Resistors in Series

Connecting Resistors in Series

Individual resistors can be connected together in either a series connection, a parallel connection or combinations of both series and parallel, to produce more complex resistor networks whose equivalent resistance is the mathematical combination of the individual resistors connected together.

Resistors in series or complicated Resistor Networks can be replaced by one single equivalent resistor, REQ or impedance, ZEQ and no matter what the combination or complexity of the resistor network is, all resistors obey the same basic rules as defined by Ohm’s Law and Kirchoff’s Circuit Laws.

Resistors in Series.

Resistors are said to be connected in “Series“, when they are daisy chained together in a single line. Since all the current flowing through the first resistor has no other way to go it must also pass through the second resistor and the third and so on. Then, resistors in series have a Common Current flowing through them as the current that flows through one resistor must also flow through the others as it can only take one path.

Then the amount of current that flows through a set of resistors in series will be the same at all points in a series resistor network. For example:

 

In the following example the resistors R1, R2 and R3 are all connected together in series between points A and B with a common current, I flowing through them.

Series Resistor Circuit

 

As the resistors are connected together in series the same current passes through each resistor in the chain and the total resistance, RT of the circuit must be equal to the sum of all the individual resistors added together. That is

and by taking the individual values of the resistors in our simple example above, the total equivalent resistance, REQ is therefore given as:

REQ = R1 + R2 + R3 = 1kΩ + 2kΩ + 6kΩ = 9kΩ

 

So we see that we can replace all three individual resistors above with just one single “equivalent” resistor which will have a value of 9kΩ.

Where four, five or even more resistors are all connected together in a series circuit, the total or equivalent resistance of the circuit, RT would still be the sum of all the individual resistors connected together and the more resistors added to the series, the greater the equivalent resistance (no matter what their value).

This total resistance is generally known as the Equivalent Resistance and can be defined as;  “a single value of resistance that can replace any number of resistors in series without altering the values of the current or the voltage in the circuit“. Then the equation given for calculating total resistance of the circuit when connecting together resistors in series is given as:

Series Resistor Equation

Rtotal = R1 + R2 + R3 + ….. Rn etc.

Note then that the total or equivalent resistance, RT has the same effect on the circuit as the original combination of resistors as it is the algebraic sum of the individual resistances.

If two resistances or impedances in series are equal and of the same value, then the total or equivalent resistance, RT is equal to twice the value of one resistor. That is equal to 2R and for three equal resistors in series, 3R, etc.

If two resistors or impedances in series are unequal and of different values, then the total or equivalent resistance, RT is equal to the mathematical sum of the two resistances. That is equal to R1 + R2. If three or more unequal (or equal) resistors are connected in series then the equivalent resistance is: R1 + R2 + R3 +…, etc.

 

One important point to remember about resistors in series networks to check that your maths is correct. The total resistance ( RT ) of any two or more resistors connected together in series will always be GREATER than the value of the largest resistor in the chain. In our example above RT = 9kΩ where as the largest value resistor is only 6kΩ.

Series Resistor Voltage

The voltage across each resistor connected in series follows different rules to that of the series current. We know from the above circuit that the total supply voltage across the resistors is equal to the sum of the potential differences across R1 , R2 and R3 , VAB = VR1 + VR2 + VR3 = 9V.

Using Ohm’s Law, the voltage across the individual resistors can be calculated as:

Voltage across R1 = IR1 = 1mA x 1kΩ = 1V

Voltage across R2 = IR2 = 1mA x 2kΩ = 2V

Voltage across R3 = IR3 = 1mA x 6kΩ = 6V

 

giving a total voltage VAB of ( 1V + 2V + 6V ) = 9V which is equal to the value of the supply voltage. Then the sum of the potential differences across the resistors is equal to the total potential difference across the combination and in our example this is 9V.

The equation given for calculating the total voltage in a series circuit which is the sum of all the individual voltages added together is given as:

Then series resistor networks can also be thought of as “voltage dividers” and a series resistor circuit having N resistive components will have N-different voltages across it while maintaining a common current.

By using Ohm’s Law, either the voltage, current or resistance of any series connected circuit can easily be found and resistor of a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor.

Resistors in Series Example No1

Using Ohms Law, calculate the equivalent series resistance, the series current, voltage drop and power for each resistor in the following resistors in series circuit.

