Math Help

An Engineers Quick References to Mathematics

algebra sheet

Algebra Help Math Sheet

This algebra reference sheet contains the following algebraic operations addition, subtraction, multiplication, and division. It also contains associative, commutative, and distributive properties. There are example of arithmetic operations as well as properties of exponents, radicals, inequalities, absolute values, complex numbers, logarithms, and polynomials. This sheet also contains many common factoring examples. There is a description of the quadratic equation as well as step by step instruction to complete the square.

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geometry sheet

Geometry Math Sheet

This geometry help reference sheet contains the circumference and area formulas for the following shapes: square, rectangle, circle, triangle, parallelogram, and trapezoid. It also includes the area of a circular ring as well as the area and segment length of a circular sector. This reference sheet contains formulas for area and volume of rectangular box, cube, and cylinder. This math help sheet also includes the area, side length, and volume of a right circular cone, as well as the volume of a frustum of a cone.

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trigonometry definition sheet

Trigonometry Definition Math Sheet

This trigonometry definition help sheet contains right triangle definitions for sine, cosine, tangent, cosecant, secant, and cotangent. It also contains the unit circle definitions for all trig functions. This sheet describes the range, domain and period for each of the trig functions. There is also a description of inverse trig function notation as well as domain and range.

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trigonometry laws and identities sheet

Trigonometry Laws and Identities Math Sheet

This trigonometry laws and identities help sheet contains the law of cosines, law of sines, and law of tangents. It also contains the following identities: tangent identities, reciprocal identities, Pythagorean identities, periodic identities, even/odd identities, double angle identities, half angle identities, product to sum identities, sum to product identities, sum/difference identities, and cofunction identities.

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calculus derivatives limits sheet

Calculus Derivatives and Limits Math Sheet

This calculus derivatives and limits help sheet contains the definition of a derivative, mean value theorem, and the derivative’s basic properties. There is a list of common derivative examples and chain rule examples. The following derivative rules are also described: product rule, quotient rule, power rule, chain rule, and L’Hopital’s rule. This sheet also contains properties of limits as well as examples of limit evaluations at infinity. A limit evaluation method for factoring is also included.

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calculus integrals sheet

Calculus Integrals Math Sheet

This calculus integral reference sheet contains the definition of an integral and the following methods for approximating definite integrals: left hand rectangle, right hand rectangle, midpoint rule, trapezoid rule, and Simpson’s rule. There is a list of many common integrals. Also included in this reference sheet is nice table for trigonometric substation when using integrals. Integration by substitution is defined as well as the integration by parts.

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Smith Chart

Smith Chart Graph Paper

Log-Log Graph Paper

Log-Log Engineering Graph Paper

Semi-Log Graph Paper

Semi-Log Engineering Graph Paper

Engineering Graph Paper

General Purpose Engineering Graph Paper

Calculus Integrals Math Sheet

An Engineers Quick Calculus Integrals Reference

Integrals

Definition of an IntegralReturn to Top

The integral is a mathematical analysis applied to a function that results in the area bounded by the graph of the function, x axis, and limits of the integral. Integrals can be referred to as anti-derivatives, because the derivative of the integral of a function is equal to the function.

PropertiesReturn to Top

the integral of the addition or subtraction of two functions

the integral of a function where the two points of evaluation are the same

the integral of a function where the two points of evaluation are swapped

the integral of a function multiplied by a constant

Common IntegralsReturn to Top

integral of a constant

integral of a variable raised to a power

integral of a x raised to -1 or 1 over x

integral of linear function raised to -1

integral of natural log function

integral of e to the x

integral of cosine function

integral of sine function

integral of secant squared function

integral of secant tangent function

integral of cosecant cotangent function

integral of cosecant squared function

integral of tangent function

integral of secant function

common integral with inverse tangent

common integral with inverse sine

Integration by SubstitutionReturn to Top

integration by u substitution

integral by u substitution

Integration by PartsReturn to Top

integration by parts

integral by parts

Integration by Trigonometric SubstitutionReturn to Top

Trigonometric identities can be use with integration substitution to simplify integrals. There are three common substitutions.

First Trigonometric SubstitutionReturn to Top

first trignometric substitution

To take advantage of the property

integral by trig substitution

Substitute

substitute sin function

substitute cosine function for dx

After substitution

result of first trig substitution

Second Trigonometric SubstitutionReturn to Top

second trignometric substitution

To take advantage of the property

integral by trig substitution- secant squared

Substitute

integration substition for x - secant

trig substitution for dx

After substitute

result for second trig substitution

Third Trigonometric SubstitutionReturn to Top

third trigonometric substitution

To take advantage of the property

integral by trig substitution - tangent squared

Substitute

integration substitution for x - tangent

trig substitution for dx - secant squared

After substitute

result for third trig substitution

Calculus Derivatives and Limits Math Sheet

An Engineers Quick Calculus Derivatives and Limits Reference

Limits Math Help

Definition of LimitReturn to Top

The limit is a method of evaluating an expression as an argument approaches a value. This value can be any point on the number line and often limits are evaluated as an argument approaches infinity or minus infinity. The following expression states that as x approaches the value c the function approaches the value L.

definition of a limit

Right Hand LimitReturn to Top

The following expression states that as x approaches the value c and x > c the function approaches the value L.

right hand limit definition

Left Hand LimitReturn to Top

The following expression states that as x approaches the value c and x < c the function approaches the value L.

left hand limit definition

Limit at InfinityReturn to Top

The following expression states that as x approaches infinity, the value c is a very large and positive number, the function approaches the value L.

limit at infinity

Also the limit as x approaches negative infinity, the value of c is a very large and negative number, is expressed below.

limit at negative infinity

Properties of LimitsReturn to Top

Given the following conditions:

conditions for limit properties

The following properties exist:

limit property with constant

limit property with the sum of two functions

limit property with the multiplcation of two functions

limit propety with the division of two functions

limit property with a function raised to a power

Limit Evaluation at +-InfinityReturn to Top

limit of e raised to the x at infinity

limit of the natural log at infinity

limit of a constant over x raised to a constant

limit of a constant over x raised to a constant when x raised r is real

limit of x raised to a constant for even r

limit of x raised to a constant for odd r

Limit Evaluation MethodsReturn to Top

Continuous FunctionsReturn to Top

If f(x) is continuous at a then:

limit of a continuous function

Continuous Functions and CompositionsReturn to Top

If f(x) is continuous at b:

limit of a the composition of continous functions

Factor and CancelReturn to Top

limit evaluation method using factoring

L'Hospital's RuleReturn to Top

limit evaluation method using L'Hopital's rule

Derivatives Math Help

Definition of a DerivativeReturn to Top

The derivative is way to define how an expressions output changes as the inputs change. Using limits the derivative is defined as:

definition of a derivative using limits

Mean Value TheoremReturn to Top

This is a method to approximate the derivative. The function must be differentiable over the interval (a,b) and a < c < b.

derivatives mean value theorem

Basic ProperitesReturn to Top

If there exists a derivative for f(x) and g(x), and c and n are real numbers the following are true:

derivative of a function with a constant

derivative of the sum of two functions

derivative of a constant

Product RuleReturn to Top

The product rule applies when differentiable functions are multiplied.

derivative product rule - derivative of two functions multiplied

Quotient RuleReturn to Top

Quotient rule applies when differentiable functions are divided.

derivative quotient rule - derivative of the division of two functions

Power RuleReturn to Top

The power rule applies when a differentiable function is raised to a power.

derivative power rule- derivative of a function raised to the power

Chain RuleReturn to Top

The chain rule applies when a differentiable function is applied to another differentiable function.

derivative of two functions applied to one another

Common DerivativesReturn to Top

derivative of a variable

derivative of the sin function

derivative of the cosine function

derivative of the tangent function

derivative of the secant function

derivative of the cosecant function

derivative of the cotangent function

derivative of the inverse sine function

derivative of the inverse cosine function

derivative of the inverse tangent function

derivative of a constant raised to variable

derivative of e raised to the power of x

derivative of the natural log function

derivative of the natural log absolute value function

derivative of the log function

Chain Rule ExamplesReturn to Top

These are some examples of common derivatives that require the chain rule.

chain rule example with function raised to power

chain rule example with e raised to a function

chain rule example of the natural log of function

chain rule example of the sin of a function

chain rule example of the cosine of a function

chain rule example of the tangent of a function

chain rule example of the secant of a function

chain rule example of the inverse tangent of a function

Trigonometry Laws and Identities Math Sheet

An Engineers Quick Trigonometry Laws and Identities Reference

Trig Laws Math Help

Law of SinesReturn to Top

law of sines formula

Law of CosinesReturn to Top

law of cosines formula 1

law of cosines formula 2

law of cosines formula 3

Law of TangentsReturn to Top

law of tangents formula 1

law of tangents formula 2

law of tangents formula 3

Mollweid's FormulaReturn to Top

mollweid's formula

Trig Identities Math Help

Tangent and Cotangent IdentitiesReturn to Top

tangent identity formula

cotangent identity formula

Reciprocal IdentitiesReturn to Top

sine reciprocal identity

cosine reciprocal identity

tangent reciprocal identity

cosecant reciprocal identity

secant reciprocal identity

cotangent reciprocal identity

Pythagorean IdentitiesReturn to Top

pythagorean identity sin and cosine

pythagorean identity tangent and secant

pythagorean identity cotangent and cosecant

Even and Odd IdentitiesReturn to Top

even and odd identity sin function

even and odd identity cosine function

even and odd identity tangent function

even and odd identity cosecant function

even and odd identity secant function

even and odd identity cotangent function

Periodic IdentitiesReturn to Top

periodic identity sin function

periodic identity cosine function

periodic identity tangent function

periodic identity cosecant function

periodic identity secant function

periodic identity cotangent function

Double Angle IdentitiesReturn to Top

double angle identity sin function

double angle identity cosine function 1

double angle identity cosine function 2

double angle identity cosine function 3

double angle identity tangent function

Half Angle IdentitiesReturn to Top

half angle identity sine function

half angle identity cosine function

half angle identity tangent function

Sum and Difference IdentitiesReturn to Top

sum and difference identity sine function

sum and difference identity cosine function

sum and difference identity tangent function

Product to Sum IdentitiesReturn to Top

product to sum indentity sine function

product to sum indentity cosine function

product to sum indentity sine and cosine functions

product to sum indentity cosine and sine functions

Sum to Product IdentitiesReturn to Top

sum to product identiy sine addition function

sum to product identiy sine subtraction function

sum to product identiy cosine addition function

sum to product identiy cosine subtraction function

Cofunction IdentitiesReturn to Top

cofunction identity sine function

cofunction identity cosine function

cofunction identity tangent function

cofunction identity cosecant function

cofunction identity secant function

cofunction identity cotangent function

Trigonometry Definition Math Sheet

An Engineers Quick Trigonometry Definition Reference

Trig Definition Math Help

Right Triangle DefinitionReturn to Top

To define the trigonometric functions of an angle theta assign one of the angles in a right triangle that value. The functions sine, cosine, and tangent can all be defined by using properties of a right triangle. A right triangle has one angle that is 90 degrees. The longest side of the triangle is the hypotenuse. The side opposite theta will be referred to as opposite. The other side next to theta will be referred to as adjacent. The following properties exist:

