Load ripple frequency r. How to reduce rectified voltage ripple

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 that 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

When building an audio system, I paid attention to an interesting fact; I and other listeners noticed that the sound quality of the equipment is affected by the time of day, or rather, late in the evening and early in the morning the sound is noticeably better than during the day. What is the reason?!

I think it’s no secret that our household electrical network (ES) leaves much to be desired. It so happened that the main parameter of the ES, which is monitored by power plant workers and maintenance personnel, is its oscillation frequency of 50 Hz, and as for the purity of the supply voltage and the stability of the voltage in our homes, no one cares. Although the last statement is a little controversial, since there is GOST 13109-97 and technical regulations for the parameters of the electrical network. From my own experience, I felt a departure from the parameters established in GOST for power supply when my DAC refused to work stably and this is understandable, since the voltage in the ES dropped to 180V, this was well monitored by the decrease in the brightness of incandescent lamps in the house. The thing is that I live in a private house and it is not uncommon for me when the voltage in the network drops to 20%. Another disadvantage of the ES was that the neighbors’ frequent welding and other work also contributed to the “ecology” of the equipment’s power supply.

This problem can be partially solved using a voltage stabilizer, but it will not save you from contaminated power supply, since the autotransformer included in these devices is not capable of working as a low-pass filter.
My search for the necessary devices did not give the desired result, since the topic dedicated to the purity of electronic systems is covered extremely rarely and there is also little information on radio electronics forums. There are power regenerators on the market, but they are either very expensive or often based on a UPS. The advantage of these products is offset by their disadvantage, namely the high noise of the pulse converter and a strong deviation from the sine wave shape of the output signal.

After some thought, I decided to develop my own mains power regenerator (RSP) that satisfies my requirements, namely:

1. Stability of supply voltage 230V with an accuracy of no worse than 2% (with a load of 40W)
2. RSP output power 60-100W (quite enough to power a sound source)
3. The coefficient of harmonic components on a 40W active load is no more than 0.5% (while in a household ES this parameter is approximately 5%)
4. Stability of supply voltage frequency (master oscillator frequency 100Hz) ± 0.5%
5. Galvanic isolation from ES
6. Low acoustic noise level.

Let me clarify right away that the 100Hz frequency was not chosen by chance. The determining factor was the optimal operating mode of the RSP load at this frequency, namely the sound reproducing equipment or DAC as in my version.

The fact is that when the frequency of the supply voltage of power transformers of devices connected to the RSP increases, their operating mode improves, namely:

1. Makes the operation of the supply transformer easier
2. The magnetic induction of the transformer is reduced, which leads to a decrease in the dissipation of the magnetic field, as well as the absence of a constant saturation voltage of the transformer iron in the power supply device and, as a result, more favorable conditions for its operation are created.

All this helps to improve the sound properties of the powered equipment, but more on that below.
Another advantage of the 100Hz power supply frequency is the improvement in the operation of the power supply rectifier, since after the diode bridge, pulsating voltages are obtained 2 times more often than when powered directly from a 220V 50Hz household network and it is equal to 200Hz. And from theory it is known that as the voltage ripple frequency increases, the capacitance of the smoothing filter after it can be reduced since it is easier for the capacitor to smooth out the ripples of the rectified voltage of a higher frequency. By the way, this is due to the lower capacity of the smoothing capacitor in switching power supplies.

Below is a diagram for measuring pulsations in Fig. 1 and oscillograms that show the process of operation of the diode bridge with capacitor C1 disconnected with a supply frequency of 50 Hz Fig. 2a and with a supply frequency of 100Hz Fig. 2b.

Rice. 1 Circuit for measuring ripple

Rice. 2a The process of operation of a diode bridge without smoothing capacitor C1 with a supply frequency of 50 Hz

Rice. 2b The process of operation of a diode bridge without smoothing capacitor C1 with a supply frequency of 100 Hz

Below are oscillograms of the operation of the ripple measurement circuit on the load with capacitor C1 at a supply voltage with a frequency of 50 Hz (Fig. 3a), as well as 100 Hz (Fig. 3b.

Rice. 3a Ripple voltage at the load when the circuit is powered with voltage at a frequency of 50 Hz

Rice. 3b Ripple voltage at the load when the circuit is powered with voltage at a frequency of 100 Hz

From Fig. 3a and Fig. 3b, it is clear that when the filter is powered with a load with a frequency twice as high, the ripples are reduced by 1.65 times
Ripple at 100Hz is 3.34V/2.02V = 1.65 times less than when powered by a 50Hz ES.

