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Characteristic Impedance Calculator for the Measurement of PCB Tracks and Coaxial Cables Using a Vector Network Analyser

Calculates Delay, Velocity Factor, Effective Dielectric Constant and Characteristic Impedance of a PCB track. This calculator can also be used for measuring coaxial cable and will then give Relative Dielectric Constant rather than Effective Dielectric Constant. The operation of this calculator can be better understood by first reading Measuring Characteristic Impedance and Effective Dielectric Constant of PCB tracks using a Vector Network Analyser

Frequency at + 900 (fa) :   MHz Delay( tav):   ns
SHORT R:   Ohms Velocity Factor: 
SHORT J:   Ohms Effective Dielectric Constant (εeff): 
OPEN R:   Ohms Characteristic Impedance Real (R):   Ohms
OPEN J:   Ohms Imaginary (j):   Ohms
Characteristic Impedance (Zo):   Ohms
Frequency at - 900 (fb) :   MHz Averaged Measurement Frequency:   MHz
SHORT R:   Ohms
SHORT J:   Ohms
OPEN R:   Ohms
OPEN J:   Ohms
Completed Phase Revolutions: 
Mechanical Length:   mm  

This calculator uses Visual Basic and will work in Internet Explorer and other browsers with Visual Basic plug-ins. For more information see About our calculators

The time delay (ta) at a + 900 point is found by dividing the total phase shift at the measured + 900 point by the phase shift per second due to frequency

[Delay at plus ninety degrees formula] Formula 1.

Where f is the frequency in Hz at + 900

rev is the number of completed revolutions of phase before the + 900 point is reached

Similarly the time delay  (tb) at a - 900 point is found by dividing the total phase shift at the measured - 900 point by the phase shift per second due to frequency

[Delay at minus ninety degrees formula]Formula 2.

The average time delay (tav) for + 900  and - 900 is then

[Average delay formula]Formula 3.

Finding the Velocity Factor

Equivalent delay in free space for a similar distance 

[Delay in free space formula]   Formula 4.

Where l is the length of the track in mm

c is the speed of light in free space

[Velocity Factor Formula]Formula 5.

[Effective Dielectric Constant formula]Formula 6.

An average of the measurement frequencies is found

[Average Frequency formula]Formula 7.

The principal of deriving the Characteristic Impedance from an OPEN and SHORT measurement is based on Transmission Lines and Networks by Walter C. Johnson, McGraw-Hill 1963 p155 Para 4.7 Measurement of the Characteristics of lines.

[Short and Open formula]Formula 8

 This calculation is combined for two adjacent measurements and so ripple (measurement error) caused by the mismatch of the VNA to the transmission line is also removed.

[Formula for Short and Open removing ripple]Formula 9.

W J Highton 4/4/2008

This calculator is provided free by Chemandy Electronics in order to promote the FLEXI-BOX

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