Aug 5 2019

# Principle of Switching Power Supply

Introduction

This video shows us that how does a switching power supply work from schematic, explanation, example and modifications.

Catalog

## 1. Principle of Switching Power Supply

### 1.1 Basic Principle of Switching Power Supply

The switching power supply is a power supply that uses modern power electronics technology to control the ratio of the turn-on and turn-off time of the switching transistor to maintain a stable output voltage. The simple structure is shown in figure 1.

Figure 1. Basic Circuit of Switching Power Supply

The switching transistor VT is connected in series between the input voltage VI and the output voltage Vo. When the base of the transistor VT inputs a switching pulse signal, the VT is periodically switched, that is, alternately turned on and off in turns. Assuming that VT is an ideal switch, the voltage drop between the base and the emitter is approximately zero when the VT is saturated, and the input voltage Vi is applied to the output via VT; On the contrary, during the time that VT is cut-off, the output is zero. After VT is periodically switched, the pulse voltage is obtained at the output end, and the average DC voltage is obtained by the filter circuit. The output voltage is as shown in formula 1:

1

Ton is the switch-on time, T is the switching period, and D is the duty cycle. It can be seen that the switching regulated power supply can control the value of output DC voltage by changing the switching pulse duty cycle, that is, the switch-on time.

### 1.2 Workflow of Switching Power Supply

The switching power supply usually consists of six parts, as shown in figure 2.

The first part is the input circuit, which contains low-pass filtering and one-step rectification.  Vi is obtained after the 220V AC is low-pass filtered and bridge-rectified. This voltage is sent to the second part for power factor correction. The purpose is to improve the power factor. The form is to keep the input current in phase with the input voltage. The third part is the power conversion, which is completed by the electronic switch and the high-frequency transformer. It converts the high-power factor DC voltage into a high-frequency square wave pulse voltage that meets the design requirements. The fourth part is the output circuit, which is used to rectify and filter the high-frequency square wave pulse voltage into a DC voltage output. The fifth part is the control circuit. After the output voltage is divided and sampled, it is compared with the reference voltage of the circuit and amplified. The sixth part is the frequency oscillation generator, which generates a high-frequency wave band signal, which is superimposed with the control signal to perform pulse width modulation to achieve adjustable pulse width. With high-frequency oscillation, there is power conversion, so the essence of the switching power supply is power conversion.

Figure 2. Working Principle Block Diagram of Switching Power Supply

### 1.3 Modulation Method of Switching Power Supply

The modulation methods of the switching power supply circuit mainly include three types: PWM, PFM, and PSM. The switching frequency of pulse width modulation (PWM) mode is constant. By changing the width of the on-pulse to change the duty cycle, it achieves the control of the output energy, which is called fixed-frequency widening; the pulse width of pulse frequency modulation (PFM) mode is constant. By adjusting the switching frequency, its duty ratio is changed so as to realize the control of the output energy, which is called fixed-width modulation; the pulse width of pulse skipping modulation mode is constant, and the output energy is adjusted by selectively skipping certain duty cycles.

### 1.3.1 Pulse Width Modulation(PWM)

The PWM modulation mode is the most commonly used control method in the switching power supply. The load-side feedback signal is compared with the internally generated sawtooth wave, and a constant-frequency widened square wave signal is output to control the switch tube, and switch-on time of the switch tube is adjusted in real time according to the load condition so as to stabilize the output voltage. Its working waveform is shown in figure 3.

Figure 3.Working Principle Diagram of PWM

At present, the PWM control mode is the most commonly used in the switching power supply, and it has the following advantages: high efficiency in the case of heavy load, good voltage adjustment rate, high linearity, small output ripple, and is suitable for current or voltage control mode. But it also has the following disadvantages: the input voltage modulation capability is weak, the frequency characteristics are poor, and the efficiency is reduced under light load.

### 1.3.2 Pulse Frequency Modulation(PFM)

PFM is a modulation method often used in switching power supplies. By comparing the feedback signal of the load end with the reference signal, the output error signal adjusts the operating frequency, and then outputs a square wave signal of constant width and variable frequency to control the switch tube, and adjusts the switch-on time of the switch tube in real time according to the load condition, thereby stabilizing the output voltage. Its working waveform is shown in figure 4.

Figure 4. Working Principle of PFM

### 1.3.3 Pulse Skipping Modulation(PSM)

PSM is a new control method in switching power supplies, which is called pulse cross-cycle modulation. The load end feedback signal is converted to a digital level, and the feedback signal level is detected on the rising edge of the clock to determine whether to operate in the clock cycle, and the switch-on time of the switch tube is adjusted to stabilize the output voltage. Its working waveform is shown in figure 5.

Figure 5. Working Principle of PSM

At present, the PSM control mode has been used for switching power supplies, and it has the following advantages: high rate when the load is light, high operating frequency, good frequency characteristics, and less frequency of power tube switching, suitable for small power management ICs. However, it also has the following disadvantages: the output ripple is large, and the input voltage adjustment capability is weak.

## 1.4 Control Method of Switching Power Supply

The switching power supplies we usually use are based on PWM mode, so we focus on the control technology in PWM mode. There are two main types of PWM control technology: one is voltage mode PWM control technology, and the other is current mode PWM control technology.

