Buck-Boost Converter

What is Buck-Boost Converter?

• We can define Buck-Boost Converter as a type of DC – DC converter whose generated output voltage that is either higher or smaller than the applied input voltage.

• Buck-Boost Converter is alike a flyback converter, but difference is that it uses inductor and flyback converter uses transformer.

• Buck-Boost Converter is a combination of Buck Converter and Boost Converter.

Below figure shows a Buck-Boost Converter Module;

Buck-Boost Converter Module

To know more about Buck Converter please visit the article, "What is Buck Converter".

There are two different topologies of buck-boost converter. Inverting topology and non-inverting topology. In detail both are explained below;

The inverting topology

• Like buck converter and boost converter the inverting buck-boost converter is like a switched-mode power supply and its circuit topology is same like buck converter and boost converter.

• The polarity of the output voltage is opposite as compare to the applied input voltage.

• For simple or basic inverting buck-boost converter we can see or get a negative output voltage with respect to the ground.

• The duty cycle of the switching transistor or MOSFET, the output voltage of buck-boost converter is adjustable or changeable.

• The driving circuitry becomes complicate, when we see that the switching component does not have a terminal at ground. Which can be a disadvantage.

• But, this disadvantage is of no importance. If the power supply is isolated from the load circuit because at this condition the power supply and polarity of diode can be upturned or reversed.

• At the reversed condition, the switch can be on either the supply side or at the ground side.

Working of inverting topology

• An Inverting buck-boost converter is shown in below figure. It is the schematic of a basic inverting buck-boost converter which is working in continuous conduction mode (CCM).

Inverting Buck-Boost Converter

• We can see an output capacitor, in the power stage a metal-oxide semiconductor field-effect transistor (MOSFET) is present, a diode, and an inductor is present.

• Anode of the diode is connected to the load.

• Anode of the diode is also connected to negative terminal of electrolytic capacitor.

• When the MOSFET (M1) is ON, the voltage through the inductor (L1) is Vin, and the current in the inductor ramps up with the rate that is proportional to the applied input voltage Vin.

• This results in storing energy in the inductor L1. While M1 is ON, the output capacitor C1 supplies the entire load current.

• When the M1 is OFF, the diode (D1) is forward-biased and the inductor current ramps down at a rate proportional to output voltage Vout.

• While M1 is OFF, energy is transferred from the inductor L1 to the output load and output capacitor C1.

The non-inverting topology

• Below figure shows a non-inverting buck-boost converter. Here we can see a buck (step-down) converter is joint with a boost (step-up) converter.

Non-Inverting Buck-Boost Converter

• The output polarity of this type of converter is same like the polarity of the applied input. But the output level may vary i.e. may be higher or lower depending on the design and component selection.

• We can see in the figure that there is only one inductor is used even there is buck mode and boost mode is combined.

• This single inductor controlled by switches instead of diodes. At a time only one switch is in ON condition.

• If it uses many inductors with only one switch same like seen in Cuk or SEPIC topologies, then it is called as "four-switch buck-boost converter".

• The popular non-inverting buck-boost topologies are; Zeta, SEPIC and two-switch buck-boost converter.

• All these above mentioned buck boost topologies generate positive output but these topologies have extra power components and less efficiency as compared to a basic inverting buck-boost converter.

Working of non-inverting topology

• We can see in figure of non-inverting buck-boost conductor; two high frequency switching MOSFETS are used along with the two diodes and these diodes have a low forward junction voltage when it conducts.

Operation of buck converter

• We can understand the operation of buck-boost inductor on the basis of inductor's "reluctance", which allows quick change in current (current across inductor).

• Initially current through the inductor is zero. This means at the initial stage when MOSFET is not working i.e. switch is open and there’s no current across the inductor i.e. nothing is charged.

• When the MOSFET switch is first closed, the blocking diode stops current from flowing through it as it is reversed biased, so the current passes through the inductor.

• Initially the Inductor will keep the current low by dropping most of the source voltage, as the inductor doesn't like fast current change. With the time the inductor allows the current to increase slowly with the decrease in voltage drop. By this inductor will store energy i.e. magnetic field.

