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IntroductionInductor is a passive component that used extensively with capacitors and resistors to create filters for analog circuits and in signal processing. Also it is an energy storage device in many switched-mode power supplies. As a major value of inductor, inductance is the ratio of wire current and the magnetic flux which is created by the flow of electrical current in the magnetic field. When a DC current passes through the inductor, there are only fixed magnetic lines around it, which do not change with time. However, when an alternating current is passed through the coil, the magnetic lines around inductor that will change with time.Inductors and Inductance DefinitionCatalogIntroductionⅠ Inductor Working PrincipleⅡ What Does Inductor Do?Ⅲ Inductor Main ParametersⅣ Inductor ClassificationⅤ Chip Inductor5.1 Purpose of a Chip Inductor5.2 Chip Inductor Classification5.3 Three Methods for Reading Chip InductorsⅠ Inductor Working PrincipleWhen ac current is applied to an inductor coil, its own current changes, making its own magnetic flux to change, and then causing induced electromotive force. This phenomenon is called self-inductance. The direction of self-induced current always be affected. When the alternating current increases, the direction of self-inductance current is opposite to that of AC current. When the AC current is weaken, the direction of self-inductance current is the same as that of alternating current, which has blocking effect.1) Self-inductionWhen current flows through the coil, a magnetic field is generated around the coil. When the current in the coil changes, the surrounding magnetic field also changes accordingly. This changing magnetic field can cause the coil itself to generate induced electromotive force (EMF is used to represent the terminal voltage of the ideal power supply for active components).2) Mutual InductanceWhen two inductor coils are close to each other, the change of the magnetic field of one coil will affect the other one, and this effect is mutual inductance. The magnitude of the it depends on the degree of coupling between the self-inductance and the two coils. The components made by this principle are called mutual inductors.Ⅱ What Does Inductor Do?The inductor mainly plays the role of filtering, oscillating, delaying, tuning and frequency selection in the circuit, as well as filtering signal, filtering noise, stabilizing current and suppressing electromagnetic wave interference. The most common role of inductance in a circuit is to form an LC filter circuit together with a capacitor. Capacitors have the characteristic of "block DC and pass AC", while inductors have the function of "pass DC and block AC". It can be made into low-frequency and high-frequency choke coils by making use of its properties. Common filter inductors are for this purpose.➡️Pass DC: It means that in a direct current circuit, the inductor acts as a wire and has no effect.➡️Block AC: In an AC circuit, the inductor will have impedance, that is, XL. The current in the entire circuit will become smaller, which has a certain blocking effect on AC. The self-induced electromotive force is always opposed to the current change in the coil. Mainly can be divided into high-frequency choke coil and low-frequency choke coil.➡️Inductor has the function of generating self-induced EMF, which is also called energy storage function. Like a capacitor, it is also an important energy storage component, which is widely used in switching power supplies. In addition, the phase relationship between the voltage across the inductor and the current: the voltage leads the current by 90 degrees, which is just the opposite of the capacitor. Using this characteristic, inductors and capacitors form LC series and parallel circuits, which can be used for frequency selection. In reality, they have been widely used in circuits, especially in radio circuits.If the direct current accompanied by many interference signals is passed through the LC filter circuit, then the AC interference signal will be consumed by the inductance into heat. When the pure DC current passes through the inductor, the AC interference signal in it will also become magnetic induction and heat energy, the higher frequency is most likely to be blocked by the inductor, which used to suppress the higher frequency interference signal.➡️Tuning and Frequency SelectionThe inductance coil and the capacitor are connected in parallel to form an LC tuning circuit. That is, the natural oscillation frequency f0 of the circuit is equal to the frequency f of the non-AC signal, and the inductance and capacitive reactance of the loop are also equal, so the electromagnetic energy oscillates between the inductor and the capacitor. This is the resonance phenomenon of the LC loop. During resonance, since the inductance and capacitive reactance of the circuit are equal and opposite, the inductance of the total current of the loop is the smallest and the current is the largest (referring to the AC signal of f=f0), so the LC resonance circuit has the function of selecting the frequency, therefore an AC signal of a certain frequency is selected.➡️ChokeIt is used to block low-frequency alternating current, and pulsating direct current flows to pure direct-current in circuits. Go further, it is commonly used in the middle of two filter capacitors at the output of a rectifier circuit. The choke and capacitor form a filter circuit. In the high-frequency circuit: to prevent the high-frequency current from flowing to the low-frequency end, which is commonly as the high-frequency choke of old regenerative radio.➡️FilterIt also prevents the rectified pulsating DC current from flowing to the pure DC circuit. The choke (to simplify the circuit and reduce the cost, replace the choke with a pure resistance) and two capacitors (electrolytic capacitors) form a filter circuit. The use of capacitor charging and discharging and AC choke coil to block the alternating current to smooth direct current and obtain the pure direct current.