Choosing Oscilloscope Bandwidth and Sampling Rate for Power Measurements

There are four related terms for oscilloscope bandwidth: analog bandwidth, digital bandwidth, system bandwidth and trigger bandwidth. Digital bandwidth is equal to half of the sampling rate and has little practical significance. Trigger bandwidth is a concept "hard" created by oscilloscope manufacturers. It refers to the frequency of the maximum input sinusoidal signal at which the oscilloscope trigger circuit can work normally. For high-end oscilloscopes, the trigger circuit will not work when the input signal frequency exceeds a certain size! System bandwidth refers to the bandwidth of the measurement system composed of the oscilloscope front-end amplifier, probe, test fixture, etc. Generally, unless otherwise specified, bandwidth refers to the analog bandwidth of the oscilloscope, that is, the cutoff frequency point of the amplitude-frequency characteristic curve of the oscilloscope front-end amplifier. The amplifier of the oscilloscope is a low-pass filter, and its amplitude-frequency characteristic curve is shown in Figure 1. The bandwidth is the
cutoff frequency point when the input voltage amplitude is reduced to -3dB (70.7%) of the input.
 

When the signal under test is serial data, if the rise time of the serial data is greater than 20% UI (the time length of one bit), then the oscilloscope bandwidth only needs to reach 1.8 times the bit rate of the signal under test to cover 99.9% of the signal energy. If the rise time is greater than 30% UI, 1.2 times the bit rate of the signal is sufficient. In real circuits, the rise time of serial data is mostly greater than 30% at the receiving end. Therefore, for a 3Gbps SATA signal, a 4GHz oscilloscope can be used after passing through the fixture. You can use 4GHz, 6GHz, and 13GHz tests and compare them.

· Power is not a serial signal, so the above rules do not apply. Long, long ago, the industry generally used the "3 to 5 times" rule to select the bandwidth of a DC transmission, that is, the bandwidth is "3 to 5 times" the frequency of the measured signal. In fact, the rise time is not emphasized here, and this rule is not universal enough. Howard Johnson, the father of SI, gave a principle of selecting bandwidth from the rise time of the oscilloscope with his personal authority, but he did not give a detailed derivation.

Howard believes that when the oscilloscope rise time is less than 1/3 of the rise time of the measured signal, the error of the measurement result is less than 5%. The oscilloscope rise time is approximately equal to 0.35/oscilloscope bandwidth. The 0.35 here is derived based on the ideal low-pass filter model RC circuit, and the actual value may be 0.45, 0.5, etc. Therefore, we can deduce the required oscilloscope rise time based on the signal rise time, and then select the oscilloscope bandwidth based on the oscilloscope manual or the 0.35 relationship.

Regarding bandwidth selection, the industry is full of unprofessional and irresponsible remarks. This is worthy of vigilance.

Let's get back to the question itself. The bandwidth selection of the switching power supply depends on the specific measurement requirements. The signals that the switching power supply needs to measure may include:

· Measure the bandwidth selection of the switch tube (mainstream is MOSFET)

During power supply debugging, the drain-source power supply Vds, drive voltage Vgs, drain-source current Ids, etc. of the switch tube should be repeatedly measured to determine the dead time of the upper and lower switch tubes to prevent the switch tube from "shooting through" and causing the power supply to explode. The drive signal waveform should be measured. If the rising edge of the waveform is slow, the switch tube loss will be greater. If the rising edge is steep, the switch tube loss will be smaller, but the drain-source overshoot will be greater. The most important measurement is to ensure that the peak-to-peak value of the Vds voltage does not exceed the maximum limit of the switch tube Vds under various dynamic conditions. These dynamic conditions include the load jump from no load to full load, and from full load to no load; the load jumps back and forth between 50%-75%-50%, 25%-50%-25%, and the peak voltage of Vds during the soft start process. There are many factors that affect the accurate measurement of Vds under these dynamic conditions, which will not be detailed here. I deeply agree with the importance of this test item in the minds of power engineers. If this value is not measured accurately, the switch tube may be easily damaged, or the withstand voltage of the switch tube may exceed the actual requirement, affecting the cost. The larger the Vds rating of the switch tube, the more expensive it is. Therefore, many power engineers are entangled in this.