### 1.4.1 Voltage Mode PWM Controller

The switching power supply was originally based on voltage mode PWM technology. The basic working principle is shown in figure 6. The output voltage Vo is compared with the reference voltage to obtain an error signal VE. This error voltage is compared with the sawtooth signal generated by the sawtooth generator. The PWM comparator outputs a rectangular wave drive signal with a duty cycle change. This is the working principle of the voltage mode PWM control technology. Since this system is a single loop control system, its biggest drawback is that there is no current feedback signal. Since the current of the switching power supply flows through the inductor, the corresponding voltage signal has a certain delay. However, for a regulated power supply, it is necessary to constantly adjust the input current to adapt to the change of input voltage and load requirements, thereby achieving the purpose of stabilizing the output voltage. Therefore, it is not enough to use the method of sampling the output voltage because the voltage regulation response is slow. Even when the large signal changes, the power switch tube is damaged due to the oscillation, which is the greatest weakness of voltage mode PWM control technology.

Figure 6. Principle of Voltage Mode PWM Control Technology

### 1.4.2 Current Mode PWM Controller

Current mode PWM control technology was developed due to the shortcomings of voltage mode PWM control technology. The so-called current mode PWM control is to directly compare the output inductor current detection signal with the output signal of the error amplifier at the input end of the PWM comparator to realize the control of the output pulse duty cycle, so that the peak current of the output inductor follows the error voltage change. This control method can effectively improve the voltage regulation rate and current regulation rate of the switching power supply, and can also improve the transient response of the entire system. The working principle of current mode PWM control technology is shown in figure 7.

Current mode PWM control technology is mainly divided into peak current control technology and average current control technology. The two control technologies detect and feed back the peak value and average value of current change during one conduction period.

Peak current control technology: Peak current mode control directly controls the inductor current of peak output side and then indirectly controls the pulse width of PWM. The peak inductor current is easy to detect and logically consistent with the change of average inductor current. However, the peak inductor current cannot be in one-to-one correspondence with the average inductor current, because the same peak inductor current can correspond to different average inductor currents with different duty cycles and the only factor that determines the value of the output voltage is the value of the average inductor current. When the system PWM duty ratio D>50%, the fixed frequency peak current mode control mode has inherent open-loop instability, and it is necessary to introduce appropriate slope compensation to remove the disturbance of the average inductor current by different duty cycles and to make the controlled peak inductor current finally converges to the average inductor current. When the slope of the applied slope compensation signal is increased to a certain extent, the peak current mode control is converted to voltage mode control. Because the slope compensation signal is completely replaced by the triangular wave in the oscillating circuit, it becomes the voltage mode control, but the current signal at this time can be regarded as a current feed-forward signal. The peak current mode control is a double closed loop control system (the outer loop is the voltage loop and the inner loop is the current loop), and the current inner loop is instantaneously and quickly operated according to the pulse by pulse. In the double loop control, the current inner loop is only responsible for the dynamic change of the output inductor, so the voltage outer loop only needs to control the output voltage, and does not need to control the energy storage circuit. Therefore, peak current mode control has a much larger bandwidth than voltage mode control.

Figure 7. Working Principle of Current Mode PWM Control Technology

Average current control technique: Average current control requires detection of inductor current, inductor current detection signal and a given VE. After the comparison, the control signal VC is generated by the current regulator and is compared with the sawtooth modulation signal to generate a PWM pulse. Current regulators typically use a PI-type compensation network and filter out high frequency components in the sampled signal.

Comparison of two current control technologies: Peak current type control technology is convenient and fast, but requires stability compensation; average current type control technology is characterized by stability and reliability, but the response speed is slower and the control is more complicated. Therefore, in practical applications, the peak current control mode is more common than the average current control mode.

## 1.5 Working Mode of Switching Power Supply

Take the flyback converter used in this design as an example, the so-called flyback means that the primary polarity of the transformer is opposite to the secondary polarity, as shown in figure 8. It is composed of a switching tube VT, a rectifier diode D1, a filter capacitor C and an isolation transformer. If the primary upper end of the transformer is positive, the secondary upper end is negative, and the switching tube VT operates in PWM mode. The flyback converter has a high efficiency, a simple circuit, and can provide multiple outputs, so it has been widely used.

Figure 8. Basic Circuit of Flyback Converter

The flyback PWM converter has two modes: continuous current and interrupted current. For the current flowing through the switching tube of the primary winding W1, its current is impossible to be continuous because the current of the switching tube VT is necessarily zero after the disconnection. But at this time, the current is inevitably caused in the secondary winding W2. For a flyback converter, continuous current means that the combined ampere of the two windings of the converter is not zero during one switching cycle, and the current interruption means that the synthetic ampoule is zero during the turn-off period of the switching tube VT. When the current is continuous, the flyback converter has two switching modes, as shown in (a) and (b) of figure 9; and when the current is interrupted, the flyback converter has three switching modes, as shown in (a) (b) (c) of figure 9.

Figure 9. Equivalent Circuit in Different Switching Modes

### 1.5.1 Working Principle of Flyback Converter When Current Is Continuous

As shown in Figure 9(a), At t=0, the switching transistor VT is turned on, and the power supply voltage Vis applied to the W1, primary winding of the transformer. At this time, the induced voltage in the secondary winding W turns off the diode D1  and the load current is supplied from the filter capacitor C. At this point, the secondary winding of the transformer is open, only the primary winding works, which is equivalent to an inductor. The inductance is L1, the primary current Lp increases linearly from the minimum value IPmin, and the increase rate is:                                                           1-2）

When t=Ton, current Ip reaches maximum IPmax

(1-3)

During this process, the core of the transformer is magnetized and its magnetic flux Φ also increases linearly. The increment of flux Φ is:

(1-4)

As shown in figure 9(b), when t=Ton, the switching tube VT is turned off, the primary winding is opened, and the induced electromotive force of the secondary winding is reversed to turn on the diode D1. The energy stored in the magnetic field of the transformer is released through the diode D1, charging the capacitor C on the one hand and supplying power to the load on the other hand. At this point, only the secondary winding of the transformer operates, which is equivalent to an inductor, and its inductance is L2. The voltage on the secondary winding is Vo, the secondary current Is drops linearly from the maximum ISmin and its decline rate is:

(1-5)

When t = T, the current Is reaches a minimum ISmin

(1-6)

During this process, the transformer core is demagnetized and its magnetic flux Φ is also linearly reduced. The amount of decrease in magnetic flux Φ is:

(1-7)

### 1.5.2 Basic Relationship of Flyback Converter When Current Is Continuous

In the regulated voltage operation, the amount of increase  in the flux of the switch-through core is necessarily equal to the amount of decrease  when switch VT is turn-off, that is, . From formula (1-4) and (1-7), we can get:

(1-8)

In the formula,  is the turns ratio of the primary and secondary windings of the transformer.

When K12=1

(1-9)

The voltage that the switching tube VT subjected to when it is turned off is the sum of Vi and the induced electromotive force in the primary winding W1, that is,

(1-10)

When the power supply voltage Vi is constant, the voltage of the switching transistor VT is related to the duty ratio D, so the value of the maximum duty ratio Dmax must be limited. The voltage of the diode D1 is equal to the sum of the output voltage V and the input voltage Vconverted to the secondary voltage:

(1-11)

The load current Io is the average value of the current flowing through the diode D1:

(1-12)

According to the working principle of the transformer, the following two formulas are established.

(1-13)

(1-14)

From formula (1-3) and formula (1-12) to (1-14), we can get:

(1-15)

(1-16)

IPmax and ISmax are respectively the maximum current values flowing through the switching tube VT and the diode D1.

### 1.5.3 Working Principle and Basic Relationship of Flyback Converter When Current Is Interrupted

Formula (1-9) still works if the critical current is continuous. At this time, the maximum current of the primary winding is IPmax, then , and the load current is

(1-17)

(1-18)

When D=0.5, IoG reaches its maximum

(1-19)

Then formula (1-18) can be written as

(1-20)

Formula (1-20) is the critical continuous boundary of the inductor current.

When the inductor current is interrupted,  is not only related to the duty cycle D but also the value of load current Io. Suppose  is freewheeling relative time of Is, we can get  because the amount of increase and decrease in core flux is equal by one switching cycle. So, , and , , then:

(1-21)

Formula (1-21) shows that when the current is interrupted, the output voltage is not only related to the duty cycle D, but also related to the magnitude of the load current Io. When the duty cycle D is constant, reducing the load current Io can make the output voltage Vo rise.

In the case of current interrupt mode, the energy stored in the primary inductor depends on the peak current:

(1-22)

Energy is delivered once per cycle,

(1-23)

This formula tells us that once the input voltage is fixed, only T can increase the output power by reducing the switching frequency or reducing the inductance. And if the switching frequency is also selected, the power can only be increased by reducing the inductance. However, the actual inductance has a minimum value, and the flyback converter operating in the discontinuous mode has a maximum output power limit, generally less than 50W.

## 1.6 Summary

This chapter mainly introduces the basic working principle and the working flow of the switching power supply. It also introduces the modulation mode of the switching power supply. At present, the PWM control mode is the most commonly used in the switching power supply. It has the following advantages: high efficiency in the case of heavy load, good voltage regulation, high linearity, and small output ripple and is suitable for current or voltage control mode. Therefore, this design will use PWM modulation.

There are two main types of PWM control technology: one is voltage mode PWM control technology, and the other is current mode PWM control technology. Since the current control method reacts quickly to the input voltage, this design will use current control method.

This chapter also describes the operating mode of the switching power supply. Since the discontinuous mode feedback loop is stable and the power of this design is small, the discontinuous mode is adopted.

## 2. Control Devices Used in Switching Power Supplies

### 2.1.1 Magnetization Curve and Hysteresis Loop

Figure 10. Magnetization Curve and Hysteresis Loop of the Transformer Core

As shown in figure 10, as forward and bridge converters, most of them work in zone 1 and 2. The characteristics of these two zones are: the external magnetic field is small and the magnetization process is reversible. In zone 1, . μ1 is the initial permeability. And is obviously linear. For power transformers with low output power and low frequency, the value of B at work can be calculated extremely accurately. In zone 2, . Here B is the Rayleigh constant and this area has not been linear. But the magnetization process is still reversible. Usually for these two areas, we still take an approximate formula for engineering applications: . Because of the reversibility, the forward converter has almost no hysteresis (In fact, due to the process and other reasons, there is still irreversible magnetization, but it is relatively not obvious). For power supply with same input and output, if the forward and reverse excitation topologies are used respectively, the efficiency of the forward transformer must be higher than that of the flyback transformer as long as the operating frequency is the same.

For a flyback transformer, the working area is zone 1, 2, and 3. Among them, zone 3 belongs to the irreversible magnetization zone. This region is the main formation region of hysteresis, so the flyback transformer has a component of hysteresis loss. It works in the middle magnetic field range. Even if the change range of the magnetic field is small, the change of B is very significant. The magnetic permeability increases rapidly and reaches the maximum value. This area is also the area with maximum magnetic permeability. It is obvious that the magnetic permeability of zone 1, 2, and 3 is not equal, but in the calculation of the parameters of the transformer, we use the formula . Here μe is the effective permeability and makes the B——H curve of zone 1,2, and 3 equate to the ratio of B and H obtained by a straight line. It should be noted that this formula is adapted to a flyback converter operating in DCM mode. Flyback converters operating in CCM mode must use incremental permeability for accurate calculations. The calculation of the energy storage inductance in the forward converter is also considered to be used in the DCM mode using μe, and the CCM mode using the incremental permeability.