➡️OscillationWe often say that rectification is to transform AC into DC, so oscillation is the reverse process of it. We call the circuit that completes this process an "oscillator." Oscillator waveform: there are sine wave, sawtooth wave, trapezoidal wave, square wave, rectangular wave, spike wave. The frequency ranges from a few Hz to tens of GHz. It is widely used in the field of wired power and radio.Ⅲ Inductor Main ParametersThe main parameters of inductor include inductance, allowable deviation, quality factor, distributed capacitance and rated current.1) InductanceInductance is also called self-inductance, which is a physical quantity that represents the self-inductance of an inductor. The size of the inductance mainly depends on the number of turns  of the coil, the winding method, the core and its material, etc. Generally, the more coil turns and the denser the coils, the greater the inductance. A coil with a magnetic core has a larger inductance than a coil without a magnetic core. What’s more, a coil with a larger magnetic core has a larger inductance.The basic unit of inductance is Henry, represented by the letter "H". Commonly used units are millihenry (mH) and microhenry (μH). The relationship between them is:1H=1000mH1mH=1000μH2) Allowable DeviationThe allowable deviation refers to the allowable error value between the nominal inductance and the actual inductance.Generally, inductors used in circuits such as oscillation or filtering require high accuracy, with an allowable deviation of ±0.2%~±0.5%; while the accuracy requirements of coils used for coupling and high-frequency blocking are not high; the allowable deviation is ±10 %~15%.3) Quality FactorQuality factor, also called Q value, is the main parameter to measure the quality of an inductor. It refers to the ratio of the inductance presented by the inductor to its equivalent loss resistance when it works under a certain frequency of AC voltage. The higher the Q value of an inductor, the smaller its loss and the higher its efficiency.The Q factor is related to the DC resistance of the coil wire, the dielectric loss of the coil frame, and the loss caused by the core and shield.4) Distributed CapacitanceDistributed capacitance refers to the capacitance that exists between the turns of the coil, the coil and the magnetic core, the coil and the ground, and the coil and the metal. The smaller the distributed capacitance of the inductor, the better its stability. Distributed capacitance can make the equivalent energy dissipation resistance larger. To reduce it, silk-covered wire or multi-strand enameled wire is commonly used, and sometimes honeycomb winding method is also used.5) Rated Current The rated current refers to the maximum current value that the inductor can withstand under the allowable working environment. If the operating current exceeds the rated current, the inductor will change its performance parameters due to heat, and even burn out due to overcurrent.Ⅳ Inductor ClassificationAccording to the form of inductor: fixed inductance, variable inductance.According to the nature of the magnetic conductor: air core coil, ferrite coil, iron core coil, copper core coil.According to work nature: antenna coil, oscillating coil, choke coil, trap coil, deflection coil.According to winding structure: single-layer coil, multi-layer coil, honeycomb coil.According to working frequency: high frequency coil, low frequency coil.According to structural characteristics: magnetic core coil, variable inductance coil, color code inductor coil, non-magnetic core coil, etc. Ⅴ Chip Inductor5.1 Purpose of a Chip InductorChip inductors are electromagnetic induction components wound with insulated wires. It is a commonly used electronic component. The function of the chip inductor: it is simple to say that it can isolate and filter the AC signal or form a resonant circuit with capacitors, resistors, etc. The inductor coil and capacitor in parallel can form an LC tuning circuit. Any current flowing through the chip inductor will generate a magnetic field, and its magnetic flux will act on the circuit.When the current passing through the chip inductor changes, the DC voltage potential generated in the chip inductor will prevent the current from changing. When the current passing through the inductor coil increases, and the current passing through the inductor coil decreases, the self-induced electromotive force is in the same direction as the current, which prevent the current from decreasing and release the stored energy at the same time. The direction of flow is opposite to prevent the increase of current, and at the same time, part of the electric energy is converted into magnetic field and stored in the inductor. Therefore, with inductor filtering, not only the pulsation of load current and voltage is reduced, the waveform becomes smooth, and the rectifier diode is turned on.The role of shielded chip inductors is different from that of the general one. The general chip inductors are not shielded in the circuit to achieve the desired effect. The shielded current instability of this kind inductor in some circuits plays a good blocking role. A metal shield surrounds the positively charged conductor, and the inside of the shield will induce the same amount of negative charge as the charged conductor. A positive charge equal to that of a charged conductor appears on the outside. If the metal shield is grounded, the positive charge on the outside will flow into the ground, and there will be no electric field on the outside, that is, the electric field of the positive conductor is shielded.The shielding inductance also plays a role of coupling in the circuit. In order to reduce the coupling interference voltage of the alternating electric field to the sensitive circuit, the inductance can be set with a metal shield with good conductivity between the interference source and the sensitive circuit, in addition, the