Let see the operation of buck converter in step wise in detail;

• Below figure shows the mode of operation of buck converter when MOSFET M1 is ON. In this mode the high frequency square wave generated by IC keep the MOSFET M1 ON and OFF. MOSFET M2 is turned off in this case.

Buck converter operation when M1 is ON

• When the gate terminal of MOSFET M1 is high, M1 starts to work and makes current to flow though inductor L1. This current charges L1, capacitor C1 and supply further to the connected load.

• The diode D1 is turned off because of the positive voltage on its cathode i.e. it is reversed biased.

• Below figure shows the mode of operation of buck converter i.e. current flow when MOSFET M1 is OFF. Now the inductor L1 is fully charged and now it is the only source of the current.

Buck converter operation when M1 is OFF

• The magnetic field generated across the inductor L1 starts to collapse and generates back E.M.F. this E.M.F. opposites the voltage polarity across L1.

• This polarity change turns on the diode D1 and current flows through the diode D2 and further to the connected load.

• Further as the current across inductor L1 decreases, the charge stored in capacitor C1 during the ON time of MOSFET M1, now adds to the current flowing across the load. This additional current from C1 keeps output voltage (Vout) constant during the M1 OFF time.

• This gives an advantage of less ripple at the output.

Operation as a Boost Converter

• Below figure shows the mode of operation of boost converter when MOSFET M1 is continuous ON. In this mode the high frequency square wave generated by IC is applied to the MOSFET M2 gate terminal.

Boost converter operation when M2 is ON

• When MOSFET M2 is ON and it’s conducting, the input current passes across the inductor L1 and through M2, and further current flow to the negative terminal of supply. This current charges or creates magnetic field around inductor L1.

• Also in this step the diode D2 not conducts i.e. current not flows across the diode D2 because high speed conducting MOSFET M2 keeps anode terminal of diode D2 at ground potential.

• Now for this ON period, the charge developed by previous oscillating cycles on the capacitor C1 acts as a supply for the load.

• The slow discharge of capacitor C1 throughout the ON period and its immediate recharging creates high frequency ripple on the output voltage.

• This high frequency ripple is at a potential of approx. Vs + Vout.

• OFF-Period of MOSFET M2 can be understand by below figure;

Boost converter operation when M2 is OFF

• As the OFF-period of MOSFET M2 starts, the inductor L1 charges and capacitor C1 partially discharges.

• As the inductor L1 charged it generates a back E.M.F. The value of this E.M.F. depends on the rate of change of current as MOSFET M2 switches OFF and ON the total inductance. This inductance is hold by the coil (inductor).

• So, depending on the circuit design the back E.M.F. can be of any voltage range.

• Now the polarity of the voltage across inductor L1 has now reversed and this voltage is added to the input voltage Vs. This gives an output voltage that is equal or greater than the applied input voltage Vs.

• Diode D2 is now forward biased i.e. it starts to conduct and so the current further flows through the load.

• At the same time this current from diode D2 re-charges the capacitor C1. Which will be further use in next period of MOSFET M2 ON.

Applications of Buck-Boost Converter

• We can see Buck-boost (step-down and step-up) converters mostly in the applications like; most of industrial machines or tools where different power supply voltages are needed for machine or tool operation, industrial computer hardware’s and automotive systems.

• Battery dependent systems; where at the full charge of battery, the high voltage can’t be supply to the system, then buck regulator circuit works. But as the battery charge comes to end the boost regulator circuit starts to work and boost the available voltage to the required level, so the system works properly.

• These types of battery depended systems can be seen in automotive applications i.e. mostly in e-bikes or e-cars.

• In the applications mentioned above, the applied input voltage could be either higher or lower than the required output voltage.

Conclusion

By joining these two regulator designs i.e. buck regulator and boost regulator we can have a regulator circuit which can handle a wide range of input voltages. These input voltages may be both higher or lower than that required by the circuit.

Both buck and boost regulator uses same types of components and we have to just re-arrange them, depending on the applied input voltage level.