For the maximum hysteresis loop, if the magnetization process cannot return according to the original path, there is inevitably energy consumption. The power consumed by magnetization for one circle is equal to the area surrounded by the magnetization curve. In order to reduce power consumption, we always hope that the hysteresis loop is as thin as possible when selecting the core because this is more similar to a straight line that crosses the coordinate zero. When using the formula , it is closer to the actual situation. Since  is an approximate formula, and Bmax of the magnetic core is lowered with the rise of temperature, the value of △B must be left with a margin when designing the transformer. (DCM mode should normally not exceed 2/3 of its nominal value Bmax. It should be noted that this value corresponds to the highest temperature at which the product may work). If the margin is small, the current limit of the overcurrent protection of the power supply must be considered. Normally, when a properly designed power supply makes open-loop operation within the full voltage input range at full load, the core of the transformer will not saturate.

For a transformer, if all of the secondary windings are not connected, the primary winding is equivalent to an inductor, and all current flowing through the primary winding is magnetized. In the DC state, the transformer is equivalent to a short-circuit component and cannot transfer energy. When the magnetizing current is large, the transformer will be saturated. At this time, the efficiency of transmitting energy drops sharply. In actual engineering measurement, all other windings are generally short-circuited for measurement when measuring the leakage inductance of a certain winding.

When the secondary winding is open, the primary current is the excitation current. The primary inductance at the corresponding secondary open circuit can be approximated as the magnetizing inductance. For a fixed transformer, the exciting current is mainly determined by the voltage applied to the primary winding, and the magnetizing inductance is a real inductance. The ideal transformer is just a black box that transmits energy.

For a forward transformer and a converter operating like a forward transformer, a magnetic reset is needed, and the magnetizing inductance is passed through a reset circuit to achieve a volt-second balance. The flyback power supply does not require a magnetic reset because the process of the flyback converter itself is a magnetic reset process. There are some common reset circuits such as LC resonant reset, RC or RCD reset, active clamp, and single winding reset.

### 2.1.2 Control of Air Gap

A flyback transformer is essentially an inductor. The whole current of it is the excitation current. The energy storage formula of the inductor is: . To increase its energy storage, it seems that there are two ways: first, increase the inductance (that is, increase the number of turns). In this way, the volume of the transformer will be greatly increased. Another problem is that since  of the magnetic core is constant, the maximum operating current is inevitably reduced, so it is unwise to increase the inductance to increase the energy storage. The second is to increase the working current. The current requirements for magnetic core energy storage increase, eventually leading to an increase in the total energy storage of the core.

Although the magnetic permeability after opening the air gap is smaller than the magnetic permeability when the air gap is not opened, the magnetic field strength (which is proportional to the current) reaching the magnetic saturation of the magnetic core is greatly increased. It is conducive to storing more energy. The increase of the reluctance after the air gap increases the magnetic flux leakage, especially around the air gap. If the leakage inductance is to be reduced, the coil can be wound directly on the air gap, but the coil around the air gap will be in a strong changing magnetic field, and a local eddy current will be generated in the wire, and the enameled wire is burned and discolored after a long time. For an air gap-dispersed iron powder core, the best way to reduce the leakage inductance is to uniformly and uniformly wrap the entire core. The following is a calculation formula for the transformer air gap.

First, according to the magnetic circuit Ohm's law:

（2-1）

N is the number of turns of the coil, Rm is the magnetic resistance, NI is the magnetic potential (similar to the electromotive force), and  is the magnetic flux.

Ampere's loop law: , substitute it into formula (2-1) and we can get:

(2-2)

(2-3)

(2-4)

(2-5)

Now we can get the formula of magnetoresistance:

(2-6)

From the magnetic path of the open air gap, we can know that the total reluctance is equal to the sum of the material reluctance and the air gap reluctance. Since the magnetic permeability of the material is much larger than the magnetic permeability of the air gap. Therefore, the magnetic resistance of the material is much smaller than the magnetic resistance of the air gap, so the magnetic resistance of the material is ignored.

(2-7)

From energy storage formula of inductor:

(2-8)

From Ampere's loop law:

(2-9)

We export:

(2-10)

μ0 is vacuum permeability

I is the primary peak current

B is the value of magnetic induction during rated operation

Se is the effective cross-sectional area of Ae

### 2.1.3 Control of Leakage Inductance

Figure 11. Distribution of Flux Linkage in Actual Transformer

Figure 11 shows a two-winding transformer, Np is primary and Ns is secondary.  is the magnetic flux that primary coupled to the secondary,  and   are magnetic fluxes that are not coupled to each other, that is, leakage inductance. Due to the presence of the primary leakage inductance, the energy will be transferred to the secondary after a delay. In actual use, the transformer has two winding methods: sequential winding method and sandwich winding method. These two winding methods have different effects on EMI and leakage inductance. The sequential winding method generally has a leakage inductance of about 5% of the inductance, but since the primary and secondary have only one contact surface and the coupling capacitance is small, the EMI is better. The sandwich winding method generally has a leakage inductance of about 1% to 3% of the inductance. The winding sequence of the sandwich winding method is generally first primary, then one second to one third of the secondary secondary. And the smaller the aspect ratio, the smaller the leakage inductance of the transformer. However, since the primary and secondary have only two contact surfaces and the coupling capacitance is large, EMI is relatively difficult. Generally, when the power is below 30~40W, the leakage energy is acceptable, so sequential winding method is more often used. When the power is above 40W, the energy of the leakage inductance is large, and generally only the sandwich winding method can be used.