metal shield is grounded. The coupling interference voltage to the sensitive circuit depends on the product of the alternating electric field voltage, the coupling capacitance and the ground resistance of the metal shield. As long as the metal shield is well grounded, the coupling interference voltage can be reduced. The electric field shielding is mainly based on reflection, so the thickness of the shielding body does not need to be too large, and the structural strength is the main consideration.5.2 Chip Inductor Classification1) Winding TypeIt is characterized by a wide range of inductance (mH～H), high inductance accuracy, low loss (that is, large Q), large allowable current, strong manufacturing process inheritance, simplicity, and low cost, and the shortcoming is size. For example, the ceramic core winding type chip inductor can maintain a stable inductance and a fairly high Q value at such a high frequency, so it occupies a place in the high-frequency circuit.NL series inductors are wire-wound type, 0.01~100uH, accuracy 5%, high Q value, which can meet general needs. NLC type is suitable for power circuit, rated current up to 300mA.NLV type is high Q value, environmentally friendly (reconstituted plastic), and can be interchanged with NL.NLFC has a magnetic screen and is suitable for power cords.2) Layer TypeIt has good magnetic shielding, high sintering density and good mechanical strength. The disadvantages of it are low pass rate, high cost, small inductance, and low Q value.Compared with wire wound chip inductors, it has many advantages: Small size is helpful to the miniaturization of the circuit.Closed magnetic circuit will not interfere with surrounding components, and will not be interfered by neighboring components, which is beneficial to high-density installation.Integrated structure, high reliability; good heat resistance and solderability.Regular shape is suitable for automatic surface mounting production.MLK type inductor has the characteristics of small size, good solderability, magnetic screen, high-density design, monolithic structure, and high reliability.MLG type has a small inductance and uses high-frequency ceramics, which is suitable for high-frequency circuits.MLK type working frequency is 12GHz, with high Q and low inductance (1n~22nH).3) Film TypeIt has the characteristics of maintaining high Q, high precision, high stability and small size in the microwave frequency band. The internal electrodes are concentrated on the same layer, and the magnetic field distribution is concentrated, which can ensure that the device parameters after mounting do not change much, and show good frequency characteristics above 100MHz.4) Weaving TypeIts characteristic is that the inductance per unit volume at 1MHz is larger than other chip inductors, small in size, and easy to install on the substrate. It is usually used as a miniature magnetic component for power processing.In actual applications, the inductor should be selected according to the situation, circuit requirement, and the material cost.5.3 Three Methods for Reading Chip Inductors1) Digital Position Identification (generally rectangular chip resistors use this nominal method)This method is to use three digits on the resistor to indicate its resistance. Its first and second digits are significant digits, and the third digit represents the number of "0"s added after the significant digits, no letters will appear in this place.For example: "472'" means "4720Ω"; "151" means "1510Ω". If it is a decimal, use "R" to mean "decimal point". It occupies one significant digit, and the remaining two are significant digits.For example: "2R4" means "2.4Ω"; "R15" means "0.15Ω".2) Resistor Color Code (generally cylindrical fixed resistors use this nominal method)Chip resistors are the same as general resistors. Most of them use four rings (sometimes three rings) to indicate their resistance. The first ring and the second ring are significant numbers, and the third ring is the magnification. For example: "brown, green and black" means "15Ω"; "blue, gray, orange and silver" means "68kΩ", the error is ±10%.3) E96 Number Mixes with LetterThis method also uses three digits to indicate the resistance value, that is, "two digits plus one letter". Two digits represent the E96 series resistance. Its third digit is the magnification expressed by the letter code. For example: "51D" means "332×103; 332kΩ"; "249Y" means "249×10-2; 2.49". Frequently Asked Questions about Inductor Uses1. What is inductor and its function?An inductor is arguably the simplest of all electronic components. It's a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. Typically, an inductor will consist of an insulated wire that's wound into a coil, much like a resistor. 2. What is the basic principle of inductor?An inductor is a passive electronic component which is capable of storing electrical energy in the form of magnetic energy. Basically, it uses a conductor that is wound into a coil, and when electricity flows into the coil from the left to the right, this will generate a magnetic field in the clockwise direction. 3. What is the function of inductor in AC circuit?Inductors store their energy in the form of a magnetic field that is created when a voltage is applied across the terminals of an inductor. The growth of the current flowing through the inductor is not instant but is determined by the inductors own self-induced or back emf value. 4. Does an inductor block AC?We know that inductor has inductive reactance property by which it opposes the flow of current through it. The equation of inductive reactance is, ... For this reason, an inductor can totally block the very high-frequency AC. 5. Why AC is blocked by inductor?Since inductor behaves like a resistor, DC flows through an inductor. The AC flowing through L produces timevarying magnetic field which in turn induces self- induced emf (back emf). ... For an ideal inductor of zero ohmic resistance, the back emf is equal and opposite to the applied emf.