 

All the data can be found by using Ohm’s Law, and to make life a little easier we can present this data in tabular form.

Resistance	Current	Voltage	Power
R1 = 10Ω	I1 = 200mA	V1 = 2V	P1 = 0.4W
R2 = 20Ω	I2 = 200mA	V2 = 4V	P2 = 0.8W
R3 = 30Ω	I3 = 200mA	V3 = 6V	P3 = 1.2W
RT = 60Ω	IT = 200mA	VS = 12V	PT = 2.4W

Then for the circuit above, RT = 60Ω, IT = 200mA, VS = 12V and PT = 2.4W

The Voltage Divider Circuit

We can see from the above example, that although the supply voltage is given as 12 volts, different voltages, or voltage drops, appear across each resistor within the series network. Connecting resistors in series like this across a single DC supply has one major advantage, different voltages appear across each resistor producing a very handy circuit called a Voltage Divider Network.

This simple circuit splits the supply voltage proportionally across each resistor in the series chain with the amount of voltage drop being determined by the resistors value and as we now know, the current through a series resistor circuit is common to all resistors. So a larger resistance will have a larger voltage drop across it, while a smaller resistance will have a smaller voltage drop across it.

The series resistive circuit shown above forms a simple voltage divider network were three voltages 2V, 4V and 6V are produced from a single 12V supply. Kirchoff’s Voltage Law states that “the supply voltage in a closed circuit is equal to the sum of all the voltage drops (IR) around the circuit” and this can be used to good effect.

The Voltage Division Rule, allows us to use the effects of resistance proportionality to calculate the potential difference across each resistance regardless of the current flowing through the series circuit. A typical “voltage divider circuit” is shown below.

Voltage Divider Network

 

The circuit shown consists of just two resistors, R1 and R2 connected together in series across the supply voltage Vin. One side of the power supply voltage is connected to resistor, R1, and the voltage output, Vout is taken from across resistor R2. The value of this output voltage is given by the corresponding formula.

If more resistors are connected in series to the circuit then different voltages will appear across each resistor in turn with regards to their individual resistance R (Ohms Law IxR) values providing different but smaller voltage points from one single supply.

So if we had three or more resistances in the series chain, we can still use our now familiar potential divider formula to find the voltage drop across each one. Consider the circuit below.

The potential divider circuit above shows four resistances connected together is series. The voltage drop across points A and B can be calculated using the potential divider formula as follows:

We can also apply the same idea to a group of resistors in the series chain. For example if we wanted to find the voltage drop across both R2 and R3 together we would substitute their values in the top numerator of the formula and in this case the resulting answer would give us 5 volts (2V + 3V).

In this very simple example the voltages work out very neatly as the voltage drop across a resistor is proportional to the total resistance, and as the total resistance, (RT) in this example is equal to 100Ω or 100%, resistor R1 is 10% of RT, so 10% of the source voltage VS will appear across it, 20% ofVS across resistor R2, 30% across resistor R3, and 40% of the supply voltage VS across resistor R4. Application of Kirchoff’s voltage law (KVL) around the closed loop path confirms this.

Now lets suppose that we want to use our two resistor potential divider circuit above to produce a smaller voltage from a larger supply voltage to power an external electronic circuit. Suppose we have a 12V DC supply and our circuit which has an impedance of 50Ω requires only a 6V supply, half the voltage.

Connecting two equal value resistors, of say 50Ω each, together as a potential divider network across the 12V will do this very nicely until we connect the load circuit to the network. This is because the loading effect of resistor RL connected in parallel across R2 changes the ratio of the two series resistances altering their voltage drop and this is demonstrated below.

Resistors in Series Example No2

Calculate the voltage drops across X and Y.

a) Without RL connected

b) With RL connected

 

As you can see from above, the output voltage Vout without the load resistor connected gives us the required output voltage of 6V but the same output voltage at Vout when the load is connected drops to only 4V, (Resistors in Parallel).

Then we can see that a loaded voltage divider network changes its output voltage as a result of this loading effect, since the output voltage Vout is determined by the ratio of R1 to R2. However, as the load resistance, RL increases towards infinity (∞) this loading effect reduces and the voltage ratio ofVout/Vs becomes unaffected by the addition of the load on the output. Then the higher the load impedance the less is the loading effect on the output.