Sine DefinitionReturn to Top

definition of the sine function

Cosine DefinitionReturn to Top

definition of the cosine function

Tangent DefinitionReturn to Top

definition of the tangent function

Cosecant DefinitionReturn to Top

definition of the cosecant function

Secant DefinitionReturn to Top

definition of the secant function

Cotangent DefinitionReturn to Top

definition of the cotangent function

Unit Circle DefinitionReturn to Top

unit circle definition for sine

unit circle definition for cosine

unit circle definition for tangent

unit circle definition for cosecant

unit circle definition for secant

unit cirle definition for cotangent

Properties of Trig FunctionsReturn to Top

DomainReturn to Top

The possible angle input for each function is defined below:

domain of sine function

domain of cosine function

domain of tangent function

domain of cosecant function

domain of secant function

domain of cotanent function

RangeReturn to Top

The ranges of values possible for each of these functions are:

range of sine function

range of cosine function

range of tangent function

range of cosecant function

range of secant function

range of cotangent function

PeriodReturn to Top

The periods for each of these trig functions are:

period of sine function

period of cosine function

period of tangent function

period of cosecant function

period of secant function

period of cotangent function

Inverse Trig FunctionsReturn to Top

Definition of Inverse Trig FunctionsReturn to Top

The definitions of the inverse trig functions are:

definition of inverse sine

definition of inverse cosine

definition of inverse tangent

Inverse Trig functions are also notated as:

inverse notation of asin

inverse notation of acos

inverse notation of atan

Domain of Inverse Trig FunctionsReturn to Top

domain of inverse sin

domain of inverse cosine

domain of inverse tangent

Range of Inverse Trig FunctionsReturn to Top

range of inverse sin

range of inverse cosine

range of inverse tangent

Geometry Math Sheet

An Engineers Quick Geometry Reference

Geometry Math Help

SquareReturn to Top

A square is a four sided regular polygon. The circumference of a square with sides of length s is:

circumference of a square

The area of a square is:

area of a square

RectangleReturn to Top

The rectangle is a 4 sided polygon, quadrilateral, with right angle corners. The circumference of a rectangle with side lengths of x and y is:

circumference of a rectangle

The area of a rectangle is:

area of a rectangle

 

CircleReturn to Top

The circle is a shape where all points along the shape are equal distance from a specific point. This point is the center of the circle and the distance to the center of the circle is the radius. The circumference of a circle of radius r is:

circumference of a circle

The area of a circle is:

area of a circle

 

TriangleReturn to Top

The triangle is a 3 sided polygon. Triangles can be classified by their sides:

  1. Equilateral triangles: All sides are equal in length.
  2. Isosceles triangles: Two sides are equal in length.
  3. Scalene triangles: All sides have different lengths.

Triangles can also be classified by their angles:

  1. Right triangle: One angle is 90 degrees.
  2. Oblique triangle: Has no angle equal to 90 degrees.
  3. Obtuse triangle: One angle is greater than 90 degrees.
  4. Acute triangle: All angles are less than 90 degrees.

The circumference of a triangle is the sum of all sides of the triangle.

circumference of a triangle

The area of a triangle is determined by its base and height.

area of a triangle

ParallelogramReturn to Top

A parallelogram is a 4 sided polygon or quadrilateral with two sets of parallel sides. The opposite sides are equal in length. The circumference of a parallelogram is:

circumference of a parallelogram

The area of a parallelogram is:

area of a parallelogram

Circular SectorReturn to Top

The circular sector is section of a circle enclosed by two radii. The length of the arc of a circular sector, where r is the radii and theta is the angle, is:

sector arc length

The area of the circular sector is:

area of sector

Circular RingReturn to Top

The circular ring or donut shape is composed of a circle with a centered small circle removed from the area. The area of a circular ring, where R is the outer diameter and r is the inner diameter, is:

area of a circular ring

TrapezoidReturn to Top

A trapezoid is a 4 sided polygon or quadrilateral with one set of parallel sides. The circumference of the trapezoid is:

circumference of a trapezoid

The area of a trapezoid is:

area of a trapezoid

SphereReturn to Top

The sphere is a 3 dimensional object, whose surface is continuous and all points of the surface are an equal distance from a fixed point, the center. The surface area of a sphere, where r is the radius, is:

surface area of a sphere

The volume of a sphere is:

volume of a sphere

CubeReturn to Top

A cube is a three dimensional object bounded by 6 equal square sides. The surface area of a cube , where the length of a side is l, is:

surface area of a cube

The volume of a cube is:

volume of a cube

Rectangular BoxReturn to Top

A rectangular box is a three dimensional object bounded by rectangular or square sides. The surface area of a rectangular box, where the lengths of the sides are a, b, c, is:

surface area of a rectangular box

The volume of a rectangular box is:

volume of a rectangular box

CylinderReturn to Top

The cylinder, also know as the right circular cylinder, is formed by rotating a line, of length h, around a fixed axis parallel to that line. A cylinder has two ends that are equally sized circles parallel to one another and the circular side is at a right angle to these circular ends. The surface area of cylinder is:

surface area of a cylinder

The volume of a cylinder is:

volume of a cylinder

Right Circular ConeReturn to Top

The right circular cone is a three dimensional object created by rotating a right triangle about the vertical side. The surface area of a right circular cone is:

area of a right circular cone

Where the slant height, s is:

slant height of a right circular cone

The volume of a right circular cone is:

volume of a right circular cone

Frustum of a ConeReturn to Top

The frustum of a cone is a portion of cone with the top removed. The top and bottom surfaces are parallel to one another. The volume of a frustum of a cone, where the top radius is r and the bottom radius is R, is:

volume of the frustum of a cone

Pythagorean TheoremReturn to Top

The Pythagorean theorem is based upon the right triangle. And If the three sides of the right triangle are a,b, and c, where c is the hypotenuse, the formula is:

pythagorean theorem equation

pythagorean theorem solution

Algebra Help Math Sheet

An Engineers Quick Algebra Reference

Algebra Math Help

Arithmetic OperationsReturn to Top

The basic arithmetic operations are addition, subtraction, multiplication, and division. These operators follow an order of operation.

AdditionReturn to Top

Addition is the operation of combining two numbers. If more than two numbers are added this can be called summing. Addition is denoted by + symbol. The addition of zero to any number results in the same number. Addition of a negative number is equivalent to subtraction of the absolute value of that number.

SubtractionReturn to Top

Subtraction is the inverse of addition. The subtraction operator will reduce the first operand (minuend) by the second operand (subtrahend). Subtraction is denoted by - symbol.

MultiplicationReturn to Top

Multiplication is the product of two numbers and can be considered as a series of repeat addition. Multiplication of a negative number will result in the reciprocal of the number. Multiplication of zero always results in zero. Multiplication of one always results in the same number.

DivisionReturn to Top

Division is the method to determine the quotient of two numbers. Division is the opposite of multiplication. Division is the dividend divided by the divisor.

Arithmetic PropertiesReturn to Top

The main arithmetic properties are Associative, Commutative, and Distributive. These properties are used to manipulate expressions and to create equivalent expressions in a new form.

AssociativeReturn to Top

The Associative property is related to grouping rules. This rule allows the order of addition or multiplication operation on numbers to be changed and result the same value.

associative property

CommutativeReturn to Top

The Commutative property is related the order of operations. This rule applies to both addition and subtraction and allows the operands to change order within the same group.

commutative property

DistributiveReturn to Top

The law of distribution allows operations in some cases to be broken down into parts. The property is applied when multiplication is applied to a group of division. This law is applied in the case of factoring.

distributive property

Arithmetic Operations ExamplesReturn to Top

algebra operations 1

algebra operations 2

algebra operations 3

algebra operations 4

algebra operations 5

algebra operations 6

algebra operations 7

algebra operations 8

algebra operations 9

algebra operations 10

Exponent PropertiesReturn to Top

exponent addition property

exponent multiplication property

exponent multiply base property

negative exponent property

negative exponent with division property

exponent division propery

exponent of zero property

exponent fraction property

invert exponent property

fraction exponent

Properties of RadicalsReturn to Top

radical property

double radical property

multiply radical property

divide radical property

exponent radical propery odd

exponent radical propery even

Properties of InequalitiesReturn to Top

inequalities subtraction property

inequalities division less than property

inequalities division greater than property

Properties of Absolute ValueReturn to Top

absolute value definition

negative absolute value property

absolute value zero property

absolute value multiply property

absolute value divide property

absolute value sum propety

Complex Numbers

Definition of Complex NumbersReturn to Top

Complex numbers are an extension of the real number system. Complex numbers are defined as a two dimension vector containing a real number and an imaginary number. The imaginary unit is defined as:

imaginary number definition

The complex number format where a is a real number and b is an imaginary number is defined as:

complex number format

Unlike the real number system where all numbers are represented on a line, complex numbers are represented on a complex plane, one axis represents real numbers and the other axis represents imaginary numbers.

Properites of Complex NumbersReturn to Top

definition of a complex number

format of complex numbers

property of the square of a complex number

property of a negative complex number

complex numbers addition property

complex numbers subtraction property

complex numbers multiplication property

complex numbers conjugate property

complex numbers absolute value property

complex numbers magnitude property

complex numbers absolute value squared property

Logarithms

Definition of LogarithmsReturn to Top

A logarithm is a function that for a specific number returns the power or exponent required to raise a given base to equal that number. Some advantages for using logarithms are very large and very small numbers can be represented with smaller numbers. Another advantage to logarithms is simple addition and subtraction replace equivalent more complex operations. The definition of a logarithms is:

log and inverse log definition

Definition of Natural LogReturn to Top

natural log definition

Definition of Common LogReturn to Top

common log definition

Logarithm PropertiesReturn to Top

log of number equal to base property

log of one property

log of base raised to power property

base raised to log property

log power to multiplication property

log multiplication property

log divisin property

Factoring

PolynomialsReturn to Top

A polynomial is an expression made up of variables, constants and uses the operators addition, subtraction, multiplication, division, and raising to a constant non negative power. Polynomials follow the form:

polynomial definition

The polynomial is made up of coefficients multiplied by the variable raised to some integer power. The degree of a polynomial is determined by the largest power the variable is raised.

Quadratic EquationReturn to Top

A quadratic equation is a polynomial of the second order.

quadratic equation

The solution of a quadratic equation is the quadratic formula. The quadratic formula is:

quadratic solution

Common Factoring ExamplesReturn to Top

quadratic factoring example 1

quadratic factoring example 2

quadratic factoring example 3

quadratic factoring example 4

cubic factoring example 5

cubic factoring example 6

cubic factoring example 7

cubic factoring example 8

Square RootReturn to Top

The square root is a function where the square root of a number (x) results in a number (r) that when squared is equal to x.

square root definition

Also the square root property is:

square root property

Absolute ValueReturn to Top

absolute value properties 1

absolute value properties 2

absolute value properties 3

Completing the SquareReturn to Top

Completing the square is a method used to solve quadratic equations. Algebraic properties are used to manipulate the quadratic polynomial to change its form. This method is one way to derive the quadratic formula.

completing the square

The steps to complete the square are:

  1. Divide by the coefficient a.
  2. Move the constant to the other side.
  3. Take half of the coefficient b/a, square it and add it to both sides.
  4. Factor the left side of the equation.
  5. Use the square root property.
  6. Solve for x.

Functions and Graphs

Expressions evaluated at incremental points then plotted on a Cartesian coordinate system is a plot or graph.

Constant FunctionReturn to Top

When a function is equal to a constant, for all values of x, f(x) is equal to the constant. The graph of this function is a straight line through the point (0,c).

constant function

Linear FunctionReturn to Top

A linear function follows the form:

linear function

The graph of this function has a slope of m and the y intercept is b. It passes through the point (0,b). The slope is defined as:

slope

An addition form for linear functions is the point slope form:

point slope

Parabola or Quadratic FunctionReturn to Top

A parabola is a graphical representation of a quadratic function.

quadratic function

The graph of a parabola in this form opens up if a>0 and opens down if a<0. The vertex of the parabola is located at:

parabola vertex

Other forms of parabolas are:

parabola other form

The graph of a parabola in this form opens right if a>0 or opens left if a<0. The vertex of the parabola is located

parabola vertex

CircleReturn to Top

The function of a circle follows the form:

circle definition

Where the center of the circle is (h,k) and the radius of the circle is r.

