the diagram in Figure 3.4 there is a plotted line of the aperiodicity boundary, determined by the condition with a face point at the values of X = Υ = 3.
The Vishnegradsky stability criterion outlined above is a separate case of the Routh-Hurwitz stability criterion. This criterion can be formulated as follows, in the form proposed by Hurwitz: if the system is described by a linear differential equation, the characteristic equation of which is:
then in order for it to be stable, that is, for all the real roots and real parts of the complex roots of the characteristic equation to be negative, it is necessary and sufficient that all the coefficients of the equation have the same sign, and the diagonal determinant is of order n-1, composed of the coefficients of the equation, and all of its diagonal minors would be positive:
The diagonal determinant is composed as follows:
Thus, in order for the system to be stable, it is necessary that all coefficients have the same sign and all determinants be greater than 0.
The order of compiling diagonal minors can be analyzed using the example of a fifth-degree equation:
Then we get:
For a third order equation:
And also.
Note that for and we have the Vyshegradsky stability conditions
Both the Vishnegradsky criterion and the Routh-Hurwitz criterion determine the stability of the system based on the coefficients of the characteristic equation and are called algebraic stability criteria. Let's look at some examples of resistance research using the Routh-Hurwitz criterion.
Example 1. Characteristic equation of the system
For this:
Just as all the coefficients of this equation are greater than zero, so the determinants are also greater than zero - the system is stable.
Pulse width modulation consists of changing the width (duration) of pulses following each other at a constant frequency. Pulse-width modulation (PWM) - approximation of the desired signal (multilevel or continuous) with a real binary one (with two levels - on/off), so that on average, over a period of time, their values are equal . The main regulating factor is the relative duration of the pulses or the duty cycle
where T is the pulse repetition period. With single-ended PWM, the reference voltage is a periodic sawtooth oscillation. In this case, modulation is carried out by changing the position of only one pulse edge. For bidirectional PWM, a triangular (preferably equilateral) reference voltage is required. Double-sided PWM has higher performance than single-sided PWM, so it is used more often. If the input signal is bipolar, then the polarity and average value of the output voltage must change. In this case, two types of modulation are possible: multi-polar PWM and unipolar PWM.
1. Task formulation
In this course work, a pulse-width modulator with the following parameters is developed:
Table 1. Contents of the task
2. Development of a functional diagram of the device
Let's consider the functional diagram and operating principle of the device.
 |
Figure 1 – Functional diagram
A rectangular pulse generator is needed to generate pulses on the next block - CLAY.
Based on the task, we determine that the reference voltage should be “triangles”. At the output of GLIN we have triangular pulses, which are the same reference voltage supplied to the comparator.
A comparator is a device whose negative input is supplied with a reference signal in the form of triangles, and the positive input is supplied with a modulated continuous analog signal.
According to the instructions, the modulated signal is a sinusoid with a frequency of 200 Hz.
Also, according to the instructions, the amplitude of the output signals should be 10V. The required amplitude is provided by an electronic key.
3. Function blocks
3.1 Square pulse generator
A quartz oscillator is a generator of oscillations synthesized by a quartz resonator that is part of the generator. Typically has a low power output.
External stress on a quartz plate causes its deformation. And this, in turn, leads to the appearance of charges on the surface of quartz (piezoelectric effect). As a result, mechanical vibrations of the quartz plate are accompanied by synchronous vibrations of the electric charge on its surface and vice versa.
To ensure communication between the resonator and the rest of the circuit elements, electrodes are applied directly to the quartz, or a quartz plate is placed between the plates of the capacitor.
We use the Pierce Generator. The circuit uses a minimum of components: one digital inverter, one resistor, two capacitors, and a quartz crystal that acts as a highly selective filter element.
A generator with an RC frequency-setting circuit, its operating principle is based on the process of charging and discharging capacitor C through resistor R. Through this resistor, the OOS is carried out with direct current, and through the capacitor-POS with alternating current.
The second inverter in the generator circuit is designed to reduce the duration of the fronts of the generated rectangular oscillation. This is necessary to reduce the influence of the subsequent circuit on the stability of the master oscillator oscillations, as well as for more reliable operation of the frequency divider digital counters.
Figure 2 – Block 1. Rectangular voltage generator
Frequency divider circuit to the desired frequency. To implement the divider, you will need a 561IE16 microcircuit.
