The Resolution Revolution In Oscilloscopes

Figure 1: Teledyne LeCroy's WavePro HD exemplifies
today's high-resolution, high-bandwidth instruments

Oscilloscopes have been around for a very long time now, and older oscilloscope users will remember the heyday of those analog boat anchors of the '60s and '70s. Many have survived and are still usable if you don't need much bandwidth (and have the means to calibrate them if necessary). I used to scout local hamfests looking for bargains on them. Many techs and engineers cut their teeth on those behemoths. You could learn a lot about design if you poked around inside them, too.

Which Windowing Function to Use in FFTs?

Figure 1: Examples of a Hamming
function (blue) and Hanning function
(red)

When performing a fast Fourier transform on an acquired waveform, you'll often encounter situations where the waveform doesn't sit neatly within the oscilloscope's acquisition window so that the voltage is the same at the window's beginning and end. The ensuing discontinuity from window to window results in high-frequency artifacts, and the way to address this issue is a technique known as "windowing."

About Windowing in Fast Fourier Transforms

Figure 1: Windowing a waveform that's not periodic within
the acquisition window reduces spectral leakage

The second artifact in FFT calculations is more serious and is also the source of some confusion. A good source for information on this topic of windowing is an application note published by National Instruments.

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.