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Ohm's law Calculations and Calculator

Ohm’s law many of us heard many times. To understand ohm’s law is very important for electrical and electronics engineer, technicians, hobbyist, etc. Here we will discuss in detail about Ohm’s law definition, Ohm’s law calculations and calculator.

Ohm's Law

Ohm’s law Calculator

Enter any two known values and press "Calculate" to get solutions of the others.
Fields should be reset to 0 or clear before each new calculation.

Volts

Amps

Ohms

Watts

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This Ohm’s law calculator will help you to perform ohm’s law calculations easily. Even manually calculated values using ohm’s law formula you can compare with the results of this calculator.

Ohm’s law Calculations and Calculator Excel Sheet

An excel sheet for Ohm's law calculation you can access by clicking on below button. Download it and save in your laptop, computer, tablet or mobile;

Ohm's law Calculator

Now let discuss Ohm’s law definition and its calculation in detail;

What is Ohm’s law

Definition of Ohm’s law is, “the current through a conductor between two points is directly proportional to the voltage across the two points”.

Introduce Resistance as constant of proportionality. Resistance in below equation is constant and not dependent of the current.

The German physicist Georg Ohm invented this law. As per him, at a constant temperature, the current flowing through a fixed linear resistance is directly proportional to the voltage applied across it, and inversely proportional to the resistance.

In other words, we can say that, the relationship between Voltage, Current and Resistance is called as Ohm’s law.

Ohm's law is an empirical relation i.e. experimental relation which precisely defines the conductivity of the many of electrically conductive materials over different level of current.

Non-ohmic material do not follow Ohm's law.

Ohm’s law equation

The mathematical equation for the same can be given as; Resistance = Voltage / Current.
Where,
Current (I) = current through the conductor in the units of amperes.
Voltage (V) = voltage measured across the conductor in the units of volts.

Resistance (R) = resistance of the conductor in the units of ohms.

Ohm’s law formula

For calculating voltage, V
V = I x R

For calculating voltage, I
I = V / R

For calculating voltage, R
R = V / I

Ohms law triangle

We can remember the ohm’s law formula's by the help of picture, which is called as Ohms law triangle.

The voltage, current and resistance in this triangle occupies different spaces and are fixed in these spaces i.e. no variation of spaces is allowed.

In triangle initial position starts with Voltage which is at top. Current and Resistance is at below.

The voltage, current and resistance positions are fixed in the triangle as per Ohm’s law.

Check below triangles to understand Ohm’s law in easy way;

Ohm's Law Triangle

Electric Power and Ohm’s law

We can define electric power as, it is the rate per unit time, an electric circuit transfers electrical energy. Watt one joule per second is the SI unit of power.

It is represented by the letter P.
In terms of voltage and current the Power can be given as; P = V x I

Electric Power formula using ohm’s law

Also using ohm’s law electric power formula, we can write as;

P = V² ÷ R

P = I² x R

Power Triangle

We can remember the formula for power by the help of picture, which is called as power triangle.

The power, current and resistance in this triangle occupies different spaces and their positions are fixed in these spaces.

In triangle initial position starts with Power which is at top. Current and Resistance is at below.

Check below triangles to understand electrical power formula's in easy way;

Power Triangle

Ohm’s law wheel

Now we know very well all the formulas related to ohm’s law formula and electric power formula.

By using these formulas, we can design ohms law wheel. According to Voltage, Current, Power, and Resistance twelve different formulas are mentioned in ohms law wheel.

Ohm's Law Wheel

Also, on the basis of same we can create Ohm's law Table of Formulas;

Ohms Law Table of Formulas

Conclusion

The person who mostly deals with electrical and electronics terms or mostly with resistance the Ohm's law is an important rule to solve the current, voltage, resistance and power issues. The calculations presented here surely will help to calculate Ohm's law manually and to understand the Ohm's law concept. The calculator presented here will ease the calculation process.

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Resistor for LED Calculator

In almost all applications where LED’s are used, a resistor in series with LED is connected. Selection of resistor for LED is not a difficult task only step wise process has to follow which is given in this article.

