The voltage received from the rectifiers is not constant, but pulsating. It consists of constant and variable components. The larger the variable component in relation to the constant one, the greater the ripple and the worse the quality of the rectified voltage.

The alternating component is formed by harmonics. The harmonic frequencies are determined by the equality

f(n) = kmf ,

where k is the harmonic number, k = 1, 2, 3, ..., m is the number of pulses of the rectified voltage, f is the frequency of the network voltage.

The quality of the rectified voltage is assessed ripple factor p, which depends on the average value of the rectified voltage and the amplitude of the fundamental harmonic in the load.

The order of the harmonic components n = km contained in the rectified voltage curve depends only on the number of pulses and does not depend on the specific one. The harmonics of the smallest numbers have the greatest amplitude.

The effective value of the voltage of the harmonic component of order n depends on the average value of the rectified voltage Ud of an ideal unregulated rectifier:

In real circuits, the transition of current from one diode to another occurs over a certain finite period of time, measured in fractions and called commutation angle. The presence of commutation angles significantly increases the amplitude of harmonics. As a result, they grow rectified voltage ripple.

The alternating component of the rectified voltage, consisting of low and high frequency harmonics, creates an alternating current in the load, which has an interfering effect on other electronic devices.

For reducing rectified voltage ripple between the output terminals of the rectifier and the load include anti-aliasing filter, which significantly reduces the ripple of the rectified voltage by suppressing harmonics.

The main elements of smoothing filters are (chokes) and, and at low powers, transistors.

The operation of passive filters (without transistors and other amplifiers) is based on the frequency dependence of the resistance value of the reactive elements (inductor and capacitor). Reactance of inductor Xl and capacitor Xc: Xl = 2πfL, Xc = 1/2πfC,

where f is the frequency of the current flowing through the reactive element, L is the inductance of the inductor, C is the capacitance of the capacitor.

From the formulas for the resistance of reactive elements it follows that with increasing frequency of the current, the resistance of the coil increases, and the resistance of the capacitor decreases. For direct current The resistance of the capacitor is infinity, and the resistance of the inductor is zero.

This feature allows the inductor to freely pass the direct component of the rectified current and delay harmonics. Moreover, the higher the harmonic number (the higher its frequency), the more effectively it is delayed. On the contrary, a capacitor completely blocks the direct current component and allows harmonics to pass through.

The main parameter characterizing the efficiency of the filter is smoothing (filtering) coefficient

q = p1 / p2,

where p1 is the ripple factor at the rectifier output in a circuit without a filter, p2 is the ripple factor at the filter output.

In practice, passive L-shaped, U-shaped and resonant filters are used. The most widely used are L-shaped and U-shaped, the diagrams of which are shown in Figure 1

Figure 1. Circuits of passive smoothing L-shaped (a) and U-shaped (b) filters to reduce rectified voltage ripple

The initial data for calculating the inductance of the filter choke L and the capacitance of the filter capacitor C are the ripple factor of the rectifier, the circuit design option, as well as the required ripple factor at the filter output.

The calculation of filter parameters begins with determining the smoothing coefficient. Next, you need to randomly select the filter circuit and the capacitance of the capacitor in it. The capacitance of the filter capacitor is selected from the range of capacitances given below.

In practice, capacitors of the following capacities are used: 50, 100, 200, 500, 1000, 2000, 4000 μF. It is advisable to use smaller capacitance values ​​from this series at high operating voltages, and larger capacitances at low voltages.

The inductance of the inductor in an L-shaped filter circuit can be determined from the approximate expression

for a U-shaped scheme –

In the formula, the capacitance is substituted in microfarads, and the result is obtained in henry.

Rectified voltage ripple filtering

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The ripple factor is most often talked about when considering a variable electricity. Then the ripple factor of voltage or current is considered. There is an internal division of the voltage (current) ripple coefficients into: voltage (current) ripple coefficient, voltage (current) ripple coefficient by the average value, by the effective value.

In general, the voltage waveform at the output of a rectifying device has a constant (called useful) and alternating (pulsating) components.

DEFINITION

Voltage (current) ripple coefficient they call a value equal to the ratio of the amplitude value (maximum value) of the variable component of the pulsating voltage (current) to the direct component.

