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This paper introduces a switching power supply with the half-bridge circuit. Its input voltage is AC 220V ±20V, the output voltage is DC 4V ~16V, the maximum current is 40A, and the working frequency is 50kHz. And its design idea, working principle, and characteristics of the power supply are introduced emphatically. 12V 10A switching power supply (with schematic and explanation)   Catalog   I. Introduction II. Main Technical Indicators III. Main Functions Description 3.1 AC EMI Filter and Rectifier Filter Circuit 3.2 Half-bridge Power Converter 3.3 Design of Power Transformer 3.4 Design of Auxiliary Power Supply 3.5 Drive Circuit 3.6 Fan Wind Speed Control Circuit 3.7 PWM Control Circuit 3.8 Current Fold back Circuit FAQ       I. Introduction Power supplies with the voltage of 5~15V and current at 5~40A are most commonly used in scientific research, production, experiments and other applications. The maximum current of the general experimental power supply is only 5A or 10A, For this purpose, a switching power supply with continuously adjustable voltage at 4V~16V and maximum output current of 40A has been developed. It adopts half-bridge circuit, with power MOS transistor as switching device and the switching frequency is 50kHz. Light weight, small volume and low cost are advantages of it.   II. Main Technical Indicators   1) Output Voltage: AC 220V±20％  2) Input Voltage: DC 4～16V(adjustable) 3) Output Current: 0~40A 4) Output Voltage Adjustment Rate: ≤1％ 5) Ripple Voltage Up: p≤50mV 6) Current / Voltage Display Function and Fault Alarm Indication   Basic Working Principles and Schematic Diagrams The schematic block diagram of the power supply is shown in Fig.1. After 220V AC voltage is filtered by EMI and rectifier, about 300V DC voltage is added to the half-bridge converter to drive the power MOS tube with the dual pulse signal generated by the pulse width modulation(PWM) circuit. The quasi-square-wave voltage is gained by coupling and isolating the power transformer, and a stable DC output voltage can be obtained by rectifying filter feedback control. Fig. 1 Working Block Diagram of Integral Power Supply   III. Main Functions Description   3.1 AC EMI Filter and Rectifier Filter Circuit Fig.2 AC EMI Filter and Input Rectifier Filter Circuit The power line of the electronic equipment is an important way of electromagnetic interference (EMI) to get into or out of the electronic equipment, but installing the power line filter at the entrance of the power line of the equipment can effectively cut off the transmission path of EMI. And it composed of IEC plug power filter and PCB power filter.   The main purpose of the IEC plug power filter is to prevent the interference from the power grid from entering the power supply box, and for PCB power filter the purpose is to suppress the high frequency noise generated when the power switch is switched. Bridge rectifier circuit is used when AC input voltage is 220V, if JTI jumper is short-connected, then 110V is suitable.   Because the input voltage is high and the capacitor capacity is large, the surge impulse current will be produced at the moment when the power network is switched on, and the general surge current value is tens of times that of the steady current.   This may result in the damage of rectifier bridge and input fuse, or the saturation damage to power devices of high frequency transformer cores, and the reduction of the service life of high voltage electrolytic capacitors, etc. So the input soft start circuit composed of resistance R1 and relay K1 is added in front of rectifier bridge to avoid those damages.   3.2 Half-bridge Power Converter The power supply uses half-bridge converter circuit, as shown in Fig.3, its operating frequency is 50kHz, the main parts on the primary side are power transistors: Q4 and Q5, and capacitors: C34 and C35. Q4 and Q5 alternately conduct and cutoff, A positive and negative square wave pulse voltage of U1/2 is generated through the primary winding N1 of a high frequency transformer. The energy is transferred from transformer to the output, and Q4 and Q5 use IRFP460 power MOS transistor. Fig.3 Switching Power Supply Schematic   3.3  Design of Power Transformer   1) Setting of the Working Frequency The working frequency has a great influence on the volume, weight and circuit characteristics of the power supply. The output filter inductance and capacitance volume decrease with high working frequency, but the switching loss increases, the heat quantity increases and the radiator volume increases. Therefore, according to the factors such as components and cost performance, optimizing the operating frequency of power supply, the formula is fs=50kHz, T=1/fs=1/50kHz=20μs.   2)Core Selection ①Selecting the EE type ferrite core made of R2KB ferrite material, has many advantages, such as versatility, large lead space, convenient wiring operation, economics, and so on. ②Determination of Working Magnetic Induction Intensity: Bm The saturation magnetic induction intensity of R2KB soft magnetic ferrite material is Bs=0.47T, considering that Bs will decrease at high temperature, and in order to prevent the saturation of high-frequency transformer at the moment of closing,  selecting Bm=1 / 3Bs= 0.15T ③Calculation and Determination of Core Type The geometric cross-sectional area S and the window area Q of the magnetic core have a certain functional relationship with the output power Po. For half-bridge converters, when the pulse waveform is an approximately square wave, having SQ= (1) η—Efficiency j—Current density, generally 300~500A/cm2 kc—Fill factor of magnetic core, ferrite core kc=1 Ku—Filling coefficient of copper, related to the wire diameter, winding process, winding number, and so on, is generally about 0.1~0.5. The units of each parameter: Po—W，S—cm2, Q—cm2, Bm—T, fs—Hz, j—A/cm2. The values each parameter:  Po=640W，Ku=0.3,j=300A/cm2,η=0.8,Bm=0.15T, plugging these into formula(1) to get SQ=4.558cm4. From the manufacturer manual of EE55 magnetic core: S=3.54cm2, Q=3.1042cm2, calculating SQ=10.9cm4, the SQ value of EE55 magnetic core is larger than the calculated value. EE55 magnetic core is the option.   3) Calculating Turns of Primary and Secondary Side Windings Calculate the primary number turns of windings according to the lowest input voltage and the full load(the duty ratio is maximum). It is known that the DC input voltage of Umin=176V after rectifying and filtering is Udmin=1.2 × 176 = 211.2V. For the half-bridge circuit, the voltage applied on the primary winding of the power transformer is equal to half of the input voltage, that is Upmin=Udmin/2=105.6V, assuming Dmax=0.9(the maximum duty ratio), getting tonmax= T × Dmax= 20 × 0.9 μs.   Design of an Output Voltage 4~16V Switching Power Supply   Fig.4 Schematic Diagram of Auxiliary Power Supply Upmin×tonmax×104=105.6×9.0×10－6×104, plugging into formula N1=8.9 turns,  the maximum output voltage is Uomax=16V when calculating secondary turns; the secondary circuit uses full wave rectifier, Us as the inductive voltage on the secondary winding and Uo as the output voltage and Uf as the rectifier diode voltage drop, taking 1 V as the voltage drop, Uz is filter inductor equal circuit voltage drop taking 0.3V, getting Us=19.22V×N2=N1×8.9=1.8 turns; For the convenience of winding the transformer, if the secondary winding is 2 turns, then the primary winding will be corrected to N1=N2=10 turns.   4) Selected Wire Diameter When selecting the wire diameter of the winding, the skin effect of the wire should be considered. It is generally required that the wire diameter be less than two times the penetration depth, and the penetration depth Δ is determined by formula (2), Δ= (2), and the unit of penetration depth Δ is m. In formula ω is the angular frequency: ω=2πfs; μ is magnetic conductivity, for the relative permeability of copper wire: μr=1 , 则μ=μ0×μr=4π×10－7H/m; γ is the conductivity of copper, γ = 58 × 10 —6Ωm. The operating frequency of the transformer is 50kHz, and the penetration depth of the copper conductor is Δ=0.2956mm at this frequency, thus the diameter of the winding wire must be copper wire whose diameter is less than 0.59mm. In addition, the current density of copper wire is generally 3 ~ 6 A / mm2, the 0.56mm enamelled wire with 8 strands in parallel for the primary is 10 turns, and the thick 0.15mm flat copper strip with 2 turns in the secondary.   3.4 Design of Auxiliary Power Supply The auxiliary power supply using RCC converter (Ringing Choke Converter), is shown in Fig.4. The input voltage is AC 220 V, as rectifier filter voltage, and the output DC voltage is 12.5 V, the output DC current is 0.5 A. In the circuit, Q8 and transformer primary winding N1 and feedback winding N3 constitute self-excited oscillation. R72 is starting resistance. Q9, R77 constitutes primary overcurrent protection of auxiliary power supply. D20, C81, ZD1, Q11, R75, N76 constitutes voltage detection and voltage stabilizing circuit. The DC component of the base current of Q 8 keeps the output voltage constant, and the transformer is made of EE19 material and LP3 material. The primary is 180 turns, the feedback winding is 5.5 turns, the secondary is 11 turns, the primary inductance is 2.6 MHz, the core gap is 0.4mm.   3.5 Drive Circuit The drive circuit is shown in Fig.5. TL494 outputs the pulse signal of 50kHz and drives the power MOS transistor through the coupling of a high-frequency pulse transformer. The secondary pulse voltage is a timing MOS switch, during which Q7 ends, and the drain circuit formed by it does not work. Q7 conducts when the second pulse voltage is 0, rapidly releasing the gate charge of MOS, and accelerating MOS cutoff. R70 is the spike to suppress the driving pulse, R68, D15, R67 used to speed up driving and suppress the oscillation caused by driving pulse, D17, and the connected pulse transformer windings form a demagnetization circuit.  Fig.5 Driving Circuit Schematic Diagram 3.6 Fan Wind Speed Control Circuit Fan wind speed control circuit is shown in Fig.6. Based on the decreasing trend of diode forward tube pressure drop with increasing temperature, D9 and D10 are used as radiator temperature samplers close to the radiator. When the temperature of the radiator rises with the increase of output power, the level of the positive phase input of the operational amplifier N2A decreases, the output low level causes the transistor Q3 to start conducting, and the voltage on the fan rises.   The rotational speed rises and finally reaches the maximum speed. When the load is lighter and the radiator temperature is lower than 50 ℃, the output of N2A is high level, Q3 is not conductive, and auxiliary electricity 12.5V stepped down by resistance R57 supplying to fan, thus the fan is running at low speed and low noise. The circuit can improve the working life of the fan, increase the reliability of the circuit and reduce the noise caused by the fan in the case of a small load.   Fig.6 Fan Wind Speed Control Circuit 3.7 PWM Control Circuit The general pulse width modulator (TL494,) used in the control circuit has the advantages of generality and low cost, as shown in Fig.7. The output voltage is sampled by R40, RV2, RV1, R41 and then sent to the TL494 pin 1 after the R5 impedance matching. RV1 installed in power front panel to realize the output voltage adjustment. R103 and C14 sample the output inductor L1 front signal which delivering through R5 to TL494 pin 1 to improve power supply stability and eliminate the influence of L1 on loop stability.   