"What is the RMS Value of AC Circuits?" - "Ⅱ Determine RMS Value of AC Signals" -> "How to Determine the RMS Value of AC Signals" - "2.1 Sinusoidal Waveform" -> "How to Calculate RMS for a Sinusoidal Waveform" - "2.2 RMS Value Equation Steps" -> "What Are the Steps to Derive the RMS Value Equation?" - "2.3 RMS Mean on a Multimeter" -> "How Do Multimeters Measure RMS?" - "2.4 The Other Waveform" -> "How to Calculate RMS for Other Waveforms"- Missing or improvable schema types detected: Article, FAQPage, HowTo (for the equation steps).- Sections with vague/unsupported claims: "Nowsaday many electrical appliances, e.g. adjustable speed drives, tend to introduce harmonics..." (Updated with 2026 context on IEEE 519 and ASDs).- Estimated content freshness score: 4/10-->IntroductionSummary: The Root Mean Square (RMS) value of an alternating current (AC) signal represents the equivalent direct current (DC) voltage that produces the same heating effect across a resistor. This 2026 guide explains how to calculate RMS voltage for sinusoidal and non-sinusoidal waveforms, details the mathematical derivation steps, and explores why RMS is the standard measurement for AC power delivery.The RMS (Root Mean Square) value of any time-varying signal is directly related to the amount of heat being produced in a circuit or across a specific electrical element. If you need to know how to calculate the root mean square or RMS voltage of a sine wave given the peak voltage, this article provides the exact formulas. We will help you calculate the RMS value of AC circuits and provide the step-by-step process to derive the formula using basic math and calculus.What is RMS Value? | Easiest ExplanationCatalogIntroductionⅠ RMS Value of AC CircuitsⅡ Determine RMS Value of AC Signals2.1 Sinusoidal Waveform2.2 RMS Value Equation Steps2.3 RMS Mean on a Multimeter2.4 The Other WaveformWhat is the RMS Value of AC Circuits?The RMS value represents the effective direct current (DC) equivalent of a given alternating current (AC) signal that produces the exact same amount of heat and power across a specific circuit element. In electrical engineering, the physical meaning of RMS is the effective voltage value of an AC signal used to perform work. The work done in the process of converting electric current into other forms of energy is called electrical work, which depends on current, voltage, and energizing time.The higher the voltage applied to electrical appliances, the greater the energized current, and the longer the energizing time, the more work the current will do. The RMS value is also called the effective value because it is evaluated from the perspective of electrical work.The effective value of alternating current equals the DC voltage that obtains the same power consumption (heating) on an identical resistance.Because AC fluctuates, the correct result must be obtained after time averaging (integration).The instantaneous value of direct current cannot be used to replace the effective value.In statistical data analysis, the square of all values is summed, the mean value is calculated, and finally, the square root is taken to obtain the root mean square value.Figure 1. Peak to Peak VoltageIn physics, we often use the RMS value to analyze the noise of a power supply. When the voltage of the resistor is the AC voltage V(t), the power V²/R changes with time. If the energy consumed per cycle is divided by the number of cycles, this is the average power. Furthermore, if the power of a DC voltage applied to the same resistor is the same as the average power of the AC voltage, the DC equivalent voltage is the root-mean-square value of the AC voltage. How to Determine the RMS Value of AC SignalsLiterally, RMS means take the SUM, get the MEAN, and then take the ROOT; in that order, and you'll get the RMS value. As shown here, the general equation of RMS value has been derived, which can be used to find the RMS value of any time-varying signal. Just obey the rules.How to Calculate RMS for a Sinusoidal WaveformTo calculate the RMS voltage of a pure sinusoidal waveform, you multiply the peak voltage by 0.7071 (or divide by the square root of two). The following formulas apply strictly to PURE sine wave signals. In 2026, the widespread use of non-linear loads like adjustable speed drives (ASDs) and LED lighting frequently introduces harmonic distortion into electrical systems, meaning real-world signals are rarely pure sine waves.Calculate the effective value from the definition, that is, alternating current and direct current respectively pass through the same resistor. If the two consume the same electric energy (or produce the same Joule heat) in the same time, then the direct current value is called the effective value of the alternating current. The accumulation of signal power over time is the work done by the signal. The most primitive is derived for sine waves, but in fact, it is applicable to all waveforms.Use definite integral to calculate the work by the AC signal in the load R at one cycle. It is equal to the work done by a DC quantity (effective value) in one cycle of the load R.VR:  Instantaneous power of R: Average power of R: The power of the stable DC voltage Vdc is , if this power is the same as the average power of AC, thenWhere, Vdc is called the RMS value of the AC signal (Vrms)With Vrms, calculate the average power of the load resistor R:The RMS voltage calculation is ultimately used to give a measure of the average continuous power carrying capability of a signal. The instantaneous voltage values are squared (the V² term) which is then summed up (the integration) before converting back to voltage by the square root operation. Once the RMS voltage value is known, then you can make accurate estimates on true power delivery over time, independent of the signal's polarity.To put it simply, for example, a square wave signal with an amplitude of 100V and a duty cycle of 0.5, if calculated based on the average value, its voltage is only 50V, and calculated according to the root mean square value is 70.71V. Why is this? For example, there is a set of 100-volt battery packs, which will stop for 10 minutes after each power supply for 10 minutes, which means that the duty cycle is half. If this batteries set drives a 10Ω resistor, 10A of current and 1000W of power will be generated in 10 minutes, and the current and power will be zero during a power failure.Then in a period of 20 minutes, the average power is 500W, which is equivalent to the power generated by 70.71V charging a 10Ω resistor directly. The 50V DC voltage can only produce 250W of power when charges a 10Ω resistor. For motors and transformers, as long as the root mean square current does not exceed the rated current, they will not burn out even if they are overloaded within a certain period of time.What Are the Steps to Derive the RMS Value Equation?To calculate the RMS of a time-varying signal y(t), you must square the function, find its mean over one complete period, and take the square root. The exact mathematical steps are as follows:Square the waveform: Calculate the square of the instantaneous signal, y²(t).Find the mean: Take the average (integral) value of y²(t) over one complete period.Take the root: Calculate the square root of that average value to find the final RMS figure.Example:(1) a2 is a constant, so .(2) cos(ωt) is a complete cosine curve.(3)How Do Multimeters Measure RMS?Most standard multimeters measure the peak voltage of an AC signal and automatically multiply it by 0.707 to display the RMS value, assuming a pure sine wave. In daily life, ordinary voltmeters are scaled according to this effective value of the sine wave.Effective Value: The effective value of the sine wave is U = maximum Um × 0.707.Average Value: The average value is generally not used for power calculations; it refers to the average of each instantaneous value in the positive or negative half cycle. The average value of the sine wave is Up = Maximum Um × (2/π) = 0.637Um.Note that measuring alternating current with a standard voltmeter is strictly based on the sine wave effective value scale. If you are measuring a non-sine wave, such as a square or pulse wave, a standard meter reading is inaccurate. You must use a "True RMS" multimeter for distorted waveforms.How to Calculate RMS for Other WaveformsDifferent waveform shapes require different mathematical constants to calculate their RMS values accurately. Below are the derivations for half-sinusoidal and square waves.Waveform TypeRMS Voltage FormulaAverage Voltage FormulaPure Sine Wave0.707 × Peak0.637 × PeakHalf Sine Wave0.500 × Peak0.318 × PeakSquare Wave1.000 × Peak1.000 × Peak1) Half Sinusoidal Waveform2) Square WaveWhen we want to average the electrical signal, if the process is completed over the entire period or less, we need to give accuracy. For basic and symmetrical AC signals, regardless of frequency, peak value or period, averaging over a complete period always results in 0V. Therefore, it is more appropriate to average these signals during the half period.In short, average voltage tells you that your voltage fluctuates around some average value, while RMS voltage shows you how much is that fluctuation. In addition, Square of RMS could be understood as the average power on a resistor of 1 Ohm. ↪️Recommended RMS Value Calculation Tool: RMS Voltage Calculator – From Average Value, Peak & Peak to Peak Value Frequently Asked QuestionsWhat does RMS stand for in electronics?RMS stands for Root Mean Square. In electronics, it is a mathematical method used to determine the effective direct current (DC) equivalent of an alternating current (AC) signal. The RMS value represents the exact amount of AC voltage required to produce the same heating effect as a steady DC voltage.How do you calculate the RMS voltage of a sine wave?To calculate the RMS voltage of a pure sine wave, multiply the peak voltage by 0.7071 (which is one divided by the square root of two). For example, an AC signal with a peak voltage of 170V has an RMS voltage of approximately 120V.Why is RMS voltage used instead of average voltage?RMS voltage is used because the true average voltage of a complete AC sine wave cycle is zero, as the positive and negative halves cancel each other out. RMS squares the instantaneous values, making them all positive, which accurately reflects the signal's true power delivery capability.What is the difference between RMS and peak power?RMS power represents the continuous, average power an amplifier can output or a speaker can handle over a long period without distortion or damage. Peak power is the absolute maximum burst of power a device can handle for a fraction of a second. RMS is the more reliable metric.