If we represent the rectified voltage in the form of a Fourier series, as the sum of a constant component () and a certain number () of harmonics having amplitudes, then the voltage ripple coefficient () can be determined by the formula:

where n is the harmonic number.

In this case, the component is considered a useful result of the rectifier's activity, in contrast to pulsations. If the ripple shape is complex, then the maximum value may not be the first harmonic, but usually k is understood as it. It is used in calculations and recorded in the technical documents of the equipment.

Varieties of voltage (current) ripple coefficients

The average voltage (current) ripple coefficient is a value equal to the ratio of the average value of the variable component of the pulsating voltage (current) to the constant component.

The voltage (current) ripple coefficient based on the effective value is a parameter that is found as the ratio of the effective value of the variable component of the pulsating voltage (current) to its constant component.

Often, consumers do not care which of the harmonics at the output of the rectifying device has the greatest range. Of interest is the total range of pulsations, which is characterized by the absolute pulsation coefficient (), which is determined by the expression:

Or use the formula:

The voltage ripple factor is measured using an oscilloscope or two voltmeters.

The ripple factor is one of the most significant characteristics of a rectifier - a device that is designed to convert the alternating voltage of an electrical energy source into direct voltage.

Units

The pulsation coefficient is considered as a dimensionless quantity or it can be indicated as a percentage.

Examples of problem solving

EXAMPLE 1

Exercise	What are the ripple coefficients for the first harmonic, the absolute ripple coefficients in two calculation options, if the constant voltage at the output of the rectifying device is 20 V, and the ripple voltage is ?
Solution	We find the voltage ripple coefficient for the first harmonic using the expression: where n =1. Let's carry out the calculations: We find the absolute voltage ripple coefficient (option 1) using the formula: Let's calculate: The second option for the absolute voltage ripple factor: Let's calculate it:
Answer

EXAMPLE 2

Exercise

When an alternating voltage is applied in the form of a sinusoid to the primary winding of the matching device (Fig. 1), it will have a voltage at the terminals of the secondary winding: The diode conducts electric current for only half the period of the alternating voltage. In the positive half of the period, when the potential at the anode of the diode (VD) is greater than zero, it is open and the entire voltage of the secondary winding of the transformer is applied to the diode. What will be the current ripple coefficient based on the average value?

Calculation of filters for PWM

The article will discuss the calculation of the simplest filter circuits for smoothing pulse width modulation. What is PWM, where is it used and how to implement it, read in a separate article.

The first thing you should focus on is the purpose of the circuit for which you are going to build a filter. Simplifying a little, PWM circuits can be divided into two types:

An example of a signal PWM is, for example, the simplest DAC; by power PWM we most often mean the PWM signal at the output of power switches, for example in pulsed sources nutrition (IIP). Strictly speaking, in power supplies the PWM signal itself is also used in the signal circuit (transistor control) and at the output of such sources the signal repeats the shape of the control signals, but has a higher power, therefore they require filters that allow higher powers to pass through.

PWM filtering in signal circuits

For simple signal circuits with high-resistance loads, the most optimal filtering circuit is an integrating RC circuit, which is essentially a simple low-pass filter. The concept of "integrating RC circuit" is used when considering impulse responses this chain.

Fig.1. The simplest low-pass filter is an integrating RC circuit and its frequency response.

The main characteristic of the filter is cutoff frequency (Figure 1 shows the angular cutoff frequency - ω s) - the amplitude of oscillations of a given frequency at the filter output is attenuated to a level of ~0.707 (-3 dB) from the input value. The cutoff frequency is determined by the following formula:

Here R and C are the resistance of the resistor in ohms and the capacitance of the capacitor in farads. It must be remembered that for the smoothing filter to work correctly, the time constant of the RC chain ( τ = R C) should be as short as possible to the PWM period, then the full charge-discharge of the capacitor will not occur in one period.

Next important parameter, which allows one to calculate the attenuation of oscillations at a given frequency is transmission coefficient filter is the ratio K = U out / U in. For a given RC chain, the transmission coefficient is calculated as follows:

Knowing these formulas and taking into account the constant voltage drop across the resistor, you can approximately calculate the filter with the necessary characteristics- for example, by specifying the available capacity or the required level of pulsation.