"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. The RMS value represents the exact amount of AC voltage required to produce the same heating effect as a steady DC voltage." } }, { "@type": "Question", "name": "How do you calculate the RMS voltage of a sine wave?", "acceptedAnswer": { "@type": "Answer", "text": "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." } }, { "@type": "Question", "name": "Why is RMS voltage used instead of average voltage?", "acceptedAnswer": { "@type": "Answer", "text": "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." } }, { "@type": "Question", "name": "What is the difference between RMS and peak power?", "acceptedAnswer": { "@type": "Answer", "text": "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. 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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.

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.

IntroductionCurrent divider equations and voltage divider formulas help you better understand resistor functions in electronic circuits. The current divider circuit is a parallel circuit in which the source current or power supply current divided into a multiple parallel paths. In a parallel circuit, the terminals of all components are connected together, sharing the same two end nodes. This results in the current to flow or pass through different paths and branches. However, the current through each component can have a different value. While a voltage divider circuit is a very common circuit that takes a higher voltage and converts it to a lower one by using a pair of resistors.The main feature of a parallel circuit is that, although the branch circuit currents are different, the voltages of all connection paths are the same. Therefore, there is no need to find the voltage of each resistor, so that the branch current can be easily found by Kirchhoff's current law (KCL) and Ohm's law.Figure 1. Voltage and Current Divider Current CircuitsCatalogIntroductionⅠ Resistive Voltage Divider CircuitⅡ Resistive Current Divider CircuitⅢ Duality (Electrical Circuits)Ⅳ Frequently Asked Questions about Resistor Voltage Divider and Current Divider Rules and FormulasIn this section, through the discussion of the commonly used resistor series voltage divider circuit and resistors in parallel divider circuit to find their rules. This article contains plenty of equations based on Kirchhoff's current law and Ohm's law for you to master voltage divider and current divider circuits.  A Discussion of the Useful Voltage Divider and Current Divider Circuits.Ⅰ Resistive Voltage Divider CircuitIn electronics, a voltage divider (also known as a potential divider) is a passive linear circuit that produces an output voltage that is a fraction of its input voltage. It is a simple circuit which turns a large voltage into a smaller one. The basic voltage divider circuit with two resistors in series as shown in the Figure 2. is analyzed, and some useful formulas are obtained:Figure 2. Basic Voltage Divider CircuitThe following equation is given by Kirchoffs Current Law (KCL):The following equation is given by Kirchoffs Voltage Law (KVL):Equation of voltage current relation of circuit elements:Substituting the Ohm's law of the resistance element into the KVL equation, the calculation formula for the current i is obtained:Then substitute it into the Ohm's law of the resistance element, the voltage division formula for calculating the resistance voltage is obtained:Generally speaking, when N resistors are connected in series, the voltage on the Kth resistor can be calculated according to the following voltage division formula:The resistor series voltage divider formula shows the relationship between the voltage of a certain resistor and the total voltage. The voltage division formula expresses that the voltage of a resistor is proportional to its resistance value, that is, when the resistance increases, the voltage also increases.According to the voltage reference direction obtained by the above voltage divider circuit formula, it can be seen that it has nothing to do with the selection of the current reference direction. When the reference direction of the voltage variable uk or us involved in the formula changes, a negative sign will appear in the formula.As shown in the Figure 3, find the voltage Uab when R=0Ω, 4Ω, 12Ω, ...∞.Figure 3. Voltage Reference DirectionThe voltage Uac and Ubc can be obtained by using the resistor series voltage divider formula:Substituting the resistance R into the above formula, after obtaining the voltage Ubc, then using KVL to obtain the voltage Uab, the calculation result is as follows:It can be seen from the calculation results that as the resistance R increases, the voltage Ubc gradually decreases, and the voltage Uab changes from negative to positive, indicating that its actual direction will varies with the change of the resistance R.The Figure 4. below shows the dual-supply DC voltage divider circuit. Try to find the range of potential change at point a when the sliding end of the potentiometer moves.Figure 4. Dual-supply DC Voltage Divider CircuitSolution: Replace the two potentials of +12V and -12V with two voltage sources to obtain the circuit shown in Figure 4. (b).When the sliding end of the potentiometer moves to the bottom end, the potential at point a is the same as that at point c:When the sliding end of the potentiometer moves to the top, the potential at point a is the same as that at point b:When the sliding end of the potentiometer gradually moves from bottom to top, the potential at point a will continuously change between -10V to 10V.Here discusses the change law of load current i and voltage u when an actual supply powers to a variable resistor load. As shown in the Figure 5, RL is a variable resistance load, and R0 represents the internal resistance of the power supply:Figure 5. Variable Resistor LoadLoad current i:Among them, k=RL/R0 represents the ratio of the load resistance to the internal resistance of the power supply, and isc=us/R0 represents the current when the load is short-circuited.Load voltage u:Among them, uoc=us represents the voltage when the load is open.Power absorbed by load resistor:When the coefficient k=RL/R0 takes different values, a series of relative values of current, voltage and power are calculated, as shown in the following table:K=RL/R000.20.40.60.81.02.03.04.05.0∞i/isc10.8330.7140.6250.5550.50.3330.250.20.1670u/uoc00.1670.2860.3750.4440.50.6670.750.80.8331p/pimax00.5560.8160.9380.98810.8890.750.640.5560According to the above data, the curve of voltage, current and power changing with load resistance can be drawn, as shown in the Figure 6:They show:1. When the load resistance gradually increases from zero, the load current gradually changes from the maximum value isc=us/R0 to zero. When the load resistance is equal to the internal resistance of the power supply, the current is equal to half of the maximum value.2. When the load resistance gradually increases from zero, the load voltage gradually increases from zero to the maximum value uoc=us. When the load resistance is equal to the internal resistance of the power supply, the voltage is equal to half of the maximum value.3. When the load resistance is equal to the internal resistance of the power supply, the current is equal to half of the maximum value, the voltage is equal to half of the maximum value, and the power absorbed by the load resistance reaches the maximum value, and pmax=0.25uocisc.The non-linear change law of the current when the load resistance changes can be seen from the resistance scale of an ordinary multimeter. The circuit model of a multimeter electric blocking is a series connection of a voltage source and a resistor. When we use a multimeter to measure unknown resistance, we should first short-circuit the multimeter and adjust the zero potentiometer pointer to 0Ω. At this time, the current is the largest and the meter pointer is fully deflected. When the short-circuit wire is removed, the pointer of the multimeter returns to ∞, and the measured current is zero at this time.When the multimeter is connected to the measured resistor, as the resistance value changes, the current of the meter head will change accordingly, the pointer will be deflected to the corresponding position, and the measured resistance value can be directly read according to the scale on the surface. There is a special case, when the measured resistance value is just equal to the internal resistance of the multimeter, the current is half of the full deflection current, and the pointer stays in the middle position. Conversely, the internal resistance can be known from the reading in the middle of the multimeter’s electrical barrier scale. For example, the reading of a 500-type multimeter when the pointer stays in the middle position is 10, the internal resistance when using a ×1k electrical barrier is 10kΩ, and the internal resistance is 1kΩ when using a ×100 electrical barrier. If necessary, use Voltage Divider Calculator to calculate the output voltage of a resistor divider circuit for a given set of resistor values and source voltage. Ⅱ Resistive Current Divider CircuitA current divider is defined as a linear circuit that produces an output current that is a fraction of its input current. The following formula describing a current divider is similar in form to that for the voltage divider. The Figure 7. shows a circuit in which a current source supplies power to two parallel resistors, and some useful formulas are drawn from its analysis. Figure 7. Resistive Current Divider CircuitThe following equation is given by Kirchoffs Voltage Law (KVL):The following equation is given by Kirchoffs Current Law (KCL):Equation of current voltage relation of circuit elements:Substituting the Ohm's law of the resistance element into the KCL equation, the calculation formula for the voltage u is obtained:Then substitute Ohm's law into the resistive current divider equation for calculating the resistor current:The resistive current divider formula of two parallel resistors expressed by resistance parameters is:Generally speaking, when n resistors are connected in parallel, the current on the Kth resistor can be calculated according to the following formula:The resistive current divider in parallel formula