Resistor for LED Calculator

Also, Resistor for LED Calculator has been provided which will help you to calculate the LED resistor in easy way. Also, you can cross check your calculated LED resistor value is matching with the value generated by LED resistor calculator.

This calculator for LED resistor is very useful and easy to use.

Click below button to get Resistor for LED Calculator or LED Resistor Calculator

Please click on below symbol and download the "Resistor for LED Calculator" in your computer, laptop, tablet or mobile.

Resistor for LED Calculator

Now let discuss the steps to calculate Resistor for LED and same steps has been used to develop Resistor for LED Calculator;

Use of Resistor for LED’s

LEDs are more common for almost many of applications as an indicator or light. This is because it has good power efficiency. Also, it has good life span as compare to incandescent or fluorescent lamps.

Full form of LED is Light Emitting Diode. It’s a type of diode. Like diode it also has polarity i.e. anode and cathode. With suitable application of power across it i.e. the power matching to LED specifications, LED works and produce light.

We have to follow the polarity requirement of the LED, same like diode otherwise it will fail. Because LED allows low value of reverse polarity voltage approximately 5 volts.

Know you know that LED is a diode so, the current across the LED should not cross the limit otherwise it will cause failure to the LED.

This is the reason why resistor in the series with the LED is used. In simple words the LED resistor controls the current across the LED.

Resistor with LED

Now let see the necessities or requirements for the current control resistor that must be used with a LED;

We know that LED’s are available in different colours. Each colour LED is made by different materials and these material have different voltage requirements. So, each colour LED has different electrical requirements and hence different specifications.

In LED specifications we refer a term, “Forward Voltage (Vf)”. This is the voltage which makes LED to work.

Below are forward voltage requirements of some common LED’s;

• Red = approximately 1.7 volts

• Green = approximately 2.2 volts

• Orange = approximately 2.0 volts

• Yellow = approximately 2.1 volts

• White = approximately 3.2 volts

• Blue = approximately 3.2 volts

Now we can clearly see the variation in the forward voltage. By knowing the forward voltage, we have to pass current in proper amount across the LED. So, resistor in series with LED is used, where resistor controls the current according to forward voltage.

Correct resistor for LED

Without using a resistor, if we apply direct DC voltage to a LED, it will work.

But if the applied voltage and current is not matching to the requirement of LED, the LED will glow dim or bright or may be it get heated and fails.

In simple words, less current across LED, the LED will glow dim. More current across LED, the LED will glow bright.

If current crosses the electrical requirement of LED, the LED will fail.

So, a resistor we have to connect in series with the LED whose current we want to control.

Calculation for selection of LED resistor

Resistor in series with LED

The resistor selection depends on Ohm’s law i.e. R = V/I.

V is the applied DC voltage. This can be calculated as; V = (applied Vdc) – Vf.

I is the amount of current which should flow across the LED to make it ON.

Applied DC voltage should me more than forward voltage (Vf) of LED. i.e. if you apply 12Vdc and LED has Vf of 3.2V so, a drop of 3.2V is easily possible across the LED and it works. But less than 3.2 will never make LED to glow.

The typical forward voltage and forward current requirement of LED you can easily find in LED specification sheet.

Now our formula becomes;

R = (Vdc – Vf) / If

Now let try with an example;

Vdc = 12V

Vf = 3.2V

If = 0.010A

Then,

R = (12 – 3.2) / 0.010

R = 880 ohm. Select standard resistor value; R = 910 ohm.

Now calculate the power rating of resistor.

P = V x I

P = (12 – 3.2) x 0.010

P = 0.088W

We can select 0.25W for this application as it is more than the calculated one. If we use the wattage rating less then calculated value, the resistor become hot.

While creating "Resistor for LED Calculator" we followed same formulas.

Many LED’s in a circuit

Consider a case, there’s a requirement of many LED’s in an application.

We can use multiple LED’s of same colour or different colour in parallel connection.

By this same voltage from voltage source will be available at each LED string, but the current requirement will increase according to number of LED’s.

As current increase the wattage requirement of each resistor will also increase.