RC PWM filter calculator

Please note that if you want to obtain a smoothed sinusoidal signal from a PWM signal, it is necessary that the filter cutoff frequency be higher than the maximum signal frequency, which means the PWM frequency must be even higher.

PWM filtering in power circuits

In power circuits, at low load resistances (for example, electric motor windings), losses in the filter resistor become very significant, therefore similar cases Low-pass filters are used on inductors and capacitors.

Fig.2. Low-pass filter on the LC circuit and its frequency response.

An LC filter is an elementary oscillating circuit that has its own resonance frequency, so its real frequency response will be slightly different from the frequency response shown in Figure 2.

Since this article is about a filter for power circuits, when calculating the filter, it must be taken into account that the fundamental harmonic of the incoming voltage must also be attenuated by the filter, therefore, its resonant frequency must be lower than the PWM frequency.

Formula for calculating the resonance frequency of an LC circuit:

f = 1/(2 π (L C) 0.5)

If the resonance frequency of the circuit coincides with the PWM frequency, the LC circuit may go into generation mode, then confusion may occur at the output, therefore I suggest you carefully avoid this misunderstanding. In addition, when designing this filter, there are several more nuances that would be nice to observe to obtain the desired result, namely:

1. To eliminate resonance phenomena on one of the high-frequency harmonic components, it is advisable to find the capacitance of the capacitor from the condition that the wave impedance of the filter is equal to the load resistance:
2. To smooth out ripples with such a filter, it is desirable that the capacitive reactance of the capacitor for the lowest pulsation frequency be as small as possible as the load resistance, and also much less than the inductive reactance of the inductor for the first harmonic.

The complex gain of an LC filter is calculated using the following formula:

where n is the number of the harmonic component of the input signal, i- imaginary unit, ω = 2πf, L - inductance of the inductor (H), C - capacitor capacity (F), R - load resistance (Ohm).

It is obvious from the formula that the higher the harmonic, the better it is suppressed by the filter, therefore, it is enough to calculate the level only for the first harmonic.

To move from a complex representation of the transmission coefficient to an exponential one, you need to find the modulus of a complex number. For those who (like me) slept on math classes at the institute, let me remind you that the modulus of a complex number is calculated very simply:

2. Secondary power sources.
Basic circuits, parameters and characteristics

2.1. Structural scheme VIEPa

Rectifier devices convert the alternating voltage of the supply network into direct voltage at the load. They are used as secondary power sources (SPPS), the block diagram of which is shown in Fig. 2.1.

Rice. 2.1. VIEP block diagram

Power transformer Tr reduces AC network voltage U 1 frequency f=50 Hz to the required value U 2. In addition, the transformer provides galvanic isolation of the power supply network and the VEP load. Rectifier IN converts AC voltage U 2 into rectified pulsating voltage of the same polarity U d. Anti-aliasing filter F reduces rectified voltage ripple U d. Stabilizer St maintains constant output voltage U out when network voltage fluctuates U 1 or change in the load of the VIEP.

2.2.Basic rectification circuits

Low-power power supplies (up to several hundred watts) usually use rectifiers powered by single-phase mains voltage. In single-phase rectifiers, three main circuits for connecting diodes are used: a single-phase half-wave circuit with one diode, single-phase full-wave circuits: a midpoint circuit (zero circuit) with two diodes and a bridge circuit with four diodes.

DC power supplies of medium (up to 1000 W) and higher (over 1000 W) power use rectifier devices powered by three-phase voltage. A three-phase rectifier can be made by NPO using a half-wave circuit with three diodes or a full-wave circuit with six diodes, which is called a three-phase bridge or Larionov circuit.

2.3. Single-phase rectification circuits

2.3.1.Half-wave rectification circuit

The single-phase half-wave rectification circuit (Fig. 2.2) is the simplest. Semiconductor diode VD1, having one-way conductivity, is connected in series with the load Rd.