### 2.1.4 Analysis of Control Process of Flyback Power Supply

In the flyback power supply, the primary current and the secondary current are actually not mutated. In theory, the current of the primary winding and the current of the secondary winding are smoothly transitioned by magnetic coupling, and the current of each winding itself can be mutated but actually no mutation. The detailed working process is as follows: After the MOS is turned off, the primary current charges the MOS output capacitor and the transformer stray capacitance (In fact, the stray capacitance is a discharge. In order to simplify the description, it is collectively described as charging), and then the DS terminal voltage of the switch tube rises resonantly. Since the current is very large, the value of Q in the resonant circuit is very small, so it is basically a linear rise. When the voltage at the DS terminal rises until the voltage at the secondary reaches the sum of output voltage and the voltage of the rectifier, the secondary should be turned on. However, due to the influence of the secondary leakage inductance, the voltage will rise to overcome the influence of the secondary leakage inductance, so that the voltage reflected to the primary is also slightly higher than the normal reflected voltage. Under such conditions, the secondary current starts to rise and the primary current begins to decrease. But don't forget the primary leakage inductance. Because it can't be coupled, its energy should be released. At this time, the leakage inductance, MOS output capacitance and the transformer stray capacitance resonate, the voltage is high, and several oscillations are formed. The energy is consumed in the clamp circuit.It is noted that the current of the leakage inductance is always in series with the primary current, so the process of dropping the leakage current is the process of rising the secondary current. And the process of dropping the leakage current is determined by the difference between the voltage on the capacitor of the clamp circuit and the reflected voltage. The larger the difference, the faster the drop. The faster the conversion process, the more obvious the efficiency, and the process of conversion is the process of voltage and current superposition. When using RC for absorption, since the difference between the voltage on C and the reflected voltage is not too large at steady state, the conversion process is slow and the efficiency is low. When using TVS for absorption, the allowable voltage and the reflected voltage are much different, so the conversion is fast and the efficiency is high. Of course, RC consumes more power than TVS, but it is cheaper.

When the power supply uses RCD as the absorption loop, during the secondary current setting process, the DC voltage applied to the capacitor is not  and it is higher than this voltage. The energy absorbed by the RCD absorption loop is composed of two parts, one is the leakage inductance energy, and the other is the primary inductance energy storage. If the RC time constant is 1/10 to 1/5 of the switching period, the loss will be large, and in the flyback process, the secondary energy will be absorbed in a large amount, resulting in a decrease in power efficiency.

### 2.1.5 Design of Absorption Control Circuit

The ringing of the switch tube and output rectifier will happen in each power supply. Over-voltage caused by excessive ringing may cause damage to the device and cause high-frequency EMI problems or loop instability. The solution is usually to add an RC absorption loop. First, measure the ringing frequency with an oscilloscope without adding an absorbing circuit under light load. Remember to use the probe with low-capacitance because the capacitance of the probe will cause the ringing frequency to change, and the design result will not be accurate. Secondly, it is better to measure the ringing frequency at the highest voltage of operation because the frequency of ringing will change with the increase of voltage, which is mainly because the output capacitance of MOS or diode will change with the voltage.

The cause of ringing is the oscillation of the equivalent RLC circuit. For a low-loss circuit, this oscillation may last for several cycles. To prevent this oscillation, we must first know a parameter of this oscillation. For MOS, the leakage inductance is the main inductance that causes oscillation and this value can be measured. For the diode, the capacitance is the main factor, which can be detected by the manual. To calculate its impedance: if we know L, then ; if we know C, . Try R=Z first, it is usually enough to control the ringing. However, the loss may be high and a capacitor needs to be connected in series to reduce the power loss of the damping circuit at this time. The value of C can be calculated as follows: . Increasing the value of C will increase the loss and the damping effect is enhanced. Reducing the value of C will reduce the loss, and the damping effect is weakened. The loss of resistance is:  . In practice, some adjustments are made based on the calculated value according to the experiment.

### 2.1.6 EMI Control of the Transformer

In power transformers with low power, there are generally two types of shielding layers: copper foil and windings. The principle of copper foil is to cut off the path of stray capacitance between the primary and secondary, so that they all form a capacitance to the ground and the shielding effect is excellent. but the process will be a little bit complicated and cost are increased. Winding shields have two principles at work: cutting off the capacitor path and balancing the electric field. Therefore, the turns, winding direction and position of the winding have a great influence on the EMI results. In short, there is one point: the voltage induced by the shield winding is opposite to the voltage direction when the shielded winding is operating. The position of the shield winding has a large impact on the standby power consumption of the power supply. EMI shielding can be connected to the original ground wire or the high-voltage end of the original side. There is almost no difference in EMI because there is a high-voltage capacitor and the common-mode signal up and down (Generally, it is dominated by common mode interference after it is greater than 1M) Is equipotential. The external shield of the transformer can be disconnected or connected to the primary ground. The effect on EMI depends on the internal condition of the winding. Please pay attention to the safety problem.Connected to the primary ground wire, the magnetic core is the primary, that is, the magnetic core is on the primary side, and the safety distance between the primary and the secondary side should be noted. The shield winding has an effect on the operation of the transformer. In order to play a good role, the shield winding is generally close to the primary, so that it forms a capacitor with the primary winding. The shield winding is usually connected to the primary ground or high voltage. This capacitor is equivalent to D-S side connected to the MOS and it is obviously causing a large turn-on loss and also affects standby power consumption. Of course, the addition of shielding will also increase the leakage inductance.