Let's return directly to the RSP circuit, I used a Wien bridge as a sinusoidal voltage generator, and as a PA I used a field-effect transistor circuit with an output power of about 100 W, which is quite enough for my needs. The RSP power supply uses a 250W transformer and a diode bridge with a filter unit with a total capacity of 39600 µF, which is more than enough for this solution. The power supply diagram is shown in Fig. 4

Rice. 4 RSP power supply

The operating principle of the RSP is as follows:
When the power supply of the RSP is turned on, the power supply capacitors are charged and the operating mode of the sinusoidal oscillation generator (Fig. 6) is established, at this time the soft-start operates, creating a delay in the supply of the input signal from the generator to the PA using relay contacts closing the circuit of the generator output and the PA input.

Operating time of the soft-start circuit Fig. 5, is set using the circuit R2, C4 and is calculated by the formula r=R2(Mom)xC4(mkF)=t(seconds).

Rice. 5 Soft-start scheme

After the time set in the soft-start circuit of 2 seconds has expired, in my version, the output amplified oscillations in the PA with a frequency of 100 Hz are fed to step-up transformer Tr1.

The winding data of step-up transformer Tr1 is as follows:
Magnetic core brand OL55/100-40.
Overall power of the magnetic circuit Pgab. = 227W
Number of turns in the primary winding w1=30 turns, PEV2 wire 1.2mm
Number of turns in the secondary winding w2=600 turns, PEV2 wire 0.51mm

Let's consider the operation of a sinusoidal oscillation generator.
The generator circuit is shown in Fig. 6. This circuit is a sinusoidal voltage generator. The circuit R1, C1 and R2, C2 sets the oscillation frequency, with the indicated elements in the diagram this frequency is 50Hz, for better symmetry these elements must be quite accurate, no worse than ±1%. Resistor R19 is necessary to adjust the amplitude of the output signal.

Rice. 6 Sine wave generator

After the sine generator comes the PA for RSP, its diagram is shown in Fig. 7

Fig.7 Power amplifier for RSP

As can be seen from the diagram, the PA includes the DA1 chip, this is an op-amp on which the level of distortion of the entire amplifier especially depends, for this reason in this circuit it is advisable to install an op-amp with low noise, for example NE5534 with a noise level of 5nV√Hz. Transistors VT1 and VT2 are necessary for preliminary boosting of the current signal required for output transistors VT3, VT4. The no-load current is set by trimming resistor R5; in my version it is 20mA.
In general, a mind in class “D” is ideal as a mind for these purposes. Its undeniable advantages, namely low energy dissipation into heat (high efficiency) and, as a result, lower weight and dimensions make it preferable in this scheme. But such schemes have disadvantages; this is the additional complexity of winding transformers and setting up the amplifier stage. Therefore, I decided to make a PA according to the classical circuit with a minimum quiescent current for this circuit, about 20 mA.

Below is the form of the mains voltage in the ES Fig. 8a and after the RSP Fig. 8b on an active load of 40 W, as well as spectrograms of harmonic distortion directly in the ES Fig. 9a and after RSP Fig.9b.

Rice. 8a Voltage waveform in a household ES on the left and its spectrogram on the right

Rice. 8b The shape of the mains voltage at the output of the RSP transformer on the left and its spectrogram on the right

From the oscillograms and spectrograms it is clear that the RSP has a noticeably better quality of sinusoidal voltage. Another advantage of this device, as described above, is the absence of magnetization on the supply side, since the matching transformer is not able to pass the DC component.
Galvanic isolation by the output transformer also improves the power supply situation of the equipment. The fact is that many people neglect the phasing of the supply transformers of audio equipment. In my opinion, it is necessary to phase every power transformer, especially in equipment without grounding, since if the phasing of power transformers, for example a PA and a sound source (DAC, player), is incorrectly phased, currents flow through the interconnect cable braid with a frequency of 50 Hz. This can be easily checked using a digital multimeter of good sensitivity; to do this, you need to measure the alternating voltage on the body of the switched on device relative to grounding on each device separately, having previously disconnected all connecting wires from it, except for the supply ones.

If the phasing of power transformers is incorrect, the sound of the equipment deteriorates. Many reputable manufacturers of audio equipment use indicators for correct phase activation in their devices.

Rice. 9 Photos of the assembled RSP

Conclusion

Mains power regenerators really improve the sound of an audio system, since high-quality power supply to the sound source (DAC, player) greatly affects its operation, because it is the sound source that has the highest resolution in the entire system, and this parameter is difficult to implement with poor power supply. I also wanted to note that this device can be used for other purposes, for example as an AC voltage stabilizer. One of my friends used RSP circuitry to power the AC motor in a vinyl record player, since in his motor the rotor speed directly depended on the frequency of the supply voltage and he adjusted the exact engine speed by adjusting the frequency of the sinusoidal voltage generator.