indicates the relationship between the current of a resistor and the total current. It shows that the resistance current is proportional to its conductance value. For example, the current will increases when the conductance increases.According to the current reference direction obtained by the above formula, it can be seen that it has nothing to do with the selection of the voltage reference direction. When the reference direction of the current is or ik changes, a negative sign will appear in the formula.Figure 8. Resistive Divider CircuitAccording to the characteristics of two resistors in parallel, the current in the 3Ω and 6Ω resistors is obtained:Then, the current in the 12Ω and 6Ω resistors is obtained:Calculate the current i5 in the short-circuit line according to the KCL equation of node a:i5 can also be calculated according to the KCL equation of node b:It should be noted that the current i5=1A in the short circuit is different from the total current.  If necessary, the Current Divider Calculator can be used to determine the current going through any branch in a parallel circuit. Enter a current source and resistance values to calculate the current through each resistor. The calculator will display the current through each resistor entered. Ⅲ Duality (Electrical Circuits)According to the above-mentioned analysis of the resistive voltage divider circuit and current divider circuit, there is a certain similarity between them.Figure 9. Duality Circuit ExamplesThe equations of the resistor divider circuit are listed as follows:It can be seen that the equations of these two circuits have a dual relationship. If the current i in the KCL equation of a certain circuit is replaced with the voltage u, the KVL equation of another circuit is obtained; the voltage u in the KVL equation of a certain circuit is replaced with the current i, and the KCL equation of another circuit is obtained. This similar relationship in circuit structure is called topological duality. Similarly, replace u in the VCR equation of a certain circuit with i, i with u, R with G, G with R, etc., you can get the VCR equation of another circuit. This similar relationship of the element VCR equation is called element duality. If two circuits are both topological duality and component duality, they are called dual circuits.The circuit equations of the dual circuit are dual, and the various formulas and results derived therefrom are also dual. For example, the dual formula derived for the dual circuit of Figure 9 (a) and (b) is as follows:This section is a simple analysis of dual circuits, dual formulas, dual theorems and dual analysis methods in order to better grasp the basic concepts of circuit theory and various analysis methods. Here are a few test questions that can be used to test how well you learn about voltage divider and current divider circuits:1) Find the voltages u1 and u2 in the circuit shown in the following figure:2) Find the current i1 and i2 in the circuit shown in the following figure:3) Find the current i2, is and voltage u in the circuit shown in the following figure: Ⅳ Frequently Asked Questions about Resistor Voltage Divider and Current Divider Rules and Formulas1. What is VDR and CDR?The Voltage Divider Rule formula (VDR) shows how the voltage distributes among different resistors in a series circuit. Similarly, the Current Divider Rule formula (CDR) shows how current distributes in a parallel circuit. 2. What is the current divider rule with examples?When two resistors are connected in a parallel circuit, the current in any branches will be a fraction of the total current (IT)). If both the resistors are of equal value, then the current will divide equally through both the branches. 3. Why does a voltage divider need two resistors?One resistor can be used to drop voltage (if the load draws current) but to divide voltage you need something to create a division ratio. To be a voltage divider the output voltage needs to be a constant proportion of the input voltage. ... Note that this need for two resistors only applies to DC. 4. Where are current divider used?By using a current divider, the current flowing through a component can be minimized and thus smaller component size can be used. For example, in a case where larger resistor wattage is required; adding multiple resistors in parallel decreases the heat dissipation, and smaller wattage resistors can do the same job. 5. What is voltage divider formula?A voltage divider is applying a voltage across a series of two resistors. We may draw in a few different ways, but they should always essentially be the same circuit. Thus formula is given as follows: V_{out} = frac{R_b}{R_a+R_b} times V_{in}

