Math Help

An Engineers Quick References to Mathematics

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

Calculus Derivatives and Limits Math Sheet

An Engineers Quick Calculus Derivatives and Limits Reference

Trigonometry Laws and Identities Math Sheet

An Engineers Quick Trigonometry Laws and Identities Reference

Trigonometry Definition Math Sheet

An Engineers Quick Trigonometry Definition Reference

Geometry Math Sheet

An Engineers Quick Geometry Reference

Algebra Help Math Sheet

An Engineers Quick Algebra Reference

Internal PCB Trace Width

Calculate the required internal trace width for a specified current

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

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

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

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

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

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

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

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/degreeC
red – 50 ppm/degreeC
orange – 15 ppm/degreeC
yellow – 25 ppm/degreeC
blue – 10 ppm/degreeC
violet – 5 ppm/degreeC

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

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

5 Band Resistor Calculator

Calculate the resistance of a 5 band resistor

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

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 345 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 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

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

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

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

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

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

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

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

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

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

Edge Coupled Stripline Impedance

PCB Differential Stripline Impedance Calculator

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}=symetric 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

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

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

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

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”

Stripline Impedance

PCB Symmetric Stripline Impedance Calculator

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

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

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

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

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

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:

zo=\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

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

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

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

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)