A variable resistor, potentiometer or pot as it is more commonly called, is a good example of a multi-resistor voltage divider within a single package as it can be thought of as thousands of mini-resistors in series. Here a fixed voltage is applied across the two outer fixed connections and the variable output voltage is taken from the wiper terminal. Multi-turn pots allow for a more accurate output voltage control.The effect of reducing a signal or voltage level is known asAttenuation so care must be taken when using a voltage divider network. This loading effect could be compensated for by using a potentiometer instead of fixed value resistors and adjusted accordingly. This method also compensates the potential divider for varying tolerances in the resistors construction.

The Voltage Divider Circuit is the simplest way of producing a lower voltage from a higher voltage, and is the basic operating mechanism of the potentiometer.

As well as being used to calculate a lower supply voltage, the voltage divider formula can also be used in the analysis of more complex resistive circuits containing both series and parallel branches. The voltage or potential divider formula can be used to determine the voltage drops around a closed DC network or as part of a various circuit analysis laws such as Kirchoff’s or Thevenin’s theorems.

Applications of Resistors in Series

We have seen that Resistors in Series can be used to produce different voltages across themselves and this type of resistor network is very useful for producing a voltage divider network. If we replace one of the resistors in the voltage divider circuit above with a Sensor such as a thermistor, light dependant resistor (LDR) or even a switch, we can convert an analogue quantity being sensed into a suitable electrical signal which is capable of being measured.

For example, the following thermistor circuit has a resistance of 10KΩ at 25°C and a resistance of100Ω at 100°C. Calculate the output voltage (Vout) for both temperatures.

Thermistor Circuit

 

At 25°C

 

At 100°C

 

So by changing the fixed 1KΩ resistor, R2 in our simple circuit above to a variable resistor or potentiometer, a particular output voltage set point can be obtained over a wider temperature range.

Resistors in Series Summary

So to summarise. When two or more resistors are connected together end-to-end in a single branch, the resistors are said to be connected together in series. Resistors in Series carry the same current, but the voltage drop across them is not the same as their individual resistance values will create different voltage drops across each resistor as determined by Ohm’s Law ( V = IxR ). Then series circuits are voltage dividers.

In a series resistor network the individual resistors add together to give the equivalent resistance, (RT ) of the series combination. The resistors in a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor or the circuit.

In the next tutorial about Resistors, we will look at connecting resistors together in parallel and show that the total resistance is the reciprocal sum of all the resistors added together and that the voltage is common to a parallel circuit.

Passive Attenuators

Passive Attenuator Basics

An Attenuator is a special type of electrical or electronic bidirectional circuit made up of entirely resistive elements. An attenuator is a two port resistive network designed to weaken or “attenuate” (hence their name) the power being supplied by a source to a level that is suitable for the connected load.

A passive attenuator reduces the amount of power being delivered to the connected load by either a single fixed amount, a variable amount or in a series of known switchable steps. Attenuators are generally used in radio, communication and transmission line applications to weaken a stronger signal.

The Passive Attenuator is a purely passive resistive network (hence no supply) which is used in a wide variety of electronic equipment for extending the dynamic range of measuring equipment by adjusting signal levels, to provide impedance matching of oscillators or amplifiers to reduce the effects of improper input/output terminations, or to simply provide isolation between different circuit stages depending upon their application as shown.

Attenuator Connection

 

Simple Attenuator Networks (also known as “pads”) can be designed to produce a fixed degree of “attenuation” or to give a variable amount of attenuation in pre-determined steps. Standard fixed attenuator networks generally known as an “attenuator pad” are available in specific values from 0 dB to more than 100 dB. Variable and switched attenuators are basically adjustable resistor networks that show a calibrated increase in attenuation for each switched step, for example steps of -2dB or -6dB per switch position.

Then an Attenuator is a four terminal (two port) passive resistive network (active types are also available which use transistors and integrated circuits) designed to produce “distortionless” attenuation of the output electrical signal at all frequencies by an equal amount with no phase shift unlike a passive type RC filter network, and therefore to achieve this attenuators should be made up of pure non-inductive and not wirewound resistances, since reactive elements will give frequency discrimination.