{ "@context": "https://schema.org", "@graph":[ { "@type": "Article", "headline": "RMS (Root Mean Square) Value of AC Circuits", "datePublished": "2021-07-02T15:10:32Z", "dateModified": "2026-03-14T15:51:00+08:00", "author": { "@type": "Organization", "name": "ApogeeWeb" }, "publisher": { "@type": "Organization", "name": "ApogeeWeb", "logo": { "@type": "ImageObject", "url": "https://www.apogeeweb.net/favicon.ico" } } }, { "@type": "FAQPage", "mainEntity":[ { "@type": "Question", "name": "What does RMS stand for in electronics?", "acceptedAnswer": { "@type": "Answer", "text": "RMS stands for Root Mean Square. In electronics, it is a mathematical method used to determine the effective direct current (DC) equivalent of an alternating current (AC) signal. 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IntroductionIn the lighting industry, people often have a misunderstanding about dimming LED lights. And the reality is that the application of LED light source dimming technology in engineering is often unsatisfactory. Why is this the case? Is the LED light source dimming technology immature, or the technology is difficult to master? So this article analyzes the LED dimmer to help readers to fully understand and master it.Dimming all kinds of LEDs?CatalogIntroductionⅠ Dimming LED Lights1.1 What is Dimming?1.2 LED Dimming Circuit Example1.3 LED Dimming Using SCRⅡ Dimming LED Using PWM2.1 LED Dimming Current2.2 LED PWM Dimmer2.3 LED PWM Dimming Advantages2.4 LED PWM Dimming Problems2.5 DALI PWM Dimmer IntroductionⅢ Main LED Dimmers ComparisonsⅠ Dimming LED Lights1.1 What is Dimming?LED dimmer switch is an electrical device that changes the luminous flux of the light source in the lighting device and adjusts the illuminance level. The purpose of the dimmer is to adjust the different brightness of the light. By reducing or increasing the rms voltage, the light output of different intensities produced by the average power lamp is promoted. Although variable voltage devices can be used for various purposes, this regulation is aimed at controlling lighting. Regarding the LED dimmer switch, we must first understand the volt-ampere characteristics of the LED. That is, the characteristics of the current flowing through the LED PN junction with voltage. Generally, the reverse characteristic curve changes steeply. When the voltage exceeds a certain threshold, the current will rise exponentially, thereby breaking down the LED PN junction. The forward voltage of the LED is also determined by its forward current. It can be seen from the figure that the change of the forward current will cause the corresponding change of the forward voltage, to be precise, the decrease of the forward current will also cause the decrease of the forward voltage. Therefore, when the current is lowered, the voltage of the LED will also decrease, which will change the relationship between the power supply voltage and the load voltage.Figure 1. Diode Volt-Ampere Characteristics CurveTherefore, from the volt-ampere characteristics of the LED, we can know that the dimming of the light source cannot be achieved simply by reducing the input voltage or input current of the LED. In addition, the waveform of the sine wave of the LED is different from the waveform of the incandescent lamp, so it cannot simply change its conduction angle to achieve the purpose of dimming.LED dimming methods can be divided into analog dimming and digital dimming. Analog dimming is to achieve dimming by changing the current in the LED loop. The power supply voltage remains unchanged, and the current in the loop is changed by changing the resistance value to achieve the effect of changing the brightness of the LED. Many analog dimming is an extension of this method. Its advantage is that the current can be continuous, but the range of adjustable current is often limited by hardware, and there are few adjustment gears. This method is not ideal for high-precision lighting equipment.Digital dimming, also known as PWM (Pulse Width Modulation) dimming, uses PWM waves to turn on and off the LED to change the on-time of the forward current to achieve the effect of brightness adjustment. This method is based on the fact that the human eye is not sensitive enough to the brightness flicker. If the frequency of brightness and darkness exceeds 100Hz, the average brightness is seen by the human eye, not the LED flickering. PWM adjusts the brightness by adjusting the ratio of light and dark time. In a PWM cycle, because the perceived brightness of human eyes to flicker is a cumulative process, that is, the brighter time accounts for the greater the proportion of the entire cycle. The longer the time, the brighter the human eye feels.1.2 LED Dimming Circuit ExampleFor example, in an LED lamp with an input of 24V, 8 1W high-power LEDs are connected in series. When the forward current is 350mA, the forward voltage of each LED is 3.3V, then 8 pieces in series is 26.4V, so a constant current source greater than 24V should be used. However, in order to dimming, the current is reduced to 100mA. At this time, the forward voltage is only 2.8V, and 8 pieces are connected in series to 22.4V. The load voltage becomes lower than the input voltage, so that a constant current source larger than 24V cannot work, and finally the LED will flicker.In this case, you may choose a step-down (wide voltage) constant current source, such as a 10V-30V constant current source for dimming. However, if this type is adjusted to a low forward voltage, the LED load current will also become very low. So the step-down ratio is very large, beyond the normal working range of constant current source, which will make LED unable to work and cause flicker. In addition, LED works at low brightness for a long time, which will reduce its efficiency and increase the temperature rise. Because the efficiency of the step-down constant current source is related to the voltage ratio, the larger the voltage drop ratio, the lower the efficiency. And greater power loss on the chip will damage the life of the constant current source and the LED light source.1.3 LED Dimming Using SCROrdinary incandescent lamps and halogen lamps usually use thyristors for dimming. Because they are pure resistance devices, and do not require the input voltage to be a sine wave. Their current waveform is always the same as the voltage waveform, no matter how the voltage waveform deviates from the sine wave, changing the effective value of the input voltage will dim the LED light .However, the adjustment of LED light source by thyristor dimming will cause unexpected problems, that is, the LC filter at the input will cause the thyristor to oscillate. This oscillation is indifferent to the incandescent lamp, human eyes can't see it at all because of thermal inertia. However, this dimming method will cause the driving power of LED produce audio noise and flicker. It will also destroy the waveform of the sine wave, thereby reducing its power factor value (usually lower than 0.5), which greatly reduces the system efficiency of the LED. Moreover, the thyristor dimming waveform increases the harmonic coefficient, and the non-sinusoidal waveform will cause serious electromagnetic interference on the line to pollute the power grid.Ⅱ Dimming LED Using PWM2.1 LED Dimming CurrentHere, you may ask: Lower voltage or current or thyristor dimming methods are not suitable for LED light source dimming, so what is the most suitable method?Is it an analog (0-10V) dimming method? May be not. Analog dimming faces a severe challenge, which is the output current accuracy. Almost every LED driver needs some kind of series resistance to distinguish the current, and the tolerance, offset and delay in the analog (0-10V) dimming drive cause a relatively fixed error, which will reduce the accuracy of the output current, and the final output current cannot be specified, controlled or guaranteed. Therefore, to ensure the dimming effect of the LED light source, one of the important rules is to reduce the output current error and improve the current accuracy in a closed loop system.2.2 LED PWM DimmerThe PWM dimming method can solve the above problems very well. Because diode characteristics, LED can realize fast switching, and its allowable switching speed can be as high as microseconds or more. Therefore, as long as the power supply is changed to a pulse constant current source, the brightness can be changed by PWM. This PWM dimming. This method is like a sluice that opens and closes in microseconds or more. The switching frequency of it is so fast that humans can’t recognize the state of its opening with the naked eye. As a result, people can only identify the speed of its switching frequency by the amount of water downstream. In addition, because the sluice changes the duty cycle of the output water flow (effective water flow), it does not change the instantaneous water pressure and flow rate, so the opening and closing action of the sluice gate will not affect the hydropower generation. The amount of water flowing down and power generation are just changed. Therefore, the