EllipseReturn to Top

The function of an ellipse follows the form:

ellipse definition

Where the center of the ellipse is (h,k)

HyperbolaReturn to Top

The function of a Hyperbola that opens right and left from the center follows the form:

hyperbola definition

The function of a Hyperbola that opens up and down from the center follows the form:

hyperbola definition

Where the center of the hyperbola is (h,k), with asymptotes that pass through the center with slopes of:

hyperbola center

Internal PCB Trace Width

Calculate the required internal trace width for a specified current

Trace Width Calculator

Stripline Trace Width Calculator

stripline impedance diagram

Inputs

Max Current
I
Trace Width Unit
W
Trace Thickness
T
Temperature Rise
Trise

Additional Inputs

Ambient Temperature
Tamb
Length
L

Output

Trace Width: 
 

Additional Output

Trace Temperature: 
 
Resistance: 
 
Voltage Drop: 
 
Power Dissipation: 
 
 

Tool Description

Trace width is a requirement that designers specify to ensure that the trace can handle the required current capacity. This tool calculates the trace width based upon the following design specifications:

  • Max Current
  • Trace Thickness
  • Max Desired Temperature Rise

This tool also calculates the following additional valuable information related to the trace:

  • Resistance
  • Votlage Drop
  • Trace Power Dissipation

After a user specifies the max current, trace thickness, and desired max temperature rise, the tool calculates the trace width. This tool is based on charts in IPC-2221

External PCB Trace Width

Calculate the required trace width for a specified current

Trace Width Calculator

Microstrip Trace Width Calculator

microstrip impedance diagram

Inputs

Max Current
I
Trace Width Unit
W
Trace Thickness
T
Temperature Rise
Trise

Additional Inputs

Ambient Temperature
Tamb
Length
L

Output

Trace Width: 
 

Additional Output

Trace Temperature: 
 
Resistance: 
 
Voltage Drop: 
 
Power Dissipation: 
 
 

Tool Description

Trace width is a requirement that designers specify to ensure that the trace can handle the required current capacity. This tool calculates the trace width based upon the following design specifications:

  • Max Current
  • Trace Thickness
  • Max Desired Temperature Rise

This tool also calculates the following additional valuable information related to the trace:

  • Resistance
  • Votlage Drop
  • Trace Power Dissipation

After a user specifies the max current, trace thickness, and desired max temperature rise, the tool calculates the trace width. This tool is based on charts in IPC-2221

Internal PCB Trace Max Current

Calculate the maximum current of an internal trace

Trace Max Current Calculator

Stripline Max Current Calculator

stripline impedance diagram

Inputs

Trace Width
W
Trace Thickness
T
Temperature Rise
Trise

Additional Inputs

Ambient Temperature
Tamb
Length
L

Output

Max Current: 
 

Additional Output

Trace Temperature: 
 
Resistance: 
 
Voltage Drop: 
 
Power Dissipation: 
 
 

Tool Description

Trace max current is a requirement that designers specify to ensure that the trace can handle the required current capacity. This tool calculates the max trace current based upon the following design specifications:

  • Trace Width
  • Trace Thickness
  • Max Desired Temperature Rise

This tool also calculates the following additional valuable information related to the trace:

  • Resistance
  • Votlage Drop
  • Trace Power Dissipation

After a user specifies the trace width, trace thickness, and desired max temperature rise, the tool calculates the max current. This tool is based on charts in IPC-2221

Pi-Match

Impedance Matching Circuit

Impedance Matching Circuits

Choose Type

PI Network Impedance Matching

pi low pass circuit topoplogy

Inputs

Frequency
F
Source Resistance
RS
Ohm
Source Reactance
XS
Ohm
Load Resistance
RL
Ohm
Load Reactance
XL
Ohm
Q Factor
Q
Ohm
Circuit DC Current

Outputs

L: 

C: 

Q: 

Plots:

  • Mag & Phase
  • Real & Complex

Freq: 

 

Mag: 

 

Phase: 

 
 

PI Match Impedance Calculator

The Pi match circuit gets its name because the circuit topology can look like a pi symbol. This tool will help you create a matching circuit so that optimal power transfer occurs between unmatched loads. This technique doesn’t work for wide band requirements, but is a simple way to achieve this at a specific frequency. This calculator will give you the circuit topology as well as the component values.

PI Match Circuit Description

There are some important items to understand when using this tool. The circuit topology can change depending on the inputs. For example in some topologies there may be 2 inductors and one capacitor and in a different configuration it may be 2 capacitors and one inductor. There is one menu item to select if there is to be any DC current or not, that also affects the topology. The inputs ask for source resistance and source reactance. If you are unsure what the reactance is set it to zero for a first pass approximation.

The outputs of this tool give you the component values as well as a graph of the impedance looking into the pi circuit from the source. This allows you to double check the calculator and make sure that it selected appropriate values, by making sure the impedance correctly matches the input impedance. Also remember that the circuit input reactance will be opposite in polarity with the source reactance when matching.

PI Match Circuit Formulas

For Pass DC Current


Z_{input}=\left ( \left ( \left ( R_{L}+jX_{L} \right )//\left ( \frac{1}{j\omega\cdot C_{L}} \right ) \right )+j\omega\cdot L \right )//\left ( \frac{1}{j\cdot \omega\cdot C_{s}} \right )

For Block DC Current

Z_{input}=\left ( \left ( \left ( R_{L}+jX_{L} \right )//\left ( j\omega\cdot L_{L} \right ) \right )+\frac{1}{j\omega\cdot C} \right )//\left ( j\omega\cdot L_{s} \right )

T-Match

Impedance Matching Circuit

Impedance Matching Circuits

Choose Type

T-Match Topology

low pass circuit topoplogy

Inputs

Frequency
F
Source Resistance
RS
Ohm
Source Reactance
XS
Ohm
Load Resistance
RL
Ohm
Load Reactance
XL
Ohm
Q Factor
Q
Ohm
Circuit DC Current

Outputs

L: 

C: 

Q: 

Plots:

  • Mag & Phase
  • Real & Complex

Freq: 

 

Mag: 

 

Phase: 

 
 

T Match Impedance Calculator

The T match circuit gets its name because the circuit topology looks like the letter “T”. This tool will help you create a matching circuit so that optimal power transfer occurs between unmatched loads. This technique doesn’t work for wide band requirements, but is a simple way to achieve this at a specific frequency. This calculator will give you the circuit topology as well as the component values.

T Match Circuit Description

There are some important items to understand when using this tool. The circuit topology can change depending on the inputs. For example in some topologies there may be 2 inductors and one capacitor and in a different configuration it may be 2 capacitors and one inductor. There is one menu item to select if there is to be any DC current or not, that also affects the topology. The inputs ask for source resistance and source reactance.

The outputs of this tool give you the component values as well as a graph of the impedance looking into the circuit from the source. This allows you to double check the calculator and make sure that it selected appropriate values, by making sure the impedance correctly matches the input impedance. Also remember that the circuit input reactance will be opposite in polarity with the source reactance when matching.

T Match Circuit Formulas

For Pass DC Current


Z_{input}=\left ( \left ( R_{L}+jX_{L}+j\omega\cdot L_{L} \right )//\left (\frac{1}{j\cdot \omega\cdot C} \right ) \right )+j\omega\cdot L_{s}

For Block DC Current

Z_{input}=\left ( \left ( R_{L}+jX_{L}+\left ( \frac{1}{j\cdot \omega\cdot C_{L}} \right )\right )//\left ( j\omega\cdot L \right ) \right )+\left ( \frac{1}{j\cdot \omega\cdot C_{S}} \right )

L-Match

Impedance Matching Circuit

Impedance Matching Circuits

Choose Type

L-Match Topology

low pass circuit topoplogy

Inputs

Frequency
F
Source Resistance
RS
Ohm
Source Reactance
XS
Ohm
Load Resistance
RL
Ohm
Load Reactance
XL
Ohm
Circuit DC Current

Outputs

L: 

C: 

Q: 

Plots:

  • Mag & Phase
  • Real & Complex

Freq: 

 

Mag: 

 

Phase: 

 
 

L Match Impedance Calculator

The L match circuit gets its name because the circuit topology can look like the letter “L”. This tool will help you create a matching circuit so that optimal power transfer occurs between unmatched loads. This technique doesn’t work for wide band requirements, but is a simple way to achieve this at a specific frequency. This calculator will give you the circuit topology as well as the component values.

L Match Circuit Description

There are some important items to understand when using this tool. The circuit topology can change depending on the inputs. In all topologies there is one inductor and one capacitor, but the location of these components changes. There is one menu item to select if there is to be any DC current or not, that also affects the topology. The inputs ask for source resistance and source reactance. If you are unsure what the reactance is set it to zero for a first pass approximation.

The outputs of this tool give you the component values as well as a graph of the impedance looking into the L circuit from the source. This allows you to double check the calculator and make sure that it selected appropriate values, by making sure the impedance correctly matches the input impedance. Also remember that the circuit input reactance will be opposite in polarity with the source reactance when matching.

L Match Circuit Formulas

For Pass DC Current


Z_{input}=\left ( \left ( R_{L}+jX_{L}+\left ( \frac{1}{j\cdot \omega\cdot C} \right )\right )//\left ( j\omega\cdot L \right ) \right

For Block DC Current

Z_{input}=\left ( \left ( R_{L}+jX_{L}+\left ( j\omega\cdot L \right )\right )// \right )\left ( \frac{1}{j\cdot \omega\cdot C} \right )

External PCB Trace Max Current

Calculate the maximum current of a trace

Trace Max Current Calculator

Microstrip Max Current Calculator

microstrip impedance diagram

Inputs

Trace Width
W
Trace Thickness
T
Temperature Rise
Trise

Additional Inputs

Ambient Temperature
Tamb
Length
L

Output

Max Current: 
 

Additional Output

Trace Temperature: 
 
Resistance: 
 
Voltage Drop: 
 
Power Dissipation: 
 
 

Tool Description

Trace max current is a requirement that designers specify to ensure that the trace can handle the required current capacity. This tool calculates the max trace current based upon the following design specifications:

  • Trace Width
  • Trace Thickness
  • Max Desired Temperature Rise

This tool also calculates the following additional valuable information related to the trace:

  • Resistance
  • Votlage Drop
  • Trace Power Dissipation

After a user specifies the trace width, trace thickness, and desired max temperature rise, the tool calculates the max current. This tool is based on charts in IPC-2221

6 Band Resistor Calculator

Calculate the resistance of a 6 band resistor

Resistance Calculator

Choose Type

6 Band Resistor

resistor
1st Digit
2nd Digit
3rd Digit
Multiplier
Tolerance
Tempco
Black
0
0
x1
Brown
1
1
1
x10
± 1%
100
Red
2
2
2
x100
± 2%
50
Orange
3
3
3
x1K
± 3%
15
Yellow
4
4
4
x10K
± 4%
25
Green
5
5
5
x100K
± 0.5%
Blue
6
6
6
x1M
± 0.25%
10
Violet
7
7
7
x10M
± 0.10%
5
Grey
8
8
8
x100M
± 0.05%
White
9
9
9
x1G
Gold
÷ 10
± 5%
Silver
÷ 100
± 10%

Outputs

Resistance: 

 

Tolerance: 

Tempco: 

 

Introduction

A resistor is a perhaps the most common building block used in circuits. Resistors come in many shapes and sizes this tool is used to decode information for color banded axial lead resistors.