Smirnov Alexey Nikolaevich (), e-mail: [email protected]

List of radioelements

Designation	Type	Denomination	Quantity	Note	Shop	My notepad
	Rice. 1 Circuit for measuring ripple
VD1	Diode bridge		1			To notepad
C1		47 µF	1			To notepad
R1	Resistor	75 Ohm	1			To notepad
	Generator		1			To notepad
	Oscilloscope		1			To notepad
S1	Switch		1			To notepad
	Rice. 4 RSP power supply
VR1	Linear regulator	LM7815	1			To notepad
VR2	Linear regulator	LM7915	1			To notepad
VD1-VD4	Diode	20ETS08	4			To notepad
VD1-VD4	Rectifier diode	DF08MA	8			To notepad
C1-C4	Electrolytic capacitor	2200 µF	4			To notepad
C5, C8	Capacitor	100 nF	2			To notepad
C6, C7	Electrolytic capacitor	470 µF	2			To notepad
S9-S16	Electrolytic capacitor	4700 µF	8			To notepad
S17, S18	Electrolytic capacitor	1000 µF	2			To notepad
S19, S20	Capacitor	1 µF	2			To notepad
R1, R2, R5, R6	Resistor	10 ohm	4			To notepad
R3, R4, R7, R8	Resistor	100 Ohm	4			To notepad
R9-R12	Resistor	0.5 ohm	4	5 W		To notepad
T1	Transformer	250 W	1			To notepad
T2	Transformer	20 W	1			To notepad
S1	Switch		1			To notepad
	Power plug		1			To notepad
XT1, XT2	Connector		2			To notepad
	Connector	Gen Power	1			To notepad
	Rice. 5 Soft-start scheme
D1	Programmable timer and oscillator	NE555	1			To notepad
D1	Chip	MC14069U	1			To notepad
VR1	Linear regulator	LM7812	1			To notepad
VT1	Bipolar transistor	KT972A	1			To notepad
VD1-VD4	Diode bridge	DF08S	1			To notepad
VD5	Rectifier diode	1N4007	1			To notepad
C1	Electrolytic capacitor	2200 µF	1			To notepad
C2	Electrolytic capacitor	470 µF	1			To notepad
C3, C5, C6	Capacitor	100 nF	3			To notepad
C4, C7	Electrolytic capacitor	47 µF	2			To notepad
R1	Resistor	330 Ohm	1	selection		To notepad
R2	Variable resistor	200 kOhm	1			To notepad
R3	Resistor	100 Ohm	1			To notepad
R4, R5	Resistor	10 kOhm	2			To notepad
R6	Resistor	220 Ohm	1			To notepad
Rel1	Relay		1			To notepad
	Rice. 6 Sine wave generator
D1	Operational amplifier	TL072	1			To notepad
VT1	MOSFET transistor	BF245A	1			To notepad
VD1, VD2	Diode		2			To notepad
VD3	Zener diode	1N750	1			To notepad
C1-C3	Capacitor	0.22 µF	3			To notepad
C4	Electrolytic capacitor	2.2 µF	1			To notepad
C5	Capacitor	1 µF	1			To notepad
C6, C7	Electrolytic capacitor	220 µF 16 V	2			To notepad
S8, S9	Capacitor	0.1 µF	2			To notepad
R1, R2, R7	Resistor	5.1 kOhm	3			To notepad
R3	Resistor	4.7 kOhm	1			To notepad
R4, R11	Resistor	2 kOhm	2			To notepad
R5	Resistor	62 kOhm	1			To notepad
R6	Resistor	8.2 kOhm	1			To notepad
R8	Resistor	36 kOhm	1			To notepad
R9	Resistor	1 MOhm	1			To notepad
R10	Resistor	68 kOhm	1			To notepad
R12, R13	Resistor	100 Ohm	2			To notepad
R19	Variable resistor	22 kOhm	1			To notepad
	Connector	Gen signal	1			To notepad
	Connector	Gen power	1			To notepad
	Fig.7 Power amplifier for RSP
DA1	Operational amplifier	TL071	1			To notepad
VR1	Linear regulator	LM7812	1			To notepad
VR2	Linear regulator	LM7912	1			To notepad
VT1	Bipolar transistor	KT815A	1			To notepad
VT2	Bipolar transistor

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 signal PWM is, for example, the simplest DAC; power PWM most often means the PWM signal at the output of power switches, for example, in switching power supplies (SMPS). Strictly speaking, in power supplies the PWM signal itself is also used in the signal circuit (controlling transistors) 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 a high-resistance load, 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 the impulse characteristics of a given circuit.

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 of the PWM period, then the complete charge-discharge of the capacitor will not occur in one period.

The next important parameter that allows you 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 a filter with the required characteristics - for example, by specifying the available capacitance or the required level of ripple.

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, with low load resistances (for example, electric motor windings), losses in the filter resistor become very significant, so in such 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 oscillatory 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:

The normal operation of all active elements of electronic equipment - transistors, thyristors and microcircuits - is designed for constant voltage supply. But current sources such as dry cell batteries and rechargeable batteries are short-lived, consume the electrical energy they store, and therefore require periodic replacement or recharging. Hence, chemical sources of electrical energy can be considered acceptable exclusively for powering portable equipment or equipment operated in the absence of constant current sources. It is more convenient to power stationary professional and household equipment from an alternating current network, using an AC-to-DC voltage converter. A rectifier is such a converter.