Let understand this by an example;

Vdc = 12V

Vf = 3.2V

Number of LED strings in parallel = 5

Single LED current requirement = 0.010A

Total current requirement, I =5 x 0.010 = 0.050A

Using the formula;

R = (12 – 3.2)/0.050

R = 176 ohm. Select standard resistor value; R = 180 ohm.

Wattage we can calculate;

P = V x I = (12 – 3.2) x 0.050 = 0.44

We can select 0.25W for this application as it is more than the calculated value.

For different colour LED’s we have to calculate current requirement of each string and add all current.

In this case also voltage will be same and we have to subtract forward voltage from supply voltage.

Calculation of power rating of resistor value will remain same like previous performed calculations. As mentioned before you have to select high wattage resistor as compare to calculated one.

In "Resistor for LED Calculator" we had already included the calculator for both resistor for LED in series and resistor for LED in parallel.

To know more about resistor, please visit below articles;

"Resistor and Working of Resistor"

"Electrical Resistance and Resistivity"

"Standard Resistor Values"

Conclusion

We had seen that the selection of resistor for LED is simple and we have to follow the Ohm’s law. But we have to give importance to LED’s specification sheet before performing any calculations. So, that the voltage, current and wattage should be in the limit and do not damage the resistor. The Resistor for LED Calculator will help you to easily calculate these values.

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RoHS 3 Directive

We know that full form of RoHS is Restriction of Hazardous Substances. It influences the whole electronics and electrical products. Here we will see the details about RoHS 3 directive and the particulars which will make our electrical and electronics products RoHS 3 compliant.

More details about RoHS, RoHS Substances and WEEE you can get from;

"RoHS and RoHS Substances"

"RoHS and WEEE for e-Waste"

What is RoHS 3 directive?

Let before understanding the RoHS 3 directive let get some details about RoHS 1 and RoHS 2.

The initial RoHS is Directive 2002/95/EC, where it restricts the use of six hazardous materials present in electrical and electronic products. This is also called as RoHS 1. RoHS is mandatory for all relevant electrical and electronics products in the EU market from July 1, 2006.

Then RoHS 2 is presented i.e. directive 2011/65/EU. It contains CE-marking directive.

Now RoHS 3 is introduced to update the present RoHS directive. RoHS 3 is also known as 2015/863 directive. With the introduction of RoHS 3 directive four extra or additional restricted substances (phthalates) are included or added to the list of previous six substances. Also it adds Category 11 products i.e. All other electrical and electronic equipment. These are not covered in other RoHS categories.

RoHS 3

Why to proceed for RoHS 3 compliant products?

Initially the RoHS 1 directive (2002/95/EC) and RoHS 2 directive (2011/65/EU) restricts six hazardous substances. The list of six hazardous substances and their permitted content as follows;

• Lead(Pb) : 0.1%

• Mercury: 0.1%

• Cadmium(Cd): 0.01%

• Hexavalent chromium (Cr6+) : 0.1%

• Polybrominated Biphenyls (PBB): 0.1 %

• Polybrominated Diphenyl Ethers (PBDE): 0.1 %

RoHS 3 directive EU 2015/863 added four more hazardous substances in the old list of six substances. The list of newly added four hazardous substances and their permitted content as follows;

• Bis(2-Ethylhexyl) phthalate (DEHP): max 0.1%

• Benzyl butyl phthalate (BBP): max 0.1%)

• Dibutyl phthalate (DBP): max 0.1%

• Diisobutyl phthalate (DIBP): max 0.1%

These newly added substances i.e. phthalates are the chemicals whose applications are for softening the plastics.

Think if these substances are present in toys. These substances cause a severe problem to human being and damages vital human and animal organs. Because of these severe issues RoHS 3 is introduced.

RoHS 3 Compliant

RoHS 3 exemptions

Let discuss about all RoHS exempted and impacted categories, here category for RoHS 3 exemptions also included.

As per the latest amendment categories 1, 2, 3, 4, 5, 6, 7, 10 and 11 are impacted from compliance according to schedule 1 of the WEEE Directive. Category 11 is newly added.

Category 8 and category 9 of the RoHS directive are presently exempted from compliance.

