This month's blog post is based off a customer question that we received this month. The question was around arbitrary waveforms (arbs), the number of points for the arb, and waveform fidelity. I have spoken about arbs in the past: click me for Matt's old blog post. Just to quickly reiterate, there are two options for arbs on the N6705 DC Power Analyzer and the N7900 Advanced power System. There is the Constant Dwell (CD) Arb that allows up to 64,000 point with a minimum Dwell time of 10 us per point and there is the standard List Arb that allows up to 512 points with a dwell as low as 1 us per point.
The question that we are trying to answer today is: When is 512 points more than 64,000 points? It is an interesting question to think about. It is definitely not true in cases where you have a non-repeating waveform. The CD Arb will always be the preferred method there and will give you the best fidelity (smallest dwell times).
The answer is when you have long DC levels in your waveform. Let's look at the proposed waveform below (please pardon the picture, I hand drew this on my tablet; also note that it is not to scale):
If you look at this waveform, the total time is 11.5 s. It's a pretty simple waveform that goes from 4 V to 6 V with a 0.05 s ramp between the two values. We need to pay attention to those times.
Lets with the math behind programming a CD Arb. With a CD arb, there is a single dwell time so you basically sample the waveform 64000 times. Lets use that to calculate a dwell time:
11.05 s/64000 = 172.66 us
This means that every point is going to last 172.66 us, no matter if it is in the constantly changing ramp or at a DC level. This means that when the waveform is at 6 V for 10 s, you will use 57,918 points. That is 90% of your points just sitting at 6V! For the 0.05 s ramp, you will only be using 290 points. The ramp is where the waveform is actually changing but due to the nature of how the CD Arb works, you cannot increase the number of points allocated to the ramp.
Let's take a look at the 512 point list now. We know that the first point of the list will be 4 V for 1 s and that the last point of the list will be 6 V for 10 s. That leaves us with 510 points to do the 0.05 s ramp which results in s dwell time of 98 us. This will give us more points in the ramp area and a better looking waveform overall.
That is all I have for this month. Please feel free to use the comments if you'd like to get in touch with us.