IntroductionA voltage regulator is a circuit that generates a fixed output voltage of a preset magnitude that remains constant regardless of changes to its input voltage or load conditions. It converts an unstable dc voltage into a stable dc voltage. Its power supply composed of discrete components has the advantages of large output power and wide adaptability. In recent years, integrated regulated power supplies have been widely used. Among them, three-terminal series regulators are the most common for low-power regulated power supplies. The commonly used integrated voltage regulators in the circuit mainly include 78xx series, 79xx series, adjustable integrated voltage regulator, precision voltage reference integrated voltage regulator, etc.What is a Voltage Regulator and How Does It Work?CatalogIntroductionⅠ Voltage Regulator ClassificationⅡ Main ParametersⅢ Applying NotesⅣ Typical Examples: LM317 & LM7805Ⅰ Voltage Regulator ClassificationVoltage regulators are generally divided into linear voltage regulator and switching voltage regulator. Linear voltage regulator is a circuit used to maintain a steady voltage, which is divided into low dropout type and general dropout type. Switching voltage regulator is a type of switch mode power supply circuit that is designed to efficiently reduce dc voltage from a higher voltage to a lower one, which is divided into step-down type, step-up type and integrated type with opposite input and output polarity.According to the number of outlet terminals and usage of the voltage regulator, it can be roughly divided into three-terminal fixed type, three-terminal adjustable type, multi-terminal adjustable type and single-chip switch type.The three-terminal fixed type voltage regulator integrates sampling resistors, compensation capacitors, protection circuits, high-power adjustment tubes, etc. on a chip. So that the entire integrated circuit block has only 3 terminals: input, output and public. It is very convenient to use. Its disadvantage is that the output voltage is fixed, so a series of products with various output voltages and current specifications must be produced to match.The three-terminal adjustable integrated voltage regulator only needs two external resistors to obtain various output voltages.The multi-terminal adjustable type is an early integrated voltage regulator. With small output power and many pins, it is not convenient to use, but the precision is high and the price is cheap.The monolithic switch type integrated regulated power supply develops in recent years, and its efficiency is particularly high. Its working principle is different from the above three types. It is a converter that converts DC to AC (high frequency) and then DC. Usually there are two types of pulse width modulation and pulse frequency modulation, and the output voltage is adjustable.Ⅱ Main Parameters1) Voltage Regulation RateIt is an important indicator that characterizes the voltage regulation performance of the integrated voltage regulator, also known as the voltage regulation coefficient or stability. It represents how stable the output voltage V0 of the regulator is when the input voltage V1 changes.2) Current Regulation RateIt is also known as current stability coefficient, and shows the ability of the regulator to suppress output voltage fluctuations caused by changes in load current (output current) when the input voltage remains unchanged.3) Ripple Rejection RatioIt reflects the ability of the regulator to suppress the mains ripple voltage introduced at the input.4) Output Voltage Temperature CoefficientIt is also known as the output voltage temperature change rate, and refers to when the input voltage and output current (load current) remain unchanged, the output voltage of the regulator changes with temperature.5) Long-term Stability of the Output VoltageIt refers to the magnitude of the change in the output voltage value over time (when the output current, input voltage and ambient temperature remain unchanged). It is usually the maximum amount of change in the output voltage of the regulator within a specified time.6) Output Noise VoltageIts absolute value represents the noise performance of the regulator directly. There is also a percentage value of the output noise voltage Vn and the output voltage V0 of the regulator to characterize the noise performance.7) Thermal StabilityIt refers to the thermal stability of the voltage regulator. It is usually the percentage value of the relative change in the output voltage caused by its unit power consumption.8) Temperature StabilityIt is the percentage value of the relative change of the regulator's output voltage within the specified maximum change range of operating temperature. Ⅲ Applying Notes① There are many types of integrated voltage regulator. According to the adjustment method there are linear and switch type. Based on the output method, there are fixed and adjustable types. Because of the obvious advantages of the three-terminal voltage regulator, it is more convenient to use and operate.② Before connecting to the circuit, it is necessary to distinguish the pins and their functions to avoid damage to the integrated block. The input and output ends of the three-terminal integrated voltage regulator with an output voltage greater than 6v need to be connected with protective diodes to prevent the rapid discharge of the output capacitor, which will cause damage to the three-terminal integrated voltage regulator when the input voltage drops suddenly.