List of ROHS product categories;

Category 1 – Large household appliances: refrigerators, stoves, washers, air conditioners

Category 2 – Small household appliances: vacuum cleaners, hair dryers, coffee makers, irons

Category 3 – Computing & communications equipment: computers, printers, copiers, phones

Category 4 – Consumer electronics: DVD players, TVs, stereos, video cameras

Category 5 – Lighting: lamps, lighting fixtures, light bulbs

Category 6 – Power tools: drills, saws, nail guns, sprayers, lathes, trimmers, blowers

Category 7 – Toys and sports equipment: videogames, electric trains, treadmills

Category 8 – Medical devices and equipment

Category 9 – Control and monitoring equipment

Category 10 – Automatic dispensers: vending machines, ATM machines

Category 11 – All other electrical and electronic equipment

Categories 8 and 9 restrictions will go into effect from July 22, 2021. This is an extension given to medical devices and control – monitoring equipment’s. These are the medical and control devices and will take time for replacement. Immediately ban will affect the medical treatments and process.

Below lines are from;

COMMISSION DELEGATED DIRECTIVE (EU) 2015/863 of 31 March 2015

“The restriction of DEHP, BBP, DBP and DIBP shall apply to medical devices, including in vitro medical devices, and monitoring and control instruments, including industrial monitoring and control instruments, from 22 July 2021.”

RoHS 3 effective date

RoHS 3 effective date as per the amended standard;

From July 22, 2019 for all electrical and electronic apparatus other than categories 8 and 9, the restriction on the added four substances is in effect.

From July 22, 2021 categories 8 and 9 restrictions will go into effect.

These RoHS 3 deadlines every manufacturer should note otherwise they won’t get in EU market.

RoHS 3 declaration for products

Manufacturers can now include a new paragraph or statement (along with the old declaration of RoHS 1 and RoHS 2) on the declaration where they can declare;

Confirmation with the latest amendment along with latest directive number.

Mention limits for all the ten substances (adding four phthalates to the list).

For more details about RoHS 3 declaration please contact testing and certification agencies in your respective country.

Conclusion

We know now the importance of RoHS and how it is protecting human and environment from the hazardous substances. Introduction or inclusion of RoHS 3 directive definitely will help everyone and will make us aware about hazardous substances present in a product.

Even manufacturer now knows their responsibility and can’t sell product without declaration.

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Standard Resistor Values

What are Standard Resistor Values?

Standard Resistor Values are the chosen values of resistance which are grouped in different series.

The selection of these resistor values is depends on logarithmic sequence, which decides the placement of different resistance values in such a way that they relate with each other by tolerance.

The advantage of having Standard Resistor Values is that, every resistor manufacturers follows the standard and manufactures these values, by which these resistor values are easily available with competitive price.

Also for a circuit design while selecting a resistor, designer can get reference from list of Standard Resistor Values and choose resistance value matching to his calculated resistance value.

Generally these values are available in the resistor tolerance range of ±1%, ±2%, ±5%, ±10% and ±20%.

To know more about resistors please visit below mentioned articles;

"Resistor and Working of Resistor"

"Electrical Resistance and Resistivity".

E series of Standard Resistor Values

E series is the name of the group of series of the standard resistor values. Here in the series the values are decided such that the upper side tolerance of one resistance value should not cross the lower side tolerance of another resistance value.

The standard resistor values structure is also called as EIA standard resistor values because this is approved by EIA (Electrical Industries Association).

The E series standard resistor values are globally recognized and have been accepted by all organisations who deal with international standards.

E-series of Standard Resistor Values are published in standard IEC 60063:1963.

What is Standard Resistance?

Let understand the Standard Resistance with an example. Consider a resistor of resistance value 1Ω, which have a resistance tolerance of ±20%. This means, the minimum resistance of this resistor will be 0.2Ω and the maximum resistance of this resistor will be 1.2Ω. So, as per resistor standard values the next available resistor value after 1.2Ω will be 1.5Ω.

Further same standard resistor value rule will be followed by 1.5Ω for both side i.e. minimum and maximum resistor tolerance. The minimum resistance value of 1.5Ω with ±20% resistance tolerance is 1.2Ω, which is touching the 1.2Ω value, not overlapping it.