Simple Passive Attenuator

Attenuators are the reverse of amplifiers in that they reduce gain with the resistive voltage divider circuit being a typical attenuator. The amount of attenuation in a given network is determined by the ratio of: Output/Input. For example, if the input voltage to a circuit is 1 volt (1V) and the output voltage is 1 milli-volt (1mV) then the amount of attenuation is 1mV/1V which is equal to 0.001 or a reduction of 1,000th.

However, using voltage, current or even power ratios to determine or express the amount of attenuation that a resistive attenuator network may have, called the attenuation factor, can be confusing, so for the passive attenuator its degree of attenuation is normally expressed using a logarithmic scale which is given in decibels (dB) making it easier to deal with such small numbers.

Degrees of Attenuation

An attenuators performance is expressed by the number of decibels the input signal has decreased per frequency decade (or octave). The decibel, abbreviated to “dB”, is generally defined as the logarithm or “log” measure of the voltage, current or power ratio and represents one tenth 1/10th of a Bel (B). In other words it takes 10 decibels to make one Bel. Then by definition, the ratio between an input signal (Vin) and an output signal (Vout) is given in decibels as:

Decibel Attenuation

Note that the decibel (dB) is a logarithmic ratio and therefore has no units. So a value of -140dB represents an attenuation of 1:10,000,000 units or a ratio of 10 million to 1!.

In passive attenuator circuits, it is often convenient to assign the input value as the 0 dB reference point. This means that no matter what is the actual value of the input signal or voltage, is used as a reference with which to compare the output values of attenuation and is therefore assigned a 0 dB value. This means that any value of output signal voltage below this reference point will be expressed as a negative dB value, ( -dB ).

So for example an attenuation of -6dB indicates that the value is 6 dB below the 0 dB input reference. Likewise if the ratio of output/input is less than one (unity), for example 0.707, then this corresponds to 20 log(0.707) = -3dB. If the ratio of output/input = 0.5, then this corresponds to 20 log(0.5) = -6 dB, and so on, with standard electrical tables of attenuation available to save on the calculation.

Passive Attenuators Example No1

A passive attenuator circuit has an insertion loss of -32dB and an output voltage of 50mV. What will be the value of the input voltage.

 

The antilog (log-1) of -1.6 is given as:

 

Then if the output voltage produced with 32 decibels of attenuation, an input voltage of 2.0 volts is required.

Attenuator Loss Table

Vout/Vin	1	0.7071	0.5	0.25	0.125	0.0625	0.03125	0.01563	0.00781
Log Value	20log(1)	20log (0.7071)	20log (0.5)	20log (0.25)	20log (0.125)	20log (0.0625)	20log (0.03125)	20log (0.01563)	20log (0.00781)
in dB’s	0	-3dB	-6dB	-12dB	-18dB	-24dB	-30dB	-36dB	-42dB

 

and so on, producing a table with as many decibel values as we require for our attenuator design.

This decrease in voltage, current or power expressed in decibels by the insertion of the attenuator into an electrical circuit is known as insertion loss and minimum loss attenuator designs match circuits of unequal impedances with a minimum loss in the matching network.

Now that we know what a passive attenuator is how it can be used to reduce or “attenuate” the power or voltage level of a signal, while introducing little or no distortion and insertion loss, by an amount expressed in decibels, we can begin to look at the different attenuator circuit designs available.

Passive Attenuator Designs

There are many ways in which resistors can be arranged in attenuator circuits with the Potential Divider Circuit being the simplest type of passive attenuator circuit. The potential or voltage divider circuit is generally known as an “L-pad” attenuator because its circuit diagram resembles that of an inverted “L”. But there are other common types of attenuator network as well such as the “T-pad” attenuator and the “Pi-pad” (π) attenuator depending upon how you connect together the resistive components. These three common attenuator types are shown below.

Attenuator Types

The above attenuator circuit designs can be arranged in either “balanced” or “unbalanced” form with the action of both types being identical. The balanced version of the “T-pad” attenuator is called the “H-pad” attenuator while the balanced version of the “π-pad” attenuator is called the “O-pad” attenuator. Bridged T-type attenuators are also available.

In an unbalanced attenuator, the resistive elements are connected to one side of the transmission line only while the other side is grounded to prevent leakage at higher frequencies. Generally the grounded side of the attenuator network has no resistive elements and is therefore called the “common line”.