PWM dimming method does not change the instantaneous voltage and current of the input LED PN junction, but changes the duty cycle of the output current to change LED brightness.2.3 LED PWM Dimming Advantages1) There will not be any LED chromatogram shift, because the LED always works between the full amplitude current and 0.2) It has a very high dimming accuracy, because the pulse waveform can be controlled to a high precision.3) Even if the light is dimmed in a wide range, there will be no flicker. Because it will not change the working conditions of the constant current source (boost ratio or step-down ratio), problems such as overheating are less to occur.4) It can be combined with digital (DALI/DSI/DMX 512) control technology for control, because the digital control signal can easily be transformed into a PWM signal.2.4 LED PWM Dimming Problems1) Because the LED is in a fast switching state, if the working frequency is very low, the human eye will feel flicker. In order to make full use of the residual visual phenomenon of the human eyes, its operating frequency should be higher than 100Hz, preferably 200Hz.2) Eliminate the howling caused by dimming. Although the human eye can't detect it above 200Hz, it is within the range of human hearing until 20kHz. At this time, it is possible to hear the slightest voice. There are two ways to solve this problem: One is to increase the switching frequency above 20kHz, out of the range of human hearing, another is to find out the sound-producing device and deal with it.At present, some manufacturers have solved the above problems well. A good LED light source dimming technology needs a good LED control signal technology to match and cooperate in order to become an effective, stable and reliable system. For example, the LED PWM dimming method has the advantage that the digital control signal can easily be converted into a PWM signal. At the same time, in the digital control signal of lighting, DALI (Digital Addressable Lighting Interface) has the unparalleled superiority of other lighting digital control methods, and it is also the mainstream of the current digital control application in the lighting industry. Therefore, the matching of PWM dimming mode and DALI takes into account their respective advantages, where PWM dimming technology solves the final dimming problem of LED light sources, and DALI solves the control, feedback and networking of each LED light.Figure 2. LED PWM Dimming Circuit2.5 DALI PWM Dimmer IntroductionThe biggest feature of DALI technology is that each lamp has an independent address. Through the DALI system software, a single lamp or any lamp set can be accurately dimmed and switched, regardless of whether the lamps are on strong current loop or not. That is to say, the lighting control has nothing to do with the strong current circuit. The DALI system software can independently address single or multiple lamps on the same strong current circuit or different circuits, to achieve individual control and arbitrary grouping set. This concept brings great flexibility to lighting control, which can meet different LED lighting requirements. Even after installation, they can still modify the control requirements at will, without having to do anything to the wiring.The following are the application advantages of PWM dimming method combined with DALI.1) The design is simple and easy to implement.In the design, as long as they are connected to each other through the digital signal interface, they are connected in parallel to the 2-core control line. All design process can be programmed by computer software during installation and debugging, which not only saves design costs, but also improve working efficiency.2) Simple and economical installationThe DALI control line has no special requirements for the wire and no polarity requirements during installation. It only requires the main power line to be separated from the control line. The control line does not need to be shielded. When the current on the control line is 250mA and the line is 300 meters long, the drop does not exceed 2V. The control line and the power line can be parallel, no need to bury the line separately. The compact design of the control components does not require a special control cabinet, so installation is simple and economical.3) Simple and convenient operationThe PWM LED driver with DALI control can automatically handle filament preheating, ignition, dimming, switching, fault detection and other functions. The user interface is very friendly. Users can operate and control without deep understanding, such as sending a change. According to the command of the scene, each relevant LED driver calculates the dimming rate according to the difference between the current brightness and the required installation brightness to achieve that all the LED light sources are synchronized to the required scene brightness.4) Accurate and reliable controlDALI is a digital signal, which is different from an analog signal. The signal of 1010 can realize disturbance-free control, and will not distort the control signal due to long-distance voltage drop. Therefore, even if the DALI digital signal control line and the strong wire are in the same line and tube, it will not be disturbed. The DALI signal is two-way transmission, which not only transmits control commands forward, but also feeds back the information of the LED driver's status, fault information, switch, and actual brightness value to the system.5) Wide range of applicationsNowadays, DALI interface is not only used for fluorescent lamp ballast dimming, various electronic transformers for halogen lamps, electronic ballasts for gas discharge lamps. DALI technology also employed in wide range of LED light control makes it more and more widely. Ⅲ Main LED Dimmers Comparisons1) SCR DimmingFigure 3. SCR Dimming Circuit Diagram✅Advantages: It has the advantages of high adjustment accuracy, small size, light weight, easy remote control, etc., which occupies a leading position in the market.❎Disadvantages: The front-cut LED dimmer is prone to generate noise, so it is not recommended for high-demand occasions. The minimum load will vary depending on the LED dimmer and light source. It is necessary to consider derating to adapt to the spike caused by the driver. The typical derating percentage should be 25%-30% of the maximum rated load of the dimmer circuit. 2) CMOS DimmingFigure 4. CMOS Dimming Circuit Diagram✅Advantages: There is no minimum load requirement, so that better performance can be achieved on a single LED lighting device or a very small load.❎Disadvantages: High cost, complicated dimming circuits, lack of high-power products, and poor stability. 3) 0-10V DimmingFigure 5. 0-10V Dimming Circuit Diagram✅Advantages: Simple application, good compatibility, high precision, better dimming effect than phase-cut dimming.❎Disadvantages: Need to add additional control lines and controllers. The dimming effect is related to the wire diameter, cable material, power current, and power supply quantity of 0-10V dimming. 4) DALI DimmingFigure 6. DALI Dimming Circuit Diagram✅Advantages: Accurate and smooth dimming, two-way communication, and strong anti-interference ability, mainly used in single lamp control.❎Disadvantages: Like 0-10V products, additional control circuits and controllers need to be added. 5) DMX512 DimmingFigure 7. DMX512 Dimming Circuit Diagram✅Advantages: Powerful control functions bring rich lighting effects to architectural lighting, night lighting, studios and variety shows.❎Disadvantages: Special wiring layout and types are required, and certain programming is required to set the basic colors and scenes, which is more costly for later maintenance. The ideal transmission distance of DMX signal is less than 200 meters. And meanwhile, in actual use, the signal is greatly interfered by the outside world. 6) SLC and Ready2mains DimmingFigure 8. LED Dimming via Ready2mains✅Advantages: The digital dimming signal is transmitted through the AC wire, without additional signal wires and wiring. Digital signal transmission has good anti-interference performance and excellent dimming effect.❎Disadvantages: At present, there are relatively few products using this type of digital dimming technology, so there are relatively few compatible products. Frequently Asked Questions about LED Dimmer1. What are LED dimmers?An LED dimmer is the term for a device that performs a dimming control operation within such an LED lighting device. LEDs react instantaneously to alterations in power input, making solid state lighting especially suitable for dimming scenarios. 2. Why do my LED dimmer lights flicker?LED bulb flickering can be traced in almost every instance to a non-compatible dimmer switch in the lighting circuit. ... LED bulbs don't have glowing filaments. When the dimmer switch goes off and on many times per second, the LED bulb becomes a flickering strobe light. 3. Do you need a special dimmer for LED lights?Use an LED Dimmer switchA standard dimmer switch cannot be used with an LED light as you will never be able to dim the LED light either completely or not very well. LED lights need their own special electronic dimmer switch to have a fully functioning and dimming light. 4. How do LED dimmer switches work?In the case of PWM, dimmable LEDs work by creating a dimming effect. Unlike traditional lighting such as incandescent, dimmable LED bulbs don't rely on voltage to dictate their level of brightness. Instead, they essentially rely on a cycle of being on and off. 5. What is the best dimmer switch for LED lights?Best Overall: Lutron Toggler Single-Pole/3-Way Light Dimmer.Best Budget: GE Slide Dimmer Rocker Wall Switch, Single Pole.Best Smart: Kasa Smart Dimmer Switch HS220.Best for Bedrooms: Lutron Maestro LED+ Dimmer Switch, Single-Pole or Multi-Location.Best for LED: Lutron Diva LED+ Dimmer Switch, Single-Pole or 3-Way.