Various transistors, microcircuits and other devices are designed to be powered by different voltages, so the presence of alternating voltage in the electrical network turns out to be very convenient, since using a transformer on its secondary windings, you can easily obtain any other voltage values ​​from the standard 220 V network voltage. It would be much more difficult to obtain different voltages in the presence of a DC network.

The simplest rectifier device is a half-wave rectifier, the diagram of which is shown in Fig. 35. Its distinctive feature is that the diode passes current only during one half of the period of the alternating voltage, when it is positive

on the top terminal of the transformer secondary winding according to the diagram. That's why the circuit is called half-wave.

If a capacitor C were not connected in parallel with the load R, the voltage waveform across the load would be as shown by the dashed line, and the voltage across the load would pulsate instead of being constant. The capacitor smoothes out the ripples of the rectified voltage. After switching on, at the first positive half-cycle, the capacitor quickly charges. The charging current flows through the secondary winding of the transformer through the open diode, capacitor and back to the secondary winding. The resistance of this circuit is small and is determined by the resistance of the winding and the open diode. Therefore, the capacitor charges quickly. At point A, the voltage of the charged capacitor is almost equal to the voltage on the winding, and later it turns out to be greater than it, due to which the diode is turned off and the charging of the capacitor stops.

Now the capacitor begins to discharge to the load R. The load resistance is significantly greater than the circuit resistance

charge. Therefore, the discharge of the capacitor occurs slowly, until point B, when the voltage on the transformer winding again becomes greater than the voltage on the capacitor, and its charging begins again. The resulting voltage across the capacitor and load is shown as a solid line. It contains a direct component (the rectified voltage itself) and an alternating component, which is called ripple voltage. Obviously, the lower the load resistance (or the greater the current consumed by the load from the rectifier), the greater the ripple amplitude and the lower the rectified voltage, since in this mode point B will be located lower. The larger the capacitance of the capacitor, the slower it will discharge and the smaller the amplitude of the pulsations and the greater the rectified voltage. Therefore, high-capacity electrolytic capacitors are used in rectifier circuits.

The highest rectified voltage is determined by the amplitude of the alternating voltage on the secondary winding of the transformer. For this reason, the operating voltage of the capacitor must be at least this voltage value.

The choice of diode in this circuit is associated with the following requirements. The average rectified diode current is equal to the load current. The direct pulse current of the diode is equal to the ratio of the voltage amplitude on the secondary winding of the transformer to the resistance of this winding. Finally, during the negative half-cycle, a reverse voltage equal to twice the amplitude of the voltage on the secondary winding is applied to the diode.

The disadvantage of a half-wave rectification circuit is obvious: due to the large time interval between moments A and B, which slightly exceeds half the period, the capacitor has time to noticeably discharge, which leads to an increased amplitude of ripples of the rectified voltage. Further smoothing of these ripples is made difficult by the fact that the ripple frequency is equal to the supply voltage network frequency of 50 Hz. In this regard, rectifiers assembled according to a half-wave circuit are used only with high load resistances, that is, with low current consumption,

when the discharge time constant of the capacitor is large and it does not have time to noticeably discharge during the negative half-cycles of the voltage.

These disadvantages are less pronounced in the half-wave rectification circuit, which is shown in Fig. 36. Here

two diodes are used and the secondary winding of the transformer is doubled, equipped with a midpoint. During one half-cycle, the capacitor is charged through one diode, and the second one is locked at this time; during the second half-cycle, the second diode is unlocked, and the first one is locked. The voltage waveform across the load in the absence of a capacitor is shown by a dashed line, and in the presence of a capacitor - by a solid line. The time during which the capacitor is discharged is reduced by more than half in this circuit. For this reason, the rectified voltage is greater, and the ripple amplitude is much less than when using a half-wave rectifier. It is also important that the pulsation frequency is twice the frequency of the supply network and is 100 Hz, which greatly facilitates their subsequent smoothing.

Despite these advantages, the full-wave rectification circuit with a midpoint also has disadvantages, which include the complexity of the transformer, as well as

the impossibility of creating two completely identical halves of the secondary winding. This leads to the fact that the voltage amplitudes on the halves of the secondary winding are different. Due to the fact that the capacitor is charged alternately from each half of the secondary winding, a component with a frequency of 50 Hz appears in the ripples of the rectified voltage, although it is less than with single-half-cycle rectification. The full-wave rectifier circuit was widely used in the era of tube technology, when two-anode kenotrons with a common cathode were used. It turned out to be convenient to use them in a circuit where the cathodes of the diodes are connected and one filament winding can be used for both diodes. Semiconductor diodes do not have a heater, and with their introduction, the full-wave circuit with the middle point of the secondary winding of the transformer, having lost this advantage, turned out to be completely replaced by a bridge rectification circuit, which in outdated literature is called the Graetz circuit.