The rise time of the switch tube depends on the specific model of the switch tube. Generally, the switching frequency of a low-power power supply can reach 1MHz or even greater, and the corresponding rise time of the switch tube is smaller. The switching frequency of a high-power power supply switch tube is small, only 100KHz or even smaller, and the rise time is large. However, the rise time of most switch tubes reaches 100ns. Even if the rise time of the switch tube is only 30ns, 1/3 of the rise time is 10ns, and the rise time of a 100MHz oscilloscope is only 3.5ns. Therefore, it is sufficient to use a 100MHz bandwidth oscilloscope to measure the switch tube of the switching power supply. In fact, there are very few switch tubes with a rise time of only 30ns, and it is sufficient to limit the bandwidth to 20MHz. However, this point has been questioned by some power supply engineers. He believes that for the high-voltage signal of Vds, it is necessary to look at the local rise time of the tip seal burr and study the energy it contains.

It should be noted here that the measurement of the switch tube, especially the upper half bridge of the half-bridge or full-bridge circuit, is generally measured with a high-voltage differential probe because it is a floating high voltage that is not grounded. Currently, more than 90% of high-voltage differential probes and current probes are third-party OEMs, and the maximum bandwidth is only 100MHz. Although the nominal bandwidth is 100MHz, it is often not designed and calibrated in an integrated manner with an oscilloscope. Therefore, the system bandwidth composed of a 100MHz oscilloscope is only 70MHz. However, if a 200MHz oscilloscope is used, the system bandwidth composed of a 100MHz probe can reach 100MHz, if you think that the signal energy of the Vds peak burr must be measured at 100MHz.

· Measurement of bandwidth selection for monitoring circuits in power systems

Some complex power supply systems are composed of many power modules and need to use DSP or Power PC as the control core. There are some peripheral storage units, keyboard monitoring units, etc. This will involve the measurement of clock signals, CAN control signals, I2C, SPI and other signals. The rates of these signals are not high except for the clock frequency. If you want to measure the DSP clock signal, it is best to choose a bandwidth of 500MHz or even 1GHz, but power engineers rarely measure this clock signal seriously. The bandwidth of other signals only needs to be 20MHz. [page]

Bandwidth selection for measuring power supply ripple and power supply noise

Power ripple and power noise have formed a conventional understanding in China. Power ripple is understood as the fluctuation of the output voltage of the power module itself, which has nothing to do with the complex power supply network on the circuit board. In other words, it is the fluctuation of the voltage at the source end (Source end) of the power output; power noise refers to the fluctuation of the voltage at the chip pin when the power module works in the actual circuit system and transmits the power energy to the chip pin through the power distribution network (PDN), or the fluctuation of the voltage at the end (Sink end) of the power output. In short, the voltage fluctuation is called ripple at the source end and noise at the end.

The signal frequency components of power supply ripple are mainly the power frequency 100Hz and the switching frequency, and the bandwidth is generally limited to 20MHz. Someone asked me, why is it 20MHz instead of 10MHz or 5MHz? This is indeed an interesting question!

For power supply noise measurement, I recommend a bandwidth of 500MHz. There is a lot of discussion and debate on this topic, but I will not go into detail in this article.

Bandwidth selection for measuring fast transient pulse discharges of power products

I have met some customers who want to buy oscilloscopes just to measure the EMI fast transient pulse discharge process. Unfortunately, I have never found an opportunity to personally measure this type of signal with these customers. The specific measurement method is to divide the high voltage signal through a dedicated "voltage divider" component and then connect it to the oscilloscope through a BNC coaxial line. The bandwidth of the oscilloscope should be above 1GHz, preferably 2GHz, and the sampling rate must be 10GS/s. In fact, the bandwidth of the "voltage divider" here affects the system bandwidth because it is part of the measurement system.