Rice. 2.2. Half-wave rectification circuit

Timing diagrams (Fig. 2.3) of rectifier voltages and currents show that in such a circuit the current i d flows through the load only during the positive half-cycle of the voltage u 2, coming from the secondary winding of the transformer (Fig. 2.3 a, b). As a result, under load Rd pulsating voltage appears u d positive polarity (Fig. 2.3 c). In the negative half-cycle of the voltage u 2 diode VD1 closes, current i d =0 and the diode is exposed to reverse voltage u 2, the maximum value of which is equal to the amplitude U 2 m, i.e. the voltage across the diode (Fig. 2.3 d).

Rectified ripple voltage across the load u d described by an expression in ranges, etc. and can be represented by the sum of constant and variable components

The non-sinusoidal variable component can be represented by a series of harmonics, i.e. a series of sinusoidal components with increasing frequency and decreasing amplitude with the serial number. Then the pulsating voltage can be represented as a harmonic Fourier series

Rice. 2.3. Half-Wave Timing Diagrams

which for a half-wave rectification circuit will be written as the expression:

Using the Fourier series, the main parameters of the rectification circuit are determined.

The DC component is calculated as the average value of the rectified voltage at the load when the rectifier is operating in no-load mode over the period of the network voltage

The average value of the ripple current in the load is determined by the expression: .

The alternating component of the rectified voltage is characterized by its maximum value (fundamental harmonic): , where – amplitude of the fundamental harmonic.

The efficiency of the rectifier is determined by the value of the ripple coefficient, which is determined by the ratio of the amplitude of the fundamental harmonic U m to the average value of the rectified voltage

In this case, the ripple frequency of the fundamental harmonic coincides with the ripple frequency of the rectified voltage and is equal to the network voltage frequency:

The advantage of a half-wave circuit is its simplicity. Disadvantages: large dimensions of the transformer, large ripple factor, low frequency fundamental harmonic. Therefore, such a rectification circuit finds limited use, mainly for powering low-power circuits and high voltage, for example: cathode ray tubes.

2.3.2.Full-wave circuit with midpoint

A single-phase full-wave circuit with a midpoint (Fig. 2.4) is a parallel connection of two half-wave rectifiers, the diodes of which operate on a common load.

Rice. 2.4. Full-wave circuit with midpoint

When voltage is applied u 1 voltages appear on the primary winding of the transformer on each half of the secondary winding u 21, u 22(Fig. 2.5 a). Secondary windings W 21 And W 22 included consistently and accordingly. The diodes of the circuit conduct current alternately, each during a half-cycle (Fig. 2.5 b, c). During the first half period to the diode VD1 a positive half-wave voltage is applied u 21, in the diode-winding circuit W 21 current flows i 21(see Fig. 2.5 b). Diode VD2 is closed at this time, since it is connected to it through a diode open at this time VD1 reverse voltage is applied to both windings of the transformer (Fig. 2.5 f). In the next half period the diode will open VD2, and current i 22 the diode - winding circuit will flow W 22. (see Fig. 2.5 c). Thus, through the load resistance Rd currents alternately pass in the same direction i 21 And i 22. As a result, under load Rd half-waves of current are formed i d and voltage u d of the same sign (Fig. 2.5 d, e).

The voltage rectified by this circuit, like the voltage of a half-wave circuit, is pulsating, i.e., can be expanded into a harmonic Fourier series.

Where is the average value of the rectified voltage across the load. When the rectifier operates in idle mode, it is determined by the expression:

Rice. 2.5. Timing Diagrams for a Midpoint Circuit

Hence the effective value of the voltage in the secondary winding of the transformer:

Rectified current value I d is determined by the expression:

Current amplitude in the secondary winding of the transformer and the effective value .

In a full-wave circuit, the amplitude of the main harmonic component has decreased to a value of , and therefore the ripple coefficient has also decreased:

.

From the timing diagrams (see Fig. 2.5 a, d) it is clear that the voltage at the load reaches its maximum value U 2 m twice during the period of rectified voltage. Therefore, the load voltage ripple frequency U d equal to twice the mains voltage frequency:

In a midpoint rectification circuit, the currents in the secondary windings flow alternately (in the winding W 21 from end to beginning, and in the winding W 22 from beginning to end), so the transformer core is not biased and a purely sinusoidal current acts in the primary winding, which leads to a decrease in typical power and better utilization of the transformer. Compared to a half-wave rectification circuit, the value of the rectified voltage has doubled U d and current I d, the pulsation coefficient decreased.