3.2 Voltage ramp generator
This block is a triangular voltage generator. Currently, generators with a low nonlinearity coefficient (ε<0,0) и слабым влиянием нагрузки на форму выходного напряжения создаются с использованием операционных усилителей.
In particular, generators based on an integrator controlled by a rectangular input voltage pulse are common. The elements of the circuit are a power supply, charging resistor R 6, capacitor C3 and discharge transistor VT1. The output voltage of the generator is the voltage across the capacitor, amplified by the operational amplifier. The op-amp is covered by negative (R 5 and R 9) and positive (resistor R 10) feedback.
Figure 3 – CLAY
The generator works as follows. At the moment when field-effect transistor VT1 is closed, capacitor C3 is charged through resistors R10 and R7. As soon as we apply a pulse to VT1, the capacitor of this field-effect transistor discharges.
3.3 Comparator
This block is a comparator, the essence of which is to compare two incoming signals and obtain pulses of different durations at the output. A reference signal is supplied to the negative input, i.e. "triangular pulses", and on the positive - the modulated continuous analog signal itself. The pulse frequency corresponds to the frequency of the triangular pulses. That part of the period in which the input signal is above the reference signal is one at the output, and below it is zero.
Figure 4 - Comparator
3.4 Electronic key
To obtain output pulses of the required amplitude, we use transistor VT2 and the “NAND” element DD5. Resistor R13 limits the current to the base input of the transistor. Resistor R15 is a load.
Figure 5 – Electronic key circuit
4. Calculation part and selection of circuit elements
4.1 Calculation of the pulse generator
Figure 6 shows a generator consisting of an active element - an inverter - and a passive element - a quartz resonator.
Figure 6 – Crystal oscillator
Instead of one inverter, you can install any odd number of inverters.
Figure 7 – Equivalent equivalent circuit
The equivalent circuit of a quartz resonator is shown in Figure 7.
The Pierce generator is one of the most popular circuits. It is the basis of almost all generators on one valve. Quartz behaves like a large inductance since it is connected in parallel. The role of load on the output of the resonator is played by capacitors C1 and C2. Capacitors C1 and C2 play the role of load capacitance of the quartz resonator.
We choose a quartz resonator as a resonator: KX-49 whose nominal frequency is 2.4576 MHz. Table 2 shows the parameters of the quartz resonator.
Table 2 KX-49 parameters
| With L | R 1 | C 0 | F |
| 30pF | 200 Ohm | 7pF | 2.4576 MHz |
Resistor R1 is designed to automatically start the generator when the power is turned on. The same element determines the gain of the inverter, and the greater this gain is, the more rectangular oscillations will be formed at its output, and this, in turn, will lead to a decrease in the current consumed by the quartz oscillator. Let's choose the value of resistor R1 equal to 1Mohm.
Resistor R2 increases the impedance of the circuit so that, together with capacitor C2, increases the phase shift. This is necessary so that the generator operates at the desired frequency, and not at a higher one. The resistor also isolates the inverter output from the resonator circuit and thereby maintains a rectangular pulse shape. The resistor value should be approximately equal to the load impedance Z L, which can be calculated using the given formula:
Pulses with a frequency of f = 2.4576 MHz are supplied to the counter IE16, from Q7 of the counter output we receive pulses with a frequency of f/ 256 = 9.6 kHz.
4.2 Calculation of a linear voltage generator
The circuit in Figure 5 is selected as a linearly varying voltage generator.
The GLIN under consideration is made on the basis of a voltage integrator (DD2, RC circuit, power supply U1), controlled by a square pulse generator and power supply U1. When the transistor is turned off, an uncontrolled (initial) drain current flows through it. When the transistor is open, the current through the transistor must be determined by the value of the load resistance and the supply voltage.
When the linearly varying voltage Uc(t) at the output of the integrator reaches the operating voltage value, a control signal is sent, under the influence of which the key transistor VT1 opens, discharging the capacitor. The process is then repeated with the period:
We set the frequency to 9.6 kHz.
It is advisable to choose the minimum voltage Ucm in order to eliminate the influence of the scatter in the parameters of the resistors used on the nonlinearity coefficient of the generated voltage.
The maximum voltage on the capacitor is related to the duration dependence
t
We select U1 = 5V, U2 = 0V, then Ucm = 5V.
We choose R 6 = R 5 = 10 kOhm, then C 3 = 96 nF.
Based on the following, we find R9.