③ In order to ensure the stability of the output voltage, the minimum input voltage difference should be guaranteed. For example, the minimum pressure difference of the three-terminal integrated voltage regulator is about 2v, and it should be kept above 3v during general use. At the same time, it should be noted that the maximum voltage difference of input and output does not exceed the specified range.④ In order to expand the output current, the three-terminal integrated voltage regulator is allowed to be used in parallel.⑤ When using, the welding should be firm and reliable. If a heat dissipation device is required, it should meet the required size.If you have a bad regulator, it may cause many components such as the fuel pump, ignition system, or other parts which require a minimum amount of voltage to not function correctly. You may experience the engine sputtering, a rough idle, or simply a lack of acceleration when you need it. Ⅳ Typical Examples: LM317 & LM7805The LM317 device is an adjustable three-terminal positive-voltage regulator capable of supplying more than 1.5 A over an output-voltage range of 1.25V to 37V. It serves a wide variety of applications including local, on card regulation. This device can also be used to make a programmable output regulator, or by connecting a fixed resistor between the adjustment and output, the LM317 can be used as a precision current regulator.LM317 Specifications Adjustable output voltage as low as 1.2VOutput voltage: 1.25-37V DCGuaranteed 1.5A output currentOutput current: 5mA-1.5ATypical linear adjustment rate: 0.01%Max input-output voltage difference: 40V DCTypical load regulation rate: 0.1%Min input-output voltage difference: 3V DCRipple rejection ratio: 80dBOperating temperature: -10± 85℃Output short circuit protectionStorage temperature: -65± 150℃Over-current, overheat protectionOutput voltage: 1.25-37V DCAdjusting tube safe working area protectionOutput current: 5mA-1.5A The linear voltage regulator LM7805 has over-voltage protection, over-current protection, and over-heat protection functions, which makes its performance very stable. It is a 5V regulator, and is able to achieve output current above 1A, and has a good temperature coefficient. So the product has a wide range of applications. Have a look to get more specific info by the following video:Why is the LM7805 is a very Popular Voltage Regulator?As a member of 78xx series of fixed linear voltage regulators, the following is a very good summary of the basics on linear voltage regulator 7805:ParameterSymbolConditionsMinTypicalMaxUnitOutput VoltageVoTj=25℃4.85.05.2V5.0mA<Io<1.0APo<15WVi=7v to 20v4.755.05.25VLinear Adjustment rate△VlineTj=25℃, Vi=7V to 25V 3.0100mVTj=25℃Vi=8V to 12V 1.050mVLoad Adjustment Rate△VloadTj=25℃,lo=5.0mA to 1.5A  100mVTj=25℃lo=250mA to 750mA  50mVStatic CurrentIqTj=25℃  8mAStatic Current Rate△Iqlo=5mA to 1.0A  0.5mAVi=7V to 25V  0.8mAOutput Voltage Drift△Vo/△Tlo=5mA -1.1 mV/℃Output Noise VoltageENf=10Hz to 100KHzTj=25℃  40μV/VoRipple Rejection RatioSVRf=120Hz,Vi=8V to 18V62  dBVoltage DifferentialVdlo=1.0ATj=25℃ 2.0 VOutput ImpedanceRof=1KHz 17 mΩShort-circuit CurrentIscVi=35VTj=25℃ 750 mAPeak CurrentIscpTj=25℃ 2.2 AIf you want to make a 5V power supply with a 7805, output currents up to 1A can be drawn from the IC provided that there is a proper heat sink. A 9V transformer steps down the main voltage, 1A bridge rectifies it and capacitor C1 filters it and 7805 regulates it to produce a steady 5V DC. Then you can test it, turn on the DC power supply and adjust the output voltage of about 8V or slightly larger. Or alternatively you can use a battery 9V-12V as voltage source. Look at the voltmeter panel when you set the voltage. Prepare a DC voltmeter readings on voltage range 50V to measure the output voltage of the IC 7805. Frequently Asked Questions about Voltage Regulator1. What is voltage regulator and how it works?A voltage regulator generates a fixed output voltage of a preset magnitude that remains constant regardless of changes to its input voltage or load conditions. ... A switching regulator converts the dc input voltage to a switched voltage applied to a power MOSFET or BJT switch. 2. What is a voltage regulator used for?Voltage regulator, any electrical or electronic device that maintains the voltage of a power source within acceptable limits. The voltage regulator is needed to keep voltages within the prescribed range that can be tolerated by the electrical equipment using that voltage. 3. What are the three 3 basic types of voltage regulators?There are three types of Switching voltage regulators: Step up, Step down, and Inverter voltage regulators. 4. What happens when voltage regulator goes bad?If you have a bad regulator, it may cause many components such as the fuel pump, ignition system, or other parts which require a minimum amount of voltage to not function correctly. You may experience the engine sputtering, a rough idle, or simply a lack of acceleration when you need it. 5. Where are voltage regulators used?Electronic voltage regulators are found in devices such as computer power supplies where they stabilize the DC voltages used by the processor and other elements. In automobile alternators and central power station generator plants, voltage regulators control the output of the plant.