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I am reading High Speed Digital Design: A Handbook of Black Magic. It was mentioned that if length of transmission line (Microstrip or stripline) is less than 1/10th of the wavelength of highest frequency component, then transmission line matching is not important. I am trying to visualize the phenomenon which will make matching insignificant for shorter transmission lines. I still think mismatch will cause reflection at the point of mismatch.

Can someone help me in understanding it? I am not sure if my question requires a detailed explanation and may be unsuited as a question over here. If this is the case, then please help me with finding relevant reading sources and some terms to google.

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    \$\begingroup\$ Think about the time it takes for the signal to reflect vs. the rise time of your signal \$\endgroup\$ – PlasmaHH Apr 10 '18 at 14:05
  • \$\begingroup\$ Think about the amount of stored energy, and the phase shifts of that energy, versus ability to upset the waveshape. \$\endgroup\$ – analogsystemsrf Apr 10 '18 at 15:51
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I still think mismatch will cause reflection at the point of mismatch.

Yes it will - with any length transmission line there will be reflections due to mismatch. However, with digital signals, if the reflection effect is somewhat below a certain value then its effect on digital signal integrity is small and can be ignored. Some folk use 1/10 and others use 1/20 as this limit.

The effect that a reflection has on a line of short length is to modulate the digital edges a slight amount - the reflected signal is about the same amplitude as the incident wave but pretty much close to having the same timings.

As the line length gets longer the reflected signal is smaller but one that has bigger timing differences to the incident wave hence the problem looks more like an amplitude wobble on the signal and a modulation of the logic 0 level. However, the reult at the end of the cable (the receiver) is of no consequence as shown below.

Consider also that an intentional mismatch at the end of a digital line can effectively be used to maintain the logic levels: -

enter image description here

Look at scenario (a) - it uses only a series driver resistor and no terminator at the receiver (unlike (b)). It's never as clear-cut as you think.

Consider this digital pulse travelling from left to right: -

enter image description here

Picture source.

It's not 100% a perfect scenario in that the thicker black wire is meant to show an cable impedance change BUT, you can see that what the receiver receives is the original signal with the loss of some amplitude and the reflection travelling back is what disrupts the incident wave back at the source. For an open ended termination at the receiver (as per scenario (a)) you get a perfectly recovered amplitude signal at the receiver/

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    \$\begingroup\$ Can you explain why reflection will be below a certain value if length of transmission line is less than 1/10 of wavelength. \$\endgroup\$ – abhiarora Apr 10 '18 at 14:12
  • \$\begingroup\$ I guess what I mean to say is that the reflection and incident voltage together may look pretty similar to the incident voltage on its own because the time shifting effects the reflection may have on the incident voltage will not cause problems. I'll refresh my answer to make that clear. \$\endgroup\$ – Andy aka Apr 10 '18 at 14:17
  • \$\begingroup\$ There's a similar question here: electronics.stackexchange.com/questions/178112/… \$\endgroup\$ – davidmneedham Apr 10 '18 at 14:18

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