In a balanced attenuator configuration, the same number of resistive elements are connected equally to each side of the transmission line with the ground located at a center point created by the balanced parallel resistances. Generally, balanced and unbalanced attenuator networks can not be connected together as this results in half of the balanced network being shorted to ground through the unbalanced configuration.

Switched Attenuators

Instead of having just one attenuator to achieve the required degree of attenuation, individualattenuator pads can be connected or cascaded together to increase the amount of attenuation in given steps of attenuation. Multi-pole rotary switches, rocker switches or ganged push-button switches can also be used to connect or bypass individual fixed attenuator networks in any desired sequence from 1dB to 100dB or more, making it easy to design and construct switched attenuator networks, also known as a step attenuator. By switching in the appropriate attenuators, the attenuation can be increased or decreased in fixed steps as shown below.

Switched Attenuator

 

Here, there are four independent resistive attenuator networks cascaded together in a series ladder network with each attenuator having a value twice that of its predecessor, (1-2-4-8). Each attenuator network may be switched “in” or “out” of the signal path as required by the associated switch producing a step adjustment attenuator circuit that can be switched from 0dB to -15dB in 1dB steps.

Therefore, the total amount of attenuation provided by the circuit would be the sum of all four attenuators networks that are switched “IN”. So for example an attenuation of -5dB would require switches SW1 and SW3 to be connected, and an attenuation of -12dB would require switches SW3and SW4 to be connected, and so on.

Attenuator Summary

• An attenuator is a four terminal device that reduces the amplitude or power of a signal without distorting the signal waveform, an attenuator introduces a certain amount of loss.
• The attenuator network is inserted between a source and a load circuit to reduce the source signal’s magnitude by a known amount suitable for the load.
• Attenuators can be fixed, fully variable or variable in known steps of attenuation, -0.5dB, -1dB, -10dB, etc.
• An attenuator can be symmetrical or asymmetrical in form and either balanced or unbalanced.
• Fixed attenuators also known as a “pad” are used to “match” unequal impedances.
• An attenuator is effectively the opposite of an amplifier. An amplifier provides gain while an attenuator provides loss, or gain less than 1 (unity).
• Attenuators are usually passive devices made to from simple voltage divider networks. The switching between different resistances produces adjustable stepped attenuators and continuously adjustable ones using potentiometers.

To simplify the design of the attenuator, a "K" (for constant) value can be used. This "K" value is the ratio of the voltage, current or power corresponding to a given value of dB attenuation and is given as:

We can produce a set of constant values called “K” values for different amounts of attenuation as given in the following table.

Attenuator Loss Table

dB	0.5	1.0	2.0	3.0	4.0	5.0	6.0	10.0	20.0
“K” value	1.0593	1.1220	1.2589	1.4125	1.5849	1.7783	1.9953	3.1623	10.000

and so on, producing a table with as many “K” values as we require.

Fixed value attenuators, called “attenuator pads” are used mainly in radio frequency (Rf) transmission lines to lower voltage, dissipate power, or to improve the impedance matching between various mismatched circuits.

Line-level attenuators in pre-amplifier or Audio Power Amplifiers can be as simple as a 0.5 watt potentiometer, or voltage divider L-pad designed to reduce the amplitude of an audio signal before it reaches the speaker, reducing the volume of the output.

In measuring signals, high power attenuator pads are used to lower the amplitude of the signal a known amount to enable measurements, or to protect the measuring device from high signal levels that might otherwise damage it.

In the next tutorial about Attenuators, we will look at the most basic type of resistive attenuator network commonly called a “L-type” or “L-pad” attenuator which can be made using just two resistive components. The “L-pad” attenuator circuit can also be used as a voltage or potential divider circuit.

Resistor Colour Code

Resistor Colour Code

We saw in the previous tutorial that there are many different types of Resistor available and that they can be used in both electrical and electronic circuits to control the flow of current or to produce a voltage in many different ways. But in order to do this the actual resistor needs to have some form of “resistive” or “resistance” value. Resistors are available in a range of different resistance values from fractions of an Ohm ( Ω ) to millions of Ohms.