For all the values present in the decade this process is followed and finally it creates a set of different resistance values named as Standard Resistor Values or Resistor Standard Values.

Available Resistor Values with E series

Now we know about E series of Standard Resistor Values. Each E series represents different available resistor values.

Let understand it in detail, here each set of standard resistor values have an identification number i.e. E-series number. Here “E” is constant and “series” denotes the number i.e. 1, 3, 6, 12, 24, 48, 96 and 192.

E1 has 1 resistor values in each decade, E3 has 3 resistor values in each decade, E6 has 6 resistor values in each decade, E12 has 12 resistor values in each decade, E24 has 24 resistor values in each decade, and it continues further.

A decade of the E6 resistor values

Resistor Tolerance with E series

E1 resistor series have very wide tolerance range and now days it didn’t exist.

Further let understand the E series resistor tolerance with E3 series. As mentioned above 3 resistor values are available in E3 series these are; 1, 2.2 and 4.7. The resistor tolerance is much more than 20%. This is a basic series and rarely used now days because requirement of today’s applications need narrow resistor tolerance, but this series has wide tolerance range.

This series we can found in the application related to electrolytic capacitors where the tolerance requirement is unbalanced i.e. minimum tolerance requirement is less and maximum tolerance requirement is more or vice versa, like tolerance of -20 at minimum side and +70% at maximum side. Also, we can found these series in applications where or for components where pull-up resistor value requirement are not critical.

Next is E6 series which have 6 resistor values in each decade. The resistor tolerance is ±20%.

Let see further E6 series in detail. In E6 series each decade is divided into 6 steps. The size of every step is equal to:

10E(1/6)= 1.44

Below diagram explains it in more detail;

Resistor Tolerance with E series

Further is E12 series which have 12 resistor values in each decade. The resistor tolerance is ±10%.

E24 series have tolerance range of ±5%. E48 series have tolerance range of ±2%. E96 series have tolerance range of ±1%. E192 series have tolerance range of ≤±0.5%.

Below tables shows summary of different E series and their resistance tolerance;

E series	Available Resistor Values	Resistor Tolerance
E1	1	Very wide tolerance
E3	3	> 20%
E6	6	20%
E12	12	10%
E24	24	5% (some-times 2% also available)
E48	48	2%
E96	96	1%
E192	192	0.5%, 0.25%, 0.1%

Standard Resistor Values Table

Please click on below image to get excel sheet having Standard Resistor Values table.

Standard Resistor Values Table

Below table shows list of Standard Resistor Values in tabular format;

