Frequency & trace length

trace length frequency

Please tell in details the relationship between Frequency & trace length.

frequency trace

There is no relatiom between frequency and trace lenght . There is relation between frequency and wavelenght( speed of light = frequncy * wavelenght ) . When wavelenght became somewhat close to lenght of trace( in order 10 for example) , you must consider each trace like transmition line. That means that you shoud keep control over characteristic impedance of source, trace and load.

calculate trace length from frequency

if frequency of signal is too high. you must consider the length of the trace because of the insert loss

trace loss at frequency

The primary factor relating trace length to frequency is dielectric loss. Every board material has a characteristic dielectric loss factor. It is sometime expressed as "loss tangent".

A trace has both self inductance and capacitance relative to its signal return path. The capacitor dielectric loss between the signal trace and its return path is the one to be most concerned about at very high frequencies. The loss tangent is the ratio at any particular frequency between the real and imaginary parts of the impedance of the capacitor. A large loss tangent means there is a lot of dielectric energy absorption.

As the trace gets longer, the amount of energy absorbed increases. The effect is to attenuate the higher frequency components of the waveform. Fast risetime pulses tend to get rounded as the high frequency components of the pulse edges are attenuated.

When you send a high-speed signal through a PCB trace, the signal loss from dielectric absorption depends on the frequency f, the trace delay td, and the loss tangent. The dielectric-loss is approximately:

Loss(f) = exp[-(Pi)x(f)x(td)x(loss tangent)]

Notice that I have not mentioned the series drop of the self inductance as a frequency dependent loss. This is because the trace has both iductance and capacitance, and the two combined give a characteristic impedance relative to the return path. The inductance cannot be considered alone, and together with the capacitance creates a constant 'characteristic impedance' which does not vary with frequency - except through the mechanism of the loss tangent as discussed above.

A secondary frequency dependent effect of trace length on signal is skin effect. This is the tendency of the signal to travel only in the outer 'skin' of the conductor at high frequency. As the frequency increases, the effective resistance of the trace increases because the thickness of the conducting 'skin' decreases. Since the overall 'resistance' is a function of length, longer traces at higher frequencies will have more loss due to resistive attenuation. This is more important with high current signals, since it is roughly equivalent to the familiar "i squared x R" losses at lower frequencies.

There is a brief illustration with equations at:
**broken link removed**

More can be found on the web by doing a search for 'skin effect' and 'loss tangent'.