6 Band Description

The number of bands is important because the decoding changes based upon the number of color bands. There are three common types: 4 band, 5 band, and 6 band resistors. For the 6 band resistor:

Band 1 – first significant digit.
Band 2 – second significant digit
Band 3 – third significant digit
Band 4 – Multiplier
Band 5 – Tolerance
Band 6 – Temperature Coefficient (Tempco)

Resistance Value

The first 4 bands make up the resistance nominal value. The first 3 bands make up the significant digits where:
black – 0
brown – 1
red – 2
orange – 3
yellow – 4
green – 5
blue – 6
violet – 7
grey – 8
white – 9

The multiplier band is color coded as follows:
black – x1
brown – x10
red – x100
orange – x1K
yellow – x10K
green – x100K
blue – x1M
violet – x10M
grey – x100M
white – x1G
gold – .1
silver – .01

An example of a resistance value is:

band 1 = orange = 3,
band 2 = yellow = 4,
band 3 = green = 5,
band 4 = blue = 1M

value = 345*1M = 345 Mohm

Resistance Tolerance

The fifth band is the tolerance and represents the worst case variation one might expect from the nominal value. The color code for tolerance is as follows:
brown – 1%
red – 2%
orange – 3%
yellow – 4%
green – .5%
blue – .25%
violet – .1%
gray – .05%
gold – 5%
silver – 10%

An example calculating the range of a resistor value is:

If the nominal value was 345 Ohm and the 5th band of the resistor was gold (5%) the value range would be nominal +/- 5% = 327.75 to 362.25

Resistance Temperature Coefficient

Resistors values can change with temperature. The 6th band represents the temperature coefficient or tempco and is represents the amount the resistance value will change with temperature. It is in units of ppm/degree C. The band colors represents the following:

brown – 100 ppm/ºC
red – 50 ppm/ºC
orange – 15 ppm/ºC
yellow – 25 ppm/ºC
blue – 10 ppm/ºC
violet – 5 ppm/ºC

An example if a resistor had a nominal value of 1K ohm and a tempco of 100 ppm/ºC and we wanted to know how much a resistor would change of 25ºC.

100*25/1e6*1K= 2.5 ohm variation over 25ºC.

5 Band Resistor Calculator

Calculate the resistance of a 5 band resistor

Resistance Calculator

Choose Type

5 Band Resistor

resistor
1st Digit
2nd Digit
3rd Digit
Multiplier
Tolerance
Black
0
0
x1
Brown
1
1
1
x10
± 1%
Red
2
2
2
x100
± 2%
Orange
3
3
3
x1K
± 3%
Yellow
4
4
4
x10K
± 4%
Green
5
5
5
x100K
± 0.5%
Blue
6
6
6
x1M
± 0.25%
Violet
7
7
7
x10M
± 0.10%
Grey
8
8
8
x100M
± 0.05%
White
9
9
9
x1G
Gold
÷ 10
± 5%
Silver
÷ 100
± 10%

Outputs

Resistance: 

 

Tolerance: 

 

Introduction

A resistor is a perhaps the most common building block used in circuits. Resistors come in many shapes and sizes this tool is used to decode information for color banded axial lead resistors.

5 Band Description

The number of bands is important because the decoding changes based upon the number of color bands. There are three common types: 4 band, 5 band, and 6 band resistors. For the 5 band resistor:

Band 1 – First significant digit.
Band 2 – Second significant digit
Band 3 – Third significant digit
Band 4 – Multiplier
Band 5 – Tolerance

Resistance Value

The first 4 bands make up the resistance nominal value. The first 3 bands make up the significant digits where:
black – 0
brown – 1
red – 2
orange – 3
yellow – 4
green – 5
blue – 6
violet – 7
grey – 8
white – 9

The 4th band or multiplier band is color coded as follows:
black – x1
brown – x10
red – x100
orange – x1K
yellow – x10K
green – x100K
blue – x1M
violet – x10M
grey – x100M
white – x1G
gold – .1
silver – .01

An example of a resistance value is:

band 1 = orange = 3,
band 2 = yellow = 4,
band 3 = green = 5,
band 4 = blue = 1M

value = 345*1M = 345 Mohm

Resistance Tolerance

The fifth band is the tolerance and represents the worst case variation one might expect from the nominal value. The color code for tolerance is as follows:
brown – 1%
red – 2%
orange – 3%
yellow – 4%
green – .5%
blue – .25%
violet – .1%
gray – .05%
gold – 5%
silver – 10%

An example calculating the range of a resistor value is:

If the nominal value was 345 Ohm and the 5th band of the resistor was gold (5%) the value range would be nominal +/- 5% = 327.75 to 362.25

4 Band Resistor Calculator

Calculate the resistance of a 4 band resistor

Resistance Calculator

Choose Type

4 Band Resistor

resistor
1st Digit
2nd Digit
Multiplier
Tolerance
Black
0
x1
Brown
1
1
x10
± 1%
Red
2
2
x100
± 2%
Orange
3
3
x1K
± 3%
Yellow
4
4
x10K
± 4%
Green
5
5
x100K
± 0.5%
Blue
6
6
x1M
± 0.25%
Violet
7
7
x10M
± 0.10%
Grey
8
8
x100M
± 0.05%
White
9
9
x1G
Gold
÷ 10
± 5%
Silver
÷ 100
± 10%

Outputs

Resistance: 

 

Tolerance: 

 

Introduction

A resistor is a perhaps the most common building block used in circuits. Resistors come in many shapes and sizes this tool is used to decode information for color banded axial lead resistors.

4 Band Description

The number of bands is important because the decoding changes based upon the number of color bands. There are three common types: 4 band, 5 band, and 6 band resistors. For the 4 band resistor:

Band 1 – First significant digit.
Band 2 – Second significant digit
Band 3 – Multiplier
Band 4 – Tolerance

Resistance Value

The first 4 bands make up the resistance nominal value. The first 2 bands make up the significant digits where:
black – 0
brown – 1
red – 2
orange – 3
yellow – 4
green – 5
blue – 6
violet – 7
grey – 8
white – 9

The 3rd band or multiplier band is color coded as follows:
black – x1
brown – x10
red – x100
orange – x1K
yellow – x10K
green – x100K
blue – x1M
violet – x10M
grey – x100M
white – x1G
gold – .1
silver – .01

An example of a resistance value is:

band 1 = orange = 3,
band 2 = yellow = 4,
band 3 = blue = 1M

value = 34*1M = 34 Mohm

Resistance Tolerance

The fourth band is the tolerance and represents the worst case variation one might expect from the nominal value. The color code for tolerance is as follows:
brown – 1%
red – 2%
orange – 3%
yellow – 4%
green – .5%
blue – .25%
violet – .1%
gray – .05%
gold – 5%
silver – 10%

An example calculating the range of a resistor value is:

If the nominal value was 34 Ohm and the 4th band of the resistor was gold (5%) the value range would be nominal +/- 5% = 32.3 to 35.7

RF Unit Converter

Make conversions between common RF units

Rf Unit Converter

Impedance

Ohm

Voltage

Vpeak

Vrms

uV

uV EMF

uV PD

dBuV

dBuV EMF

dBuV PD

Power

W

mW

uW

dBm

dBuW

dBuW EMF

dBuW PD

dBpW

dBpW EMF

dBpW PD

Enter value in Voltage or Power field and all other values will be calculated

 

RF Unit Converter Introduction

This tool is a unit converter for voltage and power. There is an input for impedance that allows the relationship between power and voltage.

Ohm

The unit for resistance or impedance. Resistance can define the relationship between voltage and current and voltage and power. Based upon ohms law the voltage and current relatinship is:


r = \frac{v}{i}

and power is


power = \frac{v^{2}}{r}

Vpeak – Peak Voltage

Peak voltage of an AC signal is the peak amplitude.

Vrms – RMS Voltage

The Root Mean Square Voltage or Vrms is:


V_{rms}=\frac{V_{peak}}{\sqrt{2}}

uV – Microvolt (RMS)

This value is the RMS voltage in microvolts.


\mu V=\frac{V_{peak}}{\sqrt{2}}\cdot 10^{-6}

uV EMF

This value is microvolt with no termination or load.


\mu V_{emf}=\frac{2\cdot V_{peak}}{\sqrt{2}}\cdot 10^{-6}

uV PD

This value is microvolt with with a load. When a signal has a matched load then half of the voltage is droped across the load. This value is the same value as uV, The unit is just explicitly defined as having the load.


\mu V_{pd}=\frac{V_{peak}}{\sqrt{2}}\cdot 10^{-6}

dBuV – dB Microvolts RMS

This unit is the decible of RMS microvolt.


dB\mu V=20\log \left ( \mu V \right )

dBuV EMF – dB Microvolts EMF

This unit is the decible of EMF microvolt.


dB\mu V_{emf}=20\log \left ( \mu V_{emf} \right )

dBuV PD – dB Microvolts PD

This unit is the decible of EMF microvolt.


dB\mu V_{pd}=20\log \left ( \mu V_{pd} \right )

W – Watts

Watts is a unit of power.


W=\frac{V_{rms}^{2}}{Z_{o}}

mW – Miliwatts

One thousandth of a watt.


mW=\frac{W}{10^{3}}

uW – Microwatts

One millionth of a watt.


\mu W=\frac{W}{10^{6}}

dBm

dBm is a power measurement and is the decibal of the power in mW.


dBm=10\log \left ( mW \right )

dBuW

dBuW is a power measurement and is the decibal of the power in uW.


dBm=10\log \left ( \mu W \right )

dBuW EMF

dBuW EMF is a power measurement and is the decibal of the power in uW. In a system with no termination or load.


dBm=10\log \left ( 2\cdot \mu W \right )

dBuW PD

dBuW PD is a power measurement and is the decibal of the power in uW. In a system with a matched load.


dBm=10\log \left (\mu W \right )

dBpW

dBpW is a power measurement and is the decibal of the power in pW.


dBm=10\log \left ( \mu W\cdot 1e6 \right )

dBpW EMF

dBpW EMF is a power measurement and is the decibal of the power in pW. In a system with no termination or load.


dBm=10\log \left ( 2\cdot \mu W\cdot 1e6 \right )

dBpW PD

dBpW PD is a power measurement and is the decibal of the power in pW. In a system with a matched load.


dBm=10\log \left (\mu W\cdot 1e6 \right )

Edge Coupled Trace Inductance

Calculate the Inductance of Two Edge Coupled Traces

Edge Trace Inductance Calculator

Edge Coupled Trace Inductance Calculator

edge coupled traces

Inputs

Trace Width
W
Trace Seperation
S
Trace Length
L
Relative Permeability
μr

Outputs

Inductance: 
 

Introduction

Coplanar traces are common in printed circuit boards. Coplanar traces where one trace is the signal and the other trace is the return path apply to this inductance calcualtor.

Wire Loop Inductance Description

The inductance of the coplanar trace calculation requires 4 variables:

  • W – Trace Width
  • S – Trace Seperation
  • L – Trace Length
  • ur – relative Permiablity

This structure requires that these spacings be uniform down the entire length of the trace.

Coplanar Trace Inductance Model.

The inductance of the coplanar trace is:


L_{coplanar}\approx \frac{\mu _{o}\mu _{r}}{\pi}\cosh^{-1}\left ( \frac{s}{w} \right )

where


\left ( d>>w, w>t \right )

Broadside Trace Inductance

Calculate the Inductance of Two Broadside Coupled Traces

Broadside Trace Inductance Calculator

Broadside Coupled Trace Inductance Calculator

broadside coupled traces

Inputs

Trace Width
W
Trace Seperation
H
Trace Length
L
Relative Permeability
μr

Outputs

Inductance: 
 

Introduction

The broadside coupled trace is a common technique for routing differential pair signals.