Disadvantages of the circuit: the need to output the middle point of the secondary winding, the need to balance the secondary windings to ensure equality, a large reverse voltage on the diodes, an increase in the dimensions of the transformer.

2.3.3.Full-wave bridge circuit

In the circuit under consideration (Fig. 2.6), the rectifier consists of four semiconductor diodes, assembled according to the bridge diagram, in one of the diagonals of which ab the voltage of the secondary winding of the transformer is connected, and to the other CD– load resistance Rd. The positive pole of the load is the common connection point of the cathodes of the diodes (point d), negative – the connection point of the anodes (point With).

Rice. 2.6. Full-wave bridge circuit

The operation of the circuit is shown in Fig. 2.7, which shows the shapes of currents and voltages for an idealized bridge circuit in its different sections. The voltage and current of the secondary winding of the transformer change over time according to the harmonic law (Fig. 2.7a)

;

During the positive half-cycle of the supply voltage point potential A is positive, and the points b– negative. Diodes VD1 And VD3 will be turned on in the forward direction and the current pulse i 13 will pass from the positive terminal of the secondary winding through the diode VD1, load Rd and through an open diode VD3 to the negative terminal of the secondary winding of the transformer (Fig. 2.6). The shape of this current will follow the shape of the current i 2 secondary winding of the transformer (Fig. 2.7b). Going through the load Rd, current pulse i 13 releases tension on it u d(Fig. 2.7e), which, without taking into account voltage losses on the diodes, repeats the shape of the positive half-wave voltage, i.e., has a ripple amplitude. During the first half-cycle, the diodes VD2 And VD4 locked because they are turned on in the opposite direction. These diodes are exposed to a negative reverse voltage, the maximum value of which is (Fig. 2.7f).

When the voltage polarity changes on the secondary winding of the transformer, the anode of the diode VD2 connects to “+”, and the cathode of the diode VD4 to “–” voltage (see Fig. 2.6). Now during the second half cycle under the influence of direct voltage will

Rice. 2.7. Bridge Timing Diagrams

there are diodes VD2 And VD4, and diodes VD1 And VD3 locked by reverse voltage (see Fig. 2.7g).

In the circuit of the secondary winding of the transformer, open diodes VD2 And VD4 and loads Rd a current pulse will pass i 24(see Fig. 2.7c) of the same shape as a current pulse i 13, isolating a voltage pulse on the load, the magnitude and polarity of which is the same as in the first half-cycle (Fig. 2.7e).

Thus, during the period of converted voltage in the load circuit Rd two current pulses pass without changing their direction and creating a load current (see Fig. 2.7d), under the influence of which a pulsating voltage is released on the load (see Fig. 2.7e), of the same type as for a circuit with a midpoint. The rectified voltage contains a constant component and an infinite series of harmonic components and can be written as a harmonic Fourier series:

The DC component is calculated as the average value of the rectified voltage across the load when the rectifier is operating in no-load mode:

When calculating the rectified current I d through the load, it should be taken into account that when current passes through an open diode, the voltage drops across it, the value of which is indicated in reference books, therefore the current in the load is determined by the expression:

The effective value of the secondary winding current is related to the load current by the relation: The fundamental harmonic component of the rectified voltage is determined by the expression:

therefore, the ripple frequency is equal to twice the frequency of the converted mains voltage:

The amplitude of the fundamental harmonic component has decreased compared to the half-wave circuit, and therefore the ripple factor has also decreased:

.