Faraday shielding generally uses thin copper sheets, and can not form a loop. The primary side shield should be connected to the primary side or a straight-line capacitor should be connected to the primary side. The secondary side shield should be connected to the secondary side. About the way of connection, it is best to take out from the copper point to eliminate the inductance. For safety, the shield should be grounded. The rated current of the shielded connected to the ground should be at least larger than the value of the power fuse current. For the magnetic core plus air gap, the external shield is used. The width of the shield is very fastidious and the principle is obvious. If the rated current of the fuse of the safety shield is smaller or the same as the power fuse, the fuse of the safety shield may  break first in the case of short circuit and may not function as a safety shield. As for external shielding, we must first meet the requirements of safety regulations. Under this premise, of course, it will be better if it is wider, but it will increase the cost as well. We just need to combine the two halves of the core. In practice, the shielded copper strip is often in direct contact with the core.

## 2. 2 Main Power Tube

The main power tube used for control is usually a MOSFET, and the components around it are parasitic components, which seriously affects the performance of the MOS as a switch. As a switching element, the main consideration is that the on and off times are short enough to operate between the minimum resistance and the maximum resistance to reduce power consumption. The actual switching time is typically 10-100ns, while the power supply has a switching period of 20-200us. The switching time is also mainly determined by the charge and discharge time of its parasitic capacitance. Both CGD and CDS are functions of the drain voltage and are non-linear.

Another important parasitic parameter is the gate resistance, which directly affects the turn-on time of the switch, and this parameter is not provided in the general specification. The drive voltage domain value of the gate is generally provided in the specification as a value of 25 °C. In fact, the domain voltage of the gate is varied with a negative temperature coefficient of -7 mV / °C.

There are also two important parasitic parameters: the source inductor and the drain inductor. The value of the parasitic inductor is mainly based on the package form of the MOS tube. Typical values are given in the specification.

## 2.3 Main Control Chip

The core part of the switching power supply is mainly composed of a precision voltage comparison chip, a PWM chip, a switch tube, a drive transformer, and a main switch transformer. The precision voltage comparison chip compares the feedback voltage of the DC output part with the reference voltage, and the PWM chip adjusts the duty ratio of the switching tube through the drive transformer according to the comparison result, thereby controlling the energy outputted to the DC part of the main switching transformer to realize the regulated output.

The PWM feedback control method can be divided into current type and voltage type. The commonly used UC3842 is a current type control mode, and its internal block diagram is shown in figure 12.

Figure 12. Internal Block Diagram of UC3842

The UC3842A is a high performance fixed frequency current mode controller designed for off-line and DC to DC converter applications. It is the most frequently used and most typical PWM control chip. These integrated circuits feature a trimmable oscillator for precise duty cycle control, temperature compensated references, and high gain error amplifiers. The current sampling comparator and the high current totem pole output are ideal for driving power MOSFETs. Other protection features include input and reference undervoltage lockout, each of them has hysteresis, CYCLE BY CYCLE current limit, programmable output dead time and single pulse measurement latch. These devices are available in 8-pin dual in-line plastic packages and 14-pin plastic surface mount packages (SO-14). The totem pole output stage in the SO-14 package has separate power and ground pins. The 16 volt (on) and 10 volt (off) low voltage lockout thresholds of UC3842A are ideal for off-line converters. The UCX843A is designed for low voltage applications with a low voltage lockout threshold of 8. 5V (on) and 7. 6V (off)  and it has the following characteristics:

1. Fine-tuned oscillator discharge current for precise duty cycle control

2. Current mode operates to 500 kHz

3. Latch pulse width modulation which can limit current cycle by cycl

4. Internally trimmed reference voltage with undervoltage lockout

5. High current totem pole output

6. Undervoltage lockout with hysteresis

7. Low starting and operating current

### 2.3.1 Function Description of Each Control Module

Oscillator: The frequency is determined by the selection values of timing element RT and CT. The capacitor CT is charged by a reference voltage of 0.5V through a resistor RT to about 2. 8V, and then discharged by an internal current sink to 1. 2V. During CT discharge, the oscillator generates an internal blanking pulse to keep the middle input of the NOR gate high, which causes the output to be low and produces a controlled amount of output dead time. It should be noted that although many R and c values can produce the same oscillator frequency, there is only one combination that yields a specific output dead time at a given frequency. In many noise-sensitive applications, the converter frequency can be locked to the external system clock. For specific clock signal control, please refer to the data sheet.

Error amplifier: it provides a fully compensated error amplifier with accessible inverting input and output. This amplifier has a typical DC voltage gain of 90dB and a 10MHz gain with a 57-degree phase margin of 1 bandwidth. The non-inverting input is internally biased at 2.5v and it is not pulled out by the pin. Typically, the output voltage of the converter is divided by a resistor divider and monitored by the inverting input. The maximum input bias current is -2uA, which will cause an output voltage error. The latter is equal to the input bias current and is the product of the equivalent input divider source resistance. The error amplifier output (pin 1) is used for external loop compensation. The output voltage is offset by approximately 1.4V due to the two diode voltage drops and is divided into three parts before being connected to the inverting input of the current sampling comparator. This will ensure that no drive pulses are present at the output (pin 6) when pin 1 is at its lowest state, which occurs when the power supply is operating and the load is cancelled, or the beginning of the circuit soft start process.

Current sampling comparator and pulse width modulation latch: UC3843A operates as a current mode controller. When the output switch is turned on by the oscillator and the peak inductor current reaches the threshold level established by the error amplifier output compensation (pin 1), the error signal controls the peak inductor current on a weekly basis. Pulse-width modulation latch configuration, the current sampling comparator used ensures that only one single pulse appears at the output during any given oscillator period, and the inductor current is converted to a voltage by inserting a ground-referenced sampling resistor RS in series with the source of the output switch. This voltage is monitored by the current sample input (pin 3) and compared to the output level from the error amplifier. Under normal operating conditions, the peak inductor current is controlled by the voltage on pin 1, where:

(2-11)

Abnormal operating conditions will occur when the power supply output is overloaded or if the output voltage sample is lost. Under these conditions, the current sampling comparator threshold will be internally clamped to 1V.