3.8 Current Foldback Circuit In order to enhance the reliability of the power supply, this power supply adopts two-stage over-current protection: primary and secondary. Current transformer CT1 is initially used to detect the primary transformer current. The detected current signal is converted from R60 to voltage signal, then filtered by D2~D4 and C9, and then the voltage is divided by potentiometer RV3, and inverted by N3, finally added to the Q 1 tube base. When the primary current is abnormal, the inverter reverses the Q1 switch and adds a high level of VREF=5V to the TL494 pin 4 (the TL494 dead-zone control pin, which is turned off at a high level), TL494 is off. Overcurrent protection on the main output DC line uses R45-R56 resistance as the sampling resistance. When the output current increases, the level of pin15 becomes lower. When the output current is greater than 105% of 40A, the internal operational amplifier of TL494 acts. The pin3 level rises, limiting the increase of the output pulse width, and the power supply is in the limiting state. FAQ   1. How does a switching power supply work? The “switch” in a switching power supply is actually a semiconductor – a MOSFET that is either off or on – driven into its saturation range to transfer power across nearly zero resistance. It does this many thousands of times per second, creating the high-frequency AC intermediary.   2. What is difference between linear and switching power supply? Linear power supplies deliver DC by passing the primary AC voltage through a transformer and then filtering it to remove the AC component. Switching power supplies feature higher efficiencies, lighter weight, longer hold up times, and the ability to handle wider input voltage ranges.   3. What is a switching power supply 12v? Switching regulated 12VDC power supplies, sometimes referred to as SMPS power supplies, switchers, or switched mode power supplies, regulate the 12VDC output voltage using a complex high frequency switching technique that employs pulse width modulation and feedback. Acopian switching regulated power supplies also employ extensive EMI filtering and shielding to attenuate both common and differential mode noise conducted to the line and load. Galvanic isolation is standard in our 12VDC switchers, affording our users input to output and output to ground isolation for maximum versatility. Acopian switching regulated power supplies are highly efficient, small and lightweight, and are available in both AC-DC single and wide-adjust output and DC-DC configurations.   4. What is a DC switching power supply? A Switching DC power supply (also known as switch mode power supply) regulates the output voltage through a process called pulse width modulation (PWM). The PWM process generates some high frequency noise, but enables the switching power supplies to be built with very high power efficiency and small form factor.   5. When should you use a switching power supply? Switching power supplies are primarily used in digital systems such as telecommunication devices, computing equipment, audio equipment, mobile phone chargers, medical test devices, arc welding equipment and automotive chargers.   6. Is a switching power supply regulated? A switch mode power supply regulates an output voltage with pulse width modulation (PWM). This process creates high-frequency noise but it provides a high-efficiency rating in a small form factor. ... The low DC voltage is finally converted into a steady DC output with another set of diodes, capacitors, and inductors.   7. Is a switching power supply DC? A switching power supply takes an AC input, but rectifies and filters into DC first, is converted back into AC at some high switching frequency, steps down the voltage with a transformer, then is rectified and filtered into a DC output.   8. How do I know if my power supply is regulated? You can generally stick one probe into the middle of the connector, and hold the other against the outside. With a few exceptions, the middle is positive, so use the red lead there, and use the black lead on the outside shell. Regulated supplies, without any load, should measure very close to the target voltage of 12v.   9. Can I use a switching power supply to drive a DC motor? A simple unregulated analog power supply may be easier and be able to supply the large starting under load current more that the switching one. DC motors are not too fussy about the supply, and will usually run quite well on unfiltered DC.   10. What are the 3 types of power supply? There are three subsets of regulated power supplies: linear, switched, and battery-based. Of the three basic regulated power supply designs, linear is the least complicated system, but switched and battery power have their advantages.   You May Also Like Learn Some Basic Knowledge about Capacitor Voltage Transformer The Latest Development of Electric Vehicle Power Management Technology Design a Momentary Pushbutton in the Circuit of Laching Power Switch

  In daily production and life, ultrasonic ranging sensors are mainly used for non-contact automatic parking distance control (PDC) of automobiles, obstacle avoidance robots, construction sites and industrial working environments that require liquid level, well depth, pipeline length, etc. In general, there are two commonly used ultrasonic distance measurement methods:   - The ultrasonic ranging system based on single chip microcomputer or embedded equipment;   -  An ultrasonic ranging system based on CPLD (complex programmable logic device). In order to understand the design and application of ultrasonic ranging sensor, let us first understand the working principle of ultrasonic sensor. Introducing ultrasonic sensor & taking HC-SR04 as an example   Catalog   I What is ultrasonic sensor? II Methods for ultrasonic ranging III Principles for ultrasonic ranging IV Conclusion FAQ   I What is ultrasonic sensor?      Figure 1. Working principle of ultrasonic sensor ranging An ultrasonic sensor is a sensor that converts an ultrasonic signal into another energy signal (usually an electrical signal).  Ultrasonic is a mechanical shock wave generated in elastic media with a frequency greater than 20 kHz. Because of its strong directivity, slow energy consumption and relatively long propagation distance, it is often used in non-contact ranging.  In addition, ultrasonic has the big ability to penetrate liquid and solid, especially in the sunshine opaque solid. When an ultrasonic hits an impurity or an interface, itwill produce a significant reflection to form an echo,  and when it hits a moving object will cause a phenomenon called Doppler Effect.  Therefore, ultrasonic ranging has a good adaptability to the environment, and ultrasonic distance measurement can be well compromised in real time, precision, and price. II Methods for ultrasonic ranging At present, there are various methods for ultrasonic ranging:    -  round-trip time detection;   -  phase detection;   -  acoustic amplitude detection. The principle is that the ultrasonic sensor emits ultrasonic waves of a certain frequency, propagates through the air medium, and is reflected back after reaching the measurement target or the obstacle. After being reflected, the ultrasonic receiver receives the pulses, and the time it takes, is the round-trip time, which is related to the distance traveled by ultrasonic waves. Measuring the wave propagation time to get the wave propagation distance: Assuming that s is the distance between the measured object and the range finder, the time measured is t / s, and the velocity of ultrasonic propagation is expressed as v／m·s－1, then there is a relation (1): s=vt／2       (1) When the accuracy is required, the influence of temperature on the ultrasonic propagation speed needs to be considered, therefore the ultrasonic propagation speed is corrected according to relation (2) to reduce the error. v=331．4+0．607T        (2) Where T is the actual temperature, the unit is °C; v is the propagation speed of ultrasonic wave in the medium, and the unit is m/s. Figure 2. Working principle of ultrasonic ranging sensor   III Principles for ultrasonic ranging   The principle of ultrasonic ranging is to transmit ultrasonic waves in a specific direction through an ultrasonic transmitter, and start timing at the same time as the transmission. When ultrasonic waves propagate in the air and hit an obstacle, they will immediately return and be received by the ultrasonic receiver, and stop timing immediately. The ultrasonic ranging sensor uses the principle of ultrasonic echo ranging and uses precise time difference measurement technology to detect the distance between the sensor and the target. It has the advantages of small angle, small blind area, high measurement accuracy, non-contact ranging, waterproof, anti-corrosion, and low cost. Ultrasonic ranging sensors are usually used in a way that one transmitter corresponds to one receiver, but there are also multiple transmitters corresponding to one receiver. Therefore, the ultrasonic distance sensor can measure the return and return time of the ultrasonic wave to determine the distance of the object. This is how the ultrasonic distance sensor works. For the ultrasonic distance sensor, we recommend to use the Korean Hagisonic ultrasonic distance sensor module HG-C40U.   Figure 3. Ultrasonic distance sensor module HG-C40U   Ultrasonic distance sensor module has two optional transmission modes:   -  Free operation mode: when there is power supply, the sensor itself can send trigger and burst signals and it is usually for basic applications;   -  External trigger mode: the external system (controller or processor) controls trigger signals for advanced applications. These two modes are suitable for a variety of purposes.   In addition, the sensors also involve the choice of two input power supplies:   -  Low voltage (5V) for the processor circuit, the distance to the obstacle can be measured is 3.5m;   -  High voltage (12V) for the controller circuit, the distance to the obstacle can be measured is 5m. The data is transmitted by UART (universal asynchronous receiver-transmitter) with a resolution of less than 5mm. On the other hand, users can select different setting modes according to their own environment needs. Such as free-running / UART triggering / external trigger settings, etc.  At the same time, on the basis of baud rate of UART communication, the user can also decide whether to set up the circular buffer or not. The output signal uses high performance ASIC (application-specific integrated circuit) chip to ensure stable transmission and sensitive reception, and the communication between sensor and PC uses "interface board" (RS232, power regulator). The data show that the real received ultrasonic wave can be amplified in real time by using the monitor program on PC, the distance value can be output by UART (ASCII, mm), and then the detection signal can be converted into the rectangular TTL level signal (square wave) in real time. IV Conclusion Ultrasonic sensors are reliable, cost-effective and efficient solutions for distance sensing, level and obstacle detection. Once you understand how ultrasonic sensors work and which ultrasonic technology is most suitable rather than excellent, you can make more informed decisions about the correct sensor system for your application.   FAQ   1. What type of sensor is ultrasonic sensor? ultrasonic / level sensors measure the distance to the target by measuring the time between the emission and reception. An optical sensor has a transmitter and receiver, whereas an ultrasonic / level sensor uses a single ultrasonic element for both emission and reception.   2. How many types of ultrasonic sensors are there? four types. All together there are four types of ultrasonic sensors, classified by frequency and shape: the drip-proof type, high-frequency type, and open structure type (lead type and SMD type).   3. What is the range of ultrasonic sensor? For ultrasonic sensing, the most widely used range is 40 to 70 kHz. The frequency determines range and resolution; the lower frequencies produce the greatest sensing range. At 58 kHz, a commonly used frequency, the measurement resolution is one centimeter (cm), and range is up to 11 meters.   