IntroductionDo you know buffer amplifier or isolation amplifier? The operational amplifier is an extremely efficient and versatile device. As we all known, the op amp is a component that amplifies the weak signal, which can be made into different forms according to the circuit requirements, and the voltage follower is one of them. Most voltage follower circuit will use an Op-amp. A follower is specifically an op amp wired to have a gain of +1. IE, the output is the same polarity and voltage as the input. That is, the output signal is exactly the same as the input signal. Here op amp voltage follower is used to isolate the signal and enhance load capacity. Op-amp as Voltage FollowerIntroductionⅠ Voltage Follower OP AmplifierⅡ Voltage Follower Characteristics2.1 Op Amp Impedance Matching2.2 Buffer Amplifier & Isolation AmplifierⅢ Op Amp Follower Circuit Analysis3.1 Op Amp Voltage and Load3.2 Op Amp Voltage Follower Stability3.3 Op Amp Phase Difference Problem3.4 Adding Feedback ResistanceⅣ Op Amp Voltage Follower ApplicationⅠ Voltage Follower OP AmplifierThe op amp follower sacrifices the voltage amplification factor in exchange for the performance of increasing the input impedance and reducing the output impedance. Because the gain of the op amp is extremely high, the input impedance of the op amp follower tends to be infinite, and the output impedance tends to zero. Within the rated output current range, the feedback voltage is equal to the output voltage, the output voltage is in phase with the input voltage, and the output voltage is slightly smaller than the input voltage. It should be noted that voltage follower is a special case of negative feedback amplifier (voltage series).Op amp voltage follower is actually a simple circuit structure which play a role in impedance matching. When a weaker signal is used to drive a relatively high current, voltage follower is often added in the middle, so that it can make weak signal stronger. It improves the load capacity to a considerable extent, while ensuring that the waveform and amplitude of the signal remain unchanged.For example, a single-chip microcomputer outputs a PWM signal to control LED lights. One LED does not require much current, so there is generally no big problem, however, when multiple LEDs need to light, current may definitely not large enough. If the current output is not enough, which may affect the signal output by the single-chip microcomputer, in this way, the voltage follower comes in handy.Ⅱ Voltage Follower Characteristics2.1 Op Amp Impedance MatchingWhen the op amp gain is approximately 1, that is, the magnification is approximately 1. The "follow" in the follower means that the voltage remains unchanged before and after, and the output waveform is almost not lost. It can be composed of transistors or operational amplifiers (best). Because the op amp input impedance is large and the output impedance is small, voltage follower can reduce the impact on the signal and improve the load capacity.2.2 Buffer Amplifier & Isolation AmplifierHere is a question, how to understand the buffering effect? Is the voltage of the former having a small impact on the back circuit? No, it is equivalent to a constant voltage source. Within the design requirement, no matter how the circuit connected to the subsequent stage changes, the output voltage is constant and does not change. In this way, the magnification or other performance of the previous stage can be kept unchanged. Otherwise, if the previous-stage input impedance is large, and the latter stage is small, the signal will definitely be distorted. For example, if a sinusoidal voltage waveform with a peak value of 10V, the sinusoidal peak value loaded to the latter stage may only be 8V. After adding a voltage follower, the waveform loaded on the input of the voltage follower will basically not change, and the input-output stage voltage ratio is very close to unity. So there will be no distortion.Since the output impedance of the voltage amplifier is generally relatively high, usually in the range of several kiloohms to tens of kiloohms. If the input impedance of the subsequent stage is relatively small, part of the signal will be lost in the output resistance of the previous stage. At this time, a voltage follower is needed to buffer from it. Another advantage of applying a voltage follower is that the op amp input impedance is increased, so that the capacity of the input capacitance can be greatly reduced, which provides a prerequisite guarantee for the application of high-quality capacitors.Another question, what about isolation? Because the op amp input impedance of the voltage follower is very large, it can be approximated as an open circuit. Of course, this open circuit is for the previous circuit. In this case, the previous circuit will not affect the subsequent circuit. However, "open circuit" means what, is it really open? No, the previous voltage is transmitted, but the corresponding current is not transmitted. This is the isolation effect.For example, if the MCU outputs a PWM waveform, you want to use it to control the brightness of a small light bulb. However, the output capacity of the IO port of the general MCU is limited. You can directly use the PWM output from the IO port to drive one light bulb. More than one doesn't work. In this case, you can add a voltage follower, so that the voltage is still the original voltage, but the driving ability has improved. Of course, the output capacity is not increased out of thin air, but comes from the input power of the op amp. In electronics, the diode has current amplification capability, and its source of amplification capability also comes from the power supply.In Hi-Fi circuits, the controversy about negative feedback has been around for a long time. In fact, if there is no negative feedback, most amplifying circuits will not work well. However, due to the introduction of a large loop negative feedback circuit, the back EMF of the speaker will pass through the feedback circuit and be superimposed with the input signal. The sound quality is blurred and the clarity is reduced. Therefore, some of the final stages of the power amplifier adopt a circuit without large loop negative feedback, trying to eliminate the disadvantages by disconnecting the negative feedback loop. However, since the operating current of the final stage of the amplifier varies greatly, its distortion is difficult to control. Here, the function of the voltage follower is just for the application. Putting the circuit between the front stage and the power amplifier can cut off the interference effect of the back electromotive force of the speaker on the front stage, so that the clarity of the sound quality is greatly improved. Ⅲ Op Amp Follower Circuit Analysis3.1 Op Amp Voltage and LoadFigure 1. Op Amp Voltage Follower SchematicThe output and the inverting input terminal are connected in series with a 10k resistor to ensure excellent characteristics. An ac signal is input at the non-inverting input terminal. Of course, dc and ac are all okay, so you will get a very high voltage at the output terminal. AC voltage that is similar and has excellent load capacity, with buffering and isolation effects.3.2 Op Amp Voltage Follower StabilityThe problem of using a voltage follower to keep the operational amplifier stable, that is, how to reduce the oscillation in the amplifier circuit using negative feedback to maintain stability, there is still no final conclusion. The ideal operating state of the op amp is that the output voltage and the input voltage are in phase, that is, when the applied voltage at the negative input causes the output to increase, the op amp can reduce the increased voltage accordingly. However, there is always a difference in phase between the input and output in reality. When the phase difference between the output and the output is 180°, the negative input and the positive input are exactly the same, but the output that should have been reduced is enhanced. It becomes a state of positive and negative collapse. If it falls into this state in a specific frequency band and still maintains the original amplitude, then the output frequency and oscillation state will continue.Figure 2. Feedback Loop3.3 Op Amp Phase Difference ProblemThe main reason for the phase difference between the input and the output:1) Due to the inherent characteristics of op amps.2) Due to the characteristics of the other feedback loop in circuit.Figure 3. Gain-frequency, Phase-frequency CurveFig 3(a), Fig 3(b)and Fig 3(c) respectively represent the voltage gain-frequency characteristic and phase-frequency characteristic of the operational amplifier. As shown in the figure, the voltage gain and phase vary with frequency. The difference between the op amp gain and the gain after feedback (0dB when using a voltage follower) is the gain (feedback gain) of the feedback loop. If the feedback gain is less than 1 time (0dB), then, the phase changes by 180° and returns to the positive feedback state, the negative gain will gradually attenuate in the circuit and theoretically will not cause oscillation.On the contrary, when the phase changes by 180°, if the loop gain corresponding to the frequency is 1 time, the original amplitude will be maintained. If the loop gain corresponding to the frequency is greater than 1, the amplitude will gradually diverge. In most cases, in the process of amplitude divergence, the amplitude is limited due to the influence of nonlinear elements such as the maximum output voltage, and the oscillation state will be maintained.Therefore, the difference between the phase corresponding to the frequency when the loop gain is 0dB, 180° is an important factor for judging the stability of the negative feedback loop, and this parameter is called the phase margin. Unless otherwise specified, when a single amplifier is used as a voltage follower, sufficient phase margin must be maintained (Fig 3b.).3.4 Adding Feedback ResistanceWhen the operational amplifier is used as a follower, when the internal resistance of the signal source is large, adding a feedback resistor with the same resistance as the internal resistance of the signal source can reduce the output offset voltage and improve the follow accuracy. The follower with feedback resistance has a certain current limiting protection effect on the circuit when the circuit is "blocked", which is its advantage.The voltage follower is originally a non-inverting operational amplifier. One of the common features of it is that a common-mode voltage is added to the non-inverting terminal and the inverting terminal.Once this common-mode voltage exceeds the allowable common-mode input voltage range, for example, if the inverting terminal signal is too large, it will cause the input stage transistor to saturate. The inverting terminal signal will be directly added to the second stage of the op amp, making the inverting input becomes non-inverting input, that is, negative feedback becomes positive feedback, and the output signal passes through the feedback loop to further saturate the input stage transistor. As a result of this, the amplifier is of course no longer in normal working condition. Even if the input signal is canceled, it will not immediately return to the normal state. This phenomenon is called blocking.When it occurs, if the feedback loop resistance is not large enough, the current in the feedback loop may burn the input stage transistors and even harm the second stage. In order to avoid blocking, in addition to choosing an op amp with a large common-mode input voltage range, a clamp circuit is often added to the input of the amplifier to ensure that the common-mode voltage at the input does not exceed the allowable range.Of course, in a small-signal inverting operational amplifier, especially in circuits with capacitive elements such as integrating operational amplifiers, blocking may also occur. The processing method is the same as that of the non-inverting amplifier. Ⅳ Op Amp Voltage Follower ApplicationIn many typical circuit designs, there will be an op amp follower before the AD converter. Whether this follower is necessary or not depends on the requirements of the circuit based on the understanding of the function of the follower. First analyze the role of the voltage follower here:The function of the voltage follower here is impedance transformation.Impact 1: The input impedance becomes very high, so that the impact on the input signal can be small.Impact 2: The output impedance becomes very low, and the impact of AD input impedance on the input signal can be very small.It can be seen that the follower is very meaningful. Secondly, analyze your own circuit and the signal under test to make a decision whether to use a follower. Here are some rules to confirm:1) If the output impedance of the signal is very small, then the Impact 1 can be ignored.2) If the input impedance of AD converter is very large, then two impacts can be ignored.3) If both impacts can be ignored, no voltage follower is necessary.4) If there is an impact, a voltage follower is needed. Frequently Asked Questions about Op Amp Voltage Follower1. Which amplifier is called as voltage follower Why?This means that the op amp does not provide any amplification to the signal. The reason it is called a voltage follower is because the output voltage directly follows the input voltage, meaning the output voltage is the same as the input voltage. 2. What is the use of voltage follower?A voltage follower can be used as a buffer because it draws very little current due to the high input impedance of the amplifier, thus eliminating loading effects while still maintaining the same voltage at the output. 3. What do you mean by voltage follower circuit?A voltage follower is also known as a unity gain amplifier, a voltage buffer, or an isolation amplifier. In a voltage follower circuit, the output voltage is equal to the input voltage; thus, it has a gain of one (unity) and does not amplify the incoming signal. 4. What is an op amp buffer?An op-amp voltage buffer mirrors a voltage from a high-impedance input to a low-impedance output. 8 min read. A voltage buffer, also known as a voltage follower, or a unity gain amplifier, is an amplifier with a gain of 1. It's one of the simplest possible op-amp circuits with closed-loop feedback. 5. What is an op amp buffer circuit used for?A buffer is a unity gain amplifier packaged in an integrated circuit. Its function is to provide sufficient drive capability to pass signals or data bits along to a succeeding stage. Voltage buffers increase available current for low impedance inputs while retaining the voltage level.