Standard Resistor Values Table
These values are normally available in the multiples of; 0.1, 1, 10, 100, 1k, and 1M.
E1	E3	E6	E12	E24	E48	E96	E192	E192 (cont.)
1	1	1	1	1	1	1	1	3.16
	2.2	1.5	1.2	1.1	1.05	1.02	1.01	3.2
	4.7	2.2	1.5	1.2	1.1	1.05	1.02	3.24
		3.3	1.8	1.3	1.15	1.07	1.04	3.28
		4.7	2.2	1.5	1.21	1.1	1.05	3.32
		6.8	2.7	1.6	1.27	1.13	1.06	3.36
			3.3	1.8	1.33	1.15	1.07	3.4
			3.9	2	1.4	1.18	1.09	3.44
			4.7	2.2	1.47	1.21	1.1	3.48
			5.6	2.4	1.54	1.24	1.11	3.52
			6.8	2.7	1.62	1.27	1.13	3.57
			8.2	3	1.69	1.3	1.14	3.61
				3.3	1.78	1.33	1.15	3.65
				3.6	1.87	1.37	1.17	3.7
				3.9	1.96	1.4	1.18	3.74
				4.3	2.05	1.43	1.2	3.79
				4.7	2.15	1.47	1.21	3.83
				5.1	2.26	1.5	1.23	3.88
				5.6	2.37	1.54	1.24	3.92
				6.2	2.49	1.58	1.26	3.97
				6.8	2.61	1.62	1.27	4.02
				7.5	2.74	1.65	1.29	4.07
				8.2	2.87	1.69	1.3	4.12
				9.1	3.01	1.74	1.32	4.17
					3.16	1.78	1.33	4.22
					3.32	1.82	1.35	4.27
					3.48	1.87	1.37	4.32
					3.65	1.91	1.38	4.37
					3.83	1.96	1.4	4.42
					4.02	2	1.42	4.48
					4.22	2.05	1.43	4.53
					4.42	2.1	1.45	4.59
					4.64	2.15	1.47	4.64
					4.87	2.21	1.49	4.7
					5.11	2.26	1.5	4.75
					5.36	2.32	1.52	4.81
					5.62	2.37	1.54	4.87
					5.9	2.43	1.56	4.93
					6.19	2.49	1.58	4.99
					6.49	2.55	1.6	5.05
					6.81	2.61	1.62	5.11
					7.15	2.67	1.64	5.17
					7.5	2.74	1.65	5.23
					7.87	2.8	1.67	5.3
					8.25	2.87	1.69	5.36
					8.66	2.94	1.72	5.42
					9.09	3.01	1.74	5.49
					9.53	3.09	1.76	5.56
						3.16	1.78	5.62
						3.24	1.8	5.69
						3.32	1.82	5.76
						3.4	1.84	5.83
						3.48	1.87	5.9
						3.57	1.89	5.97
						3.65	1.91	6.04
						3.74	1.93	6.12
						3.83	1.96	6.19
						3.92	1.98	6.26
						4.02	2	6.34
						4.12	2.03	6.42
						4.22	2.05	6.49
						4.32	2.08	6.57
						4.42	2.1	6.65
						4.53	2.13	6.73
						4.64	2.15	6.81
						4.75	2.18	6.9
						4.87	2.21	6.98
						4.99	2.23	7.06
						5.11	2.26	7.15
						5.23	2.29	7.23
						5.36	2.32	7.32
						5.49	2.34	7.41
						5.62	2.37	7.5
						5.76	2.4	7.59
						5.9	2.43	7.68
						6.04	2.46	7.77
						6.19	2.49	7.87
						6.34	2.52	7.96
						6.49	2.55	8.06
						6.65	2.58	8.16
						6.81	2.61	8.25
						6.98	2.64	8.35
						7.15	2.67	8.45
						7.32	2.71	8.56
						7.5	2.74	8.66
						7.68	2.77	8.76
						7.87	2.8	8.87
						8.06	2.84	8.98
						8.25	2.87	9.09
						8.45	2.91	9.2
						8.66	2.94	9.31
						8.87	2.98	9.42
						9.09	3.01	9.53
						9.31	3.05	9.65
						9.53	3.09	9.76
						9.76	3.12	9.88
Prepared by; www.powerelectronicstalks.com

Now days in many datasheets we can see the resistor series is mentioned like; E96 + E24 and E192 + E24 i.e. addition of two E series. To meet market requirement this is purposely done by resistor manufacturers as some resistor values in E24 series are not available in E48, E96 and E192 series. So, to get lower tolerance values like; 1%, 0.5%, 0.25%, 0.1% they have added values in E24 series with other series i.e. tolerances.

Standard Resistor Value Formula

Below formula is for standard resistor value calculation;

R = D . 10E(I/N)

Where,
D = Decade multiplier i.e. 1, 10, 100, 1k, 10k
N = Tolerance of E series i.e. 1%, 2%, 5%, 10%, 20%
I = 0 … N-1
Unit of R is Ω
E is exponent

Let understand by an example, result of a calculation is 257kΩ with the tolerance of 1%.
Check in the table and select the nearest available value i.e. 2.58. Multiply this with a multiplier of 100000 you will get 258kΩ.

Conclusion

Standard resistor values helps in many ways to both resistor manufacturers and circuit designers. The resistor manufacture can produce the resistors which are mentioned in the standard and they don’t have to produce the non-standardized resistors and fill their inventory.

While designing the circuit the design engineer can easily identify and select the resistor value by looking up in the standard resistor value list. Designers can select the value which is closely matching to their calculated value.

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