4. Can ultrasonic sensor detect human? Finally, ultrasonic sensors assist in detecting people for autonomous navigation of robots. Ultrasonic sensors can be used to set multiple tripwire distances to help navigate around people. Additionally, the high read rate allows you to quickly detect when a person may enter your robot's path.   5. Is ultrasonic sensor harmful? Occupational exposure to ultrasound in excess of 120 dB may lead to hearing loss. Exposure in excess of 155 dB may produce heating effects that are harmful to the human body, and it has been calculated that exposures above 180 dB may lead to death.   6. How do ultrasonic sensors work? Ultrasonic sensors work by emitting sound waves at a frequency too high for humans to hear. They then wait for the sound to be reflected back, calculating distance based on the time required. This is similar to how radar measures the time it takes a radio wave to return after hitting an object.   7. Why is ultrasonic sensor used? Ultrasonic sensors are used primarily as proximity sensors. They can be found in automobile self-parking technology and anti-collision safety systems. ... Ultrasonic sensors are also used as level sensors to detect, monitor, and regulate liquid levels in closed containers (such as vats in chemical factories).   8. Where are ultrasonic sensors used? Ultrasonic sensors have been used throughout many applications and industries. They are used within food and beverage to measure liquid level in bottles, they can be used within manufacturing for an automated process and control maximising efficiency on the factory floor.   9. Is ultrasonic sensor waterproof? Most ultrasonic distance sensors aren't waterproof which can be a problem if you need your project to withstand the elements outdoors. ... This sensor is suitable for outdoor applications such as car reversing sensors, security alarms, industrial inspection, etc.   10. Is ultrasonic sensor analog or digital? Usually, ultrasonic sensors are integrated with an Analog-to-Digital converter (ADC).   11. How do ultrasonic sensors measure distance? As the name indicates, ultrasonic sensors measure distance by using ultrasonic waves. The sensor head emits an ultrasonic wave and receives the wave reflected back from the target. Ultrasonic Sensors measure the distance to the target by measuring the time between the emission and reception.   12. How accurate is the ultrasonic sensor? The more accurate ultrasonic sensors can achieve 0.1 – 0.2% of the detected range under perfectly controlled conditions, and most good ultrasonic sensors can generally achieve between 1% and 3% accuracy.   13. What can ultrasonic sensors detect? Ultrasonic sensors can measure the distance to a wide range of objects regardless of shape, color or surface texture. They are also able to measure an approaching or receding object.   14. Are ultrasonic sensors affected by smoke? Ultrasonic sensors are superior to infrared sensors because they aren't affected by smoke or black materials, however, soft materials which don't reflect the sonar (ultrasonic) waves very well may cause issues.   15. Which is better ultrasonic or IR sensor? Ultrasonic sensors work using sound waves, detecting obstacles is not affected by as many factors. If reliability is an important factor in your sensor selection, ultrasonic sensors are more reliable than IR sensors. If you're willing to compromise reliability for cost, infrared sensors are ideal for your application.  

Warm hint: The word in this article is about 1000 words and reading time is about 5 minutes     This article introduces you some basic and simple rectifiers and their waveforms and working principle and more.   Catalog I. Introduction 1.1 Composition of DC Stabilized Power Supply 1.2 Basic Concepts II. Detail & Analysis 2.1 Half-Wave Rectifier 2.2 Full-Wave Rectifier 2.3 Bridge Rectifier 2.4 Capacitor Filter 2.5 Inductor Filter FAQ   I. Introduction   1.1 Composition of DC Stabilized Power Supply FIG.1   2. Basic Concepts   AC voltage (current): both amplitude and direction change periodically with time. FIG.2 Sinusoidal Voltage/Current Waveform (AC): alternating voltage/current whose amplitude and direction both change sinusoidally and periodically over time. It is often called AC for short.   Effective value: the direct voltage/current thermally equivalent to the alternating voltage/current is called the effective value of the AC (voltage or current).   Peak value: the maximum instantaneous value of AC (voltage or current).   Frequency: the number of times that AC (voltage or current) changes periodically every second.   Direct voltage/current: voltage/current whose value and direction do not change with time. In fact, the direction can be guaranteed not to change over time, but it is impossible for the value to act the same way all the time. So the alternating voltage/current whose direction is always the same and the numerical value changes over time can be explained as a superposition of DC (voltage or current) and AC (voltage or current) whose amplitude and direction change with time. II. Detail & Analysis   2.1 Half-Wave Rectifier The circuit diagram and the waveforms of half-wave rectifier are shown as the following figures. FIG.3 Average value: FIG.4 Effective value: Turns ratio: According to this, the required output voltage can be obtained by selecting the appropriate N1 and N2.   2.2 Full-Wave Rectifier The following figures are the circuit diagram and the waveform of full-wave rectifier. FIG.5 FIG.6 Average value: Effective value: Transformer: The number of turns of the primary winding is N1, and the number of turns of the secondary winding is N2a=N2b. Turns ratio: According to this, the required output voltage can be obtained by selecting the appropriate N1, N2a and N2b.   2.3 Bridge Rectifier The following figures are the circuit diagram and the waveform of bridge rectifier. FIG.7 FIG.8 Average value: Effective value: Transformer: The number of turns of the primary winding is N1, and the number of turns of the secondary winding is N2. Turns ratio: According to this, the required output voltage can be obtained by selecting the appropriate N1 and N2.   2.4 Capacitor Filter The following figures are the circuit diagram and the waveform of capacitor filter. FIG.9 Filtering principles: a~b: u2=uc=u0, the capacitor C is charged in a sine wave; b~c: u2≈uc = u0, the capacitor C discharges in an exponential curve, but the sinusoidal waves of u2 basically coincide. c~d: u2＜uc=u0, the capacitor C continues to discharge exponentially, and u2 to drop in a sine wave. FIG.10 The effects of RL and C on filtering are shown in the following figure. FIG.11 （1）Basic knowledge of capacitors   Definition:   Basic equations:  Energy equation:  FIG.12 （2）Charging the capacitor Where  It is a time constant, and the initial values of current is  FIG.13 （3）Discharging the capacitor Where It is a time constant, and the initial values of current is FIG.14 （4）Output voltage   After the filtered voltage waveform is linearized, the following approximate waveform is obtained: FIG.15 Based on the relationship of similar triangles, there is And  So we have When There is  FIG.16 Rectifier diode: The current and the conduction angle of the rectifier diode in the capacitor filter circuit are shown in the following figure: FIG.17 Where iD is the current of the rectifier diode when the current is switched on, and io is the current in the load.   2.5 Inductor Filter In heavy current load, if a filter capacitor is used, the capacitance of it and the inrush current of the rectifier both will be very large. But if an industrial-frequency inductor is in series with it for filtering after the rectification, then we can solve these problems very well. The following figure is the circuit diagram of the inductor filter. FIG.18 From the energy point of view, the effects of the inductive filter and the capacitive filter are the same. Therefore, the volt-ampere characteristics of the inductive filter is similar to that of the capacitive filter, see the figure below. FIG.19 The quantitative analysis of inductive filter is more complex, so we should do it with the help of the previous analyzed results for the capacitive filter. If  then we have When the inductor filter is used, the waveform of the terminal voltage and current of the inductor and the conduction angle of the rectifier diode are shown in the following figure. Because the rectifier diode is connected in series with an inductor, the conduction angle of it can reach 180°. Therefore, in situations where harmonics are not demanding, we can use inductive filter to meet PFC (Power Factor Correction) requirements. FIG.20 （1）Basic concepts of inductor FIG.21 Definition:  Basic equations: Energy equation: （2）When inductor stores energy   After the switch is closed, here we have According to the initial conditions, the solution is Where It is a time constant, and the initial voltage is FIG.22 （3）When inductor releases energy FIG.23 After the switch is closed, here we have According to the initial conditions, here we have: Where It is a time constant, and the initial voltage is FIG.24 How Amplifiers Work: Rectifiers and Filter Capacitors   FAQ   1. What are the types of rectifiers? The Different Types of Rectifiers: a. Single Phase & Three Phase Rectifiers. b. Half Wave & Full Wave Rectifiers. c. Bridge Rectifiers. d. Uncontrolled & Controlled Rectifiers.   2. What is Rectifier used for? A rectifier is an electrical device that converts alternating current (AC), which periodically reverses direction, to direct current (DC).   3. What is an example of rectifier? Thyristors are commonly used in place of diodes to create a circuit that can regulate the output voltage. Many devices that provide direct current actually generate three-phase AC. For example, an automobile alternator contains six diodes, which function as a full-wave rectifier for battery charging.   4. Is Zener diode a rectifier? A Zener diode is a special type of rectifying diode that can handle breakdown due to reverse breakdown voltage without failing completely. Here we will discuss the concept of using diodes to regulate voltage drop and how the Zener diode operates in reverse-bias mode to regulate voltage in a circuit.   5. What is the working principle of rectifier? Principle: A junction diode offers a low resistance to current in one direction(when forward biased) and a high resistance in the other direction(when reverse biased). Thus, the diode acts as a rectifier.   6. Why zener diode is not used in Rectifier? No, we don't prefer to use a Zener Diode in a rectifier circuit because for a rectifier circuit a high maximum peak inverse voltage is required. Unlike the normal p-n junction diode, a Zener diode has a low peak inverse voltage. This is an undesirable property for the rectifier circuit.   7. What are the signs of a bad Rectifier? You'll note signs right away like poor starts, fluctuating meter readings, and dimmed headlights. around 13 volts, the bike will start to drain the battery. When this happens, it's only a matter of time before the engine stops completely.   8. What causes a rectifier to fail? Ground connections are important for good voltage, and if there is faulty voltage, the regulator rectifier can run hot. Bad grounding, corroded battery connection and poor or loose battery connections will cause faulty voltage.   9. Will a bad rectifier cause no spark? A bad regulator/ rectifier will result in a dead battery, and once the battery is competely dead you will not get a spark.   10. What is the difference between diode and rectifier? A diode is a switching device, while a rectifier is generally used for the conversion of AC voltage to DC voltage. ... A diode allows the flow of current only when it is forward biased. The diode blocks the reverse flow of current. A rectifier, on the other hand, consists of a transformer, a diode, and a filter circuit.   You May Also Like: Transformers Basics: Construction, Types, Materials and Design Characteristics and Functions of Diodes Switched Mode Power Supply Tutorial: Principles & Functions of SMPS Circuits