To prevent damage to diodes when operating in rectification circuits, it is necessary to take into account the maximum values ​​of voltage and current in the secondary winding of the transformer when choosing diodes. The maximum reverse voltage across the diode is equal to the voltage at the ends of the secondary winding. Therefore, for circuits with a midpoint , and for a half-wave and bridge circuit - . In full-wave rectification circuits, the current pulse passes through the diode only during half a cycle, so the average value of the current flowing through the diode is half the rectified current: In a half-wave circuit, the same current flows through the diode and the load:

The bridge circuit is the basic circuit for single-phase rectifiers. It can be used without a transformer, that is, it can be connected directly to the alternating current circuit if the network voltage provides the required rectified voltage. When working with a transformer, current pulses i 13 And i 24 in the secondary winding of the transformer are directed towards each other, so their constant components are compensated, and the transformer operates in a mode without constant magnetization. Compared to the midpoint circuit, the bridge circuit has smaller transformer dimensions, since only one winding is placed on the secondary side.

2.4.Anti-aliasing filters

The voltage at the output of any diode block is always pulsating, containing, in addition to constant voltage, a number of sinusoidal components of different frequencies. In most cases, food electronic devices pulsating voltage is completely unacceptable. Requirements for the permissible value of the ripple coefficient depend on the purpose and operating mode of the device. For example, for input amplifier stages the ripple factor can be within the range . To power devices, these ripples must be reduced to a minimum level at which they do not significantly affect the operation of electrical devices.

For this purpose, smoothing filters are used, which pass only the direct component of the rectified voltage to the output and attenuate its alternating components as much as possible. The main elements of filters are inductance (connected in series with the load) and a capacitor (connected in parallel with the load). The smoothing effect of these elements is due to the fact that the inductance represents a large resistance () for high-frequency currents and small resistance for low-frequency currents, and the capacitor represents a large resistance (for low-frequency currents and low resistance for high-frequency currents.

The effectiveness of ripple smoothing is assessed by the smoothing coefficient, which is the ratio of the ripple coefficient at the input and output of the filter

The smoothing coefficient shows how many times the filter reduces the ripple of the rectified voltage.

Depending on the method of connecting the capacitor and inductance, the following types of filters are distinguished: capacitive (Fig. 2.8 a), inductive (Fig. 2.8 b), L-shaped (Fig. 2.8 c), L-shaped (Fig. 2.8 d).

Rice. 2.8. Electrical circuits anti-aliasing filters

In Fig. Figure 2.9 shows oscillograms of the output voltages of a full-wave rectifier when operating without a filter (Fig. 2.9 a), when capacitive (Fig. 2.9 b) and inductive (Fig. 2.9 c) filters are turned on.

Rice. 2.9. Timing diagrams during operation: a) without filter;
b) with a capacitive filter; c) with inductive filter

When using a capacitive filter, smoothing of the ripple of the rectified voltage and current occurs due to periodic charging of the capacitor and its subsequent discharging into the load resistance. The capacitor is charged by current i d flowing through the diode for a short period of time, when the instantaneous value of the pulsating voltage at the output of the rectifier (Fig. 2.9 a) is higher than the voltage across the load (and at the capacitor). The time constant for charging a capacitor is determined by the capacitance of the filter capacitor and a small resistance equal to the sum of the direct resistance of the open diodes and the active resistance of the transformer reduced to the secondary winding. When the voltage becomes less than the voltage on the capacitor, the diodes close and the capacitor is discharged through the load resistance (Fig. 2.9 b). At large capacity capacitor and load resistance, the time constant for discharging the capacitor is significantly greater than the time constant for charging it. In this case, the discharge of the capacitor proceeds in time almost according to a linear law, and output voltage(Fig. 2.9 b) does not decrease to zero, but pulsates within certain limits. increasing the average value of the rectified voltage, which can reach a maximum value with a large capacitor capacity.

For efficient work smoothing filter, the capacitance at the fundamental harmonic frequency should be at least an order of magnitude less than the load resistance:

It follows that the use of a capacitive filter is more effective with a high-resistance load with low rectified current values, since this increases the smoothing efficiency.

When an inductive filter is connected in series with the load (Fig. 2.8 b), a changing magnetic field excited by a pulsating current induces an electromotive force of self-induction. In accordance with the Lenz principle, the electromotive force is directed so as to smooth out the current ripples in the circuit, and therefore the load voltage ripples (Fig. 2.9 c). The smoothing efficiency increases at higher values ​​of the rectified current.