IntroductionThe transistor is one of the basic semiconductor components, which has the function of current amplification in electronic circuit. It is made of two PN junctions very close to each other on a semiconductor substrate. Two PN junctions divide the entire semiconductor into three parts: The middle part is the base area, and the two sides are the emitter and the collector. What is NPN Transistor? For BeginnerCatalogIntroductionⅠ NPN Transistor Arrangement and SymbolⅡ How Do NPN Transistors Work?Ⅲ NPN Transistor Uses: A Controllable ValveⅠ NPN Transistor Arrangement and SymbolBefore explaining the principle, let's first understand the basic structure and symbols of the NPN transistor. To identify the NPN transistor pins, it will be Collector (c), Base (b) and Emitter (e).Figure 1. NPN Transistor Structure and SymbolNPN transistor is composed of two N-type semiconductors and one P-type semiconductor. Generally, an NPN transistor has a piece of P-type silicon (the base) sandwiched between two pieces of N-type (the collector and emitter). The arrangement is shown in the Figure 1. Ⅱ How Do NPN Transistors Work?Here is the main description to illustrate the basic principle and function of NPN transistors.1) Current AmplificationThe following analysis is only for NPN silicon transistors. As shown in the figure above, we call the current flowing from the base B to the emitter E the base current Ib; the current flowing from the collector C to the emitter E is called the collector current Ic. The directions of these two currents are both flowing out of the emitter, so an arrow is used on the emitter E to indicate the current direction.The amplification function of the transistor is: the collector current is controlled by the base current (assuming that the power supply can provide a large enough current to the collector), and a small change in the base current will cause a large change in the collector current: the change in the collector current is β times the change in the base current, that is, the current change is amplified by β times, so we call β the magnification of the transistor (β is generally much larger than 1). If we add a changing small signal between the base and the emitter, it will cause a change in the base current Ib. After the change in Ib is amplified, it leads to a big change in Ic. If the collector current Ic flows through a resistor R, it can be calculated according to the Ohm's Law formula U=R*I, and the voltage on this resistor will change greatly. According to the voltage on this resistor, so we can get the amplified voltage signal. In short, the change satisfies a certain proportional relationship.2) Bias CircuitWhen the transistor is used in the actual amplifier circuit, it is also necessary to add a suitable bias circuit. There are several reasons for this. First of all, due to the non-linearity of the transistor's BE junction (equivalent to a diode), the base current must be generated after the input voltage reaches a certain level (for silicon tubes, 0.7V is often used). When the voltage between the base and the emitter is less than 0.7V, the base current can be considered as zero. However, in practice, the signal to be amplified is often much smaller than 0.7V. If no bias is applied, such a small signal is not enough to cause a change in the base current (because when it is less than 0.7V, the base current is all 0).Add a suitable current to the base of the transistor (called the bias current, and the resistor in the figure used to provide this current, is called the base bias resistor). When a small signal follows this bias current are superimposed together, a small signal will cause a change in the base current, and the change in the base current will be amplified and output on the collector. Another reason is meeting the requirement of the output signal range. If there is no bias, then only those increased signals will be amplified, but the decreased signals will be invalid (because the collector current is 0 when there is no bias, and it cannot be reduced). With bias, let the collector have a certain current in advance. When the input base current becomes smaller, the collector current can be reduced; when the input base current increases, the collector current increases. Both the reduced signal and the increased signal can be amplified.3) NPN Transistor SwitchLet's talk about the saturation mode of the transistor. As shown in the figure above, because of the limitation of resistance Rc (Rc is a fixed value, then the maximum current is U/Rc, where U is the power supply voltage), the collector current cannot increase indefinitely. When the base current increases and the collector current cannot continue to increase, the transistor enters a saturated state. The general criterion for judging whether the transistor is saturated is: Ib*β>Ic.In a saturation state, the voltage between the collector and the emitter of the transistor will be very small, which can be understood as a switch. In this way, when the base current is 0, the collector current is 0 (this is called the triode cut-off), which is equivalent to the switch off; when the base current is large, it is equivalent to the switch on. In cut-off and saturation state, a transistor is equal to a switch.4) Operational StateIf we replace the resistor Rc with a bulb in the above figure, then when the base current is 0, the collector current is 0, so the bulb is off. If the base current is relatively large (greater than the current flowing through the bulb divided by the magnification β), the transistor will saturate, and the bulb will light up. Since the control current only needs to be a little larger than β of the bulb current, a small current can be used to control the on and off of a large current. If the base current increases slowly, the brightness of the bulb will also increase (which is a saturation process).The figure below is a basic transistor switch circuit. The base should connect a base resistor (R2), and the collector connects with a load resistor (R1).Operational ModeNPNCut-offUne<UonUc>UbActiveUbe>UonUc>UbSaturationUbe>UonUc<UbNPN transistor uses the B-E current (IB) to control the C-E current (IC). The E pole has the lowest potential, and usually the C pole has the highest potential during normal amplification, that is, VC>VB>VE.NPN base extremely high voltage, the collector and emitter are short-circuit and low-voltage, and the collector and emitter are open-circuit.NPN is suitable for two situations:If the input is a high level and the output needs a low level, NPN is better.If the input is a low level and the output needs a high level, NPN is better.2N2222 NPN Transistor PinoutⅢ NPN Transistor Uses: A Controllable ValveNPN is a component that uses b (base) current Ib to drive the current Ic flowing through CE, and its working principle is much like a controllable valve.Figure 2. A Controllable ValveThe blue water flow in the thin pipe on the left impacts the lever to open the valve of the large water pipe, allowing the larger red water flow to pass through the valve. The larger the blue water flow, the greater the red water flow in the big pipe. If the magnification is 100, then when the blue water flow is 1 kg/hour, then 100 kg/hour of water is allowed to flow through the large pipe. The principle of the transistor is the same. When Ib (base current) is 1mA, a current of 100mA is allowed to pass through Ice.Figure 3. NPN Transistor DiagramLet's analyze this circuit. If its magnification is 100, and ignore the base voltage. The base current is 10V÷10K=1mA, so the collector current should be 100mA. According to Ohm's law, the voltage on Rc is 0.1A×50Ω=5V. Then the remaining 5V is on the C and E poles of the transistor. Now if we let Rb be 1K, then the base current is 10V÷1K=10mA, according to the magnification of 100, is Ic 1000mA? If it is really 1A, then the voltage on Rc is 1A×50Ω=50V. The power supply voltage has been exceeded, and the transistors have become generators? This is not the case. See below:Figure 4. NPN Transistor Compared to A ValveContinue the metaphor. When the control current is 10mA, the valve on the main water pipe is opened to allow 1A current to flow, but can 1A be realized? No, because there is a resistor on it, it is equivalent to a fixed valve. It is stringed on top of the main water pipe. When the opening of the lower controllable valve is greater than the opening of the upper fixed resistor, the water flow will not increase any more, but will be equal to the water flow passing through the fixed valve opening above. Therefore, it is useless to open the lower transistor to a large opening. Therefore, we can calculate the maximum current of the fixed resistor 10V÷50Ω=0.2A, which is 200mA. That is to say, in the circuit, the base current increases and the collector current also increases. When the base current Ib increases to 2mA, the collector current increases to 200mA. When the base current increases again, the collector current will no longer increase, and it will not move at 200mA. At this time, the upper resistor also acts as a current limiter.  