Warm hints: The word in this article is about 3000 words and  reading time is about 10 minutes.   The transformer is a static electrical device, mainly composed of an iron core (or magnetic core) and coil. The coils have two or more windings, of which the ones connected to the power are called primary coils, and the rest are called secondary coils. Transformers are widely used in electrical equipment such as household appliances, electronic equipment, switching power supply, and so on. Circuit symbols commonly used T as the beginning of the number, for example, T01, T201.    This article covers the construction, functions, classification, and design of transformers and materials used for building magnetic cores in transformers.     Catalogs   I. The Composition of Transformer II. The Construction and Functions of Transformer III. High-frequency Transformer Design Program 3.1 Program structure 3.2 Matters needing attention when doing the core material   selection 3.3 Ferrite magnetic material requirements IV. Power Transformer Classification V. Principle and method of Transformer Design FAQ   I. The Composition of Transformer 1）The primary side 2）The secondary side 3）Magnetizing inductance 4）Leakage inductance 5）Open-circuit or short-circuit measurement of the primary side leads to the  Magnetic inductance and the leakage inductance turns ratio respectively:  K=Np/Ns=V1/V2   II. The Construction and Functions of Transformer 1) Electrical isolation 2) Energy storage 3) Voltage change for same power input.   III. High-frequency Transformer Design Program   3.1 Program structure (1) Core material (2) Core structure (3) Core parameters (4) Transformer Winding Parameter (5) package assembly (6) Temperature rise check   (1) Core material Soft magnetic ferrite is widely used in switching power supply because of its own characteristics. It has the advantages of high resistivity, low AC eddy current losses, low price, and easy to be machined into magnetic cores of various shapes. The disadvantages are low working magnetic flux density, low permeability, large magnetostriction, and high sensitivity to temperature changes. Which kind of soft magnetic ferrite material can satisfy the design requirement of a high-frequency transformer more fully, only when it is carefully considered and the transformer design can reach the high-cost performance.   (2) Magnetic core structure The factors considered in the selection of magnetic core structure are as follows: reducing magnetic leakage and leakage inductance, increasing the area of coil heat dissipation, which is beneficial for shielding and makes it easier to wind coils, more convenient to wire for assembly and so on.   The magnetic leakage and leakage inductance are directly related to the magnetic core structure . If the magnetic core does not need air gap, then a enclosed ring-like or square type magnetic core may be used as far as possible.   (3) Magnetic core parameters In the design of core parameters, special attention should be paid to the operating flux density only limited by the magnetization curve, but also by the losses, and also related to the working mode of power transmission. When the flux changes in one direction, there is ΔB=Bs-Br, which is not only limited by the saturation flux density but also mainly by the losses (Losses cause temperature rise, which in turn affects magnetic flux density). The operating flux density Bm=0.6～0.7ΔB.   An air gap can decrease Br and therefore increase the flux density ΔB. The exciting current can be increased after using an air gap opening, but the core volume can be decreased either. For the two-way operation of magnetic flux, the flux density ΔB is twice the maximum operating flux density Bm, that is ΔB=2Bm. In bidirectional operating mode, we should pay attention to the problem of transformer DC magnetic bias due to the inequality of volt-second areas of positive and negative excitation variation, which is caused by different reasons. A small air gap will be needed in the core, or a DC capacitor can also be added to the circuit design.   Magnetic properties of ferromagnetic materials Magnetic hysteresis loops of the core   (4) Coil parameters Coil parameters include: turns, conductor section (diameter), wire form, winding arrangement and insulation. The conductor section (diameter) depends on the current density of winding, using taking 2.5～4A/mm2. When doing some choosing of section conductor diameter don’t forget to take the skin effect into consideration and do regulations necessary after some temperature rise tests of the transformer.   General winding arrangements: the primary winding is close to the core and the secondary windings & feedback windings are gradually arranged outward. The following two winding arrangements are recommended:   1) If the voltage of the original windings is high (for example, 220V) and meanwhile that of the secondary windings is low, a more appropriate arrangement is the secondary winding being close to the core, and then goes the feedback winding, the original winding is arranged on the outermost ends, which is advantageous to the insulation arrangement of the original winding to the core;   2) If we want to increase the coupling between the primary and secondary windings, we can make half of the original windings be close to the core, then goes the feedback winding and secondary winding, and the other half of the original winding being the outermost ends, which is an arrangement advantageous to reduce the leakage inductance.   (5) Assembly structure The assembly structure of high-frequency power transformers are divided into horizontal and vertical types. If you'd like to select the planar core, sheet magnetic core and thin-film magnetic core, then a horizontal-type assembly would do you good.   (6) Temperature rise tests The temperature rise tests can be carried out by calculation and sample test. The temperature rise is lower than the allowable temperature rise above 15 degrees, the current density and the cross-section of the wire are appropriately increased. Appropriately increase the current density and decrease the cross-section of the wire, and do the exact opposite if temperature rise exceeds the allowable value, such as increasing the diameter or enlarging the core if necessary, to increase the area of coil heat dissipation.       3.2 Matters needing attention when doing the core material selection (1) Soft ferrite, due to its low price, good adaptability, and high performance at high frequency, has been widely used in switching power supply.   (2) Soft ferrite is commonly divided into two series: Mn-Zn ferrite and Ni-Zn ferrite. The Mn-Zn ferrite is composed of Fe2O3，MnCO3，ZnO and so on, which is widely used in all kinds of filters, inductors, transformers, and so on below 1MHz. The Ni-Zn ferrite is composed of Fe2O3，NiO，ZnO and so on, which is widely used in all kinds of adjustable inductor windings, anti-jamming magnetic beads, antenna matching devices, and so on above 1MHz.    (3) Mn-Zn ferrite is the most widely used core in switching power supply, and the selection of its material depends on its use. The core for the input filter part of the power supply is mostly high-conductivity magnetic core, and its material number mostly is R4K～R10K, that is, the ferrite core of relative permeability is about 4000~10000, but the main transformer and output filter are magnetic materials with high saturation flux density, where Bs is about 0.5T (5000GS).     3.3 Ferrite magnetic material requirements   Ferrite magnetic materials for switching power supply shall meet the following requirements:   (1) High saturation flux density Bs and low residual flux density Br   The residual flux density Bs has a certain influence on the transformer and winding results. Theoretically speaking, the number of turns of transformer windings can be reduced and the copper loss can be reduced because of the high Bs. In practical applications, there are different types of circuits of high-frequency converters in switching power supply.    For transformers, their operations can be divided into two categories:   1) Bipolar: The circuit topologies include half-bridge, full-bridge, push-pull, etc. In the primary winding of the transformer, the excitation current is equal and opposite in direction during the positive and negative half-cycles. Therefore, the magnetic flux changes in the magnetic core of the transformer are symmetrically moved up and down. The maximum variation range of B is  ΔB=2Bm, and the DC component of the magnetic core is basically canceling out.   2) Unipolar: The circuit topologies include single-ended forward, single-ended flyback, etc. The transformer primary winding adds a unidirectional square wave pulse voltage in one cycle (this is the case for single-ended flyback). The magnetic flux density varies from the maximum Bm to the residual flux density Br in the unidirectional-excitation transformer core. If we decrease the Br and increase the saturation flux density Bs, then the △B will be increased, and the turns and copper loss will also be reduced.   (2) Transformers or inductors are divided into three categories according to their topology:   1) An DC-filter inductor's magnetic core only works in one quadrant, the topologies of this operating state including Boost, Buck, buck/boost inductors, single end flyback converter transformer, forward and all push-pull converters and output filter inductors.   2) The core of the transformer in the forward converter also works in one quadrant, but the transformer needs to magnetic reset.   3) The core of the transformer with push-pull topology is in bidirectional alternating magnetization. These kinds of converters include push-pull, half-bridge and full-bridge converters, AC filter inductors, and so on.   (3) Low power loss at high frequency   The power loss of ferrite not only affects the power output efficiency but also leads to the heating of the magnetic core and waveform distortion.   The heating problem of the transformer is very common in practical applications, which is mainly caused by copper loss and core loss of the transformer. If the selected Bm is too low and the turns of winding are too many, it will cause the winding to heat up and transfer the heat to the core at the same time, and vice versa.   When selecting the ferrite material, we must make the power loss change with temperature characterized by a negative temperature coefficient. This is because if the core loss is the main heating, making the transformer temperature rise up, which then will lead to a further increase of core losses, thus it will form a vicious circle and eventually make the power tube, transformer, and other components burn down. Therefore, in the researches of power ferrite at home and abroad, we must solve the problem of negative temperature coefficient of magnetic material power loss itself, which is also a remarkable feature of magnetic materials having met the requirements for power supply applications, such as PC40 from Japanese company TDK and R2KB from China manufacturers and so on.   (4) A relatively moderate permeability   (5) How we choose the appropriate relative permeability?    Well, this depends on the switching frequency of your actual circuit, mostly 2000, meanwhile its applicable frequency must be below 300kHz, and sometimes can be a little higher, but the maximum will not be higher than 500 kHz.   (6) A relatively high Curie temperature   Curie temperature is the temperature at which a magnetic material loses its magnetic properties, generally above 200 ℃. However, the actual operating temperature of the transformer should not be higher than 80℃, at which the saturation flux density Bs will drop to 70% of that at the normal temperature when the temperature is above 100℃. That is, the saturation flux density of the core will drop more seriously when the operating temperature is too high. Furthermore, when the temperature is higher than 100℃, the power loss has been experiencing a positive temperature coefficient, which will lead to a vicious circle. For R2KB2 materials, the temperature corresponding to the allowable power consumption has reached 110℃ and the Curie temperature is up to 240℃, which meets the requirements of high-temperature use.     