The value of the filter inductance is chosen so that the inductive reactance is significantly greater than the load resistance.

A greater reduction in rectified voltage ripple is provided by mixed filters that use capacitors and inductors, for example, L-shaped smoothing filters (Fig. 2.8 c, d). However, when using these filters, the magnitude of the constant component of the rectified voltage at the load is reduced due to a drop in part of the voltage across the active resistances of the inductor winding or.

2.5.External characteristics of the rectifier device

The external characteristic determines the limits of change in load current, at which the rectified voltage at the load does not decrease below the permissible value when the load resistance changes. The external characteristic is described by the equation:

where is the average value of the rectified voltage in the no-load mode of the rectifier, is the active component of the resistance of the transformer windings, is the voltage drop across the diodes of one arm of the rectifier. For a circuit with a midpoint, for a bridge – , is the voltage drop across the open diode.

External characteristic 1 (Fig. 2.10) corresponds to a rectifier without a filter, characteristic 2 corresponds to a rectifier with a capacitive filter, and when an L-shaped LC filter is included in the circuit, characteristic 3 is obtained. Open circuit voltage for a full-wave circuit without a filter, and when a capacitive filter is included for The capacitor charge count may increase to the maximum value.

Rice. 2.10. External characteristics of the rectifier device

The decrease in output voltage with increasing load current is explained by the voltage drop across the circuit elements: resistance and diodes. When a capacitive filter is turned on, an additional decrease in the output voltage occurs due to a faster discharge of the capacitor into a lower load resistance. When the L-shaped LC filter is turned on, an additional decrease in voltage across the load is caused by a voltage drop across the series-connected inductive filter.

2.6. Three-phase rectification circuits

2.6.1. Three-phase midpoint rectification circuit

A three-phase rectification circuit with a midpoint (Fig. 2.11) is also called a three-phase single-cycle circuit, since only one of the half-waves of the alternating voltage of each phase is rectified. The three-phase rectification circuit includes a transformer, the primary windings of which can be connected in a star or delta, and the secondary windings can only be connected in a star. ends a, b, c secondary windings of the transformer are connected to the anodes of three diodes VD 1, VD 2, VD 3. The cathodes of the diodes are connected together and serve as the positive pole for the load circuit, and the midpoint terminal of the transformer serves as the negative pole.

Rice. 2.11. Rectification circuit

Operation of the rectifier for an active load.

Initially, let us assume that the load of the rectification circuit is active, i.e. Xd= 0. For simplicity, we will consider the diodes and transformer ideal, i.e. The resistance of the diode in the forward direction is zero, and in the reverse direction it is infinitely large, the active resistance and leakage inductance X a transformer windings and the inductance of the supply network are taken equal to zero. Then the transition of current from one diode to another is considered instantaneous. The operation of the circuit is illustrated by the diagrams shown in Fig. 2.12. From the time diagram (see Fig. 2.12 a) it is clear that the voltage u 2 a, u 2 b , u 2 c are shifted in phase by one third of a period (2p/3) and during this interval the voltage of one phase is higher than the voltage of the other two phases relative to the zero point of the transformer. The diodes of the circuit operate alternately for 1/3 of the period (2p/3). At any point in time, the diode whose anode potential relative to the transformer zero point is higher than that of other diodes conducts current. This is true for the case of connecting diodes into a cathode group. The current in each diode flows for 1/3 of the period (2p/3) and stops when the anode potential of the operating diode becomes lower than the cathode potential. The diode closes and a reverse voltage is applied to it u b(see Fig. 2.12 c). The current transition from one diode to another occurs at the moment the curves intersect phase voltages(points a, b, c, d in Fig. 2.12a). Rectified current i d passes through the load Rd continuously and consists of alternating anode currents i a 1 ,i a 2 , i a 3. Instantaneous value of rectified voltage u d(see Fig. 2.12b) at each moment is determined by the instantaneous voltage value of the phase to which the operating diode is connected. Rectified voltage u d represents the envelope of sinusoids of phase voltages u 2 secondary windings of transformer T. Rectified current curve i d at X a = 0, Xd= 0 repeats the rectified voltage curve. Current waveform i a in the diode VD 1 is shown in Fig. 2.12c. Diode current VD 1 in this case will also be a current i 2 a secondary winding of the transformer. Reverse voltage curve u b 1 on diode VD 1 is formed from sections of sinusoids of linear voltages ( u ab, u with a), because the anode of the idle diode is connected to one of the phases, and the cathode, through an open diode, is connected to another phase of the secondary winding. Instantaneous values ​​of phase-to-phase (line-to-line) voltage correspond to the ordinates of the area shaded in Fig. 2.12a. Built on them line chart reverse voltage u b 1, on diode VD 1 (see Fig. 2.12 c). S T = = 1,345Pd,