Uout = 10 V, then: R 9 = Ucmax*R 6 / Uout = 5*10000/10≈ 2 kOhm, take the closest nominal value
R 9 = R 10 = 2 kOhm
140UD7 was selected as op-amp DD3. Power supply ±10V.
4.3 Selecting a comparator
521CA3 is used as the DD4 comparator to ensure stable PWM operation.
Technical characteristics of the analog comparator 521CA3
Analogue LM111
Input current no more than 100 nA
Gain factor not less than 200000
Load current up to 50 mA
Power supply +5...+30 or ±3...±15 V
Areas of use
Zero crossing detectors
Surge detectors
Pulse width modulators
Precision rectifiers
Analog-to-digital converters
Resistor R12 in combination with diodes D1 and D2 limits the swing of the input signal. Thanks to diodes, we limit the input voltage swing to values of -12.6 V to +12.6 V, the condition is that the negative input voltage should not reach the breakdown voltage value (for example, for a diode like KD510A this value is - 50 V).
Table 3 Parameters of the selected transistor
| Name | U arr. ,IN | I ex. max, A | I arr. max, µA | F d max, kHz |
| KD510A | 50 | 0.2 | 5 | 200000 |
4.4 Electronic key calculation
The following scheme is selected as the key:
Figure 9 – Electronic key circuit
Rн =0.5 k Ohm, Uout =10V.
Ik=Uout/Rn=10/500=50mA
Using the reference book, we look for a transistor that can withstand the given collector current (0.05A). The KT315A transistor holds a constant current of up to 0.1 A.
From the reference book - h21e, for KT315A
We consider the base current Ib=Ik/h21e=0.05/30≈ 1.67 mA; a current of at least 167 μA must be supplied to the base.
R14 – matching resistance between comparator DD3 and transistor VT2. Let's choose R16 = 200 Ohm.
R out =R 15 =500 Ohm according to the instructions, select 510 Ohm from the series. at the output you need to get 10 V, then calculate the value of resistor R 14
(U supply -U out)/R 14 =U out/R 15,
from where R 14 = 2R 15 /10 = 102 Ohm, from the standard series we select a nominal value of 100 Ohm. Power dissipation 10V*1.25mA≈0.0125 W
Table 4. Parameters of the selected transistor KT315A
5. Circuit simulation
Output signal from triangle pulse generator:
Output signal from square wave generator:
Simulated signal:
Modulation process:
Output period:
Shortest pulse duration:
The duration should be 5.12 µs. The graph shows that it is 5.56 μs.
Longest pulse duration:
The pulse duration should be 97.37 µs. The graph shows that it is equal to 97.74 μs.
Conclusion
In this course work, we developed a circuit diagram and calculated the Pulse Width Modulator circuit. A sinusoid with a frequency according to the specification is supplied to the input of the PWM device - 200 Hz, at the output we have a converted PWM signal, the amplitude of which is 10 V. The range of changes in the relative duration of the output pulses of this PWM is - 0.05 ÷ 0.95. The developed pulse width modulator is quite simple. The circuit was simulated using the CircuitMaker package.
List of used literature
1. Altshuller G.B., Elfimov N.N., Shakulin V.G. Quartz resonators: a reference guide. M.: Radio and Communications, 1984.-232 pp., ill.
2. Horwitz P., Hill W. The Art of Circuit Design: Trans. from English – Ed. sixth. M.: Mir, 2001.
3. Lecture course on ECiMS (teacher I.B. Andreev).
4. Digital CMOS microcircuits, reference book, Partala O.N. – St. Petersburg: Science and Technology, 2001. - 400 pp. with illustrations.
5. L. Labutin, Quartz resonators. - Radio, 1975, No. 3.
6. Rectangular pulse generators based on CMOS chips. V. Strizhov, Circuitry, 2000, No. 2, p. 28
7. Zabrodin Yu.S., Industrial electronics: a textbook for universities. - M.: Higher. School, 1982. – 496 p., ill.
8. Pulse width modulation in converters
8.1. General information
The principles of pulse control and modulation are discussed in Chapter. 4 using the example of a simple DC regulator circuit. At the same time, definitions are given of the main types of pulse modulation used in the theory of linear pulse systems, which correspond to the practice of controlling pulsed DC converters.