IV. Power Transformer Classification Power transformers are divided into three categories according to their topology: (1) Flyback transformers; (2) Forward transformers; (3) Push-pull transformers (full-bridge/half-bridge converters)   The appropriate topologies for various core structures are shown in the following table:   Core structureTypes of converter circuitFlybackForwardPush-pullE cores++0Planar E Cores-+0EFD Cores-++ETD Cores0++ER Cores0++U Cores+00RM Cores0+0EP Cores-+0P Cores-+0Ring Cores-++    "+"=fit; "0"=normal; "-"=unfit Summary of High frequency transformer core.XLS V. Principle and Method of Transformer Design   (1) There are two main ways to design transformer: Area Product (AP) Method AP: The product of core effective cross section Ae and Area of window Aw PT-The calculation power of the transformer Ae-Core effective cross section Aw- Area of window Ko-Core window utilization coefficient, typically 0.4 Kf-Waveform coefficient, usually square wave being 4 and sine wave being 4.44 Bw-The operating magnetic intensity of core FS-Switching frequency Kj-Current density coefficient, usually 395A/cm2 X-Core structure coefficient     (2) According to the area product (AP) method, the general steps of designing transformer are as follows: 1. Select the core material to calculate the apparent power of the transformer; 2. Determine the core cross section AP and select the core size according to AP value; 3. Calculation of the primary side inductance and the number of turns; 4. Calculation of the length of air gap; 5. Calculating the line diameter according to the current density and the secondary side RMS current. 6. Determine whether the copper loss and iron loss meet the requirements (eg allowable loss and temperature rise)   Selecting the flyback topology, the basic parameters of the power supply are as follows: Input voltage: 175-264 VAC Output voltage: 21V Output current: 3A Output power P0=63W Frequency set at 60Khz Duty cycle set at 0.45 initially   1) Select the core material to determine the apparent power PT of the transformer   and select the PC40 material here considering the cost factor and check the PC40 data to get Bs=0.39T, Br=0.06T. In order to prevent the core from becoming saturated instantly, a certain margin is reserved. Let Bm= ΔBmax*0.6=0.198T, and pick up the 0.2T. For flyback topology, the transformer apparent power PT is:   2) Calculating AP values with Excel tables   Where, J is the current density, usually 395A/cm2, and Ku is the effective use coefficient of copper window, usually 0.2～0.4, now we set Ku as 0.4.    Based on the figure above, we select the core EE3528 due to its being greater than the calculated AP value, with the following parameters: Ae: 84.8mm2 AP：1.3398cm4 Wa：158mm2 AL：2600nH/H2 In order to adapt to the abrupt load current, the power supply is designed in critical mode and the critical current is: I0B=0.8×I0=2.4A     3) Calculation of the primary side inductance and the number of turns (A) Minimum input voltage Vimin=ViACmin*1.2=210V (B) Turns ratio n=[Vimin/(V0+Vf)]*[Dmax/(1-Dmax)] n=[210V/(21V+1V)*[0.45/(1-0.45)] n=7.8 (C) Peak secondary current ^IsB=2*IoB/(1-Dmax) ^IsB=2*2.4A/(1-0.45) ^IsB=8.72A (D) Secondary inductance Ls=(V0+Vf)*(1-Dmax)*[1/(Fs*1000)]/^IsB*1000000 Ls=(21V+1V)*(1-0.45)*[1/(60Khz*1000)]/8.72A*1000000 Ls=23.58Uh (E) Primary inductance Lp=n*n*Ls Lp=7.8*7.8*23.58uH Lp=1434uH   Primary and secondary peak currents (F) Calculation of peak secondary current in continuous mode ^Isp=Io/(1-Dmax)+(^IsB/2) ^Isp=3A/(1-0.45)+(8.72A/2) ^Isp=9.81A (G) Calculation of peak primary current in continuous mode ^Ipp=^Isp/n ^Ipp=9.8A/7.8 ^Ipp=1.257A (H) Calculating the turns of the primary and secondary auxiliary windings a) Number of turns in the primary side Np=Lp*^Ipp/(^B*Ae) Np=1434uH*1.257A/(0.2*84.8) Np=106.28T After rounding: Np=106T b) Number of turns in the secondary side Ns=Np/n Ns=106T/7.8 Ns=13.58T After rounding: Ns=14T c) Number of feedback turns Nv=(Vcc+Vf)/[(V0+Vf)/Ns] Nv=(14.5V+1V)/[(21V+1V)/14T] Nv=9.87T After rounding: Nv=10T   To avoid core saturation, an appropriate air gap is added to the magnetic loop, the calculation go as follows: The number of turns may need to be corrected by the air-gap flux edge effect.   4) There are two ways to calculate the wire diameters of the primary, secondary and auxiliary windings: Effective current of original side diameter: Iprms=Po/^n/Vimin Iprms=63W/0.8/210V Iprms=0.375A (A) Calculating the area of bare wire (B) Calculating the wire diameter (current density J to take 4A/mm2) Using two 0.18mm-diameter wires wound around or AWG #28 a single strand The secondary diameter: Use four wires with a diameter of 0.25mm (AWG #31) and wind around. Calculation of Skin Depth: The diameter of multi-strand parallel winding must be less than or equal to dwH, in single wire winding, however, if the diameter exceeds the dWH value,  the multi-strand wire winding should be taken into account.   5) Calculation of copper loss Pcu and iron loss Pfe (total transformer loss Ploss) (A) Calculating the loss of primary and secondary windings.  Where, MLT is the average turn length of magnetic core (B) Calculating the allowable total loss Ploss and allowable iron loss at efficiency η (C) According to the loss curve of iron core, the actual loss (iron loss per unit weight and actual iron loss) is obtained by: The Ploss is the loss of the whole circuit, including diode/MOSFET losses and other losses, the actual losses Pfe must be much smaller than the calculated one, so here is only for reference. (D) Calculating the loss per unit area by Φ=Ploss/As If the temperature rise caused by Φ is less than 25 degrees, then the design is wonderful.   6) Calculating the BW The working flux density BW should be below Bs-Br within the design specifications, that is Bw<Bs-Br, to avoid saturation of the core.   FAQ   1. What is the use of transformer? Transformers are employed for widely varying purposes; e.g., to reduce the voltage of conventional power circuits to operate low-voltage devices, such as doorbells and toy electric trains, and to raise the voltage from electric generators so that electric power can be transmitted over long distances.   2. What are the 3 types of transformers? There are three primary types of voltage transformers (VT): electromagnetic, capacitor, and optical.   3. What is the basic principle of transformer? A transformer consists of two electrically isolated coils and operates on Faraday's principal of “mutual induction”, in which an EMF is induced in the transformers secondary coil by the magnetic flux generated by the voltages and currents flowing in the primary coil winding.   4. Does a transformer convert AC to DC? A transformer is built to transfer the energy from one circuit into another circuit by way of magnetic coupling. ... An alternating current creates a magnetic flux in the core on its way through the first winding, inducing the voltage in the others. It can convert high and low voltages, it cannot convert AC to DC.   5. What are the main parts of transformer? There are three basic parts of a transformer: a. an iron core which serves as a magnetic conductor, b. a primary winding or coil of wire and. c. a secondary winding or coil of wire.   6. What are the classification of transformer? Depending upon the type of construction used, the transformers are classified into two categories viz.: (i) Core type, and (ii) Shell type. Depending upon the type of service, in the field of power system, they are classified as: (i) Power transformers, and (ii) Distribution transformers.   7. Can a transformer work on DC? As mentioned before, transformers do not allow DC input to flow through. This is known as DC isolation. This is because a change in current cannot be generated by DC; meaning that there is no changing magnetic field to induce a voltage across the secondary component.   8. How do you convert a transformer? This conversion is made by winding two separate conductors around a common iron core. Applying an alternating voltage to the primary conductor produces current which sets up a magnetic field around itself. This is known as mutual inductance.   9. What are two components of no load current in transformer? The no-load current of a transformer consists of two components: The Magnetization Current iM is the current required to produce the flux in the transformer core. The Core-loss Current ih+e is the current required to make up for hysteresis and eddy current losses.   10. Which type of transformer core is most efficient? SHELL CORE. The most popular and efficient transformer core is the SHELL CORE, as illustrated in figure (4). As shown, each layer of the core consists of E- and I-shaped sections of metal. These sections are butted together to form the laminations.   You May Also Like: Analysis of Calculation Theory for Transformer Temperature Rise Some suggestions about protecting transformers Learn Some Basic Knowledge about Capacitor Voltage Transformer      

Warm hints: The word in this article is about 3000 words and  reading time is about 10 minutes.SummaryFull bridge push-pull bi-directional DC/DC converters are mostly modeled by state space averaging method with the complex modeling process. Taking the isolated form push-pull bi-directional DC/DC converter as the research object, this article adopted the pulse-width modulation switch model method to obtain the equivalent circuit model of this converter. Based on this model, this article constructed a closedloop control system of the converter under different working modes, carried out the design and verification of voltage control loop and realized the constant voltage charge-discharge control strategy. The experimental and simulation results verify the correctness of the conclusion. CoreFull bridge push-pullPurposeTo obtain the equivalent circuit model of the converterEnglish nameBidirectional DC/DC convertersCategoryElectromechanical deviceFunctionConverting a source of direct current (DC) from one voltage level to anotherFeatureAdopting the pulse-width modulation switch model method CatalogsCatalogs1. Foreword2.2 Modeling of bi-directional DC/DC converter4 Epilogue2. Principle and design2.3 Voltage Closed-loop Control and Simulation 2.1 The working principle of circuit3 Experimental result   Introduction1. ForewordBidirectional DC/DC converters have been widely applied in many fields such as electric vehicles and battery energy storage systems. Bidirectional DC/DC converters have different circuit topologies according to their applications.I have seen some examples of using Buck/Boost converter to realize the bi-directional flow of electric energy. Because there is no transformer in the converter, so the electrical isolation of the high and low voltage side can not be realized, and only a small voltage range has been allowed. In order to solve this problem, it is proposed to use isolation transformer in bidirectional full-bridge DC/DC transform circuit, but the converter uses too many switching devices and therefore causes too many power losses. The isolated full bridge push-pull bi-directional DC/DC converter has been widely used due to the advantages of both types of converters of itself.At present, the state space averaging method is used to deduce the small signal model of bidirectional DC/DC converter, which needs a large amount of mathematical derivations and calculations. In order to simplify the modeling process, the full-bridge push-pull bi-directional DC/DC converter is modeled by using PWM-switch modeling method. The transfer function between output voltage and duty cycle of the converter is obtained in two modes: boost mode and buck mode. In addition , the voltage closed loop control system is constructed based on the derived circuit model, and the voltage loop is designed and corrected by the compensation network , realizing the constant voltage control of the full-bridge push-pull bidirectional DC/DC converter.First step in developing feedback control for a dc-dc converter is modeling. Here, we model the buck converter in terms of average