When designing a high-power switching regulator, the internal tank voltage can be reduced at a reasonable level in order to maintain the power consumption of RS. However, excessive reduction in clamp voltage of  will result in erroneous operation due to noise pickup, and a narrow spike can usually be observed at the leading edge of the current waveform. When the output load is light, it may cause power instability. This sharp pulse is generated due to the power transformer's turn-to-turn capacitance and output rectifier recovery time. Adding an RC filter to the current sampling input causes its time constant to approach the duration of the spike, which usually eliminates instability.

Output: The PWM device of 3842 has a single totem pole output stage specifically designed to drive the power MOSFET directly. It provides a peak drive current up to 1A and a typical rise and fall time of 50ns at 1nF load. The SO-14 surface mount package provides separate pins for VC (supply voltage) and power ground. Appropriate application can significantly reduce the switching transient noise applied to the control circuit, and the power supply and control ground should be properly connected.

### 2.3.2 Precautions for Peripheral Control Circuit Design

 Pin (8-pin package) Function Description 1 Compensation Error amplifier output for loop compensation 2 Voltage feedback Inverting input of error amplifier, output voltage sampling 3 Current sampling A voltage proportional to the inductor current is input to this pin, and the PWM and internal error signals are compared to control the output. 4 RT/CT Oscillating capacitor and resistor are connected to this pin 5 Ground It is the common ground of the entire PWM 6 Output Totem pole output for direct drive of external MOS 7 VCC Positive power supply for IC 8 VREF SV reference voltage inside the IC, accuracy of  1%, and it can output 20 mA current

Table 1. Description of the Functions of Each Pin of UC3842

High frequency circuit layout techniques must be used to prevent pulse width jitter. It is usually added to current sampling or voltage feedback input and there is excessive noise. Noise suppression can be enhanced by reducing the circuit impedance at these points. The printed circuit board layout should include a ground plane with only a small current signal, while the high current switch and output ground return to the input filter capacitor through the separate path. According to the circuit layout, a ceramic bypass capacitor (0.1uF) is typically required to connect directly to Vcc and Vref. This provides a low impedance path that filters out high frequency noise. All high current loops should be as short as possible and can reduce radiated electromagnetic interference by using coarse copper foil. The error amplifier compensation circuit and the converter output divider should be closer to the integrated circuit and as far as possible from the power switch and other noise-generating components.

The current mode converter works under the condition that the duty ratio is greater than 50% and the continuous inductor current will generate subharmonic oscillation. At this time, the slope compensation circuit must be added to make the whole power supply work stably.

## 2.4 Generation and Transmission of Control Signal

### 2.4.1 Signal Transmission in Isolation

With the rapid development of electronic components, the linearity of optocouplers is getting higher and higher, and optocouplers are the most widely used isolation and anti-interference devices in switching power supplies. An optical coupler (OC) is also known as an opto-isolator or optocoupler, referred to as an optocoupler. It is a device that transmits electrical signals by means of light. Generally, an illuminator (infrared light emitting diode LED) and a light receiver (photosensitive semiconductor tube) are packaged in the same package. When the input terminal is powered, the illuminator emits light, and after receiving the light, the photoreceptor generates a photocurrent, which flows out from the output end, thereby realizing the "electric-optical-electric" conversion. The optocoupler that couples the input signal to the output end with light as a medium is widely used on circuits because of its small size, long life, no contact, strong anti-interference ability, insulation between output and input, one-way transmission signal, etc. Due to its non-linearity, a typical optocoupler is limited to the isolated transmission of small signals at higher frequency. A common optocoupler can only transmit digital (switching) signals and is not suitable for transmitting analog signals. Linear optocouplers introduced in recent years are capable of transmitting continuously varying analog or analog current signals, which broadens their application areas.

The main advantage of the optocoupler is the one-way transmission signal, complete electrical isolation between the input end and the output end, strong anti-interference ability, long service life and high transmission efficiency. The optocoupler has a large isolation resistance (about 1012 ohms) and a small isolation capacitor (about a few pF). The optocoupler operating in a linear mode adds a control voltage to the input of the optocoupler, which proportionally produces a voltage at the output for further control of the next stage of the circuit. The linear photocoupler is composed of a LED and a phototransistor. When the LED is turned on and emits light, the phototransistor is turned on. The photocoupler is current-driven type, and requires a large enough current to turn on the LED. If the input signal is too small, the LED is not turned on and its output signal will be distorted. In the switching power supply, the optocoupler feedback circuit can be constructed by using a linear optocoupler, and the duty ratio is changed by adjusting the current of the control terminal to achieve the purpose of precision voltage regulation.

The technical parameters of the optocoupler mainly include LED forward voltage drop VF, forward current IF, current transfer ratio CTR, insulation resistance between input stage and output stage, and collector-emitter reverse breakdown voltage V(BR)CEO, collector-emitter saturation voltage drop VCE(sat). In addition, parameters such as rise time, fall time, delay time, and storage time need to be considered when transmitting digital signals.