Obviously, it would be impractical to have available resistors of every possible value for example,1Ω, 2Ω, 3Ω, 4Ω etc, because literally tens of hundreds of thousands, if not tens of millions of different resistors would need to exist to cover all the possible values. Instead, resistors are manufactured in what are called “preferred values” with their resistance value printed onto their body in coloured ink.

4 Coloured Bands

The resistance value, tolerance, and wattage rating are generally printed onto the body of the resistor as numbers or letters when the resistors body is big enough to read the print, such as large power resistors. But when the resistor is small such as a 1/4W carbon or film type, these specifications must be shown in some other manner as the print would be too small to read.

So to overcome this, small resistors use coloured painted bands to indicate both their resistive value and their tolerance with the physical size of the resistor indicating its wattage rating. These coloured painted bands produce a system of identification generally known as a Resistors Colour Code.

An international and universally accepted Resistor Colour Code Scheme was developed many years ago as a simple and quick way of identifying a resistors ohmic value no matter what its size or condition. It consists of a set of individual coloured rings or bands in spectral order representing each digit of the resistors value.

The resistor colour code markings are always read one band at a time starting from the left to the right, with the larger width tolerance band oriented to the right side indicating its tolerance. By matching the colour of the first band with its associated number in the digit column of the colour chart below the first digit is identified and this represents the first digit of the resistance value.

Again, by matching the colour of the second band with its associated number in the digit column of the colour chart we get the second digit of the resistance value and so on. Then the resistor colour code is read from left to right as illustrated below:

The Standard Resistor Colour Code Chart.

 

The Resistor Colour Code Table.

Colour	Digit	Multiplier	Tolerance
Black	0	1
Brown	1	10	± 1%
Red	2	100	± 2%
Orange	3	1,000
Yellow	4	10,000
Green	5	100,000	± 0.5%
Blue	6	1,000,000	± 0.25%
Violet	7	10,000,000	± 0.1%
Grey	8		± 0.05%
White	9
Gold		0.1	± 5%
Silver		0.01	± 10%
None			± 20%

Calculating Resistor Values

The Resistor Colour Code system is all well and good but we need to understand how to apply it in order to get the correct value of the resistor. The “left-hand” or the most significant coloured band is the band which is nearest to a connecting lead with the colour coded bands being read from left-to-right as follows;

Digit, Digit, Multiplier = Colour, Colour x 10 colour  in Ohm’s (Ω’s)

For example, a resistor has the following coloured markings;

Yellow Violet Red = 4 7 2 = 4 7 x 102 = 4700Ω or 4k7.

The fourth and fifth bands are used to determine the percentage tolerance of the resistor. Resistor tolerance is a measure of the resistors variation from the specified resistive value and is a consequence of the manufacturing process and is expressed as a percentage of its “nominal” or preferred value.

Typical resistor tolerances for film resistors range from 1% to 10% while carbon resistors have tolerances up to 20%. Resistors with tolerances lower than 2% are called precision resistors with the or lower tolerance resistors being more expensive.

Most five band resistors are precision resistors with tolerances of either 1% or 2% while most of the four band resistors have tolerances of 5%, 10% and 20%. The colour code used to denote the tolerance rating of a resistor is given as;

Brown = 1%, Red = 2%, Gold = 5%, Silver = 10 %

If resistor has no fourth tolerance band then the default tolerance would be at 20%.

It is sometimes easier to remember the resistor colour code by using mnemonics or phrases that have a separate word in the phrase to represent each of the Ten + Two colours in the code. However, these sayings are often very crude but never the less effective for remembering the resistor colours. Here are just a few of the more “cleaner” versions but many more exist:

• Bad Booze Rots Our Young Guts But Vodka Goes Well
• Bad Boys Ring Our Young Girls But Vicky Goes Without
• Bad Boys Ring Our Young Girls But Vicky Gives Willingly — Get Some Now (This one is only slightly better because it includes the tolerance bands of Gold, Silver, and None).

The British Standard (BS 1852) Code.

Generally on larger power resistors, the resistor colour code systems is not required as the resistance value, tolerance, and even the power (wattage) rating are printed onto the actual body of the resistor instead of using the resistor colour code system. Because it is very easy to “misread” the position of a decimal point or comma especially when the component is discoloured or dirty. An easier system for writing and printing the resistance values of the individual resistance was developed.