The rectifier bridge circuit is shown in Fig. 37. Instead of two diodes, it contains four, but does not require doubling the secondary winding of the transformer. During one half of the alternating current period, the current passes from the upper terminal of the secondary winding through the diode VD2, the load, through the diode VD3 to the lower terminal of the secondary winding. During the next half of the period, the current passes from the lower terminal of the winding through the diode VD4, the load, through the diode VD1 to the upper terminal of the secondary winding of the transformer. Thus, during both half-cycles, a current of the same direction flows in the load and the same alternating voltage of the secondary winding is rectified by the diodes. Due to this, the pulsation does not contain a component with a frequency of 50 Hz.

The bridge rectification circuit is also full-wave. The voltage waveform across the load in this circuit is the same as in a full-wave circuit with a midpoint. The operating voltage of the capacitor is also equal to the amplitude of the alternating voltage on the secondary winding. However, the diode requirements in both full-wave circuits are different from those in the half-wave circuit.

Rice. 37. Bridge rectification circuit

Due to the fact that the load current passes through the diodes alternately, the average rectified current of each diode is equal to half the load current.

The reverse voltages on the diodes of the bridge circuit are equal not to double, but to single voltage amplitude of the secondary winding. The reverse voltages on the diodes of the full-wave mid-point circuit and the values ​​of the pulse currents of both circuits are the same as in the half-wave circuit. However, the current of the secondary winding of the transformer in the bridge circuit is equal in its effective value to the load current, which is twice as much as in the half-wave circuit and in the midpoint circuit. Therefore, the cross-section of the wire of the secondary winding of the transformer in the bridge circuit must be twice as large as in the other two (the diameter of the wire is 1.41 times larger).

Doubling the number of diodes in the bridge circuit is more than compensated by the halved number of turns of the secondary winding of the transformer and the reduction in rectified voltage ripple. To simplify the installation of bridge circuits, the industry produces ready-made assemblies of four identical diodes in one housing, which are already connected to each other according to a bridge circuit. Such assemblies, for example, include assemblies of the KD906 type with an average rectified current of up to 400 mA and a reverse voltage of up to 75 V.

The disadvantage of a bridge circuit is that the rectified current passes in series through two diodes. The voltage drop across an open silicon diode reaches 1 V, and across two diodes in series the voltage drop at maximum forward current is 2 V. If the rectifier is designed for low rectified voltage,

which is commensurate with the voltage drop across the diodes, an increase in the voltage on the secondary winding of the transformer is required. This must be taken into account when calculating the rectifier.

If it is necessary to obtain a rectified voltage that exceeds the amplitude value of the voltage on the secondary winding of the transformer, you can use a half-wave rectified voltage doubling circuit shown in Fig. 38. During the first half-cycle, when the secondary winding current is directed according to the circuit from top to bottom, diode VD1 is open and capacitor C1 is charged,

Rice. 38. Half-wave voltage doubling circuit

as in a half-wave rectifier circuit. During the second half-cycle, the secondary winding current flows from bottom to top. Diode VD1 is locked, and diode VD2 is unlocked. Now capacitor C2 is charged by the total voltage of the secondary winding of the transformer and the voltage of the charged capacitor C1, which are connected accordingly. Due to this, a double voltage is formed on capacitor C2. The operating voltage of capacitor C1 is equal to the amplitude, and the operating voltage of capacitor C2 is equal to twice the amplitude of the voltage of the secondary winding of the transformer. The reverse voltages of both diodes are equal to twice the voltage amplitude of the secondary winding. The ripple frequency is equal to the network frequency - 50 Hz.

Double the voltage on capacitor C2 and the low ripple frequency are the disadvantages of this circuit. In addition, while charging capacitor C2, capacitor C1 is quickly discharged by the charging current of capacitor C2. To avoid a sharp increase in ripple and a decrease in rectified voltage, it is necessary to choose a much larger capacitance C1

containers C2. Therefore, if the use of this circuit is not dictated by the construction of the rest of the power supply circuit, it is better to use another voltage doubling circuit, shown in Fig. 39.

Here, during one half-cycle, one capacitor is charged through the diode, and during the second half-cycle, the second capacitor is charged through the second diode. The output rectified voltage is removed from both capacitors connected in series and in accordance. Each capacitor

is charged according to the circuit of a half-wave rectifier, but the total voltage turns out to be full-wave, the discharge of capacitors occurs only through the load, therefore the ripple frequency is twice the frequency of the supply network, and the shape of the output voltage is similar to that of a full-wave rectifier. The output voltage is almost equal to twice the voltage amplitude of the secondary winding. The operating voltage of both capacitors is equal to the amplitude of this voltage. The reverse voltage on each diode is equal to twice the amplitude. Thus, the use of this scheme is more profitable than the scheme shown in Fig. 38.