Broadside Trace Inductance Description

The inductance of a broadside coupled trace is easy to calculate. Broadside coupled traces are on adjacent planes and the return is identical to the trace in width and length. It is important to note that in industry we can find that some differential pairs are routed this way for a strong coupling, but the actual return for the signal is on a power plane. This calculator is for the case where the signal return is on the adjacent trace. The geometry inputs are:

  • W – trace width
  • T – trace thickness
  • H – distance between traces
  • L – trace length

Broadside Coupled Trace Inductance Model.

The inductance for a set of broadside coupled traces is defined as:


\frac{\mu _{o}\mu _{r}h}{w}

Where


(w>>h,h>t)

Coil Inductance

Calculate the Inductance of a Coil

Coil Inductance Calculator

Coil Inductance Calculator

coil of wire

Inputs

Number of Turns
N
Loop Diameter
D
Wire Diameter
d
Relative Permeability
μR

Outputs

Inductance: 
 

Introduction

A coil inductance formula is based upon the basic loop inductance. Inductance is the ability to store energy in a magnetic field, and coils are a very common way to create inductance. Many magnetic field coupling circuits, like chokes and transformers take advantage of a coil’s magnetic storage properties.

Wire Loop Inductance Description

The inductance of a wire loop is a common example of a circuit with inductance. The variables used in this tool are the diameter of the wire conductor and the diameter of the wire loop, number of turns, and the relative permeability. Coil inductance is related to individual loop inductance by the square of the number of turns.

Coil Inductance Model.

The inductance of the wire a coil is:


L_{loop}\approx N^{2}\mu _{o}\mu _{r}\left ( \frac{D}{2} \right )\cdot \left ( \ln\left ( \frac{8\cdot D}{d} \right )-2 \right )

Rectangle Loop Inductance

Calculate the Inductance of a Rectangle Loop

Rectangle Loop Inductance Calculator

Rectangle Loop Inductance Calculator

rectangle loop of wire

Inputs

Number of Turns
N
Loop Width
W
Loop Height
H
Wire Diameter
d
Relative Permeability
μR

Outputs

Inductance: 
 

Introduction

The rectangle loop is often found in windings for transformers or ferrite cores.

Rectangle Inductance Description

The inductance of a rectangle loop has three geometric variables:

  • W – rectangle long side
  • h – rectangle short side
  • d – wire diameter

Rectangle Loop Inductance Model

The inductance for a rectangle loop is:

L_{rec}=\frac{\mu _{o}\mu _{r}}{\pi }\left [ -2\left ( w+h \right )+2\sqrt{h^{2}+w^{2}}+temp \right]

where

temp=-h\ln \left ( \frac{h+\sqrt{h^{2}+w^{2}}}{w} \right )-w\ln \left ( \frac{w+\sqrt{h^{2}+w^{2}}}{h} \right)+h \ln \left ( \frac{2h}{d} \right )+w \ln \left ( \frac{2h}{d} \right )

Loop Inductance

Calculate the Inductance of a Loop

Wire Loop Inductance Calculator

Loop Inductance Calculator

loop of wire

Inputs

Loop Diameter
D
Wire Diameter
d
Relative Permeability
μR

Outputs

Inductance: 
 

Introduction

A wire loop creates inductance. Inductance is the ability to store energy in a magnetic field.

Wire Loop Inductance Description

The inductance of a wire loop is a common textbook example of a circuit with inductance. The variables used in this tool are the diameter of the wire conductor and the diameter of the wire loop. This calculation is for loop and self inductance they are the same for this example.

Loop Inductance Model.

The inductance of the wire loop.


L_{loop}\approx \mu _{o}\mu _{r}\left ( \frac{D}{2} \right )\cdot \left ( \ln\left ( \frac{8\cdot D}{d} \right )-2 \right )

Wire Over Plane Inductance

Calculate the Inductance of a Wire Over a Plane

Wire Over Plane Inductance Calculator

Wire Over Plane Inductance Calculator

wire over plane

Inputs

Wire Diameter
D
Height Above Plane
H
Length of Wire
L
Relative Permeability
μR

Outputs

Inductance: 
 

Introduction

The wire over plane is a transmission line that is common. One place that it is used is in modifications to existing circuit boards. In some instances one might be interested in only the inductance.

Description

The inductance calculated in this tool is the loop inductance created with the wire and its return path on the ground plane. It is important to notice this is not the self inductance of the wire but a closed loop. The inductance allows one to understand the amount of energy that can be stored in magnetic fields. The only variables used in this calculation are the height of the wire from the reference plane, the radius of the wire, and the relative permeability of the medium around the wire. The permeability of air is 1 for all practical purposes. The permeability of a vacuum is exactly 1.

Wire over Plane Inductance Model.

The inductance of the loop created with the wire and plane.


L_{wire}\approx \frac{\mu _{o}\mu _{r}}{2\pi}\cosh^{-1}\left ( \frac{h}{a} \right )

where

\left ( h> > a \right )

Coax Inductance

Calculate the Inductance of a Coax Cable

Coax Cable Inductance Calculator

Coax Inductance Calculator

coax cable

Inputs

Outer Diameter
D
Inner Diameter
d
Length of Wire
L
Relative Permeability
μR

Outputs

Inductance: 
 

Introduction

A coax is a common transmission line construction and most rf cables are coax. The impedance of the coax is a relationship of the capacitance per unit length and the inductance per unit length. This tool will help you find the inductance for a given length of coax cable.

Coax Inductance Description

The inductance of a coax cable can be useful to know. The variables needed in calculating this inductance are center conductor diameter, distance to outer shield, and length. You might notice that the diameter of the outer shield is not required. It is assumed that this shield is sufficiently thick. This calculation is for a loop inductance where the outer shield is the return path for the center conductor.

Coax Inductance Model.

The inductance of the loop created with the center conductor and outer shield.


L_{coax}\approx \frac{\mu _{o}\mu _{r}}{2\pi }\cdot \ln \left ( \frac{D}{d} \right )\cdot L

Parallel Wire Inductance

Calculate the Inductance of Two Parallel Wires

Parallel Wire Inductance Calculator

Parallel Wire Inductance Calculator

two parallel wires inductance

Inputs

Diameter of Wire
D
Distance Between Wires
S
Length of Wire
L
Relative Permeability
μ

Outputs

Inductance: 
 

Introduction

The inductance of two parallel conductors can be computed. It is assumed that one of the conductors is the return path for the other wire.

Self Inductance Description

The inductance for the two wire inductance might be useful in measuring the inductance for a signal and ground on a ribbon cable. The inputs to this calculator are length distance between the two conductors and diameter of the wire. These two signals make a complete loop.

Wire Self Inductance Model.

The inductance of the loop created with the two wires.


L_{wires}\approx \frac{\mu _{o}\mu _{r}}{\pi}\cosh^{-1}\left ( \frac{s}{d} \right )\cdot L

where


s>>d

Wire Inductance

Wire Self Inductance Calculator

Wire Self Inductance Calculator

Wire Self Inductance Calculator

wire segment diagram self inductance

Inputs

Diameter of Wire
D
Length of Wire
L

Outputs

Wire Self Inductance: 
 

Introduction

The inductance of a single conductor is called self inductance. Self inductance is not typically measured, since it is only part of a complete circuit loop.

Self Inductance Description

The inductance calculated in this tool is the self inductance. This self inductance is used in some simulations and is really only part of a total loop inductance. In this tool the variables required are length, and wire diameter. Notice that there is not a return path referenced in this inductance estimator. When calculating a loop inductance the self inductance as well as the mutual inductance to the return path and the return paths self inductancec is accounted for.

Wire Self Inductance Model.

The self inductance of a single wire in free space is defined below.


L=2l\left ( \ln \left ( \left ( \frac{2l}{d} \right )\left ( 1+\sqrt{1+\left ( \frac{d}{2l} \right )^{2}} \right ) \right )-\sqrt{1+\left ( \frac{d}{2l} \right )^{2}}+\frac{\mu }{4}+\left ( \frac{d}{2l} \right ) \right )

For this calculation the diameter and length units are in cm.

This formula is from the following reference.
“Inductance Calculations” , F. W. Grover, Dover Publications, 2004 .

Broadside Coupled Stripline Impedance

PCB Differential Broadside Coupled Stripline Impedance Calculator

Differential Stripline Impedance Calculator

Broadside Coupled Stripline Impedance Calculator

differntial broadside coupled stripline impedance diagram

Inputs

Trace Thickness
T
Substrate Height
H1
Trace Width
W
Trace Spacing
S
Substrate Dielectric
Er

Outputs

Odd (Z): 
Even (Z): 
Common (Z): 
Differential (Z): 
 

Edge Coupled Stripline Impedance

PCB Differential Stripline Impedance Calculator

Differential Stripline Impedance Calculator

Edge Coupled Stripline Impedance Calculator

differntial edge coupled stripline impedance diagram

Inputs

Trace Thickness
T
Substrate Height
H1
Trace Width
W
Trace Spacing
S
Substrate Dielectric
Er

Outputs

Odd (Z): 
Even (Z): 
Common (Z): 
Differential (Z): 
 

Introduction

The edge couple differential symmetric stripline transmission line is a common technique for routing differential traces. There are four different types of impedance used in characterizing differential trace impedances. This calculator finds both odd and even transmission line impedance. Modeling approximation can be used to understand the impedance of the edge couple differential stripline transmission line.

Description

An edge couple differential symmetric stripline transmission line is constructed with two traces referenced to the same reference planes above and below the traces. There is a dielectric material between them. There is also some coupling between the lines. This coupling is one of the features of differential traces. Usually it is good practice to match differential trace length and to keep the distances between the traces consistent. Also avoid placing vias and other structures between these traces.

Differential Impedance Definitions

Differential Impedance The impedance measured between the two lines when they are driven with opposite polarity signals. Zdiff is equal to twice the value of Zodd

Odd Impedance The impedance measured when testing only one of the differential traces referenced to the ground plane. The differential signals need to be driven with opposite polarity signals. Zodd is equal to half of the value of Zdiff

Common Impedance The impedance measured between the two lines when they are driven with the same signal. Zcommon is half the value of Zeven

Even Impedance The impedance measured when testing only one of the differential traces referenced to the ground plane. The differential signals need to be driven with the same identical signal. Zeven is twice the value of Zcommon

Microstrip Transmission Line Models

Models have been created to approximate the characteristics of the microstrip transmission line.

h=\frac{b-t}{2}

ke=\tanh \left ( \frac{\pi w}{2b} \right )\cdot \tanh \left ( \frac{\pi }{2}\cdot\frac{w+s}{b} \right )

ko=\tanh \left ( \frac{\pi w}{2b} \right )\cdot \coth \left ( \frac{\pi }{2}\cdot\frac{w+s}{b} \right )

k_{e}^{`}=\sqrt{1-ke^{2}}

k_{o}^{`}=\sqrt{1-ko^{2}

z_{o,e}=\frac{30\pi }{\sqrt{er}}\cdot \frac{K(k_{e}^{`})}{K(k_{e})}

z_{o,o}=\frac{30\pi }{\sqrt{er}}\cdot \frac{K(k_{o}^{`})}{K(k_{o})}

Z_{o,ss}=symmetric\:stripline(w,t,h,er)

C_{f}^{`}\left ( \frac{t}{b} \right )=\frac{.0885\eta_{r}}{\pi }\left \{ \frac{2b}{b-t}\ln \left ( \frac{2b-t}{b-t} \right )-\left ( \frac{t}{b-t} \right )\ln \left ( \frac{b^{2}}{\left ( b-t \right )^{2}}-1 \right ) \right \}

C_{f}^{`}\left ( 0 \right )=\frac{.0885e_{r}}{\pi }\cdot 2\ln \left ( 2 \right )

k_{ideal}=\text sech\left ( \frac{\pi w}{2b} \right )

k_{ideal}^{`}=\text tanh\left ( \frac{\pi w}{2b} \right )

Edge Coupled Microstrip Impedance

PCB Differential Microstrip Impedance Calculator

Differential Microstrip Impedance Calculator

Edge Coupled Microstrip Impedance Calculator

differntial microstrip impedance diagram

Inputs

Trace Thickness
T
Substrate Height
H1
Trace Width
W
Trace Spacing
S
Substrate Dielectric
Er

Outputs

Odd (Z): 
Even (Z): 
Common (Z): 
Differential (Z): 
 

Introduction

The edge couple differential microstrip transmission line is a common technique for routing differential traces. There are four different types of impedance used in characterizing differential trace impedances. This calculator finds both odd and even transmission line impedance. Modeling approximation can be used to understand the impedance of the differential microstrip transmission line.