Where S 1 = 3U 1 I 1 = 1,21Pd– calculated power of the primary winding of the transformer;

S 2 = 3U 2 I 2 = 1,48Pd– calculated power of the secondary winding of the transformer;

Pd = U d I d– load power.

In a three-phase rectifier with a midpoint, the phenomenon of forced magnetization of the transformer magnetic circuit occurs, because currents of the secondary windings of the transformer i 2 a,i 2 b, i 2 c contain a constant component equal to Id, which creates a unidirectional flux of forced magnetization of the transformer in each magnetic core. This flow, pulsating at a triple frequency relative to the frequency of the supply network, closes partly through the core, partly through the air and steel reinforcement surrounding the transformer core, causing them to heat up. As a result, the transformer core is saturated, and heat losses occur in the steel reinforcement due to eddy currents induced by the variable component of the forced magnetization flux. Saturation of the transformer magnetic circuit leads to a sharp increase in the magnetizing current (no-load current) of the transformer. To avoid saturation, it is necessary to increase the cross-section of the magnetic circuit. However, this leads to an overestimation of the weight and size parameters of the transformer and the entire rectifier installation. To eliminate additional losses caused by the variable component of the forced magnetization flux, the primary windings of the transformer must be connected in a triangle. In this case, only the constant component remains in the forced magnetization flux; the variable component with a clearly expressed third harmonic is compensated by flows that create currents of higher harmonics with a frequency that is a multiple of three contained in the currents primary windings transformer and closing along the circuit formed by these windings. The calculated power of the transformer when connecting the windings in a triangle does not change.

2.6.2.Three-phase bridge circuit

A significant number of three-phase current rectifiers are made using a bridge circuit (Larionov circuit), containing a three-phase transformer and a rectifier block of six diodes (Fig. 2.13.) The primary and secondary windings of the transformer can be connected in a star or delta circuit. However, a bridge rectification circuit can be used without a transformer. Diodes in the rectifier block are divided into two groups:

1) cathode, or odd (diodes VD 1, VD 3, VD 5), in which the cathodes of the diodes are electrically connected and their common terminal is the positive pole for the external circuit, and the anodes are connected to the terminals of the secondary windings of the transformer;

2) anodic, or even (diodes VD 2, VD 4, VD 6), in which the anodes of the diodes are electrically connected to each other, and the cathodes are connected to the anodes of the first group. The common point of connection of the anodes is the negative pole for the external circuit. The load is connected between the connection points of the cathodes and anodes of the diodes.

A three-phase bridge circuit can be thought of as a series connection of two three-phase midpoint circuits fed from a single transformer winding. At any moment of time, the diode in the cathode group will be open whose anode potential is higher than the potentials of the anodes of other diodes in the cathode group, and in the anode group - the diode whose cathode potential is lower than the potentials of the cathodes of other diodes in the anode group.

Rice. 2.13. Rectification circuit

The operation of the circuit can be monitored using timing diagrams in Fig. 2.14. Since the operating modes of the circuit for active and active-inductive loads differ slightly, we will analyze the operation of the circuit for the most common active-inductive load, taking X a = 0, X d = 0. Diodes of the cathode group open at the moment of intersection of the positive sections of the phase voltage curves (points a, b, c, d, e in Fig. 2.14a), and diodes of the anode group - at the moment of intersection of the negative sections of the phase voltage curves (points k, l , m, n). Each diode is open for one third of the period. With instantaneous switching of current in a three-phase bridge circuit, current is carried out at any point in time

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