Let us understand the status of the IO in the microcontroller.Figure 5. AT89S51/52 The circuits with 24 IO ports of P1-P3 in the single-chip microcomputer are as shown in the figure above. Usually the purpose of using electronic circuits is to allow devices to obtain a certain current to make them work. For example, to make light-emitting diodes bright, a current of more than 1mA is generally required. However, the single-chip microcomputer is a smart chip. It can make logical analysis and judgments by detecting the voltage value of each IO port, and outputs high or low voltage as the result signal. Therefore, it can be seen that the IO ports of the single-chip microcomputer focus on voltage, not the current flowing through R and the transistor. Here what is the relationship between the voltage and current of the IO port in the single-chip microcomputer?  Continue the water pipe example.Suppose we let the valve of R open larger and let the control valve below be fully closed. At this time, as shown in Figure 6, it can be seen that the pressure at point P is the same as the water tank. When we fully open the following control valve, as shown in Figure 7, the water will flow through the pipeline with a large flow, and the pressure at point P is 0 at this time. This principle is very similar to electronic circuits. The logic quantity measured at the output point P is 1 (power supply voltage) or 0 (0 potential) by transistor turning off or on. However, there is a problem with this process, that is, when the output of point P is required to be 0, the transistor will be turned on very large, and the current flowing through it will be very large. There are 32 IO ports on the single-chip microcomputer, which consumes a lot of power. Look at Figure 8. If we close the upper valve R very small and close the lower control valve fully, then the pressure at point P will still the same as the water tank, which is the same as in Figure 6 above. When we open the control valve greatly, as shown in Figure 9, although the pressure at point P is also 0, the flow of water passing through at this time is greatly reduced. In this way, we can either output 1 or 0. So very little water is consumed. The circuit in the single-chip microcomputer does exactly this. The resistance R on it is about 50K, and the maximum current is 5V÷50K=0.1mA. In other words, when P outputs 1, no current is consumed, and when P outputs 0, the current consumed is 0.1mA. Because of its large pull-up resistance R, for beginners, it is necessary to have certain methods to directly drive LEDs or other loads. Here to share the various situations when the IO port is connected to the load.Figure 10. AT89S51/52 & 74HC373Let's take a look at the situation of connecting TTL devices first. When P1.0 is connected to an input pin of 74HC373, and the input impedance of TTL is very high, about a few hundred K to M ohm level. We assume 500K resistor to P1.0 to ground. In this way, when the transistor is turned on, the P1.0 point is at a low level, and a current of 0.1mA flows through Rc and then through the transistor to the ground, and no current flows through Ri. When the transistor is cut off, the current flows through Rc and then flows to the ground through Ri. Due to the resistor voltage divider effect, there are partial voltages on Rc and Ri, and the voltage at point P1.0 is the divided voltage of Rc and Ri. Total current is 5V÷(50K＋500K)=0.009mA, then the voltage at point P1.0 is 0.009mA×500K=4.5V. TTL stipulates that output 2.4~5V is high level. So this connection is correct. Now let's take a look at the situation of using S51 to drive the LED.AT89S51 Correct ConnectionLet’s take a look at the situation in Figure 11. Obviously, only P1.0 is a high potential to light the luminous tube, so the transistor must be cut off. In this case, the current flows through Rc to the luminous tube and then to the ground. To make the luminous tube turn on, there must be a threshold voltage exceeding 2.1V at both ends of the luminous tube. Therefore, the current flowing through the luminous tube is (5V-2.1V)÷50K=0.058mA, which is too weak to conduct.Look at Figure 12. It can be seen from the figure that P1.0 must be at a low potential if the luminous tube turned on. The transistor of the P1.0 port must be turned on. At this time, the current flows all the way through Rc to the transistor and then to the ground. The other way consumes 2.1V on the luminous tube. Then current flows through with almost no resistance, but the maximum current of the triode of the IO port cannot exceed 15mA. If it exceeds, the triode will be burned out, so this connection method is incorrect. So how can these two connections be able to drive the light-emitting tube? See below: AT89S51 Incorrect ConnectionLooking at Figure 13, a resistor Ri is connected between P1.0 and Vcc. When the transistor is turned on, two currents will flow through its c, e pole, one is the 0.1mA current on the internal R, and the other is the current on Ri. In order to prevent the transistor from over-current and burn out, we must make sure the resistance value, Ri=5V÷15mA=0.333K, which is about 330 ohms. At this time, the current flowing through the transistor is about 15mA, and the light-emitting tube is not bright at this time. When the transistor is turned off, both currents will flow through the luminous tube. The current flowing through the internal resistance of S51 is (5V-2.1V)÷50K=0.06mA, which is so small that we can ignore it. The current flowing through Ri is (5V-2.1V)÷330Ω=0.0087A, which is 8.7mA. However, the current consumed when the luminous tube is off is greater than the current consumed when the luminous tube is on. If many IO ports are used to light up many LEDs, such a circuit is not economical.Look at Figure 14, after connecting a resistor in series with the luminous tube between Vcc and P1.0. When the transistor is turned on, the two currents will flow through the c, e after confluence. The current on the internal resistance is still 0.1mA. The current on the ce should be less 15mA. If exceeds 15mA, the resistance is determined as (5V-2.1V) ÷ 15mA = 0.193K, which is about 200 ohms. In this way, the current flowing through the luminous tube is about 15mA, and the luminous tube is on. When the transistor is cut off, it blocks the paths of these two currents, so no current is consumed. Low level P1.0 directly drives the light-emitting tube. It can be seen that this circuit consumes 15mA of current when the light-emitting tube is on, and does not consume current when it is off, so this circuit is effective. S51 direct drive digital tube generally also uses this principle. Frequently Asked Questions about NPN Transistor1. What is meant by NPN transistor?An NPN transistor is the most commonly used bipolar junction transistor, and is constructed by sandwiching a P-type semiconductor between two N-type semiconductors. An NPN transistor has three terminals– a collector, emitter and base. The NPN transistor behaves like two PN junctions diodes connected back to back. 2. How do NPN transistors work?The NPN transistor is designed to pass electrons from the emitter to the collector (so conventional current flows from collector to emitter). The emitter "emits" electrons into the base, which controls the number of electrons the emitter emits. ... The transistor is kind of like an electron valve. 3. What is a NPN transistor used for?NPN transistors are mainly used in switching applications. Used in amplifying circuit applications. Used in the Darlington pair circuits to amplify weak signals. NPN transistors are used in the applications where there is a need to sink a current. 4. Which is better PNP or NPN transistor?A NPN transistor has electrons as majority charge carriers whereas the PNP transistor has holes as majority charge carrier. ... mobility of electrons is more than hole,so as a result npn transistor are faster than pnp that's why they are preferred. 5. What does NPN mean?NPN stands for Negative, Positive, Negative. Also known as sinking.

