# How Can You Avoid Selecting an Oscilloscope Probe with the Wrong Bandwidth?

Blog Post created by BoonCampbell on Apr 2, 2018

Bandwidth is one of the key oscilloscope probe banner specifications, and if you pick the wrong bandwidth, you’ll get inaccurate measurements. However, picking the right bandwidth probe isn’t as simple as you might think. Avoid making these common mistakes when selecting the right probe bandwidth, and have confidence that the signal you measure is the best representation of your device under test (DUT).

## Probe Bandwidth

Probe bandwidth is a point on the frequency response curve where the amplitude has decreased by 3 dB. This 3 dB roll-off is shown below in Figure 1. Figure 1. Probe 3 dB roll-off point.

For example, measuring a 500 MHz, 1 V peak-to-peak sine wave using a 500 MHz probe results in a measurement error of –3 dB or decrease by –0.3 V peak-to-peak. This 3 dB roll-off diminishes your actual 1 Volt peak-to-peak signal to only 0.7 V peak-to-peak. You can fix this pitfall by calculating the correct bandwidth for your desired frequency. A common rule of thumb is that your probe bandwidth should be three times the sine wave frequency you wish to measure. So, to measure a 500 MHz sine wave, you need to choose a probe with 1.5 GHz or more bandwidth.

## Rise Time and Bandwidth are Related

Now let’s dive a little deeper into this theory. You need to know more than just your signal frequency. To calculate a more accurate probe bandwidth, you need to know your signal’s rise time. Rise time is the time it takes your signal to get from the 10% level to the 90% level of a rising edge. Figure 2. 10% and 90% rise time points.

Let’s use the universally accepted formula that states: bandwidth times the rise time equals 0.35 when evaluating a rising edge from 10% to 90%. Or you can configure the same formula another way: If you are working with a communication standard, often the rise time specification is listed along with other banner specs. For example, if your rise time for the 500 MHz clock signal is 350 ps (pico seconds), use the formula below to calculate the probe bandwidth you need. The calculated bandwidth now equals 1 GHz. This means the real bandwidth of your signal is 1 GHz, not 500 MHz. 500 MHz is your clock frequency for an entire cycle, but your clock’s rising edge is much faster at 1 GHz. You need a probe with a bandwidth specification of 3 times your calculated 1 GHz bandwidth, or a 3 GHz probe. By doing this, you avoid the pitfall of attenuating any of your signal’s frequency components.

## The Harmonic Nature of Square Waves

You have been calculating your bandwidth needs based on measuring a sine wave. Let’s transition into the pitfalls associated with measuring square waves. If you remember your schooling on Fourier series, you recall that it is a way to represent a function as the sum of sine waves. In Figure 3 below, an original signal is shown in yellow and is made from its fundamental harmonics. Note that the first harmonic in green has the same period and duty cycle, but its rising edges are slower, and the corners are more rounded. The first and third harmonics combined in purple have faster rising edges, and the corners are crisper. The first, third, and fifth harmonics combined in pink have faster edges, crisper corners, and detail on the top and bottom. Figure 3. Square wave signal with its harmonics below it.

Now let’s take this harmonic knowledge a little farther and use a 100 MHz square wave clock example. Figure 4 below shows the result of measuring the 100 MHz square wave with a 100 MHz probe. The harmonics of the 100 MHz signal are well below the 3 dB point of the probe, resulting in what looks like a sine wave. Any measurements made with this signal will be inaccurate. Figure 4. Distorted square wave due to the wrong bandwidth probe selection.

Now let’s measure the same 100 MHz square wave with a 500 MHz probe. The resulting crisp square wave is shown in Figure 5 below because the critical harmonics of the 100 MHz signal are captured in the measurement. You can see how much difference it makes when you use a probe with the appropriate bandwidth. Figure 5. Square wave with the correct bandwidth probe selection.

## System Bandwidth, The Weakest Link

It is also worth noting that you should consider your entire system bandwidth. You need to factor in both the bandwidth of your probe and your oscilloscope to determine the bandwidth of your probing system (probe + scope). See the formula for your probing system bandwidth below. Let’s say both your oscilloscope and probe bandwidths are 500 MHz. Using the formula above, the system bandwidth would be 353 MHz. You can see that the system bandwidth degrades greatly from the two individual bandwidth specifications of the probe and oscilloscope. Now, let’s say that the probe bandwidth is 300 MHz and the oscilloscope bandwidth is still 500 MHz. Using the above formula, the system bandwidth reduces further to 257 MHz. You can see that the total system bandwidth is always lower than your weakest link or lowest system component bandwidth.

## Accessory Choice

There is always a trade-off between measurement flexibility, usability, and resulting bandwidth. Many probe tip accessory solutions are available, but all have an impact on your bandwidth. The added inductance of longer ground leads brings with it stray capacitance, creating RC circuits that resonate within your measured bandwidth. These circuits reduce your bandwidth and the ripple on the DUT’s signals. For example, users can use longer lead solutions for quick checks to ensure the circuits are functioning. However, for critical measurements, lead length (both on the signal and ground side) should be kept to a minimum.

People often use a VNA (vector network analyzer) to measure an oscilloscope probe’s bandwidth, but VNA’s are expensive and require some training to operate them effectively. In addition, because the VNA is a 50 Ω system and passive probes should be terminated into 1 MΩ, the VNA is not a good test solution for passives.

Another way to test bandwidth is to use a sine wave source, splitter, and power meter to sweep the response. This method requires a remote interface such as GPIB or USB and programing skills in MATLAB.

An easier way to measure the bandwidth of probes with bandwidths below 1 GHz is the time domain approach, utilizing only an oscilloscope with a built-in step signal source, and ‘differentiate’ and ‘FFT’ functions. Apply a step function to your system, then apply the differentiate (or derivative) to this step response. You now have an impulse response and can take the FFT of the impulse response to obtain the system’s frequency response.

## Conclusion

Choosing a probe with adequate bandwidth is crucial to making accurate measurements and good engineering decisions. Understanding the impact of rise times, harmonics, and system constraints can help you determine your bandwidth limitations.

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