This system conforms to the British Standard BS 1852 Standard and its replacement, BS EN 60062, coding method were the decimal point position is replaced by the suffix letters "K" for thousands or kilohms, the letter "M" for millions or megaohms both of which denotes the multiplier value with the letter "R" used where the multiplier is equal to, or less than one, with any number coming after these letters meaning it’s equivalent to a decimal point.

The BS 1852 Letter Coding for Resistors.

BS 1852 Codes for Resistor Values

0.47Ω = R47 or 0R47

1.0Ω = 1R0

4.7Ω = 4R7

47Ω = 47R

470Ω = 470R or 0K47

1.0KΩ = 1K0

4.7KΩ = 4K7

47KΩ = 47K

470KΩ = 470K or 0M47

1MΩ = 1M0

Sometimes depending upon the manufacturer, after the written resistance value there is an additional letter which represents the resistors tolerance value such as 4k7 J and these suffix letters are given as.

Tolerance Letter Coding for Resistors.

Tolerance Codes for Resistors (±)

B = 0.1%

C = 0.25%

D = 0.5%

F = 1%

G = 2%

J = 5%

K = 10%

M = 20%

Also, when reading these written codes be careful not to confuse the resistance letter k for kilohms with the tolerance letter K for 10% tolerance or the resistance letter M for megaohms with the tolerance letter M for 20% tolerance.

Tolerances, E-series & Preferred Values.

Hopefully by now we understand that resistors come in a variety of sizes and resistance values but to have a resistor available of every possible resistance value, literally hundreds of thousands, if not millions of individual resistors would need to exist. Instead, resistors are manufactured in what are commonly known as Preferred values.

Instead of sequential values of resistance from 1Ω and upwards, certain values of resistors exist within certain tolerance limits. The tolerance of a resistor is the maximum difference between its actual value and the required value and is generally expressed as a plus or minus percentage value. For example, a 1kΩ ±20% tolerance resistor may have a maximum and minimum resistive value of.

Maximum Resistance Value

1kΩ or 1000Ω + 20% = 1,200Ω’s

Minimum Resistance Value

1kΩ or 1000Ω – 20% = 800Ω’s

 

Then using our example above, a 1kΩ ±20% tolerance resistor may have a maximum value of1200Ω’s and a minimum value of 800Ω’s resulting in a difference of some 400Ω’s!! for the same value resistor.

In most electrical or electronic circuits this large 20% tolerance of the same resistor is generally not a problem, but when close tolerance resistors are specified for high accuracy circuits such as filters or oscillators etc, then the correct tolerance resistor needs to be used, as a 20% tolerance resistor cannot generally be used to replace 2% or even a 1% tolerance type.

The five and six band resistor colour code is more commonly associated with the high precision 1% and 2% film types while the common garden variety 5% and 10% general purpose types tend to use the four band resistor colour code. Resistors come in a range of tolerances but the two most common are the E12 and the E24 series.

The E12 series comes in twelve resistance values per decade, (A decade representing multiples of 10, i.e. 10, 100, 1000 etc), while the E24 series comes in twenty four values per decade and the E96series ninety six values per decade. A very high precision E192 series is now available with tolerances as low as ± 0.1% giving a massive 192 separate resistor values per decade.

Tolerance and E-series Table.

E6 Series at 20% Tolerance – Resistors values in Ω’s
1.0, 1.5, 2.2, 3.3, 4.7, 6.8
E12 Series at 10% Tolerance – Resistors values in Ω’s
1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2
E24 Series at 5% Tolerance – Resistors values in Ω’s
1.0, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.2, 2.4, 2.7, 3.0, 3.3, 3.6, 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.2, 8.2, 9.1
E96 Series at 1% Tolerance – Resistors values in Ω’s
1.00, 1.02, 1.05, 1.07, 1.10, 1.13, 1.15, 1.18, 1.21, 1.24, 1.27, 1.30, 1.33, 1.37, 1.40, 1.43, 1.47, 1.50, 1.54, 1.58, 1.62, 1.65, 1.69, 1.74, 1.78, 1.82, 1.87, 1.91, 1.96, 2.00, 2.05, 2.10, 2.15, 2.21, 2.26, 2.32, 2.37, 2.43, 2.49, 2.55, 2.61, 2.77, 2.74, 2.80, 2.87, 2.94, 3.01, 3.09, 3.16, 3.24, 3.32, 3.40, 3.48, 3.57, 3.65, 3.74, 3.83, 3.92, 4.02, 4.12, 4.22, 4.32, 4.42, 4.53, 4.64, 4.75, 4.87, 4.99, 5.11, 5.23, 5.36, 5.49, 5.62, 5.76, 5.90, 6.04, 6.19, 6.34, 6.49, 6.65, 6.81, 6.98, 7.15, 7.32, 7.50, 7.68, 7.87, 8.06, 8.25, 8.45, 8.66, 8.87, 9.09, 9.31, 9.53, 9.76

