Adequate Bandwidth

I just heard from Istvan Novak, who follows the world of power integrity as closely as anyone I know. I wrote to him about a new TDK capacitor type recently mentioned on the SI-LIST:  

It is available in a range of specific ESR values.  That's good for controlling resonance in certain power supply applications.

I asked Istvan if he were aware of any others, or if it is the first of its kind.

Istvan replied, "I think it is great to have this choice, so that people can make a conscious decision in optimizing their power distribution network.  [Regarding the question of being "first"] it depends how we define being first.  This TDK part is the first mass-produced controlled-ESR ceramic capacitor.  However, in experimental sampling, controlled-ESR MLCCs have been produced by at least three other capacitor vendors since year 2000, but for various reasons those have not been put into volume production.  Also, volume-produced controlled-ESR capacitors (other than ceramics) became available in recent years before the TDK controlled-ESR ceramic.

"POSCAPs and tantalums were actually the first bypass capacitors with guaranteed plus and minus tolerance for ESR.  A [short] history of the developments and the available volume-produced controlled-ESR parts were documented in his 2007 DesignCon paper, "History of Controlled-ESR Capacitors at SUN," and Designcon TecForum TF-MP3, "Controlled-ESR Bypass Capacitors Have Arrived".

If you are not following the controlled-ESR topic, it's worth a look.

By the time you get this I'll be preparing for my annual journey to the U.K. to visit Oxford University and other sites in Europe.  In my experience, June is the best time to visit.  The weather's fine, and all the businesses are still open.

The technical note below results from some good questions I received recently about the meaning of scope bandwidth, and its effect on signal measurement accuracy. Thanks to all for your good questions

Adequate Bandwidth

The waveform in Figure 1 had its tips clipped by a low-pass filter.

The source signal comes from a DS25BR100 LVDS-style differential driver. The driver is designed to work at speeds up to 3.125 Gb/s. This particular driver provides adjustable pre-emphasis. In making this waveform I set the pre-emphasis feature to its maximum setting.

The driver outputs run through SMA connectors, 24-in. RG-316DS cables, and DC blocking capacitors straight into CH1-CH2 of a LeCroy SDA 6020 6GHz digital scope. The scope computes the difference between channels 1 and 2, showing the differential result in purple, labeled "6 GHz".

The "1 GHz" waveform uses the low-pass filtering function available on my LeCroy scope. That function selects the equivalent bandwidth of each input channel.

Analog scopes have long been available with a 20-MHz bandwidth-limit feature. That feature can be quite useful when looking at small signals.

A bandwidth-limit feature performs a service somewhat like vertical averaging in that it reduces random noise, but it does not require a repetitive signal. It's just an analog filter, so a bandwidth-limit feature works on single-shot acquisitions. The feature applies a moving-weighted-average function to the incoming waveform, smoothing the peaks and edges. Properly used, it can reduce the level of random white noise or short impulsive noise present in a signal at the expense of a slight degradation in the rise/fall time of the measured waveform. The exact frequency response of the filter function is determined by the particular profile of moving-weighted-average function used. Early implementations implemented with analog filters had only one choice: 20 MHz. 

Nowadays, digital scopes do an even better job. Using digital signal processing techniques a good digital scope can apply a very nice Gaussian, linear-phase filter to the input signal with a variety of different bandwidth limits.

The LeCroy SDA 6020 can do both digital and analog filtering. It offers front-end analog bandwidth selections of 6 GHz (full bandwidth), 4, 3, 1, 0.2, and 0.02 GHz. In addition, it can implement arbitrary filter functions in DSP software post-acquisition.

The effect of the filter depends on the speed of the signal to which it is applied. In general, a low-pass filter rounds the sharp corners of a square-edged waveform. If the waveform has sharp peaks, the filter clips them off, as shown in Figure 1. 

In signal-processing terminology, the high-bandwidth LeCroy SDA 6020 scope, combined with a 1 GHz low-pass filter function, makes a 1-GHz instrument. In other words, the figure shows what signal you would have seen with a 1-GHz instrument.

That's an interesting way to think about the issue, because it means you can explore signals using the high-bandwidth scope to see how they would be distorted if viewed through the eyes of an instrument with inadequate bandwidth.

In the case just presented, the bandwidth-limit effect clipped only tiny peaks from the signal. The remaining portion of the waveform, being fairly slow-moving, was unaffected. If you only cared about the gross ups and downs of the waveform, in effect just looking for 1's and 0's, the 1-GHz bandwidth limit makes almost no difference. On the other hand, if you are trying to accurately measure an exact degree of transmit pre-emphasis, the low-pass filtering effect of a limited-bandwidth instrument distorts your view.

Figure 2 illustrates an even more dramatic case. It depicts the common-mode output of the same differential signal, using the sum of the two input channels (CH1+CH2).  The vertical scale has been enlarged to 50 mV/div. As you can see, the common-mode signal harbors some very tall, narrow peaks. Many signals, like crosstalk and skew, have a similar appearance.

With the 1 GHz input bandwidth setting the short pulses rise to only half their correct amplitude. That's a 50% error. The 6 GHz bandwidth setting shows you the whole signal.

How do I know that 6 GHz is enough? Might there not be even more to this signal at even higher bandwidths?

I know there is not because I checked that. I pushed the 3 GHz button and saw the same result at both 3 and 6 GHz. That's a cute trick you can use to make sure your scope has adequate bandwidth. You can rarely increase the bandwidth of your instrument, but you can artificially reduce it. If the reduction makes no observable difference, then you probably have adequate bandwidth headroom [see Note 1]. If the reduction makes a noticeable difference, then a higher-bandwidth instrument might reveal even more of the signal you are trying to measure.

The most commonly used rule of thumb for determining the bandwidth you need depends on the effective rise/fall time of the measuring instrument. To determine whether your instrument is adequate, given no other information but the 3-dB bandwidth of your scope, first figure its effective rise/fall time:

tSCOPE = 0.338/f3dB

Compare that time with the rise/fall time of the signal you need to measure, tSIGNAL. The waveform-reproduction accuracy of the measured result will fall in line with this table:

Ratio  tSCOPE/tSIGNAL General accuracy
< .1 better than 0.5 %
1/3 5%
1/2 12%
1 40%
>1 do not attempt

Keep in mind that your measuring system comprises a probe (or at least a probe cable) and a sampling unit. They affect each other. The overall bandwidth of the combination is never as great as either of the individual pieces. To figure the overall effective rise/fall time of your combination, first determine the rise/fall time of each piece and then combine the pieces:

tOVERALL = sqrt{ tSCOPE2 + tPROBE2 }

These simple equations assume well-damped Gaussian filters in both the scope and probe. In some cases, especially for digital scopes at 6 GHz and above, that assumption may not be correct. In that case the equations will be indicative of behavior, but not precise. Check your scope manufacturer's web site for more precise information about the equivalent rise/fall time of various instrument/probe combinations.

Best Regards,
Dr. Howard Johnson


NOTE 1: I said your bandwidth is probably adequate because there are some pathological cases for which my simple test would not return the correct answer. For example, take a square wave with 10 ns rise/fall times, and superimpose upon that signal a 70 GHz sine wave. Any scope with a bandwidth greater than 100 MHz would show the square wave part of the signal with crystal clarity, but unless your scope goes all the way to 70 GHz, you would probably never notice the sine wave component.