How to calculate overshoot/undershoot

[likephysics]

I am measuring a digital signals with fast rise time(~2ns). Because of the oscilloscope probe inductance, there is some overshoot. How do I calculate the amount of overshoot due to the probe inductance.
I am thinking V = L di/dt

I know L, dt but how to find di?

 

[jsgruszynski]

I am measuring a digital signals with fast rise time(~2ns). Because of the oscilloscope probe inductance, there is some overshoot. How do I calculate the amount of overshoot due to the probe inductance.
I am thinking V = L di/dt

I know L, dt but how to find di?

At those edge rates it gets tricky. You are at the edge of lumped-model and distributed-model regimes for circuits. Most of what works at lower frequencies and edge rates starts to stop working at that kind of rise time.

This is so pervasive a problem that the various oscilloscope vendors have numerous application notes about how to deal with this. Some probes simply can never work by their design. Better to have the brain power of Agilent or Tek or LeCroy behind you at this point. This app note from Agilent is pretty good and yet generic about the problem. Best to talk to your scope vendor about how to fix it.

http://cp.literature.agilent.com/litweb/pdf/5988-5021EN.pdf

 

[Dickfore]

$$c dt = 2.998 \times 10^{8} \frac{\mathrm{m}}{\mathrm{s}} \times 2 \times 10^{-9} \mathrm{s} = 5.996 \times 10^{-1} \mathrm{m} = 60 \mathrm{cm}$$

If the linear dimensions of the circuit are smaller than 6 cm, I would say that lumped circuit analysis is still valid.

 

[berkeman]

I am measuring a digital signals with fast rise time(~2ns). Because of the oscilloscope probe inductance, there is some overshoot. How do I calculate the amount of overshoot due to the probe inductance.

The main goal is to minimize the stray inductance in the probe. We use two techniques for that here in our lab. The first is to use the Z-lead option for some probes. Here is an example of a Z-lead ground probe:

http://www.testpath.com/Items/Z-Lead-1-inch-Long-Pkg-of-2-for-P6243-P6245-118-880.htm

On some Tek probes, you can un-screw the final tip plastic piece, and reverse the ground shroud housing so the hole (where you normally plug in the ground wire lead) points toward the tip instead of away. You then insert the Z-lead probe in the hole in the ground shroud, and that aligns the tip of the Z-lead with the end of the probe tip. It has the Z shape so you can rotate it in and out a bit, to adjust the spacing between the probe tip and the ground tip, to accommodate different probe spots on your PCB. In any case, the signal you want to probe has to be pretty close to a ground pad or pin that you can pick up with the Z-lead tip.

The other trick is to use a coaxial probe tip adapter. You can get them in different sizes to accommodate different probe sizes. If it's just for a quick test, you can solder-tack the signal and ground parts of the adapter onto your PCB in a flying fashion. If you anticipate needing to probe high-speed signals on a test board that you are designing, you put down the adapters on the PCB in the design phase. This gives you the absolute minimum parasitic inductance you can get for your measurements, and works great. Here are some links to typical coaxial probe tip adapters:

http://www.probetronix.biz/i//tn_Coaxial_BNC_adaptor.jpg

http://search.digikey.com/scripts/DkSearch/dksus.dll?lang=en&site=US&WT.z_homepage_link=hp_go_button&KeyWords=j462-nd

And also look for Tek part numbers:
062-6421-00
131-4244-00
131-4353-00
131-2766-03

.

 

[berkeman]

There is one other option similar to the Z-lead ground probe technique. I'm not able to find any web pictures of it yet, but will post them if I can find them.

If you take your 'scope probe tip plastic off, this generally exposes a ground ring around the probe tip near the end. There is an accessory which is a small spring coil that fits around the ground ring at the tip, and has one end coming out to make a ground contact point. We've had some of these for one or two of our 'scope probe brands in the past.

But you can also make your own ground spring tip, either from a spring that fits your probe tip's ground ring, or even just from a paper clip if you bend it up into the coil shape and bend out a probe tip.

 

[likephysics]

There is one other option similar to the Z-lead ground probe technique. I'm not able to find any web pictures of it yet, but will post them if I can find them.

If you take your 'scope probe tip plastic off, this generally exposes a ground ring around the probe tip near the end. There is an accessory which is a small spring coil that fits around the ground ring at the tip, and has one end coming out to make a ground contact point. We've had some of these for one or two of our 'scope probe brands in the past.

But you can also make your own ground spring tip, either from a spring that fits your probe tip's ground ring, or even just from a paper clip if you bend it up into the coil shape and bend out a probe tip.

Berkeman, I use the techniques you mentioned in your post. All my ckts had the probe adapter on PCB. But in high density PCBs, that's not an option.
My favorite is the spring attached to the probe tip. I also made my own version using a thin copper strip. I got slightly better results than the tek spring. I guess the copper strip inductance is lesser.

These are nice measurement techniques but how do I calculate the numbers. Overshoot vs probe lead inductance?
For example, we can easily calculate rise time degradation due to probe input capacitance. But what about overshoot due to inductance?

All I found was resonance freq eqn f= 1/2*pi*sqrt(LC)

Doesn't give the overshoot, only gives the freq.
In my case, this freq is 750MHz. My signal BW is 0.35/2ns = 175MHz.
So resonance is well beyond my signal BW. Which means, I shouldn't see any overshoot on the signal.
But the resonance freq is within the BW of the scope (2GHz). Does this matter?