2 Selection of sampling rate in power supply measurement

The concept of sampling rate is very easy to understand. It means how many points are sampled per second. For example, a sampling rate of 10GS/s means that 10G points are sampled per second. "S" here means Samples. Some documents write the sampling rate as 10GSa/s. The reciprocal of the sampling rate is the sampling period, which means how long it takes to sample a point. For example, a sampling rate of 10GS/s means that a point is sampled every 100ps.

There is a famous Nyquist sampling theorem that tells us that only when the sampling rate is more than twice the highest frequency of the measured signal can the undistorted reconstructed signal be guaranteed. However, the highest frequency of the measured signal is not intuitive for non-sinusoidal signals. Even for sinusoidal signals, for the application of oscilloscopes, sampling two points in one cycle cannot reconstruct the original signal very well. Over the years, the method I recommend for judging whether the sampling rate is sufficient is to ensure that 3-5 points are sampled on the rising edge of the signal of interest. Five points are best, and when the oscilloscope conditions are limited, sampling three points will not result in large errors. The measurement results of sampling 5 and 10 points on the rising edge of interest are almost exactly the same. Based on this conclusion, let's go back to the issue of choosing the sampling rate in power supply measurement:

· Selection of sampling rate for measuring switch tube  

The recommended sampling rate for measuring power switch tubes is 250MS/s or more, because if the peak burr part of the rising edge of the switch tube can be accurately reconstructed, it takes 4ns to sample one point. Even for some switch tubes, 250MS/s is not sufficient. In actual measurement, you can zoom in on the rising edge of the Vds waveform to see if 5 points are sampled on the peak burr. The data of 250MS/s was measured and confirmed by me after I changed from a power engineer to an oscilloscope sales engineer and returned to my old employer. Ten years have passed, and I am still impressed. Interestingly, in the rich and handsome company where I worked at that time, there were many technical experts and many measurement specification documents, but no one seemed to care about how to determine the sampling rate of the oscilloscope. The boss just often told me that the real Vds peak value can be measured only after the waveform is expanded after pressing auto setup.

I was verifying that the measurement was of MOSFET IRF460. However, 50MS/s can meet the accurate measurement of most switching tubes.

Note:
(1) Some oscilloscopes use sinusoidal interpolation (sinx/x interpolation) by default, which means that a number of "calculated false points" will be inserted in the middle of the real sampling points according to the sinx/x algorithm. When you zoom in on a part of the waveform, you will see that there are still many calculated false points on the rising edge, which will be mistaken for sufficient sampling rate, leading to wrong judgment and wrong measurement results.
(2) Some oscilloscopes cannot fix the sampling rate, but can only fix the storage depth. However, because sampling rate * sampling time = storage depth, the sampling rate continues to decrease as time increases, and when you reduce the time, the sampling rate automatically increases, and there are still enough points on the spikes and glitches you see when you expand the waveform.

· Sampling rate selection for measuring the monitoring circuit of the power system

The signal with the highest frequency in this part is the DSP clock, and a sampling rate of 5GS/s or above is recommended.

Sampling rate selection for measuring power supply ripple and power supply noise   

The sampling rate for measuring power ripple is the same as that for measuring switching tubes. It is recommended to be above 250MS/s because the power ripple contains switching frequency components. However, for power noise, because it contains noise from high-speed chips transmitted through the power supply and ground planes, presenting a high-frequency component of about 200MHz, the recommended sampling rate is above 5GS/s.

Sampling rate selection for measuring fast transient pulse discharges of power products

The peak burr of this type of fast pulse signal has a very fast rising edge, and the recommended sampling rate is 10GS/s.

If the sampling rate is too low, the measurement result will be seriously distorted. For example, the peak-to-peak value of Vds should be 450V, but due to insufficient sampling, the result measured by linear interpolation may be only 350V, while the result measured by sinusoidal interpolation may be 500V. "Always be vigilant about the sampling rate" is one of the important principles of high-fidelity capture.

I hope the above explanation can help you in the most basic indicator selection and use. Welcome to follow "Engineer's Handheld Oscilloscope Library", the oscilloscope art WeChat platform scope-of-the-art, where you can get answers to all your questions.