Description

An edge couple differential microstrip transmission line is constructed with two traces referenced to the same reference plane. There is a dielectric material between them. There is also some coupling between the lines. This coupling is one of the features of differential traces. Usually it is good practice to match differential trace length and to keep the distances between the traces consistent. Also avoid placing vias and other structures between these traces.

Differential Impedance Definitions

Differential Impedance The impedance measured between the two lines when they are driven with opposite polarity signals. Zdiff is equal to twice the value of Zodd

Odd Impedance The impedance measured when testing only one of the differential traces referenced to the ground plane. The differential signals need to be driven with opposite polarity signals. Zodd is equal to half of the value of Zdiff

Common Impedance The impedance measured between the two lines when they are driven with the same signal. Zcommon is half the value of Zeven

Even Impedance The impedance measured when testing only one of the differential traces referenced to the ground plane. The differential signals need to be driven with the same identical signal. Zeven is twice the value of Zcommon

Microstrip Transmission Line Models

Models have been created to approximate the characteristics of the microstrip transmission line.

er_{eff1}=\frac{er+1}{2}+\left ( \frac{er-1}{2} \right )\cdot \left ( \sqrt{\frac{w}{w+12h}}+.04\left ( 1-\frac{w}{h} \right )^{2} \right )

er_{eff2}=\frac{er+1}{2}+\left ( \frac{er-1}{2} \right )\cdot \left ( \sqrt{\frac{w}{w+12h}} \right )

a_{0}=.7287\left ( er_{eff}-\frac{er+1}{2} \right )\cdot \left ( \sqrt{1-e^{-.179u}} \right )

b_{0}=\frac{.747\cdot er}{.15+er}

c_{0}=b_{0}-\left ( b_{0}-.207 \right )\cdot e^{-.414u}

d_{0}=.593+.694e^{-.562u}

g=\frac{s}{h}

w_{eff}=w+\frac{t}{\pi }\cdot \ln \left ( \frac{4e}{\sqrt{\left ( \frac{t}{h} \right )^{2}+\left ( \frac{t}{w\pi +1.1t\pi } \right )^{2}}} \right )\cdot \frac{er_{eff}+1}{2\cdot er_{eff}}

er_{effo}=\left ( \left ( .5\cdot \left ( er+1 \right )+a_{0}-er_{eff} \right )\cdot e^{-c_{0}\cdot g^{d_{0}}} \right )+er_{eff}

zo_{surf}=\frac{\eta_{o}}{2\pi \sqrt{2}\sqrt{er_{eff}+1}}\cdot \ln \left ( 1+\left ( 4\cdot \frac{h}{w_{eff}} \right )\cdot \left (\left ( 4\cdot \frac{h}{w_{eff}} \right )\cdot\left ( \frac{14\cdot er_{eff}+8}{11\cdot er_{eff}} \right )+ temp \right )\right )

temp=\sqrt{16\left ( \frac{h}{w_{eff}} \right )^{2}\cdot \left ( \frac{14\cdot er_{eff}+8}{11\cdot er_{eff}} \right )^{2}+\left ( \frac{er_{eff}+1}{2er_{eff}} \right )\cdot \pi ^{2}}

q_{1}=.8695\cdot u^{.194}

q_{2}=1+.7519\cdot g+1.89g^{2.31}

q_{3}=.1975+\left ( 16.6+\left ( \frac{8.4}{g} \right )^{6} \right )^{-.387}+\frac{1}{241} \cdot \ln \left ( \frac{g^{10}}{1+\left ( \frac{g}{3.4} \right )^{10}} \right )

q_{4}=\frac{2\cdot q_{1}}{q_{2}\left ( e^{-g}\cdot u^{q_{3}}+\left ( 2-e^{-g} \right )\cdot u^{-q_{3}} \right )}

q_{5}=1.794+1.14\cdot \ln \left ( 1+\left ( \frac{.638}{g+.517\cdot g^{2.43}} \right ) \right )

q_{6}=.2305+\frac{1}{281.3}\cdot \ln \left ( \frac{g^{10}}{1+\left ( \frac{g}{5.8} \right )^{10}} \right )+\frac{1}{5.1}\cdot \ln \left ( 1+.598\cdot g^{1.154} \right )

q_{7}=\frac{10+190\cdot g^{2}}{1+82.3\cdot g^{3}}

q_{8}=e^{\left(-6.5 -.95\cdot\ln (g) -\left (\frac{g}{.15}\right )^{5}\right)}

q_{9}=\ln \left ( q_{7} \right )\cdot \left ( q_{8}+\frac{1}{16.5} \right )

q_{10}=\left ( \frac{1}{q_{2}} \right )\cdot \left ( q_{2}\cdot q_{4}-q_{5}\cdot e^{\left ( \ln\left ( u \right )\cdot q_{6}\cdot u^{-q_{9}} \right )} \right )

zo_{odd}=zo_{surf}\cdot \left [ \frac{\sqrt{\frac{er_{eff}}{er_{effo}}}}{1-\left ( \frac{zo_{surf}}{\eta_{o}}\cdot q_{10}\sqrt{er_{eff}} \right )} \right ]

v=\frac{u\cdot \left ( 20+g^{2} \right )}{10+g^{2}}+ge^{-g}

ae(v)=1+\frac{\ln \left ( \frac{v^{4}+\left ( \frac{v}{52} \right )^{2}}{v^{4}+.432} \right )}{49}+\frac{\ln \left ( 1+\left ( \frac{v}{18.1} \right )^{3} \right )}{18.7}

b_{e}(e_{r})=.564\left ( \frac{er-.9}{er+3} \right )^{.053}

er_{eff,e}=\frac{er+1}{2}+\frac{er-1}{2}\cdot \left ( 1+\frac{10}{v} \right )^{-a}\cdot e^{v}\cdot b_{e}(e_{r})

zo_{even}=zo_{surf}\cdot \frac{\sqrt{\frac{er_{eff}}{er_{eff,e}}}}{1-\frac{zo_{surf}}{\eta_{o}}\cdot q_{4}\cdot \sqrt{er_{eff}}}

The source for these formulas are found in the IPC-2141A (2004) “Design Guide for High-Speed Controlled Impedance Circuit Boards” and Wadell, Brian C. Transmission Line Design Handbook. Norwood: Artech House Inc, 1991

Wire Stripline Impedance

PCB Wire Stripline Impedance Calculator

Wire Stripline Impedance Calculator

Wire Stripline Impedance Calculator

wire stripline impedance diagram

Inputs

Wire Diameter
D
Substrate Height
H
Substrate Dielectric
Er

Outputs

Impedance (Z): 
 
 

Introduction

The wire stripline transmission line is similar to a standard stripline transmission line, but with a round conductor. Modeling approximation can be used to understand the impedance of the wire stripline transmission line.

Description

A wire stripline is constructed with a round conductor suspended between two ground planes. The conductor and ground planes are separated with a dielectric. This calculator assumes the distance between the two reference planes to be an equal distance.

Microstrip Transmission Line Models

Models have been created to approximate the characteristics of the microstrip transmission line.


zo_{ws}= \frac{\eta _{o}}{2\pi \sqrt{er}}\cdot \ln \left ( \frac{4h}{\pi d} \right )

The source for these formulas are found in the IPC-2141A (2004) “Design Guide for High-Speed Controlled Impedance Circuit Boards”

Wire Microstrip Impedance

Wire Over Reference Plane Impedance Calculator

Wire Microstrip Impedance Calculator

Wire Microstrip Impedance Calculator

wire microstrip impedance diagram

Inputs

Wire Diameter
D
Substrate Height
H
Substrate Dielectric
Er

Outputs

Impedance (Z): 
 
 

Introduction

The wire microstrip transmission line is similar to a standard microstrip transmission line, but with a round conductor. Modeling approximation can be used to understand the impedance of the wire microstrip transmission line.

Description

A wire microstrip is constructed with a round conductor suspended over a ground plane. The conductor and ground plane are separated with a dielectric. As with the standard microstrip trace, an effective dielectric constant is calculated because air is on one side of the trace where another dielectric is between the wire and the ground plane.

Example

An example of a wire microstrip might most often be found in prototypes or reworked boards where a wire is used over the top of pcb or copper clad material. If there is an insulator around the wire then this calculator will be an estimate. Include both the pcb dielectric thickness as well as the wire insulation in the height calculation.

Microstrip Transmission Line Models

Models have been created to approximate the characteristics of the microstrip transmission line.


\Large er_{eff1}=\frac{er+1}{2}+\frac{er-1}{2}\cdot \left [ \sqrt{\frac{d}{d+12h}}+.04\cdot \left ( 1-\frac{d}{h} \right )^{2} \right ]


\Large er_{eff2}=\frac{er+1}{2}+\frac{er-1}{2}\cdot \left[ \sqrt{\frac{d}{d+12h}} \right ]


\Large if (\frac{d}{h}<1)


\Large er_{eff}=er_{eff1}


\Large else


\Large er_{eff}=er_{eff2}


\Large temp=\frac{2h+d}{d}


\Large zo_{wm}=\frac{\eta_{o}}{2\pi \sqrt{er_{eff}}}\cdot \ln \left ( \frac{2h+d}{d}+\sqrt{\frac{2h+d}{d}\cdot \frac{2h+d}{d}-1} \right )=\frac{\eta_{o}}{2\pi \sqrt{er_{eff}}}\cosh^{-1}\left ( \frac{2h+d}{d} \right )

The source for these formulas are found in the IPC-2141A (2004) “Design Guide for High-Speed Controlled Impedance Circuit Boards”

Asymmetric Stripline Impedance

PCB Asymmetric Stripline Impedance Calculator

Asymmetric Stripline Impedance Calculator

Asymmetric Stripline Impedance Calculator

asymmetric stripline impedance diagram

Inputs

Trace Thickness
T
Substrate Height
H1
Substrate Height
H2
Trace Width
W
Substrate Dielectric
Er

Outputs

Impedance (Z): 
 
 

Introduction

The asymmetric stripline transmission line is most commonly found in a pcb where the distance from trace to planes is not the same distance above and below. The ability to model this impedance is nice because it can often be found in designs. Modeling approximation can be used to design the asymmetric stripline trace. By understanding the asymmetric stripline transmission line, designers can properly build these structures to meet their needs.

Description

A stripline is constructed with a flat conductor suspended between two ground planes. The conductor and ground planes are separated by a dielectric. The distance between the conductor and the planes is not the same for both reference planes. This structure will most likely be manufactured with the printed circuit board process.