The current transfer ratio is usually expressed as a direct current transfer ratio. When the output voltage remains constant, it is equal to the percentage of the DC output current IC to the DC input current IF. CTR range of photocoupler using a phototransistor is mostly 20%-300% (such as 4N35) while Darlington optocouplers (such as 4N30) can reach 100%-5000%. This means that the latter requires less input current if you want the same output current. Therefore, the CTR parameters have some similarities to the HFE of the transistor. The CTR-IF characteristic curve of a common optical coupler is nonlinear, and the nonlinear distortion is particularly serious when the IF is small, so it is not suitable for transmitting an analog signal. The linear optocoupler's CTR-IF characteristic curve has good linearity especially when transmitting small signals. Its AC current transmission ratio  is very close to value of CTR, which is the DC current transmission ratio. Therefore, it is suitable for transmitting analog voltage or current signals, enabling a linear relationship between output and input.

The use of optocouplers is primarily to provide isolation between the input and output circuits. The following principles must be followed when designing the circuit: The optocoupler device chosen must meet national and international standards for isolation breakdown voltage:

In order to correctly select the type and parameters of the linear optical coupler in the isolation of the switching power supply and the design of the optocoupler feedback switching power supply, the following principles must be followed: the allowable range of the current transfer ratio (CTR) of the optocoupler is 50% - 200%. This is because when CTR < 50%, the LED in the optocoupler needs a large operating current (IF > 5mA) to properly control the duty cycle of the monolithic switching power supply IC, which increases the power consumption of the optocoupler. If CTR> 200%, when starting the circuit or when the load mutates, it is possible to falsely trigger the single-chip switching power supply, affecting the normal output; If the amplifier circuit is used to drive the optocoupler, it must be carefully designed to compensate the temperature instability and drift of the coupler; A linear optocoupler is recommended because it is characterized by a linear adjustment of the CTR value within a certain range.

The optocoupler used above operates in a linear mode. A control voltage is applied to the input end of the photocoupler, and a voltage for further controlling the next-stage circuit is proportionally generated at the output end, and the closed-loop adjustment control is performed to stabilize the power supply output.

### 2.4.2 Generation of Error Control Signals

The TL431 has a three-terminal adjustable shunt reference with a good thermal stability. It can be used as a low temperature coefficient programmable reference amplifier. Its output voltage can be arbitrarily set to any value from Vref (2.5V) to 36V with two resistors, allowing sinking current from 1mA to 100mA. The typical dynamic impedance of the device is 0.2 ohm. Inside the TL431 is a 2. 5V reference voltage, so its reference input voltage can be provided by the partial voltage of the DC output voltage, which makes it work well. It has very low output noise and a temperature coefficient of only 50ppm/C. It is ideal for use as a reference power supply.

The sampling circuit compares the obtained output signal with the 2. 5V reference source inside the TL431 to generate an error amplification signal, and at this time converts the output voltage signal into a current signal. According to the characteristics of the op amp, only when the voltage at the REF terminal (in-phase terminal) is slightly higher than 2. 5V, there will be a stable unsaturated current passing through the triode. Moreover, with the slight change of the voltage at the REF terminal, the current through the series connected transistor will vary from 1 to 100 mA. So the TL431 is by no means a zener but a real IC.

### 2.4.3 Implementation of Negative Feedback Closed Loop Control

For the circuit shown in figure 13, it is necessary to determine the values of R1, R2, R3 and R4. Let the output voltage be 5V and the auxiliary winding rectified output voltage be 12 V. The circuit uses the output voltage to compare with the reference voltage formed by the TL431 and controls the COMP terminal of the PWM through the current change of the photodiode PC817 diode-transistor, thereby changing the PWM width and achieving the purpose of stabilizing the output voltage. Because the controlled object is PWM, the first thing needed to figure out is the control characteristics of PWM. The relationship between Vcomp and Icomp is known from the PWM specification. It can be seen from figure 14.

Figure 14. Linear Working Area of PWM

It can be seen that the current of Icomp should be between 810 uA and 822 uA, and the PWM will change linearly. Therefore, the current Ice of the transistor PC817 should also vary within this range. While Ice is controlled by diode current If, we can correctly determine forward current If of diode PC817 by the relationship between Ice and If of PC817. We can see from figure 15 that when the PC817 diode forward current If is about 8 mA, the collector current Ice of the triode changes around 810 uA, and the collector voltage Vce can vary linearly over a wide range as shown in figure 16.

Figure 15. Characteristic Curve of PC817

Figure 16. Relationship between Output Voltage and Current of PC817

It meets the control requirements of the PWM. Therefore, it can be determined that the PC817 diode forward current IF is 8 mA. Once the forward current of the optocoupler is determined, the resistance value of the current limiting resistor R1 can be determined:

(2-12)

The purpose of parallel resistor R2 is to provide bias current to TL431. TL431 requires operating current to be at least 1mA, that is, when the diode current of optocoupler is at the minimum value of operation, TL431 should also be at least 1mA. Since the anode of the TL431 is not less than 2.5V, it is roughly estimated that R2 <= 2.5V / 1mA = 2.5K.

In addition, this is also a power consumption consideration. Here we select 2K and there are two factors to consider for the value of R3:

1) The current of the reference input terminal of TL431 is generally about 2uA. In order to avoid this terminal current affecting the partial pressure ratio and the influence of noise, the current flowing through the resistor R3 is generally 100 times or more of the reference segment current. Therefore, the resistance should be smaller than 2.5V/200uA=12.5.

2) Requirements of standby power consumption. If it is required to try to take a large value when <12.5K, we choose 2.5K here. Since the output voltage is 5V, R4 also selects 2.5K.

## 2.5 Summary

The main work of this chapter is to introduce the control devices used in the design, high-frequency transformers, main power tubes and main control chips. The control process of the flyback power supply and the design of the absorption control circuit are also introduced. The generation and transmission process of the control signal is elaborated in this chapter.

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