It is interesting to note that at a constant voltage value on the secondary winding of the transformer, the bridge circuit provides a rectified voltage twice as high, and the voltage doubling circuit (see Fig. 39) provides four times as high as a full-wave circuit with a midpoint. It should be mentioned that in outdated literature the voltage doubling circuit shown in Fig. 39, is called the Latour scheme.

Let's consider two more rectifier circuits with voltage multiplication. In Fig. Figure 40 shows a rectifier circuit with voltage quadrupling, built on the same principle as the circuit shown in Fig. 38. During one half-cycle, capacitors C1 are charged by the winding voltage and SZ by the sum of the winding voltage and the charged capacitor C2 minus the voltage on C1; at the same time C2 is discharged.

Capacitor C1 is charged to the amplitude, and SZ - to twice the amplitude of the voltage on the winding. During the next half-cycle, C2 is charged with the total voltage on the winding and on C1, as well as C4 with the sum of the voltages on the winding, on C1 and on SZ minus the voltage on C2; in this case, C1 and SZ are discharged. Both capacitors C2 and C4 are charged to twice the voltage amplitude on the winding. The resulting voltage is removed from capacitors C2 and C4 connected in series and in accordance. The ripple frequency of the rectified voltage in this circuit is the same as in the circuit in Fig. 38, 50 Hz.

Rice. 40. Half-wave voltage multiplication circuit

In Fig. Figure 41 shows a full-wave voltage quadrupling circuit similar to the circuit shown in Fig. 39. The reader can consider the principle of its operation independently by analogy with the previous diagrams. Here the ripple frequency is 100 Hz, and two capacitors C1 and SZ operate at a voltage equal to the single amplitude of the voltage of the secondary winding of the transformer instead of one capacitor C1 in the circuit in Fig. 40. With the same number of elements, this scheme is more profitable than the previous one.

The advantage of the circuit shown in Fig. 40, is the ability to multiply the voltage an odd number of times. So, if you remove capacitor C4 and the diode connected to it, and remove the rectified voltage from capacitors C1 and S3, you will get triple the voltage. The diagram shown in Fig. 41, allows you to obtain only a rectified voltage an even number of times greater than the voltage on the secondary winding of the transformer.

Rice. 41. Full-wave voltage multiplication circuit

Rectification with voltage multiplication is not limited to quadrupling it; by connecting additional circuits consisting of a diode and a capacitor, you can increase the multiplication factor. It is often necessary to obtain high rectified voltage, measured in kilovolts. To achieve this goal, there are two ways: either wind the high-voltage secondary winding of the transformer and rectify the high voltage obtained from it with a simple rectifier, or use a multiplication circuit. The second method is more expedient. High-voltage windings of transformers have low reliability, since it is necessary to carefully insulate them from other windings and from the core, and also to well insulate the layers of this winding from one another. In addition, the winding of high-voltage windings itself is very labor-intensive: you have to wind thousands of turns with very thin wire, which easily breaks with the slightest tension. Finally, the rectifier requires the use of high-voltage capacitors and diodes with a very high permissible reverse voltage. The output is found by connecting several capacitors and several diodes in series. But then, with the same number of capacitors and diodes, it is more expedient to assemble a rectifier with voltage multiplication, at the same time eliminating the need to wind the high-voltage winding of the transformer.

Patients at appointments are often interested in what physical activity is safe and beneficial for their heart. Most often this question arises before the first visit to the gym. There are many parameters for controlling maximum load, but one of the most informative is heart rate. Its calculation determines the heart rate (HR).

Why is it important to control your heart rate during exercise? To better understand this, I will first try to clearly explain the physiological basis of adaptation of the cardiovascular system to physical activity.

Cardiovascular system during exercise

Against the backdrop of stress, tissue demand for oxygen increases. Hypoxia (lack of oxygen) serves as a signal to the body that it needs to increase the activity of the cardiovascular system. The main task of the cardiovascular system is to ensure that the supply of oxygen to the tissues covers its costs.

The heart is a muscular organ that performs a pumping function. The more actively and effectively it pumps blood, the better the organs and tissues are provided with oxygen. The first way to increase blood flow is to speed up the heart. The higher the heart rate, the greater the volume of blood it can “pump” in a certain period of time.

The second way to adapt to stress is to increase stroke volume (the amount of blood ejected into the vessels during one heartbeat). That is, improving the “quality” of the heart: the larger the volume of the heart chambers occupied by blood, the higher the contractility of the myocardium. Due to this, the heart begins to pump out more blood. This phenomenon is called the Frank-Starling law.

