All measurement systems have some defined bandwidth over which their accuracy is maximized, and oscilloscope probes are no different. All oscilloscope probes have a bandwidth specification that is related to their input capacitance, and the probe bandwidth is designed with this capacitance in mind. Oscilloscopes also have built-in front-end filtering capabilities that limits measurement bandwidth. With these points in mind, how can an oscilloscope probe be chosen such that captured measurements have the highest accuracy?
Because bandwidth impacts the measurement capability of an oscilloscope probe, it also limits the accuracy of measurement captured with a particular probe. To see why, we have to look at the internal structure (and equivalent circuit) of an oscilloscope probe.
Bandwidth and Accuracy Relationship
The term “accuracy” in the context of measurements means that the signal captured with an instrument has the closest resemblance to the true signal being measured. Therefore, looking at an arbitrary input signal in the frequency domain, the probe bandwidth needs to exceed the signal bandwidth. Mathematically, we would write:
Most of the simpler oscilloscope probes that can be purchased from distributors have probe bandwidths reaching ~100 MHz, which essentially matches the bandwidth of most budget scopes. More advanced oscilloscopes might be supplied with a probe that offers much higher bandwidth, or you will have to purchase an additional probe from the vendor. In either case, the probe bandwidth will be a limiting factor determining what can be accurately measured.
To quantify how the probe bandwidth limits accuracy, we have to look at the internal structure of the probe.
Oscilloscope Probe Equivalent Circuit
All oscilloscope probes that do not include compensation will function as parallel RC circuits, thus they have low-pass filter behavior. The input capacitance and the probe’s parallel resistance will limit the responsiveness of the probe to a fast input AC signal. The result is that the low-pass filtering action of the probe creates some roll-off in the collected signal amplitude.
One way to quantify the bandwidth of a probe is in terms of its RC time constant. The RC time constant of the probe’s input circuitry can be used to define a bandwidth limit in terms of a rise time for a pulsed signal. If we consider that 2.2 time constants are needed to observe a 10%-90% rise time for the above RC circuit, then the bandwidth limit for an input pulse would be given by the classic knee frequency formula:
The result of this roll-off effect in the probe response is a decrease in amplitude accuracy. As the bandwidth limit is reached, the collected amplitude starts to drop, meaning the sampled amplitude is slightly lower than the real amplitude of the signal being measured. This is shown below; at 30% of the rated probe bandwidth, the error will be approximately 3%.
Amplitude accuracy due to oscilloscope probe bandwidth limitation.
Phase accuracy is more complex and it requires comparing the measured time-domain waveform with a reference oscillator or reference signal. The phase delay across the oscilloscope probe, input port, and internal phase delay must also be known. For digital, we generally do not worry about this except when evaluating digital timing applications. However, it can be very important for analog and RF applications. More on this will be discussed in another article.
Input Bandwidth Also Limits Accuracy
Oscilloscope probe bandwidth is obviously important and it can’t be ignored in the discussion of accuracy. However, the oscilloscope front end also limits the accuracy of a signal measurement. The structure of an oscilloscope’s front end and the nature of digital sampling both limit the signal bandwidth that can be accurately resolved. Bandlimiting and sampling capabilities in the oscilloscope front end can be quantified in two ways:
- Sampling rate - Defines a Nyquist frequency at which aliasing begins to occur
- Bandwidth limit - Defines amplitude roll-off at the input port of the scope
Digital oscilloscopes (which encompasses most new scopes on the market) generally specify a sampling rate. Ideally, we would like to have the following:
At least in this case, the probe is no longer the limiting factor determining accuracy, and the full measurement capability of the scope can be accessed.
When the scope’s bandwidth is known, it is important to note that this limits the bandwidth of a signal that can be accurately sampled without pre-shoot artifacts, known as the Gibb’s phenomenon. The scope’s front-end is usually a higher order filter (4th order or higher) that heavily attenuates the input signal above some cutoff. The result is that the accuracy decreases much faster as the bandwidth limit is reached. If we quantify this in terms of a pulse’s edge rate, then the scope bandwidth would need to be much larger than 0.35/(rise time).
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