behavior. Detail2. Principle and design2.1 The working principle of circuitFigure 1 shows the topology of the main circuit of full bridge push-pull bi-directional DC/DC converter. ^The power switch tubes S1～S4  are arranged in the form of a full-bridge circuit;^the power switch tubes S5～S6 are arranged in the form of a push-pull circuit;^CHV is a parallel capacitor with HVDC busbar;^CLV is a parallel capacitor with LVDC busbar;^L is a  low-voltage-side energy storage filter inductor;^HV is high-voltage-side DC bus;^LV is a low-voltage-side DC bus.Figure 1 Main circuit of bidirectional DC/DC converterFigure 2 and 3 respectively give the schematic diagrams of the PWM driving waveform of the power switch tube working in boost and buck mode, and the schematic diagram of the voltage waveform of the primary and secondary sides of the transformer. The u12 shown in the diagram is the transformer primary-side voltage and the u34 is the transformer sub-side voltage.Figure 2 Waveforms of the  power switch tube working in boost modeFigure 3 Waveforms of the  power switch tube working in buck mode2.2 Modeling of bidirectional DC/DC converterThe basic idea of PWM-switch modeling method: the nonlinear part will be linearized by taking an average value of the voltage and the current of it in one switching period when it is a stable circuit, and therefore the nonlinear circuit will turn into a linear circuit. The push-pull bidirectional DC/DC converter working in the buck mode can be equivalent to the circuit shown in Fig. 4 (the circuit in the dashed box is meant to indicate the nonlinear circuit), which turns on during [0, DTs] and turns off during [DTs, Ts], where Ts is the switching cycle and D is the duty ratio of the full bridge push-pull bi-directional DC/DC converter turn on. In the mathematical expressions presented in this article, all the uppercase variables represent the steady-state values, and all the lowercase variables represent the instantaneous values.Figure 4 Conducting circuit in buck mode operationIn the equivalent circuit shown in figure 4, the voltage and current are averaged during a PWM switching cycle, among which idc is primary instantaneous current and iL is secondary instantaneous current of transformer; iC is instantaneous current of electric capacity CLV; ucp is the instantaneous voltage between nodes c and p; uap is the instantaneous voltage between nodes a and p; n is the transformation ratio.Assuming that the duty cycle is d=D, now add an AC small signal to its value attachment (where small angle brackets denote AC small signals and the other variables following are the same), the complete instantaneous value expression for duty cycle is as shown in formula 3:Then substituting equation 3 into the original yields equation 1 and 2, so we have:Neglecting the product term of AC small signal, and equation 4 and 5 of  AC small signal can be simplified as equation 6 and 7:The mathematical relations of voltage and current working in steady state (following yields equation 8 and 9) derived from original yields equation 1 and 2, along with equation 6 and 7 can be used to obtain equivalent circuit model of bidirectional DC/DC converter in Buck mode (see the two-port circuit shown in the dashed box of figure 5). The model is linear since the constraint equations describing the two-port circuit are all linear equations. It can be learned from the above modeling process that the linear model of the full bridge push-pull bidirectional DC/DC converter can be easily established by using the switching model modeling method, which has the advantages of less calculation and simple derivation. It can be learned from the above modeling process that the linear model of the full bridge push-pull bidirectional DC/DC converter can be easily established by using the PWM-switch modeling method, which has the advantages of less calculation and simple derivation.The equation 10 gives transfer function between the output voltage and duty cycle of low voltage side bus according to laws of KCL and KVL.Figure 5 gives the equivalent circuit of bidirectional DC/DC in Buck mode obtained from equation 10, among which UHV is the operating voltage of high voltage side bus in steady state, uLV is the instantaneous voltage of low voltage side bus, n is the transformer ratio, R is the load resistance of low-voltage-side DC bus, Uap/D can be regarded as controlled voltage source, and IL/n can be regarded as controlled current source.Figure 5 Small signal equivalent circuit in Buck mode operationThe transfer function between duty cycle and output voltage in Boost mode can be obtained by using the same analysis method as Buck mode, which has shown in equation 11. R1 is the load of high voltage side bus.2.3 Voltage Closed-loop Control and SimulationFigure 6 gives the block diagram of the closed loop control system of small signal circuit model of the full bridge push-pull bidirectional DC/DC converter in two different operating modes. Charge and discharge at constant voltage in two modes can be realized by voltage closed-loop control.What we can see from figure 6:Uref is the given voltage of high-voltage-side and low-voltage-side DC bus; Hv(s) is the transfer function of sampling; Gm(s) is the transfer function of PWM; Gcv(s) is the transfer function of PI of voltage control loop; Gvd(s) is the transfer function of voltage versus duty cycle.Figure 6 Block diagram of voltage closed loop controlTo theoretically verify the correctness of mathematical model establishment and the feasibility of voltage control strategy, we use the PSIM 9.0 software tool for simulation and analysis in this article. Figures 7 and 8 have respectively shown the simulated waveforms in different operating modes. In Buck mode operation, the voltage of low voltage bus can be stabilized at 12V, so the constant voltage charging has been realized; and in Boost mode operation, the voltage of high voltage bus can be stabilized at 400V, so the constant voltage discharge has been realized, which theoretically verifies the correctness of mathematical model establishment and the feasibility of voltage control strategy. u12 and u34 are the voltages of the primary and secondary sides of the transformer respectively, uHV and uLV are voltages of high-voltage side and low-voltage side bus.Figure 7 Simulated voltage waveform in boost mode operationFigure 8 Simulated voltage waveform in buck mode operation Analysis3 Experimental resultIn order to verify the correctness of the small-signal circuit model and the feasibility of voltage feedback control, we built an experimental platform of full-bridge push-pull bi-directional DC/DC converter using TMS320F28035 as the core control chip.Table 1 gives the main circuit parameters of the bidirectional DC/DC converter based on the full bridge push-pull circuit structure.Table 1 Basic circuit parameters of converterFigure 9 gives the output voltage waveform of secondary voltage and low-voltage-side DC bus of transformer in buck mode operation when steady input voltage of high-voltage-side DC bus is 400V (provided by programmable DC power supply) and load resistance of low-voltage-side DC bus is 0.1Ω (provided by programmable DC electronic load). Here the output current of low-voltage-side DC bus iL is stable at about 120A, the output voltage uLV is about 12V, and the output power of low-voltage-side bus Po is about 1.5kW which meets the requirement of rated power designed, now we have realized  the constant-voltage charging of low-voltage-side DC bus.Figure 9 The voltage waveform in Buck mode operationFigure 10 gives the output voltage waveform of primary voltage and  high-voltage-side DC bus of transformer in boost mode operation when steady input voltage of low-voltage-side DC bus is 12V (provided by low-voltage DC power supply) and load resistance of high-voltage-side DC bus is 105Ω (provided by high voltage resistance load box). Here the output current of high-voltage-side DC bus iH is stable at about 3.7A, the output voltage of high-voltage-side DC bus uHV is stable at about 400V, and the output power of high-voltage-side bus Po is about 1.5kW which meets the requirement of rated power designed, until now we have realized  constant-voltage discharge of high-voltage-side DC bus.Due to the high level at the output, technical problems in the winding process for power transformers and the whole experimental device completing by manual welding, the rate of heat dissipation of power transformer appears to be somewhat low and the parasitic inductance and inductive coupling is also rocking the boat, and then we see the voltage waveform oscillation at zero crossing of transformer voltage in Boost mode moderation. However, under the condition of steady state parameters, this experimental platform can work normally and stably for a long time according to the design requirements and can meet the needs of practical applications.Figure 10 The voltage waveform in Boost mode operationFigure 11 is a schematic diagram of the hardware platform which is mainly composed of main circuit board, control circuit board and corresponding test equipment.Figure 11 physical photographs of experimental devices4 EpilogueAccording to the characteristics of bidirectional DC/DC converter applied in fields of battery and electric vehicle energy storage management, a bidirectional DC/DC converter based on full-bridge push-pull topology is obtained by comparing with different circuit topologies. Different from the traditional state-space average modeling, the method of PWM-switch modeling is used now to build small signal equivalent circuits in different mode operations, and the voltage loop has also been designed and corrected. The high-power constant voltage charging is realized in Buck mode moderation and the high-power constant voltage discharge is also realized in boost mode operation. Both modes can work normally and stably to meet the performance requirements of practical applications, which appear to be in high value at fields of battery and electric vehicle energy storage management. Book SuggestionSoft-Switching PWM Full-Bridge Converters: Topologies, Control, and DesignJun 23, 2014This book intends to describe systematically the soft-switching techniques for pulse-width modulation (PWM) full-bridge converters, including the topologies, control and design, and it reveals the relationship among the various topologies and PWM strategies previously proposed by other researchers. The book not only presents theoretical analysis, but also gives many detailed design examples of the converters.---by Xinbo RuanPower Electronics: Converters and RegulatorsOct 28, 2016This book is the result of the extensive experience the authors gained through their year-long occupation at the Faculty of Electrical Engineering at the University of Banja Luka. Starting at the fundamental basics of electrical engineering, the book guides the reader into this field and covers all the relevant types of converters and regulators. Understanding is enhanced by the given examples, exercises and solutions. Thus this book can be used as a textbook for students, for self-study or as a reference book for professionals.---by Branko L. Dokić and Branko BlanušaPulse-Width Modulated DC-DC Power ConvertersOct 26, 2015With improved end-of-chapter summaries of key concepts, review questions, problems and answers, biographies and case studies, this is an essential textbook for graduate and senior undergraduate students in electrical engineering. Its superior readability and clarity of explanations also makes it a key reference for practicing engineers and research scientists. Following the success of Pulse-Width Modulated DC-DC Power Converters this second edition has been thoroughly revised and expanded to cover the latest challenges and advances in the field.---by Marian K. Kazimierczuk Relevant information "Modeling and Control of Full Bridge Push-Pull Bi-Directional DC/DC Converter"About the article "Modeling and Control of Full Bridge Push-Pull Bi-Directional DC/DC Converter", If you have better ideas, don't hesitate to  write your thoughts in the following comment area. You also can find more articles about electronic semiconductor through Google search engine, or refer to the following related articles:How to Learn Analog Circuit DesignLook Forward to the Future of Semiconductor