Heart rate calculation for different load zones

As your heart rate increases during exercise, your body undergoes various physiological changes. Heart rate calculations for different heart rate zones in sports training are based on this feature. Each zone corresponds to a percentage of heart rate from the maximum possible rate. They are chosen depending on the desired goal. Types of intensity zones:

1. Therapeutic zone. Heart rate – 50-60% of maximum. Used to strengthen the cardiovascular system.
2. . 60-70%. Fighting excess weight.
3. Strength endurance zone. 70-80%. Increased resistance to intense physical activity.
4. Improvement zone (hard). 80-90%. Increasing anaerobic endurance - the ability to perform long-term physical activity when the body's oxygen consumption is higher than its intake. Only for experienced athletes.
5. Improvement zone (maximum). 90-100%. Development of sprint speed.

To safely train the cardiovascular system, use pulse zone No. 1.

1. First find the maximum heart rate (HRmax), for this:

• 220 – age (years).

• it ranges from HRmax * 0.5 to HRmax * 0.6.

An example of calculating the optimal heart rate for training:

• The patient is 40 years old.
• Heart ratemax: 220 – 40 = 180 beats/min.
• Recommended zone No. 1: 180*0.5 to 180*0.6.

Pulse calculation for the selected therapy zone:

1. 180*0,5 = 90
2. 180*0,6 = 108

The target heart rate during exercise for a 40-year-old person should be: from 90 to 108 beats/min.

That is, the loads during exercise need to be distributed so that the heart rate falls within this range.

Age (years)	Recommended heart rate (bpm)
Table with the optimal heart rate for training the cardiovascular system by age.
20	100-120
25	97-117
30	95-114
35	92-111
40	90-108
45	87-105
50	85-102
55	82-99
60	80-96
65 and older	70-84

At first glance, these heart rate indicators in pulse zone No. 1 seem insufficient for exercise, but this is not so. Training should be done gradually, with a slow increase in target heart rate. Why? The SSS must “get used to” the changes. If an unprepared person (even a relatively healthy one) is immediately given maximum physical activity, this will end in a breakdown of the adaptation mechanisms of the cardiovascular system.

The boundaries of pulse zones are blurred, therefore, with positive dynamics and the absence of contraindications, a smooth transition to pulse zone No. 2 is possible (with a pulse rate of up to 70% of the maximum). Safe training of the cardiovascular system is limited to the first two pulse zones, since the loads in them are aerobic (the supply of oxygen completely compensates for its consumption). Starting from the 3rd pulse zone, a transition from aerobic to anaerobic exercise occurs: the tissues begin to lack incoming oxygen.

The duration of classes is from 20 to 50 minutes, the frequency is from 2 to 3 times a week. I advise you to add no more than 5 minutes to your workout every 2-3 weeks. It is imperative to focus on your own feelings. Tachycardia during exercise should not cause discomfort. An elevated pulse rate during measurement and deterioration in well-being indicate excessive physical exertion.

Moderate physical activity is indicated. The main guideline is the ability to talk while jogging. If during running your heart rate and breathing rate increase to the recommended levels, but this does not interfere with conversation, then the load can be considered moderate.

Light to moderate physical activity is suitable for training your heart. Namely:

• : walking in the park;
• Nordic walking with poles (one of the most effective and safest types of cardio training);
• Jogging;
• Do not ride a bicycle or exercise bike quickly under heart rate control.

In a gym setting, a treadmill is suitable. The heart rate calculation is the same as for heart rate zone No. 1. The simulator is used in fast walking mode without lifting the belt.

What is the maximum heart rate allowed?

The heart rate during exercise is directly proportional to the magnitude of the load. The more physical work the body performs, the higher the tissue demand for oxygen and, therefore, the faster the heart rate.

The resting heart rate of untrained people ranges from 60 to 90 beats/min. Against the background of load, it is physiological and natural for the body to accelerate the heart rate by 60-80% of the resting value.

The adaptive capabilities of the heart are not unlimited, which is why there is the concept of “maximum heart rate,” which limits the intensity and duration of physical activity. This is the highest heart rate value at maximum effort until the moment of extreme fatigue.

Calculated using the formula: 220 – age in years. Here is an example: if a person is 40 years old, then his heart ratemax is 180 beats/min. When calculating, an error of 10-15 beats/min is possible. There are over 40 formulas for calculating maximum heart rate, but this is more convenient to use.

Below is a table with the permissible maximum heart rate depending on age and, with moderate physical activity (running, brisk walking).

Table of target and maximum heart rate during physical activity:

Age, years	Target heart rate in the zone 50 – 85% of maximum	Maximum heart rate
20	100 – 170	200
30	95 – 162	190
35	93 – 157	185
40	90 – 153	180
45	88 – 149	175
50	85 – 145	170
55	83 – 140	165
60	80 – 136	160
65	78 – 132	155
70	75 - 128	150

How to check your fitness level?

