About Data Truncation in Fast Fourier Transforms

Figure 1: The first precondition of using the Fourier transform
is a repetitive signal

Our last post discussed how time-domain signals acquired by an oscilloscope might be translated into the frequency domain using the discrete Fourier transform. We noted that using the Fourier transform only works if our signal is repetitive (Figure 1), and that it allows us to identify only harmonics of the first harmonic frequency, which is 1/acquisition window. Moreover, the discrete Fourier transform, if used on a large number of data points, is relatively slow to calculate.

Getting From the Time Domain to the Frequency Domain

Figure 1: A fundamental underlying assumption of a discrete
Fourier transform is a repetitive waveform

Fundamentally, oscilloscopes are time-domain instruments: We use them to acquire signals from our circuitry or device under test, and the instrument displays them in the time domain. We see the voltage of the signal in the vertical axis, and we see how that voltage changes over time in the horizontal axis.

Using 50-Ohm Coax From DUT to Oscilloscope

Figure 1: A coaxial cable presents high impedance at low
frequencies but acts as a transmission line at higher frequencies

In our recent exploration of 10x passive probes, we've determined that while these types of probes are great general-purpose tools, they're not necessarily going to do the job in specialized measurement circumstances. They're relatively low-bandwidth, low-SNR probes that impose some limitations and, in some scenarios, can deliver potentially misleading or erroneous measurement results if used without clear understanding of their capabilities.

Squeezing More Bandwidth From a 10x Passive Probe

Figure 1: Shown is a comparison of inherent oscilloscope
noise and noise at the shorted tip of a 10x passive probe

Now that we have a better understanding of what's happening under the hood of a 10x passive oscilloscope probe, we can sum up its key characteristics. The first thing to know about such probes is that they offer relatively low bandwidth (<100 MHz). This is largely a result of the probe's tip inductance.

10x Passive Probes and Cable Reflections

Figure 1: With unequal impedances at either end of the coax,
are cable reflections a concern in 10x passive probes?

We've been discussing the ubiquitous 10x passive probe here on Test Happens, beginning with an overview of the probe-oscilloscope system. We turned to the 10x passive probe itself and the issues posed by its constitutive circuitry. Then we covered what about that circuitry makes it usable at all, namely, its built-in equalization circuit.

How Tip Inductance Impacts a Probing System's Bandwidth

Figure 1: Shown are FFT plots of a 10-MHz, fast-edge square
wave reaching the oscilloscope via direct coax connection
(orange-yellow plot) and 10x passive probe fitted with a coax
tip adapter (straw-colored plot)

If you're using 10x passive probes with your oscilloscope, it's important to understand the bandwidth of your probing system and how it's affected by various methods of probing the signal of interest. There's a relatively easy way to determine this parameter by probing a fast-edge, 10-MHz signal from a square-wave generator. Doing so can also instruct us in the effects of tip inductance on the probe's bandwidth.

How Equalization Works in 10x Passive Probes

Figure 1: The adjustable equalization circuit on the oscilloscope
end of the coaxial cable compensates for the 10x passive
probe's inherent low-pass filter characteristics

We've been discussing 10x passive probes and their inner workings; our last post covered all the ways in which a 10x passive probe is apt to be a liability. They'd be basically unusable for any measurements at all but for one attribute: their equalization circuit (Figure 1). Without it, the 10x passive probe makes a pretty good low-pass filter, but the equalization circuit counters that with a high-pass filter to balance things out.