However, pulse-width modulation of voltages or currents in AC converters has a slightly different definition in power electronics, taking into account the features of PWM when solving problems of converting electricity using alternating current. As defined in IEC 551-16-30, pulse width modulation is a pulse control in which the width or frequency of the pulses, or both, are modulated within a period of the fundamental frequency to produce a specific output voltage waveform. In most cases, PWM is carried out in order to ensure the sinusoidality of the voltage or current, i.e., reducing the level of higher harmonics relative to the main (first) harmonic, and is called sinusoidal. There are the following main methods for ensuring sinusoidality: analog PWM and its modifications; selective (selective) suppression of higher harmonics; hysteresis or delta modulation;
space vector modulation.
The classic version of organizing an analog sinusoidal PWM is to change the width of the pulses that form the output voltage (current) by comparing a voltage signal of a given shape, called a reference or reference, with a triangular voltage signal having a higher frequency and called a carrier signal. The reference signal is modulating and determines the required shape of the output voltage (current). There are many modifications of this method in which the modulating signals are represented by special functions other than a sine wave. The lecture notes will discuss several basic circuits explaining these PWM methods.
The method of selective suppression of higher harmonics is currently successfully implemented using software-based microprocessor controllers. Hysteresis modulation is based on the principles of relay “tracking” of a reference signal, for example, a sinusoidal waveform. In its simplest technical design, this method combines the principles of PWM and PFM (pulse frequency modulation). However, through special circuit measures it is possible to stabilize the modulation frequency or limit the range of its change.
The space vector modulation method is based on converting a three-phase voltage system into a two-phase one and obtaining a generalized space vector. The magnitude of this vector is calculated at moments determined by the fundamental and modulating frequencies. It is considered very promising for controlling three-phase inverters, in particular, when used in electric drives. At the same time, it is in many ways similar to traditional sinusoidal PWM.
Control systems based on PWM allow not only to provide a sinusoidal shape of the average values of the fundamental harmonic of voltage or current, but also to control the values of its amplitude, frequency and phase. Since in these cases the converter uses fully controlled switches, it becomes possible to implement the operation of AC (DC) converters together with the AC network in all four quadrants in both rectifying and inverting modes with any given value of the fundamental harmonic power factor cosφ in range from -1 to 1. Moreover, with increasing carrier frequency, the possibilities of reproducing current and voltage of a given shape at the output of inverters expand. This allows you to create active filters to suppress higher harmonics.
We will consider the main definitions used in the further presentation using the example of the application of the first method in a single-phase half-bridge circuit of a voltage inverter (Fig. 8.1, A). In this conditional diagram the keys S1 And S2 are represented by fully controlled switching elements, supplemented by diodes connected in series and parallel to them. Series diodes reflect the unidirectional conductivity of switches (for example, transistors or thyristors), and parallel diodes provide conduction of reverse currents with an active-inductive load.
Diagrams of reference, modulating u M(θ) and carrier u H (θ) signals are shown in Fig. 8.1, b. Formation of key control pulses S 1 and S 2 is carried out according to the following principle. At u M (θ) > u H(θ) key S 1 is on, a S 2 switched off. At u M(θ)< u H (θ) key states are reversed: S 2 - on, a S 1 - off. Thus, a voltage is generated at the inverter output in the form of two polar pulses. In real circuits to eliminate simultaneous conduction of switches S 1 and S 2, a certain delay should be provided between the moments of generating signals to turn on these keys. Obviously, the pulse width depends on the ratio of the signal amplitudes u M(θ) and u H(θ). The parameter characterizing this relationship is called the amplitude modulation index and is determined by formula (8.1):
, (8.1.)
Where U M m and U H m - maximum values of the modulating signal u M(θ) and carrier signal u H(θ) respectively.
Rice. 8.1. Single phase semi bridge voltage inverter: A- scheme; b– voltage diagrams for pulse modulation
Carrier frequency u H(θ) is equal to the switching frequency f H keys S 1 and S 2 and usually significantly exceeds the frequency of the modulating signal f M. Frequency ratio f H and f M is an important indicator of the efficiency of the modulation process and is called the frequency modulation index, which is determined by formula (8.2):
At small values M f signals u M(θ) and u H(θ) must be synchronized to avoid unwanted subharmonics. B as maximum value My, which determines the need for synchronization, is set M f = 21. Obviously, with synchronized signals the coefficient M f is a constant value.