IntroductionA three-phase circuit consists of a three-phase source, a three-phase load, and a three-phase transmission line. The most basic characteristic of this circuit is that it has one or more groups of power supplies. Each group consists of three sinusoidal power supplies with the same amplitude, the same frequency, 120° phase difference, and the power supply and the load are connected in a specific way. Three-phase circuits are widely used in power systems such as power generation, transmission, distribution, and high-power electrical equipment.What does 3 phase mean?CatalogIntroductionⅠ Three-phase Circuit Basics1.1 Three-phase Circuit Characterized1.2 Three-phase Circuit Terms1.3 Three-phase Voltage & Current1.4 Three-phase Circuit AdvantagesⅡ Symmetrical vs Asymmetrical2.1 Symmetrical Three-phase Circuit2.2 Three-phase AsymmetryⅢ Power in Three Phase Circuit FormulasⅣ Frequently Asked Questions about Three-phase CircuitⅠ Three-phase Circuit BasicsThe three phases could be supplied over six wires, with two wires reserved for the exclusive use of each phase. However, they are generally supplied over only three wires, and the phase or line voltages are the voltages between the three possible pairs of wires. The phase or line currents are the currents in each wire. Voltages and currents are usually expressed as rms or effective values, as in single-phase analysis.1.1 Three-phase Circuit CharacterizedSpecial power supplySpecial loadSpecial connectionSpecial solution1.2 Three-phase Circuit Terms1) End wire (fire wire)2) Neutral line3) Line current4) Line voltage5) Phase current6) Phase voltage7) Three-phase three-wire system and three-phase four-wire system1.3 Three-phase Voltage & CurrentStar ConnectionSummery: Line Voltage vs Phase Voltage1) The line current is equal to the corresponding phase current.2) If the phase voltage is symmetrical, the line voltage is also symmetrical.3) The line voltage is equal to √3 times the phase voltage.4) The phase of the line voltage leads the corresponding phase voltage by 30°. Delta ConnectionSummery: Line Current vs Phase Current1) The line voltage is equal to the corresponding phase voltage.2) If the phase currents are symmetrical, the line currents are also symmetrical.3) The line current is equal to √3 times the phase voltage.4) The phase of the line current lags behind the corresponding phase voltage by 30°.1.4 Three-phase Circuit AdvantagesPower generation: Three-phase power is increased by 50% compared to single-phase power.Transmission: 25% less material than single-phase circuit transmission. That is, under certain conditions, transmitting a certain amount of power by three-phase only requires 75% of the copper of single-phase transmission.Power distribution: More economical than single-phase transformers and easier to connect to the load.Transportation: simple structure, low cost, reliable operation, convenient maintenance.In addition, three wires are usually seen in high-voltage transmission lines, whether on towers or poles, with pin or suspension insulators. Some high-voltage lines are now DC, since solid state devices make it easier to convert to and from AC. The DC lines are free of the problems created by phase, as well as eliminating the skin effect that reduces the effective area of the conductors. It is not nearly as easy to manage long-distance electrical transmission as might be thought.Ⅱ Symmetrical vs Asymmetrical2.1 Symmetrical Three-phase CircuitA symmetrical three-phase power source is usually generated by a three-phase synchronous generator, as shown in Figure (a). Among them, the three-phase windings differ by 120° in space. When the rotor rotates at a uniform angular velocity ω, an induced voltage is generated in the three-phase winding, thereby forming a symmetrical three-phase power supply as shown in Figure (b). Among them, the three ends of A, B, and C are called the start end, and the three ends of X, Y, and Z are called the end. When you connect a load to the three wires, it should be done in such a way that it does not destroy the symmetry.Instantaneous Voltage Calculation of Three-phase PowerIn the formula, take the phase A voltage uA as the reference sine quantity. The three-phase voltage waveform diagram is shown in Figure (a).The key to understanding three-phase is to understand the phasor diagram for the voltages or currents. The phasor of the three-phase power supply can be represented by the Figure (b).The characteristics of the symmetrical three-phase power supply can be derived from the above formula:From the above formula, the sum of the instantaneous value of the three-phase power supply and the sum of the phasor are always zero.The sequence in which each phase of the three-phase power passes through the same value (such as the maximum value) is called the phase sequence of the three-phase power, and the phase sequence of the above-mentioned three-phase voltage is called the positive sequence. Conversely, if phase B exceeds 120° of phase A and phase C exceeds 120° of phase B, this phase sequence is called reverse sequence. If there is no special instructions, it will generally default to positive order.2.2 Three-phase Asymmetry1) In a three-phase circuit, as long as there is asymmetrical part, it is called a three-phase asymmetry.2) The complex power absorbed by the three-phase load is equal to the sum of various complex powers.3) The instantaneous power of a three-phase circuit is the sum of the instantaneous power of each phase load.4) In a three-phase three-wire circuit, whether symmetrical or not, two power meters can be used to measure three-phase power.When the power supply voltage in the three-phase circuit is asymmetrical or the parameters in the circuit are asymmetrical, the current in the circuit is generally asymmetrical. This kind of circuit is called three-phase asymmetry. There are a lot of asymmetry parts in three-phase circuits, and the causes are different. For example, there are many low-power single-phase loads in a three-phase circuit, it is difficult to make them into a completely symmetrical circuit. When a three-phase circuit is broken or short-circuited, it is also a three-phase asymmetry circuit. In addition, some electrical equipment and instruments formally use three-phase asymmetry to work.For example, the most common low-voltage three-phase four-wire system. Due to the large number of single-phase loads in the low-voltage system, the equivalent impedances ZA, ZB, and ZC of the three phases circuit are generally different from each other, and the power supply voltage can generally be considered symmetrical. In this way, a symmetrical three-phase power supply converts to an asymmetrical three-phase load.The circuit shown in the figure has two nodes, and the voltage between the two nodes can be directly calculated according to the node voltage method.Although the power supply voltage in the above formula is symmetrical, the voltage between the neutral point of the power supply and the neutral point of load is not zero due to the load asymmetry, that is, UNN≠0. According to Kirchhoff's voltage law, the phase voltage of the load can be obtained as:The phasor diagram of each voltage corresponding to the above formula is as follows:Ⅲ Power in Three Phase Circuit Formulas1. Average PowerSuppose the power absorbed by a phase load in a symmetrical three-phase circuit is equal to Pp=UpIpcosφ, where Up is the phase voltage and Ip is the phase current of the load. Then the total three-phase power is: P=3UpIpcosφPay Attention To1) φ in the above formula is the phase difference angle (impedance angle) of phase voltage and phase current.2) cosφ is the power factor of each phase, in a symmetrical three-phase system:cosφA=cosφB=cosφC=cosφ3) The formula calculates the circuit power (or the power absorbed by the load).When the load is in a star connection, the line voltage  and line current  at the load end are substituted into the above formula:When the load is in a delta connection, the line voltage  and line current  at the load end are substituted into the above formula:2. Reactive powerThe reactive power absorbed by the load in a symmetrical three-phase circuit is equal to the sum of the reactive power of each phase:3. Apparent Power4. Instantaneous PowerSuppose the voltage and current of phase A of the three-phase load are:Then the instantaneous power of each phase is:It can be proved that their sum isThe above formula shows that the instantaneous power of a symmetrical three-phase circuit is a constant, and is equal to the average power. This is one of the advantages of a symmetrical circuit. For example, on a three-phase motor, a balanced electromagnetic torque is obtained and mechanical vibration is avoided, which is not available in single-phase motors. Ⅳ Frequently Asked Questions about Three-phase Circuit1. What is a 3 phase circuit?Three-phase power is a three-wire ac power circuit with each phase ac signal 120 electrical degrees apart. ... three-phase is that a three-phase power supply better accommodates higher loads. Single-phase power supplies are most commonly used when typical loads are lighting or heating, rather than large electric motors. 2. How many wires are in a 3 phase?four wiresThe three-phase system has four wires. Three are conductors and one is neutral. 3. What is the 3 phase power formula?3-Phase Calculations. For 3-phase systems, we use the following equation: kW = (V × I × PF × 1.732) ÷ 1,000. 4. What is the advantage of three-phase system?A three-phase circuit provides greater power density than a one-phase circuit at the same amperage, keeping wiring size and costs lower. In addition, three-phase power makes it easier to balance loads, minimizing harmonic currents and the need for large neutral wires. 5. What is meant by 3 phase balanced load?A balanced three-phase voltage or current is one in which the size of each phase is the same, and the phase angles of the three phases differ from each other by 120 degrees. ... With such a balanced load, if a balanced three-phase supply is applied, the currents will also be balanced.

