In the last post, we covered the analysis of stubs using a frequency domain perspective. We defined a low pass band in which we can neglect the effect of a stub with the criteria of not affecting the transfer function of the system.
Today we will analyze the stub effect in the time domain and we will compare both.
Time domain analysis
We will start from a simulation that includes two transmission lines in the signal path and a stub capacitivelly terminated with a very small capacitor to emulate to an open circuit that will lead to an almost full reflection.
In the simulation we will make use of the capability to use different parameters in a list (.step PARAM <var> list <n1> <n2> ...
) and also the capability to get a value (the stub delay) as the result of an arithmetic operation. In this example, I wanted to get the destination waveform when the stub delay are different fractions of the signal rise time (RT).
The simulation shows that when the stub round trip delay is significantly lower than the signal rise time, its effect is negligible. However, when comparable, the signal is significantly distorted, and in a way that is specially inconvenient because the signal transition in the destination becomes non monotonic. This is dangerous for clock signals because a single transition may create double clock if logic is very fast.
In summary, makes sense to establish the criteria that the round trip delay in the stub should be lower that the transition rise time in order to have an undistorted waveform.
Rule of thumb: in order to have a negligible effect, keep the one-way sub delay significantly lower that one half of the signal rise time.
Rules comparison
In the previous post, we suggested that the signal frequency should be lower that one half of the first notch frequency of the stub. This one takes place when the one way transmission line delay of the stub is a quarter of the signal period. Expressed in an algebraic form, this is:
The approximate relationship between signal rise time and bandwidth is:
Combining both, we get
which is similar to the previous rule of thumb to keep it below one half of the signal rise time.
Rules of thumb are not frontiers but approximate good practice limits.
Example
Let us consider a LVDS interface (used to transmit data 200 at Mbps).
The MAX9110 driver manufacturer specifies a minimum rise time 250 ps. Let us consider it as the reference Rise Time (RT). [Double check: this is 1/20 of the bit period: the driver has bandwidth enough].
For the stub to have negligible effect should have a delay of less than 125 ps.
In a typical PCB, the propagation speed of an microstrip over FR4 is about 50 % of c (light speed in vacuum), which produces a propagation delay of 6 ns/m = 6 ps/mm.
In this system, the stub to be considered negligible has to measure less than 20 mm.
Stubs tend not to be real problems in designs done following good engineering practices but when boards are really high speed, may.