Warm hints: The word in this article is about 3500 words and  reading time is about 15 minutes.   Based on the heat balance principle, the basic theory for the calculation of steady and transient temperature rise of transformer is discussed.   The calculation of transformer temperature rise is mainly used to make sure that the steady-state temperature rises produced by the transformer with rated load in long-term continuous operation will not exceed the limit specified in the standard or technical contract. In addition, the data of overload operation capacity of transformer running under various rated loads are also used to offer support to the measures taken to ensure safe overload operation of electrical systems.   However, from the author's current reading of recent info on transformer principles, design, and calculation theories available, it may be due to the limitation of space or different aspects of emphasis that they are always making an introduction to various practical formulas for transformer temperature rise calculation in a practical way. As to the involved thermal principle of calculating the transformer temperature rise is always a bit of an oversimplification I think, especially the thermal analyses demonstrating how heat energy be absorbed(or dissipate) and the temperature goes up(or goes down) during a heating process. In this article, therefore I would like to make some theoretical discussions to solve this problem and add some extra explanations needed.   Catalog   I. Brief Introduction II. Heating & Cooling Process 2.1 Heating process when the thermal power is constant 2.2 The cooling process in which the heated body is no   longer supplied with heat 2.3 Just as same as the situation of 2.1, but Τ≠0 when   t=0 III. Further Analysis of Some Formula 3.1 Mechanism of temperature-rising process of heated   body 3.2 Properties and applications of Τu in formula 2 3.3 Definition, function and derivation of the thermal   time constant Τ IV. Conclusion FAQ I. Brief Introduction   It is well known that heat is always transferred automatically from a high-temperature object to a low-temperature object. Heat can transfer (or move) in three ways: conduction, convection, and radiation, usually a combination of two or three of them may cause the transmission (also known as heat dissipation).   Before formally describing this section, I would like to quote two conclusions from laboratory research that are fundamental to thermal science:   1) the temperature rise of an object is directly proportional to the heat (heat) supplied by the outside world and inversely proportional to its own mass and Specific Heat Capacity.   2) the heat energy (calorific energy) that a heating object disperses into a cooler object(cooling medium) within a unit of time is directly proportional to the area of its radiating surface, the temperature difference, and the Heat Transfer Coefficient between the heating object and cooling medium.   Specific heat capacity: the ratio of the heat added to (or removed from) an object to the resulting temperature change per unit mass of material.   Heat transfer coefficient: when the temperature difference between the heating object and the cooling object is 1K, the heat from the unit dissipation surface area to the cooler object within a unit of time.   For the convenience of discussion, the heating object is referred to as the heated body in this paper, and the object which gets the heat released from the heated body is called the cooling body (or the cooling medium).   Take a dry transformer, for example, its winding and core are heating bodies, and the cooling body refers to the air around the transformer. For oil-immersed transformers, in addition to the winding and core known as heating bodies, the oil-filled in the transformer can also be called a heating one in relation to ambient air or cooling water. However, relative to the winding and core, oil is also called a cooling body(cooling medium).   Fig. 1 Transformers are found everywhere alternating current is used   II. Heating & Cooling Process   2.1 Heating process when the thermal power is constant Suppose that in the heating process (that is, the heat is still in a transition state, not reaches a stable state yet), the temperature rise by Τ relative to the cooling medium, the temperature rise increases dΤafter a tiny time unit dt.   The heat supplied by the outside during this dt period is a constant thermal power of Pdt(P. For windings in oil-immersed transformers, it refers to load loss; for oil, it refers to total loss). Let the heat supplied by the outside surroundings during this dt period be Pdt(P is the constant thermal power; for windings in oil-immersed transformer, P refers to load losses, and for oil, the total losses). Some of the Pdt is the heat absorbed when the temperature rise of the heated body increases by dΤ, and the other part is dispersed into the cooling medium.   In order to understand the nature of this physical phenomena in the heating process better, suppose the heated body is an isothermic one, therefore the density, specific heat capacity, and any other parameters being the same, including the heat dissipation capacity of each point on the surface.   According to the principle of thermal balance (it comes down to the law of energy conservation), the states of the heating process described above can be represented by the following equations:   Where   P——Constant value of thermal power c——Specific heat capacity of the heated body G——the mass of the heated body F——Heat dissipation surface area of the heated body k——Heat transfer coefficient  Τ——Temperature difference (or temperature rise) between the heated body and cooling body at a certain time   The first item on the right of Equation (1) indicates the heat energy absorbed by the heated body when it increases the temperature of dΤ; The second item indicates that the heat energy is dispersing to the cooling body while the heated body is storing heat.   When the temperature rise of the heating body does not go up, that is, when the temperature rise reaches a stable state, then there is dΤ=0 and Τ=Τu (Τu means the steady-state temperature rise).   At this point, from formula (1) there is:   According to the above analyses we can see: formula (1) is the mathematical expression of the heat balance principle under the transient state; formula (2) is the mathematical expression of the heat balance principle under steady-state.   From Formula (1) and Formula(2) we can get a first-order differential equation of Τ:   Where: From formula (4), the parameters on the right side of the equation are the physical parameters of the object itself, so Τ is a constant and has a dimension of time, so it is called the thermal time constant. In the physical sense, Τ is the ratio of the heat storage capacity of the heated body to the heat dissipation capacity per unit time of the heating system studied, which is an attribute of the heated body. Therefore formula (4) is considered to be the definition of Τ and the formula (4') is another expression for calculation.   To obtain the solution of formula (3) we let t=0 and Τ=0, then this is what we get:   Note that sometimes it is easier to express the formula (5) with temperature θ instead of temperature rise Τ, so it is reworded as follows: Where:   θ——The temperature of heated body at any given moment and there is θ-θа=Τ θа——The temperature of cooling body θu——The steady state temperature of the heated body that reaches a steady state Δθu——θu-θа=Τu   The rising curve in Fig. 1 shows the temperature rise of heated body changes with time t.   In order to visually see how the Τ changes with the temperature rise, Fig. 1  shows two curves with different Τ and same Τu. Fig. 2 Relation between temperature-rise(Τ)of heated body and time(t) As can be seen directly from formula (5), formula (5') and Fig. 1, the process of temperature rising of a heated body is characterized by the fact that it changes fast at the very start, then gradually slows down, and when the time t becomes equals to (4～6)Τ, it remains almost unchanged, at this point it can be assumed that Τ reaches Τu (theoretically t reaches ∞).   2.2 The cooling process in which the heated body is no longer supplied with heat   When the temperature rise of the heated reaches Τu and no heat will be emitted, the temperature rise begins to go down from Τu to zero, which we call the cooling process. At this point, its transient process equation can still be deduced by formula (1), in which you need only to let P be equal to zero.   Therefore the first-order differential equation of its temperature rise is as follows:   The solution is: All the symbols of parameter in the formula above are identical with those in formula (5), except that Τu is the initial value of temperature rise when t=0; when (4～6)Τ later, Τ≈0.   Why would we worry about Formula 6?    This is because the temperature rise of winding got at the end of the current transformer temperature rise test, is still the value of temperature rise calculated through measurements of the resistance value of the winding which will change with the temperature. The resistance value measurement is still carried out in the temperature rise test under a way of supply voltage been removed, thus the formula (6) should be used to calculate.     2.3 Just as same as the situation of 2.1, but Τ≠0 when t=0 When the heating body is supplied with constant heat power and Τ=Τ0 (≠0) when t=0 satisfied, the whole process of deduction of temperature rise calculation, with the exception of the situation of Τ=Τ0 when t = 0, is the same as 2.1, in other words, the formula of temperature rise can still be deduced from formula (5) as follows: Comparing this with the formula (5) we notice that there is a new second item occurs. Considering the physical meaning of the expression is not obvious enough, it is now rewritten (which will not change the result of the calculation) as: These two formulas above show a case that the transformer is suddenly asked to conduct a overload operation running beyond the steady load.   III. Further Analysis of Some Formula   3.1 Mechanism of temperature-rising process of heated body Formula (5) and Fig. 1 describe the rising process of heated body temperature from a mathematical point of view. This process is characterized by a rapid start and then a gradual slow down until it finally stops rising and reaches a stable temperature rise of Τu .   In this section, characteristics of heating and cooling mechanism in this process will be described from a physical point of view. So we divide the t into n small and equal time periods when t=Τu, that is Δt1=Δt2=……=Δtn=Δt (theoretically t=∞, but in practice, it is desirable to suppose that t=(4～6)T, considering the value required of Tu with a higher accuracy). Therefore, the derivative symbol "d" in this article is replaced with a increment sign "Δ".   Please note that the heat energy supplied by surroundings in each time period is equal to P·Δt (P is the constant thermal power).   Now let us take a look in the first time period Δt1. Since the temperature of heated body has already made be equal to the cooling body when t=0, that is Τ=0, according to the second item of formula (1), we can assume the heat energy emitted is also equal to 0 during the period of Δt1 until the end of present stage. Therefore, during the Δt1 period, the final increments of the temperature rise of the heated bodyΔΤ1 is determined by the total external heat energy (P·Δt). So the temperature rise at the end of first time period Δt1 is Τ1=ΔΤ.    