IntroductionA stable power supply is necessary for normal operation of the electrical system. Except for the use of solar cells or chemical batteries in certain special occasions, the direct current of most circuits is converted from the alternating current of the grid. The bridge rectifier is commonly used to convert AC into DC, which is the most commonly used circuit that uses the unidirectional conductivity of diodes for rectification. There are many types of bridge rectifiers: flat, round, square, bench-shaped (plug in and SMD), etc., having GPP and O/J structures. The maximum rectified current ranges from 0.5A to 100A, and the maximum reverse peak voltage ranges from 50V to 1600V.What is Bridge Rectifier?CatalogIntroductionⅠ Bridge Rectifier Diode CircuitⅡ Bridge Rectifier Circuit FeaturesⅢ Single Phase Rectification vs Three Phase Rectification3.1 Single Phase Bridge Rectifier Circuit3.2 Three Phase Bridge Rectifier CircuitⅣ Role of Bridge RectificationⅤ Bridge Rectifier Wiring DiagramⅥ Difference between Bridge Rectifier and Full-wave Rectifier CircuitⅠ Bridge Rectifier Diode CircuitThe bridge rectifier uses four semiconductor diodes to be connected in pairs. When the positive half of the input sine wave is turned on, the two tubes are turned on, and the positive output is obtained; on the contrary, when the negative half of the sine wave is input, the other two tubes are turned on. Since the two tubes are reversely connected, the output is still the positive part of the sine wave. In addition, the utilization efficiency of the input sine wave by the bridge rectifier is twice as high as that of the half-wave rectifier.The rectifier bridge stack is generally used in a full-wave rectifier circuit, and it is divided into a full bridge and a half bridge. The full bridge is composed of 4 rectifier diodes connected in the form of a bridge full-wave rectifier circuit and packaged as a whole. The half bridge is to seal the half of the two diode bridge rectifiers together. Two half bridges can form a bridge rectifier circuit, and a half bridge can also form a full wave rectifier circuit with a center tap of the transformer. When choosing a rectifier bridge, the rectifier circuit and operating voltage must be considered carefully.The forward current of the full bridge has various specifications such as 0.5A, 1A, 1.5A, 2A, 2.5A, 3A, 5A, 10A, 20A, 35A, 50A, etc. The withstand voltage (the highest reverse voltage) is 25V, 50V, 100V, 200V, 300V, 400V, 500V, 600V, 800V, 1000V, etc.In this chapter, the rectifier diode is regarded as an ideal component, that is, its forward conduction resistance is considered to be zero, and its reverse resistance is infinite, because of the convenience of analyzing the rectifier circuit. However, in practical applications, it should be considered that the diode has internal resistance, and the output amplitude of the waveform obtained after rectification will be reduced by 0.6~1V. When the input voltage of the rectifier circuit is large, this part of the voltage drop can be ignored. On the contrary, if the input voltage is small, for example, if the input is 3V, the output is only 2V, and the influence of the diode forward voltage drop needs to be considered.Current Direction of the Bridge Rectifier CircuitFigure 1.In the positive half cycle of u2, D1 and D3 are turned on, D2 and D4 are turned off, and the current returns from the upper end of the TR secondary to the lower end via D1→RL→D3, and a half-wave rectified voltage is obtained on the load RL.In the negative half cycle of u2, D1 and D3 are off, D2 and D4 are on, and the current returns from the lower end of Tr secondary to the upper end of Tr secondary via D2→RL→D4, and the other half-wave rectified voltage is obtained on the load RL. Ⅱ Bridge Rectifier Circuit Features(1) The rectification device used is twice that of full-wave rectification.(2) Rectified voltage pulse changing direction is the same as full-wave rectification.(3) The reverse voltage that each device bears is the peak value of the power supply voltage.(4) The utilization rate of the transformer is higher than that of the full-wave rectifier circuit. Ⅲ Single Phase Rectification vs Three Phase Rectification3.1 Single Phase Bridge Rectifier CircuitFigure 2.The single phase bridge rectifier circuit is composed of four diodes connected in the form of a bridge. Its disadvantage is that it only uses half a cycle of the power supply, and at the same time the rectification voltage has a large pulsation.The above Figure 2 (a) shows the direction of current in the single-phase bridge rectifier circuit. The solid arrow indicates the situation when the AC power supply is in the positive half cycle, and the dotted arrow indicates the situation when the AC power supply is in the negative half cycle.It can be seen that the four diodes are divided into two parts: positive half cycle and negative half cycle. However, the current direction on the load does not change. This is full-wave rectification. In addition, the single-phase bridge rectifier circuit can be implemented with an integrated device "bridge stack" in practice.In Figure 3. shows the waveform diagram of the single phase bridge rectifier circuit. According to the diagram, the average voltage is: Uo ≈ 0.9U2 (where U2 is the effective value of the output voltage of the transformer secondary side).Figure 3. Wave Form (single phase)3.2 Three Phase Bridge Rectifier CircuitFigure 4.The three phase bridge rectifier circuit is developed from a uncontrolled half-wave rectifier circuit, which is essentially a series connection of a set of common cathode and a set of common anode with three semiconductor diodes.In addition, the three phase bridge circuit must have two thyristors turned on at the same time, one in the common cathode area and the other in the common anode area to form a loop.Circuit Analysis LawThe diode with the highest anode potential in the common cathode group is turned on.The diode with the lowest cathode potential in the common anode group is turned on.Circuit Analysis ExamplesFigure 5. t1 ~ t2In the common cathode group, the potential at point U is the highest, and V1 is on.In the common anode group, the potential at point V is the lowest, and V4 is on.The voltage across the load is the line voltage Uuv. Figure 6. t2~t3In the common cathode group, the potential at point U is the highest, and V1 is on.In the common anode group, the potential at point W is the lowest, and V6 is turned on.The voltage across the load is the line voltage Uuw. Figure 7. t3~t4In the common cathode group, the potential at point V is the highest, and V3 is on.In the common anode group, the potential at point W is the lowest, and V6 is turned on.The voltage across the load is the line voltage Uvw.......SummeryIn a full-wave cycle, it can be divided into 6 intervals, each of which is powered by a pair of phase wires to the load.In a full-wave cycle, each diode is turned on for one-third of the time (the conduction angle is 120°).During the 6 periods in a cycle, the voltage of the load can be seen as a periodic change. Ⅳ Role of Bridge Rectification1. Convert the alternating current generated by the alternator into direct current to power the electrical equipment and charge the battery.2. Limit the battery current to flow back to the generator to protect the generator from being burnt out by the reverse current.Figure 8. Bridge Rectifier AC to DC Flow ChartⅤ Bridge Rectifier Wiring DiagramThe bridge rectifier circuit overcomes the shortcomings that the full-wave rectifier circuit requires the transformer secondary to have a center tap and the diode to withstand large reverse voltage, but two diodes are used. With the rapid development of semiconductor devices and low cost today, this shortcoming is not obvious, so bridge rectifier circuits are widely used in practice.It needs to be pointed out that the diode as a rectifier component should be selected according to different rectification methods and load values. If choose improperly, you may not be able to work safely, or even burn the pipe, causing waste.Figure 9. Schematic Diagram of Bridge Rectifier CircuitThe bridge rectifier circuit can also be considered as a kind of full-wave rectifier circuit. The transformer is connected to four diodes according to the method shown in Figure 9. D1～D4 are four identical rectifier diodes connected in the form of a bridge, so they are called bridge rectifier circuits. Using the guiding function of the diode, the secondary output can be directed to the load even in the negative half cycle. It can be seen from the figure that D1 and D2 lead the current through RL from top to bottom during the positive half cycle, and D3 and D4 lead the current through RL from top to bottom during the negative half cycle. In this structure, if the same DC voltage is output, the secondary winding of the transformer needs only half of the winding compared with the full-wave rectification. However, if the same amount of current is to be output, the diameter of the winding should be increased accordingly.Because the output voltage of the rectifier circuit contains larger pulsating components. In order to reduce the pulsation component as much as possible, on the other hand, it is necessary to keep the DC component as much as possible to make the output voltage close to the ideal DC. This measure is filtering. Filtering is usually achieved by using the energy storage effect of capacitors or inductors.Figure 10. Bridge Rectifier Circuit with CapacitorIn this experimental circuit, capacitor filtering is used, that is, a filter capacitor C is connected in parallel with the load resistance RL. The circuit is shown in Figure 11, and the filtered waveform is as shown in the figure below.Figure 11. Full-wave Rectification Filter WaveformThe DC component of the full-wave rectified output voltage (compared to the half-wave) is increased, and the pulsation is reduced, but the transformer needs a center tap, which is troublesome to manufacture, and the rectifier diode needs to withstand high reverse voltage, so it is generally suitable for the low output voltage.Figure 12. Half-wave Rectification Filter WaveformHalf-wave rectification is the most commonly used circuit that uses the unidirectional conductivity of a diode for rectification. Ⅵ Difference between Bridge Rectifier and Full-wave Rectifier Circuit1) Don't need a center tap on the secondary side of the bridge rectifier circuit transformer, but use 2 more rectifier diodes.2) The full-wave rectifier circuit uses less than 2 rectifier diodes, but the secondary side of the transformer should be center-tapped.3) The reverse withstand voltage of the rectifier diode used in the full-wave rectifier circuit is twice that of the bridge rectifier.4) Rectification and full-wave rectification have different requirements for the number of secondary transformers. The former requires only 1 set of coils, while the latter requires 2 sets.5) Rectification and full-wave rectification have different requirements for the secondary current of the transformer, the former is twice the latter. Frequently Asked Questions about Bridge Rectifier Circuit1. What does a bridge rectifier do?A bridge rectifier provides full-wave rectification from a two-wire AC input, resulting in lower cost and weight as compared to a rectifier with a 3-wire input from a transformer with a center-tapped secondary winding. ... Diodes are also used in bridge topologies along with capacitors as voltage multipliers. 2. How does a bridge rectifier convert AC to DC?Bridge rectifiers convert AC to DC using its system of diodes made of a semiconductor material in either a half wave method that rectifiers one direction of the AC signal or a full wave method that rectifies both directions of the input AC. 3. What happens when a bridge rectifier fails?Without capacitor smoothing, when 1 diode fails open in a bridge rectifier, both voltage and current reduce. With capacitor smoothing, when 1 diode fails open in a bridge rectifier, the voltage remains fairly constant but the current increases. 4. Why do we use 4 diodes in bridge rectifier?The bridge rectifier consisting of four diodes enables full wave rectification without the need for a centre tapped transformer. The bridge rectifier is an electronic component that is widely used to provide full wave rectification and it is possibly the most widely used circuit for this application. 5. Why is a bridge rectifier more preferable than a full wave rectifier?Bridge rectifier is driven by a single winding which carries current both cycles in load. ... Full wave is better than bridge in one more aspect i.e. the output DC voltage is slightly higher than bridge. This is because it has only 1 diode drop from AC to DC.