Example

An example of an asymmetric stripline is a 4 layer pcb were a trace on layer 3 is referenced to both layer 1 and layer 4. The trace is closest to layer 4 and layer 4 has the dominant effect on the transmission line impedance, but layer 1 would still affect the characteristic impedance of this trace.

Asymmetric Stripline Transmission Line Models

Models have been created to approximate the characteristics of the microstrip transmission line.


h_{eff}=\frac{h_{1}+h_{2}}{2}


m=\frac{6\cdot h_{eff}}{3\cdot h_{eff}+t}


zo_{air}=2\left ( \frac{zo_{ssh1}\cdot zo_{ssh2}}{zo_{ssh1}+ zo_{ssh2}} \right )


\Delta zo_{air}= .0325\cdot \pi \cdot zo_{air}^{2}\cdot \left ( \left |.5-.5\cdot \frac{2h_{1+t}}{h_{1}+h_{2}+t} \right |^{2.2} \right )\cdot \left ( \left | \frac{t+w}{h_{1}+h_{2}+t} \right |^{2.9} \right )


zo_{as}=\frac{1}{\sqrt{er}}\cdot \left ( zo_{ssheff}-\Delta zo_{air} \right )

The source for these formulas are found in the IPC-2141A (2004) “Design Guide for High-Speed Controlled Impedance Circuit Boards”

Symmetric Stripline Impedance

PCB Symmetric Stripline Impedance Calculator

Stripline Impedance Calculator

Symmetric Stripline Impedance Calculator

symmetric stripline impedance diagram

Inputs

Trace Thickness
T
Substrate Height
H
Trace Width
W
Substrate Dielectric
Er

Outputs

Impedance (Z): 
 
 

Introduction

The symmetric stripline is reliable method for creating a transmission line. The stripline is a TEM (transverse electromagnetic) transmission line. Modeling approximation can be used to design the microstrip trace. By understanding the stripline transmission line, designers can properly build these structures to meet their needs.

Description

A stripline is constructed with a flat conductor suspended between two ground planes. The conductor and ground planes are separated by a dielectric. One advantage of the stripline is that there is an improve isolation between adjacent traces when compared with the microstrip.

Stripline Transmission Line Models

Models have been created to approximate the characteristics of the microstrip transmission line.


\Large m =\frac{6h}{3h+t}


\Large w_{eff} =w+\frac{t}{\pi}\cdot\ln{\left(\frac{e}{\sqrt{\left(\frac{t}{4h+t}\right)^2+\left(\frac{\pi t}{4\cdot(w+1.1\cdot t)}\right)^m}}\right)}


\Large b=2\cdot h+t


\Large D=\frac{W}{2}\cdot \left ( 1+\frac{t}{\pi w}\cdot \left ( 1+\ln \left ( \frac{4\pi w}{t} \right ) \right )+.551\left ( \frac{t}{w} \right )^{2} \right )


\Large zo_{sst2}=\frac{60}{\sqrt{er}}\cdot \ln \left ( \frac{4b}{\pi D} \right )


\large when


\Large \left ( \frac{w}{b}< .35 \right ) or \left ( \frac{t}{b}\leq .25 \right ) or \left (\frac{t}{w}\leq .11 \right )


\Large zo_{ss}=\frac{\eta o}{2\pi \sqrt{er}}\ln \left ( 1+\frac{8h}{\pi \cdot w_{eff}}\cdot \left ( \frac{16h}{\pi \cdot w_{eff}}+\sqrt{\left ( \frac{16h}{\pi \cdot w_{eff}} \right )^{2}+6.27} \right ) \right )


\large else


\Large zo_{ss}=\frac{94.15}{\left ( \frac{\frac{w}{b}}{\left ( 1-\frac{t}{b} \right )} +\frac{\theta }{\pi }\right )}

The source for these formulas are found in the IPC-2141A (2004) “Design Guide for High-Speed Controlled Impedance Circuit Boards”

Embedded Microstrip Impedance

PCB Embedded Microstrip Impedance Calculator

Embedded Microstrip Impedance Calculator

Embedded Microstrip Impedance Calculator

embedded microstrip impedance diagram

Inputs

Trace Thickness
T
Substrate Height
H1
Substrate Height
H2
Trace Width
W
Substrate Dielectric
Er

Outputs

Impedance (Z): 
 
 

Introduction

The embedded microstrip is a similar in construction to the microstrip transmission line. Modeling approximation can be used to design the embedded microstrip trace. By understanding the embedded microstrip transmission line, designers can properly build these structures to meet their needs.

Description

An embedded microstrip is constructed with a flat conductor suspended over a ground plane. The conductor and ground plane are seperated by a dielectric. There is also a layer of dielectric material above the conductor. One case of an embedded microstrip transmision line is a microstrip trace with soldermask.

Embedded Microstrip Transmission Line Models

Models have been created to approximate the characteristics of the embedded microstrip transmission line.


\Large When \frac{w}{h_{1}}<1


\Large er_{eff}=\frac{er+1}{2}+\frac{er-1}{2}\cdot \left \{ \sqrt{\frac{w}{w+12h_{1}}}+.04\left ( 1-\frac{w}{h_{1}} \right )^{2} \right \}


\Large When \frac{w}{h_{1}}\geq 1


\Large er_{eff}=\frac{er+1}{2}+\frac{er-1}{2}\cdot \left \{ \sqrt{\frac{w}{w+12h_{1}}} \right \}


\Large w_{eff}=w+\left ( \frac{t}{\pi } \right )\cdot \ln \left \{ \frac{4e}{\sqrt{\left ( \frac{t}{h_{1}} \right )^{2}+\left ( \frac{t}{w\pi +1.1t\pi } \right )^{2}}} \right \}\cdot \frac{er_{eff}+1}{2\cdot er_{eff}}


\Large zo_{embed}=zo\cdot \left \{ \frac{1}{\sqrt{e^{\frac{-2b}{h_{1}}}+\frac{er}{zo_{surf}\cdot er_{eff}}\cdot \left ( 1-e^{\frac{-2b}{h_{1}}} \right )}} \right \}


\Large Where


\Large zo=\frac{\eta_{o}}{2\pi \sqrt{2}\sqrt{er_{eff}+1}}\cdot \ln \left ( 1+4\cdot \left ( \frac{h_{1}}{w_{eff}} \right )\cdot \left ( x_{1}+x_{2} \right ) \right )


\Large x_{1}=4\cdot \left ( \frac{h_{1}}{w_{eff}} \right )\cdot \left ( \frac{14\cdot er_{eff}+8}{11\cdot er_{eff}} \right )


\Large x_{2}=\sqrt{16\cdot \left ( \frac{h_{1}}{w_{eff}} \right )^{2}\cdot \left ( \frac{14\cdot er_{eff}+8}{11\cdot er_{eff}} \right )^{2}+\left ( \frac{er_{eff}+1}{2\cdot er_{eff}} \right )\cdot \pi ^{2}}


\Large b=h_{1}-h_{2}

The source for these formulas are found in the IPC-2141A (2004) “Design Guide for High-Speed Controlled Impedance Circuit Boards”

Microstrip Impedance

PCB Microstrip Impedance Calculator

Microstrip Impedance Calculator

Microstrip Impedance Calculator

microstrip impedance diagram

Inputs

Trace Thickness
T
Substrate Height
H
Trace Width
W
Substrate Dielectric
Er

Output

Impedance (Z): 
 
 

Introduction

The microstrip is a very simple yet useful way to create a transmission line with a PCB. There are some advantages to using a microstrip transmission line over other alternatives. Modeling approximation can be used to design the microstrip trace. By understanding the microstrip transmission line, designers can properly build these structures to meet their needs.

Description

A microstrip is constructed with a flat conductor suspended over a ground plane. The conductor and ground plane are seperated by a dielectric. The suface microstrip transmission line also has free space (air) as the dielectric above the conductor. This structure can be built in materials other than printed circuit boards, but will always consist of a conductor seperted from a ground plane by some dielectric material.

Microstrip Transmission Line Models

Models have been created to approximate the characteristics of the microstrip transmission line.

\Large When \frac{w}{h}<1

\Large er_{eff}=\frac{er+1}{2}+\frac{er-1}{2}\cdot \left \{ \sqrt{\frac{w}{w+12h}}+.04\left ( 1-\frac{w}{h} \right )^{2} \right \}

\Large When \frac{w}{h}\geq 1

\Large er_{eff}=\frac{er+1}{2}+\frac{er-1}{2}\cdot \left \{ \sqrt{\frac{w}{w+12h}} \right \}

\Large w_{eff}=w+\left ( \frac{t}{\pi } \right )\cdot \ln \left \{ \frac{4e}{\sqrt{\left ( \frac{t}{h} \right )^{2}+\left ( \frac{t}{w\pi +1.1t\pi } \right )^{2}}} \right \}\cdot \frac{er_{eff}+1}{2\cdot er_{eff}}

\Large zo=\frac{\eta_{o}}{2\pi \sqrt{2}\sqrt{er_{eff}+1}}\cdot \ln \left ( 1+4\cdot \left ( \frac{h}{w_{eff}} \right )\cdot \left ( x_{1}+x_{2} \right ) \right )

\Large Where

\Large x_{1}=4\cdot \left ( \frac{h}{w_{eff}} \right )\cdot \left ( \frac{14\cdot er_{eff}+8}{11\cdot er_{eff}} \right )

\Large x_{2}=\sqrt{16\cdot \left ( \frac{h}{w_{eff}} \right )^{2}\cdot \left ( \frac{14\cdot er_{eff}+8}{11\cdot er_{eff}} \right )^{2}+\left ( \frac{er_{eff}+1}{2\cdot er_{eff}} \right )\cdot \pi ^{2}}

The source for these formulas are found in the IPC-2141A (2004) “Design Guide for High-Speed Controlled Impedance Circuit Boards”

Stripline Crosstalk

PCB Stripline Crosstalk Calculator

Stripline Crosstalk Calculator

Choose Type

Stripline Crosstalk Calculator

stripline crosstalk diagram

Inputs

Source Rise Time
Tr
ns
Source Voltage
V
Volts
Lenght of Parallel Routes
L
Substrate Height
H
Trace 1 Height
h1
Trace 2 Height
h2
Trace Spacing
S
Substrate Dielectric
Er

Outputs

Cross Talk Coeff: 
Coupled Voltage: 
 

Introduction

Crosstalk is unwanted coupled energy between traces. There are two types of crosstalk: forward and backward. This tool calculates backward crosstalk which is usually the dominant crosstalk component.

Description

Backwards crosstalk creates a pulse width that is twice that of the propagation time of the pulse traveling the coupling distance. The amplitude of this crosstalk is what this tool calculates. The amplitude increases as the coupling length increases up to a point. At some point the amplitude will stay constant. The crosstalk coupling calculation requires information for the driver source as well as the PCB physical characteristics. This tool calculates the crosstalk coefficient as well as the coupled voltage, both can be useful in crosstalk analysis.

Stripline Transmission Line Crosstalk Models

The following models approximate the forward crosstalk in stripline transmission lines.