According to the same analytical principle, we continue with the second time period Δt2. Since the initial temperature rise at the beginning of Δt2 is the that of the first time period Δt1, it can be included that Τ1=ΔΤ1. The heat emitted during Δt2 is no longer zero, but . At the end of the Δt2, the increment value of temperature rise of heated body ΔΤ2 is determined by , so there we have ΔΤ2<ΔΤ1 (That is, the increment of temperature rise in the second period is smaller than that in the first period).   Finally, at the end of the second time period Δt2, the temperature rise Τ2 is equal to ΔΤ1+ΔΤ2. The rest may be deduced by analogy, at the end of Δtn time period, the temperature rise is , also ΔΤn=0 has been illustrated at the same time.   According to the changes of temperature increment ΔΤn in each of time period above, there always are: ΔΤ1>ΔΤ2…>ΔΤn-1>ΔΤn (ΔΤn=0), therefore demonstrating the trend that all the heat absorbed by heated body in each time period gradually goes down from P·Δt absorbed in the time period of Δt1 to 0 absorbed in the time period of Δtn. The heat energy emitted in each of the corresponding time periods is gradually increased from 0 to (from the first time period Δt1 to the end of the NO.n time period Δtn). That also means the final temperature rise (steady temperature rise) is: After the temperature rise reaches the stable value of Τu, the heated body no longer absorbs external heat energy, which indicates that all the external heat energy has been dispersed to the cooling body.   3.2 Properties and applications of Τu in formula 2 Formula 2 is a theoretical formula derived from the heat balance principle for calculating the steady-state temperature rise of the heated body. It is difficult to calculate the temperature rise directly for complex heated bodies such as transformers.   Therefore, various manufacturers and scientific research institutions have respectively obtained many practical formulas, according to their own practical experience or scientific research results and the characteristics of the heated body structure and three different heat dissipation forms, including conduction, convection, and radiation.   Furthermore, a heated body such as a transformer having a complex structure does not always have the characteristics of the homogeneous isothermal body assumed in formula 2, and the heat-dissipation capability at each point on the surface is not equal, either.   Therefore, the steady-state temperature rise (Τu) calculated from formula 2 (including the relevant practical formula based on formula 2) on the whole indicates the average value of temperature rise at different points in the heat source.   The calculation of the maximum temperature rise (temperature) of an object at a "hot spot" of concern has so far could only be mainly estimated by experience and the use of temperature rise measurements in certain heaT tests (for example, confirming the difference between the maximum temperature rise and the average value or confirming the multiple values between them to estimate).   3.3 Definition, function and derivation of the thermal time constant Τ Formula 4 is the definition expression of thermal time constant. It is obtained in the derivation of formula 5 from formula 2 and formula 1. Therefore, it is possible to think that equation 4 is obtained under the admission that when t=∞ it has dΤ=0 and Τ=Τu, the latter of which is obtained under the boundary conditions of objective reality. Because the definition of "Τ" and some functions have been described in section 2.1, here i only do some additional analyses to formula 7 which shows applications of transformer temperature rise under a short-time overload operation. Fig. 3 What is a Transformer   The basic theory of transformer and working principle of transformer   Fig. 4 Large power transformers have their core and windings submerged in an oil bath to transfer heat and muffle noise, and also to displace moisture which would otherwise compromise the integrity of the winding insulation. Heat-dissipating "radiator" tubes on the outside of the transformer case provide a convective oil flow path to transfer heat from the transformer's core to ambient air.   First of all, according to the statistics of a large number of dry and oil-immersed power transformers with different capacities, which have been manufactured at home and abroad, the value of Τ is generally not less than 1h (for oil-immersed transformer, although the T of winding is quite low, about 5 min-20 mins, the T of oil is 1h～5h.    Noting that the oil actual temperature rise is generally not lower than the temperature difference between the winding and the oil and that the thermal time constant of the oil should therefore be considered to control the temperature rise of the winding during the overload operation, that is, the temperature difference between winding and ambient air or temperature of cooling water still plays a decisive role.    Although the Τu of the transformer will obviously exceed the temperature rise limit of rated-load operation, as long as the time t has been controlled within T, it can still make the actual temperature rise running in short-time overload not excess the temperature rise limit of short-time overload operation. These permissible limits, according to the standard of the load guide of the oil-immersed power transformer, is related to the operation type within nameplate capacity, namely, normal periodicity, long-term or short-term emergency, and generally higher than that of rated temperature rise.   It can be seen from this that the function of the thermal time constant T is relatively large, so it is necessary to pay close attention to its definition, various affecting factors, and derivation of its formula. However, I have seen some people added another boundary condition except dΤ=0 during the derivation of the expression of Τ: in extreme cases, the heat will not be transferred into the surrounding medium at all, which is also called "adiabatic condition". In this regard, I would like to put forward the following different views for discussion.   (1) In this article, the derivations of formula 4 and formula 5 have only used a "boundary condition" of dΤ=0 (Τ=Τu) when t=∞, so there is no need to add another adiabatic condition for derivation.   It is said that without heat dissipation, the time required to reach a stable temperature is called time constant (Τ), but that will only be true when the second item (dissipated heat) on the right of the equation meets a condition of , now that to reach a steady temperature Τ must be equal to Τu, which is at variance with objective reality of electric accessories including transformers.   Some might say that when people calculate the temperature of a transformer at a short-circuit current, don't they also use the formula obtained under the "adiabatic condition" to calculate the temperature of the transformer? Yes, but the case being considered is only the "short time" one, that is, the formula only applies when short-circuit durations never exceed 10s (actually 2s).    The time is very small compared with the thermal time constant of winding in oil-immersed power transformer (about 5min-20mins) and that of oil (about 1lh～5h). This is still true when compared with the thermal time constant of the windings of dry-type transformers (about or above 30min). In section 3.1 of this article, such a short duration makes it is possible to consider it as an adiabatic transient system. In a broad sense, if the heat energy emitted accounts for only a very small part of the heat supplied by the outside world during a same period, it can be roughly regarded as adiabatic process. At this point, it is precisely because of the recognition of  that it is in line with objective reality.   This proves that adiabatic conditions should not be used as the basis in the derivation of expression of Τ (formula 4) and that of transient temperature rise (formula 5).   (3) From the details of the derivation process in this article, I would like to say that the true expression of temperature rise of the heated body still has not been obtained yet in the end. Think about that, a task for you, my readers.   IV. Conclusion   (1) Starting from the principle of heat balance, this article expounds the model of the heating mechanism in the rising process of temperature rise of the heated body with concise mathematics and physical language.   (2) It is clearly pointed out in this paper that the steady temperature rise of the heated body can be calculated by using formula 2, and formula 5 and formula 7 are the formulas for calculating the temperature rise of the heated body during the transient process.   (3) It is pointed out that to obtain the expression of the transient temperature rise of the thermal time constant Τ and the heated body, the adiabatic condition should not be used for the process of derivation, which is not necessary either.   (4) Due to space constraints, this article has not covered the heat dissipation mechanism of heated body, but you readers can refer to other references about heat loss or transfer in Kynix and other sites.   FAQ   1. How hot is too hot for a power transformer? Transformers designed with high-temperature insulation systems can run safely at temps up to 200°F. But remember, a hot-running transformer is an angry transformer.    2. What is ambient temperature of transformer? The average ambient temperature for a transformer over a 24 hour period should not exceed 30 degrees Celsius. For instance, if the transformer ambient temperature was 40 deg. C for 12 hours, then the transformer must not exceed 20 deg.   3. Should doorbell transformer be hot? Transformers are always going to produce some heat. It's a part of the step-down process. It should only be warm to the touch, however.   4. What is maximum ambient temperature? In general, a safe range is between 60 and 75 degrees Fahrenheit or 15 and 25 degrees Celsius, although the cooler end of that range is better. Ambient temperatures above those ranges make it difficult for a computer's cooling system to keep it at a safe operating temperature.   5. What is the name of oil used in transformer? Mineral oil and Synthetic oil are the majorly used transformer oil. These are the petroleum products, like Naphthenic based transformer oil and Paraffinic based transformer oil. Naphthenic based transformer oils are known for their heat distribution, which is one of the main problems with transformer.   6. What will happen if the regulation of a transformer is poor? If the transformer supplies a very low lagging power factor, large secondary currents will flow resulting in poor voltage regulation due to greater voltage drops in the winding. ... Therefore positive regulation produces a voltage drop in the winding while a negative regulation produces a voltage rise in the winding.   7. What is high transformer temperature? Standard Ratings and Overload Capacity：Dry-type transformers are available in three standard temperature rises: 80C, 115C, or 150C. Liquid-filled transformers come in standard rises of 55C and 65C. These values are based on a maximum ambient temperature of 40C.   8. What is hot spot temperature in transformer? Modern transformers make use of thermally upgraded paper that has been chemically treated to improve the stability of cellulose structure. The rated hot spot temperature for this kind of paper is 110°C and it can be seen that an increase of 7°C will double the aging acceleration factor.   9. How much heat does a 75 kVA transformer give off? According to Cutler-Hammer, a 75-kVA, 150°F-rise, dry-type transformer has an efficiency of 97.2% at 1/4 load and 96.7% at full load. So, figure 3% loss at 75 kVA, which would represent 2,250 W.   10.What happens when transformer is overloaded? The weakening of the system will happen faster if the transformer is frequently overloaded. The net result of small, incremental increases in loading capacity over time is a weakened insulation system. Overloading causes overheating, and eventually thermal degradation that acts thrrough cracks in the insulation.   You May Also Like: Some suggestions about protecting transformers Learn Some Basic Knowledge about Capacitor Voltage Transformer