Then by using the appropriate E-series value for the percentage tolerance required for the resistor, adding a multiplication factor to it, any ohmic value of resistance within that series can be found. For example, take an E-12 series resistor, 10% tolerance with a preferred value of 3.3, then the values of resistance for this range are:

Value x Multiplier = Resistance

3.3 x 1 = 3.3Ω

3.3 x 10 = 33Ω

3.3 x 100 = 330Ω

3.3 x 1,000 = 3.3kΩ

3.3 x 10,000 = 33kΩ

3.3 x 100,000 = 330kΩ

3.3 x 1,000,000 = 3.3MΩ

 

The mathematical basis behind these preferred values comes from the square root value of the actual series being used. For example, for the E6 20% series there are six individual resistors or steps (1.0 to 6.8) and is given as the sixth root of ten ( 6√10 ), so for the E12 10% series there are twelve individual resistors or steps (1.0 to 8.2) and is therefore given as the twelfth root of ten (12√10 ) and so on for the remaining E-series values.

The tolerance series of Preferred Values shown above are manufactured to conform to the British Standard BS 2488 and are ranges of resistor values chosen so that at maximum or minimum tolerance any one resistor overlaps with its neighbouring value. For example, take the E24 range of resistors with a 5% tolerance. It’s neighbouring resistor values are 47 and 51Ω’s respectively.

   47Ω + 5% = 49.35Ω’s, and 51Ω – 5% = 48.45Ω’s, an overlap of just 0.9Ω’s.

Surface Mount Resistors

4.7kΩ SMD Resistor

Surface Mount Resistors or SMD Resistors, are very small rectangular shaped metal oxide film resistors designed to be soldered directly onto the surface, hence their name, of a circuit board. Surface mount resistors generally have a ceramic substrate body onto which is deposited a thick layer of metal oxide resistance.

The resistive value of the resistor is controlled by increasing the desired thickness, length or type of deposited film being used and highly accurate low tolerance resistors, down to 0.1% can be produced. They also have metal terminals or caps at either end of the body which allows them to be soldered directly onto printed circuit boards.

Surface Mount Resistors are printed with either a 3 or 4-digit numerical code which is similar to that used on the more common axial type resistors to denote their resistive value. Standard SMD resistors are marked with a three-digit code, in which the first two digits represent the first two numbers of the resistance value with the third digit being the multiplier, either x1, x10, x100 etc. For example:

“103” = 10 × 1,000 ohms = 10 kiloΩ´s

“392” = 39 × 100 ohms = 3.9 kiloΩ´s

“563” = 56 × 1,000 ohms = 56 kiloΩ´s

“105” = 10 × 100,000 ohms = 1 MegaΩ

 

Surface mount resistors that have a value of less than 100Ω’s are usually written as: “390”,
“470”, “560” with the final zero representing a 10 xo multiplier, which is equivalent to 1. For example:

“390” = 39 × 1Ω = 39Ω´s or 39RΩ

“470” = 47 × 1Ω = 47Ω´s or 47RΩ

 

Resistance values below ten have a letter “R” to denote the position of the decimal point as seen previously in the BS1852 form, so that 4R7 = 4.7Ω.

Surface mount resistors that have a “000” or “0000” markings are zero-Ohm (0Ω) resistors or in other words shorting links, since these components have zero resistance.

Then we have seen that the resistor colour code system is used to identify the resistive value of a resistor. In the next tutorial about Resistors, we will look at connecting resistors together in a series chain and prove that the total resistance is the sum of all the resistors added together and that the current is common to a series circuit.