To test your capabilities, there are special tests to check your pulse, which determine a person’s level of fitness during exercise. Main types:

1. Step test. Use a special step. For 3 minutes, perform a four-stroke step (consistently climb up and down the step). After 2 minutes, the pulse is determined and checked against the table.
2. Test with squats (Martine-Kushelevsky). The initial heart rate is measured. Perform 20 squats in 30 seconds. The assessment is carried out based on the increase in heart rate and the speed of its recovery.
3. Kotov-Deshin test. It is based on assessing heart rate and blood pressure after 3 minutes of running in place. For women and children, the time is reduced to 2 minutes.
4. . Similar to a squat test. The assessment is carried out using the Ruffier index. To do this, the pulse is measured while sitting before the load, immediately after it and after 1 minute.
5. Letunov's test. An old informative test that has been used in sports medicine since 1937. Includes heart rate assessment after 3 types of loads: squats, fast running in place, running in place with hip raise.

To independently test the fitness of the cardiovascular system, it is better to limit yourself to a test with squats. If you have cardiovascular diseases, tests can only be performed under the supervision of specialists.

Influence of physiological characteristics

Heart rate in children is initially higher than in adults. So, for a 2-year-old child in a calm state, a pulse of 115 beats per minute is considered the absolute norm. During physical activity in children, unlike adults, stroke volume (the amount of blood ejected by the heart into the vessels in one contraction), pulse and blood pressure increase more strongly. The younger the child, the more the pulse accelerates even with a slight load. In this case, the OP changes little. Closer to 13-15 years, heart rate indicators become similar to adults. Over time, stroke volume becomes larger.

Elderly people also have their own characteristics of heart rate readings during exercise. The deterioration of adaptive abilities is largely due to sclerotic changes in the blood vessels. Due to the fact that they become less elastic, peripheral vascular resistance increases. Unlike young people, both systolic and diastolic blood pressure are more likely to increase in old people. The contractility of the heart becomes smaller over time, so adaptation to the load occurs mainly due to an increase in heart rate, rather than stroke volume.

There are adaptation differences depending on gender. In men, blood flow improves to a greater extent due to an increase in stroke volume and to a lesser extent due to an acceleration of heart rate. For this reason, the pulse in men is usually slightly lower (6-8 beats/min) than in women.

A person who is professionally involved in sports has significantly developed adaptive mechanisms. Bradycardia at rest is normal for him. The pulse can be below not only 60, but also 40-50 beats/min.

Why are athletes comfortable with such a heart rate? Because during training, their stroke volume increased. During physical activity, an athlete’s heart contracts much more efficiently than that of an untrained person.

How does pressure change under load?

Another parameter that changes in response to physical activity is blood pressure. Systolic blood pressure is the pressure experienced by the walls of blood vessels at the moment of heart contraction (systole). Diastolic blood pressure is the same indicator, but during myocardial relaxation (diastole).

An increase in systolic blood pressure is the body's response to an increase in stroke volume provoked by physical activity. Normally, systolic blood pressure increases moderately, up to 15-30% (15-30 mmHg).

Diastolic blood pressure also changes. In a healthy person, during physical activity it can decrease by 10-15% from the original (on average, by 5-15 mmHg). This is caused by a decrease in peripheral vascular resistance: in order to increase the supply of oxygen to tissues, blood vessels begin to dilate. But more often, fluctuations in diastolic blood pressure are either absent or insignificant.

Why is it important to remember this? To avoid false diagnosis. For example: blood pressure 140/85 mmHg. immediately after intense physical activity is not a symptom of hypertension. In a healthy person, blood pressure and pulse return to normal fairly quickly after exercise. This usually takes 2-4 minutes (depending on training level). Therefore, for reliability, blood pressure and pulse must be rechecked at rest and after rest.

Contraindications to cardio training

There are few contraindications to exercise in pulse zone No. 1. They are determined individually. Main restrictions:

• Hypertension. The danger is posed by sudden “jumps” in blood pressure. Cardio training for hypertension can be carried out only after proper correction of blood pressure.
• Coronary heart disease (myocardial infarction, angina pectoris). All loads are performed outside the acute period and only with the permission of the attending physician. Physical rehabilitation in patients with coronary artery disease has its own characteristics and deserves a separate article.
• Inflammatory heart diseases. Under a complete ban on exercise in case of endocarditis, myocarditis. Cardio training can only be done after recovery.

Tachycardia during physical activity is not just an unreasonable acceleration of heart rate. This is a complex set of adaptive physiological mechanisms.

Heart rate control is the basis of competent and safe training of the cardiovascular system.

For timely load correction and the ability to evaluate the results of cardiovascular training, I recommend keeping a diary of heart rate and blood pressure.

Author of the article: Practicing physician V. O. Chubeiko. Higher medical education (Omsk State Medical University with honors, academic degree: “Candidate of Medical Sciences”).

Beginning of the fat burning zone

143 – 155 50% – 60%
light activity zone 132 – 143