From the diagram in Fig. 8.1 it can be seen that the amplitude of the first harmonic of the output voltage U am 1 can be presented, taking into account (8.1), in the following form (8.3):
(8.3)
According to (8.3) at M a = 1 amplitude of the first harmonic of the output voltage is equal to the height of the half-wave rectangle U d/2. The characteristic dependence of the relative value of the first harmonic of the output voltage on the value of M a is shown in Fig. 8.2, from which it is clear that the change M a from 0 to 1 linearly and depends on the amplitude U am 1. Limit value M a is determined by the principle of the type of modulation under consideration, according to which the maximum value U am 1 is limited by the height of the half-wave of a rectangular shape, equal to U d/2. With a further increase in the coefficient M a modulation leads to a nonlinear increase in amplitude U am 1 to the maximum value determined by the formation of a rectangular voltage at the output of the inverter, which subsequently remains unchanged.
Expanding the rectangular function into a Fourier series gives the maximum value (8.4):
(8.4)
This value is limited by the index value M a, varying in the range from 0 to approximately 3. Obviously, the function in the interval a-b values from 1 to 3.2 is nonlinear (Fig. 8.2). The operating mode in this section is called over modulation.
Meaning M f determined by the choice of carrier signal frequency u H (θ) and significantly affects the technical characteristics of the converter. As the frequency increases, switching losses in the power switches of the converters increase, but at the same time the spectral composition of the output voltage improves and the solution to the problem of filtering higher harmonics caused by the modulation process is simplified. An important factor in choosing a value f H in many cases is the need to ensure its value in the audio frequency range of more than 20 kHz. When choosing f H you should also take into account the level of operating voltages of the converter, its power and other parameters.
Rice. 8.2. Dependence of the relative value of the amplitude of the fundamental harmonic of the output voltage on the amplitude modulation index for a single-phase half-bridge circuit
The general trend here is an increase in the values of M f low power and low voltage converters and vice versa. So the choice M f is a multicriteria optimization problem.
Pulse modulation with stochastic process. The use of PWM in converters is associated with the appearance of higher harmonics in modulated voltages and currents. Moreover, in the spectral composition of these parameters, the most significant harmonics occur at frequencies that are multiples of the frequency modulation index M f and harmonics with decreasing amplitudes grouped around them at side frequencies. Higher harmonics can cause the following main problems:
the occurrence of acoustic noise;
deterioration of electromagnetic compatibility (EMC) with other electrical devices or systems.
The main sources of acoustic noise are electromagnetic components (chokes and transformers), which are exposed to current and voltage containing higher harmonics with frequencies in the audio range. It should be noted that noise can occur at certain frequencies where higher harmonics are greatest. Noise-causing factors, such as magnetostriction, make EMC problems more difficult to resolve. EMC problems can occur over a wide frequency range, depending on the EMI sensitivity of electrical devices. Traditionally, design and technology solutions have been used to reduce noise levels, and passive filters have been used to ensure EMC.
As a promising direction for solving these problems, methods associated with changing the nature of the spectral composition of modulated voltages and currents are considered. The essence of these methods is to level the frequency spectrum and reduce the amplitude of pronounced harmonics due to their stochastic distribution over a wide frequency range. This technique is sometimes called “smearing” the frequency spectrum. The concentration of interference energy decreases at frequencies where harmonics can have maximum values. The implementation of these methods is not associated with any impact on the components of the power part of the converters and in most cases is limited by software with minor changes to the control system.
Let us briefly consider the principles of implementation of these methods. PWM is based on a change in the duty cycle γ= t And / T n, Where t and - pulse duration; T n- the period of its formation. Usually these quantities, as well as the position of the pulse on the period interval T n are constant in steady state conditions. PWM results are defined as integral average values. In this case, the deterministic values of t and and, including the pulse position, determine the unfavorable spectral composition of the modulated parameters. If these quantities are given a random character while maintaining a given value of γ, then the processes become stochastic and the spectral composition of the modulated parameters changes. For example, such a random character can be given to the position of the impulse t and on the interval of period T n or provide a stochastic change in the latter. For this purpose, a random number generator can be used, influencing the modulation frequency master generator f n =1/T n. In a similar way, you can change the position of the pulse over the interval T n with mathematical expectation equal to zero. The averaged integral value γ must remain at the level specified by the control system, as a result of which the spectral composition of higher harmonics in modulated voltages and currents will be equalized.
Questions for self-control
1. List the main PWM methods for ensuring a sinusoidal current or voltage.
2. What is the difference between unipolar and bipolar voltage modulation?
3. List the main parameters of PWM.
4. For what purpose is PWM with stochastic processes used?
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