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# Transmission line rule

#### engr_joni_ee

A general rule of thumb regarding transmission line in FR4 is, if the length of a conductor is more than 1/10 of the wavelength, then we consider it a transmission line. I have calculated some numbers. Kindly let me know if they are correct.

Clock frequency: 500 MHz
Dielectric constant: 4
Wavelength: 300 mm
Turn in to transmission line: If the trace length is more then 30 mm

Clock frequency: 1000 MHz
Dielectric constant: 4
Wavelength: 150 mm
Turn in to transmission line: If the trace length is more then 15 mm

Clock frequency: 2000 MHz
Dielectric constant: 4
Wavelength: 75 mm
Turn in to transmission line: If the trace length is more then 7.5 mm

Mathematically correct, but referred frequency isn't necessarily the "clock frequency". Usually we relate lambda/10 rule to maximal signal frequency component or e.g. derive it from signal rise time. For typical square wave signals this results in factor 10 smaller dimensions.

A general rule of thumb regarding transmission line in FR4 is, if the length of a conductor is more than 1/10 of the wavelength,
That's for an RF sinewave.
For a digital signal it's determined by the signal rise and fall times.

For digital signals, the critical length lc is defined as the line length over which the signal propagation time is half of the fastest rise time of the signal pulses. If tr = fastest rise time of the digital signal, the time of the propagation of the signal over the length lc is tpd.lc = tr/2 (by definition of lc).

Thanks for comments. Yes, I understand that the numbers in post # 1 are for sine wave signal but not for digital.

In digital, I guess if we assume that the rise time is 20 % of the clock period then the highest considerable frequency or highest significant frequency in the signal is 5 x clock frequency, right ?

The numbers for digital signal for a trace length to turn in to transmission line will be then.

Clock frequency: 500 MHz
Signal bandwidth: 2500 MHz
Dielectric constant: 4
Wavelength: 300/5 mm = 60 mm
Turn in to transmission line: If the trace length is more then 30/5 mm = 6 mm

Clock frequency: 1000 MHz
Signal bandwidth: 5000 MHz
Dielectric constant: 4
Wavelength: 150/5 mm = 30 mm
Turn in to transmission line: If the trace length is more then 15/5 mm = 3 mm

Clock frequency: 2000 MHz
Signal bandwidth: 5000 MHz
Dielectric constant: 4
Wavelength: 75/5 mm = 15 mm
Turn in to transmission line: If the trace length is more then 7.5/5 mm = 1.5 mm

I guess if we assume that the rise time is 20 % of the clock period
What's your basis for that guess?
Digital signal rise/fall times are independent of the clock period.

Data sheets usually have the 10-90% or 20-80% risetime figure, then calculate the knee frequency.