Situational Awareness: Testing Oscilloscope Outer Limits

Fig 1. 40 ps signal measured full bandwidth on a
1 GHz oscilloscope shows visible over/undershoot.

Nothing is perfect. Every test instrument has its limits, and knowing the limits to your oscilloscope’s bandwidth in response to real-world signals helps to develop situational awareness when making measurements. This is especially true when testing signals that are at or very near the specified bandwidth limit of the instrument.

The measurements we’ll demonstrate were made on a WaveSurfer 4104HD, a 12-bit, 4-channel, 1 GHz bandwidth oscilloscope that samples at up to 5 GS/s.

Fig 2. Example fast edge source
for testing oscilloscope bandwidth.

For any bandwidth/rise time test, you will need a fast edge signal source that you know exceeds the bandwidth of the measurement system, so that you can test the limits to the bandwidth. We used a commercially available circuit board (Figure 2) that generates about a 40 picosecond rise time, connected with a BNC cable to input a 50 Ohm, AC coupled, 1 V peak-to-peak signal (Figure 1).

Commercial digital oscilloscopes do a surprising amount of analog front-end signal processing, as well as digital signal processing to extend bandwidth and get a flat response. The bandwidth of the front-end amplifier sets a fundamental limit to how short a rise time we can see and measure.  Assuming that the oscilloscope amplifier’s transfer function has a single pole response, bandwidth is equal to 0.35 divided by the 10% - 90% rise time of the input signal. However, most modern oscilloscope front ends use a transfer function with multiple poles, so that the bandwidth is closer to 0.45 over the rise time. The higher order filter provides a sharper roll off with frequency and a much flatter frequency response.

Before we measure the 1 GHz oscilloscope’s response to this signal, we anticipate the result. We expect the rise time to be about 0.45/1E9 or about 0.45 nanoseconds (450 ps).  When the oscilloscope’s built-in 10-90% rise time measurement parameter is applied to the acquired signal, we see the rise time of the 40 ps fast edge is measured at 470 ps (Figure 1).  Dividing the expected 450 ps by 470 ps, the measured oscilloscope bandwidth is .957 GHz, quite close to the specified 1 GHz.

The small overshoot and undershoot seen on the signal in Figure 1, called “Gibb's Ears”, are due to the signal processing occurring in the oscilloscope. Whenever you have a signal that has a much higher bandwidth than the rated bandwidth of the oscilloscope, the signal will display a sharp wall cut off, which means the high frequency components don't fall off gradually, they fall off instantly as soon as they hit that wall (1 GHz in our example). Knowing that gives me situational awareness that this is an artifact of my oscilloscope processing, not necessarily a characteristic of the signal coming from my DUT.

You could conduct similar measurements using a known fast edge to test how your oscilloscope behaves with signals that are at the edge of its performance limits.

If you know your signal has a lot of high frequency noise, and you really only care about the lower frequency components, you could filter out some of that and improve the rise time measurement by decreasing the bandwidth going into the oscilloscope with the built-in bandwidth limiting filters. WaveSurfer 4000HD oscilloscopes have two available bandwidth limiting filters: 200 MHz and 20 MHz.

Fig 3. 40 ps signal measured with a 200 MHz bandwidth
limiting filter shows an improved response.

Applying the 200 MHz filter, we expect rise time should increase to 0.45/0.2 E9, or 2.2 ns. The measured rise time of 1.93 ns in Figure 3 is a bit below the expected 2.2 ns. Note, however, that the Gibb’s Ears have disappeared, because the signal rise time has been reduced by the bandwidth limiting filter.  If the measurement is repeated for the 20 MHz bandwidth limit, the rise time is nearly 2 ns, closer to the expected value.

The interconnect you use to input the signal can also have a significant effect on measurements, as we’ll show in our next post.

Watch Dr. Eric Bogatin demonstrate this concept in the on-demand webinar, SI/PI Measurements on a Budget.

Also see:

Four Measurement Best Practices