T_{RT} = 1.017\sqrt{\varepsilon _{r\cdot 0.475+0.67}}\cdot L\cdot 2


S_{eff}=\sqrt{S^{2}+\left (h_{2}-h_{1} \right )^{2}}


h_{1eff}=\frac{h_{1}\cdot \left ( H-h_{1} \right )}{h_{1}+ \left ( H- h_{1} \right )}


h_{2eff}=\frac{h_{2}\cdot \left ( H-h_{2} \right )}{h_{2}+ \left ( H- h_{2} \right )}

if

\frac{T_{RT}}{T_{R}}\leq 1

then

CT_{dB} = 20\log \left ( \frac{1}{1+\left ( \frac{ S_{eff}^{2}}{h_{1eff}\cdot h_{2eff} } \right )}\cdot \frac{T_{RT}}{T_{R}} \right )


V_{crosstalk} = V\cdot \frac{1}{1+\left ( \frac{S_{eff}^{2}}{h_{1eff}\cdot h_{2eff} } \right )}\cdot \frac{T_{RT}}{T_{R}}

else

CT_{dB} = 20\log \left ( \frac{1}{1+\left ( \frac{ S_{eff}^{2}}{ h_{1eff}\cdot h_{2eff}} \right )^{2}}\right )


V_{crosstalk} = V\cdot \frac{1}{1+\left ( \frac{ S_{eff}^{2}}{ h_{1eff}\cdot h_{2eff}} \right )^{2}}

Microstrip Crosstalk

PCB Microstrip Crosstalk Calculator

Microstrip Crosstalk Calculator

Choose Type

Microstrip Crosstalk Calculator

microstrip crosstalk diagram

Inputs

Source Rise Time
Tr
ns
Source Voltage
V
Volts
Length of Parallel Routes
L
Substrate Height
H
Trace Spacing
S
Substrate Dielectric
Er

Outputs

Cross Talk Coeff: 
Coupled Voltage: 
 

Introduction

Crosstalk is unwanted coupled energy between traces. There are two types of cross talk forward and backward crosstalk. This tool calculates backward crosstalk which is usually the dominant crosstalk component.

Description

Backwards crosstalk creates a pulse width that is twice that of the propagation time of the pulse traveling the coupling distance. The amplitude of this crosstalk is what this tool calculates. The amplitude increases as the coupling length increases up to a point. At some point the amplitude will stay constant. The crosstalk coupling calculation requires information for the driver source as well as the PCB physical characteristics. This tool calculates the cross talk coefficient as well as the coupled voltage, both can be useful in crosstalk analysis.

Microstrip Transmission Line Models

Models have been created to approximate the characteristics of the forward crosstalk in microstrip transmission lines.


T_{RT} = 1.017\sqrt{\varepsilon _{r\cdot 0.475+0.67}}\cdot L\cdot 2

if

\frac{T_{RT}}{T_{R}}\leq 1

then

CT_{dB} = 20\log \left ( \frac{1}{1+\left ( \frac{S}{H} \right )^{2}}\cdot \frac{T_{RT}}{T_{R}} \right )


V_{crosstalk} = V\cdot \frac{1}{1+\left ( \frac{S}{H} \right )^{2}}\cdot \frac{T_{RT}}{T_{R}}

else

CT_{dB} = 20\log \left ( \frac{1}{1+\left ( \frac{S}{H} \right )^{2}}\right )


V_{crosstalk} = V\cdot \frac{1}{1+\left ( \frac{S}{H} \right )^{2}}

Coax

Coax Impedance Calculator

Coaxial Impedance Calculator

Choose Type

Coax Calculator

coax cross section

Inputs

Inner Conductor Diam.
D1
Inner Surface Shield Diam.
D2
Substrate Dielectric
Er

Outputs

Impedance (Z): 
Delay: 
Inductance per inch: 
Capacitance per inch: 
 

Introduction

Perhaps the most common type of transmission line is the coax. The coax is a very nice way to create a transmission line. Understanding coax can be helpful when working with it. The nice part about coax is that it can be bent and flexible unlike most pcb transmission lines.

Description

The basic coax cable is constructed with an inner trace and a shield separated by dielectric. The property of coax that is nice is the transverse electric magnetic (TEM) mode, which means that the magnetic and electric fields are perpendicular to the direction of the wave propagation. The characteristic impedance is primarily determined by the distance from the conductor to the shield as well as the dielectric constant of material separating them.

Microstrip Transmission Line Models

Models have been created to approximate the characteristics of the microstrip transmission line.

The characteristic impedance of a coax is:


z_{o}=\frac{60}{\sqrt{er}}\cdot \ln \left ( \frac{d2}{d1} \right )

The time delay in ns/inch is:


delay = 84.72\cdot 10^{-12}\cdot\sqrt{er}\cdot \frac{1}{10^{-9}}

The inductance in nH/inch is:


inductance = 5.08\cdot 10^{-9}\cdot \ln \left ( \frac{d2}{d1} \right )\cdot \frac{1}{10^{-9}}

The capacitance in pF/inch is:


capacitance = 1.41\cdot 10^{-12}\cdot \ln \left ( \frac{d2}{d1} \right )\cdot \frac{1}{10^{-12}}

Twisted Pair

Twisted Pair Cable Impedance Calculator

Twisted Pair Impedance Calculator

Choose Type

Twisted Pair Calculator

twisted pair

Inputs

Diameter of Wire
D
Seperation Between Wires
S
Substrate Dielectric
Er

Outputs

Impedance (Z): 
Delay: 
Inductance per inch: 
Capacitance per inch: 
 

Introduction

Two conductors can create a transmission line. To make an effect transmission line with two wires it is best to create a twisted pair. Often when working with wires it is easy to create large return path loops if one is not paying close attention. The twisted pair helps create a more uniform inductance and capacitance per unit length of wire to ensure a constant impedance, by keeping the return path as close to the signal as possible.

Description

The geometries of the twisted pair that we should pay close attention too are the distance between the two conductors (center to center) and the diameter of the conductive wire. The effective permittivity of the material between the two conductors will be somewhere between the permittivity of the insulation on the wires and the relative permittivity of air (1).

Characteristic Properties of the Twisted Pair

Characteristic Impedance The characteristic impedance of the twisted pair is the impedance a signal will see as it travels down the conductor.

Propagation Delay The propagation delay of the signal is the time it takes for the signal to travel a specific distance. This tool calculates the time delay in inches per nanosecond.

Inductance Per Unit Length The inductance of the signal is valuable to know. Especially when creating a model for the transmission line in a simulation tool. This tool calculates the inductance in nano-henrys per inch

Capacitance Per Unit Length The capacitance of the signal is often need when creating a model for the transmission line in a simulation tool. This tool calculates the capacitance in pico-farads per inch

Twisted Pair Transmission Line Models

Models have been created to approximate the characteristics of the microstrip transmission line.


zo_{twistedpair}(ohms)=\frac{120}{\sqrt{er}}\cdot \ln \left [ \frac{2s}{d} \right ]


delay\left ( \frac{ns}{inch} \right )=84.72\cdot10^{-3}\cdot \sqrt{er}


L_{twistedpair}\left ( \frac{nH}{inch} \right )=10.16\cdot 10^{-9}\cdot \ln \left [ \frac{2s}{d} \right ]


C_{twistedpair}\left ( \frac{pF}{inch} \right )=\left ( \frac{.7065}{\ln \left ( \frac{2s}{d} \right )} \right )\cdot er

Template with Flot

Example Tool Template With Flot Plotting

Tool Template

Tool Title

tool_type

Inputs

Resistance
R
Unit
Capacitance
C
Unit

Outputs

Plots:

  • Mag & Phase
  • Real & Complex
Freq: 
 
Mag: 
 
Phase: 
 
 

Using Flot with your Templates

The regular toolbox template includes the flot js library so no need to include this inside your weblog html field.

Event Driven Calculations:

Tool keyboard events are driven by the following bindings that work off of all fieldInput and fieldSelect classes. This will alleviate harcoding events into your tool’s html.
[geshify lang=“javascript”] //Dynamically updates Plots via onkeyup event; Triggers active plot redraw; $(’.fieldInput’).keyup(function () { $(’#’+activePlot).trigger(‘click’); })
[/geshify]

Template With Sidebar

Example Template With Sidebar

Tool Template

Choose Type

Tool Title

tool_type

Inputs

Field One
Label
Unit
Field Description
Label

Outputs

Sample Output_1: 

Sample Output_2: 

Sample Output_3: 

Sample Output_4: 

 

Javascript Code:

Place all your javascript code in the tools weblog entry at the bottom of the “tool_html” field. Javascript code can be in the html file or included via a standard js include link
[geshify]
[/geshify]

Event Driven Calculations:

Tool keyboard events are driven by the following bindings that work off of all fieldInput and fieldSelect classes. This will alleviate harcoding events into your tool’s html.
[geshify lang=“javascript”] // Tool onkeyup and onchange events for updating output values $(”.fieldInput”).keyup(function(event){ testMe(); }); $(”.fieldSelect”).change(function(event){ testMe(); });
[/geshify]

Trace Resistance

PCB Trace Resistance Calculator

Trace Resistance Calculator

 

Trace Resistance

Trace Resistance Calculator

Inputs

Trace Width
W
Trace Length
L
Trace Thickness
T
Temperature
Temp

Output

Resistance (R): 
 
 

Introduction

The purpose of this calculator is to solve the resistance of a copper conductor based upon physical dimensions. The resistance of a trace can be useful in many ways. The power dissipation in a trace is calculated after one has determined the trace resistance. The trace resistance can also be helpful if a circuit requires precision resistors and the pcb traces cab effect the resistance value.

The equation for resistance of a rectangular conductor is:

R=\rho \cdot \frac{L}{T\cdot W}\cdot \left ( 1+tc\cdot \left ( temp-25 \right ) \right )

Where

\rho=resistivity

L= length

W=trace width

T=trace height

Resistivity of Copper is: 1.7E-6 ohm-cm
Temp_Co of Copper is: 3.9E-3 ohm/ohm/C

Resistor Tables

Standard Resistor Tables (Based on EIA Preferred Values)

0.1%, 0.25%, and 0.5% Resistor Table (E192)
100 101 102 104 105 106 107 109 110 111 113 114
115 117 118 120 121 123 124 126 127 129 130 132
133 135 137 138 140 142 143 145 147 149 150 152
154 156 158 160 162 164 165 167 169 172 174 176
178 180 182 184 187 189 191 193 196 198 200 203
205 208 210 213 215 218 221 223 226 229 232 234
237 240 243 246 249 252 255 258 261 264 267 271
274 277 280 284 287 291 294 298 301 305 309 312
316 320 324 328 332 336 340 344 348 352 357 361
365 370 374 379 383 388 392 397 402 407 412 417
422 427 432 437 442 448 453 459 464 470 475 481
487 493 499 505 511 517 523 530 536 542 549 556
562 569 576 583 590 597 604 612 619 626 634 642
649 657 665 673 681 690 698 706 715 723 732 741
750 759 768 777 787 796 806 816 825 835 845 856
866 876 887 898 909 920 931 942 953 965 976 988
1% Resistor Table (E96)
100 102 105 107 110 113 115 118 121 124 127 130
133 137 140 143 147 150 154 158 162 165 169 174
178 182 187 191 196 200 205 210 215 221 226 232
237 243 249 255 261 267 274 280 287 294 301 309
316 324 332 340 348 357 365 374 383 392 402 412
422 432 442 453 464 475 487 499 511 523 536 549
562 576 590 604 619 634 649 665 681 698 715 732
750 768 787 806 825 845 866 887 909 931 953 976
2% Resistor Table (E48)
100 105 110 115 121 127 133 140 147 154 162 169
178 187 196 205 215 226 237 249 261 274 287 301
316 332 348 365 383 402 422 442 464 487 511 536
562 590 619 649 681 715 750 787 825 866 909 953
5% Resistor Table (E24)
100 110 120 130 150 160 180 200 220 240 270 300
330 360 390 430 470 510 560 620 680 750 820 910
10% Resistor Table (E12)
100 120 150 180 220 270 330 390 470 560 680 820
20% Resistor Table (E6)
100 150 220 330 470 680

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