Probe a Circuit with the Power Off (EE Tip #14)

Imagine something is not working on your surface-mounted board, so you decide use your new oscilloscope. You take the probe scope in your right hand and put it on the microcontroller’s pin 23. Then, as you look at the scope’s screen, you inadvertently move your hand by 1 mm. Bingo!ComponentsDesk-iStock_000036102494Large

The scope probe is now right between pin 23 and pin 24, and you short-circuit two outputs. As a result, the microcontroller is dead and, because you’re unlucky, a couple of other chips are dead too. You just successfully learned Error 22.

Some years ago a potential customer brought me an expensive professional light control system he wanted to use. After 10 minutes of talking, I opened the equipment to see how it was built. My customer warned me to take care because he needed to use it for a show the next day. Of course, I said that he shouldn’t worry because I’m an engineer. I took my oscilloscope probe and did exactly what I said you shouldn’t do. Within 5 s, I short-circuited a 48-V line with a 3V3 regulated wire. Smoke and fire! I transformed each of the beautiful system’s 40 or so integrated circuits into dead silicon. Need I say my relationship with that customer was rather cold for a few weeks?

In a nutshell, don’t ever try to connect a probe on a fine-pitch component when the power is on. Switch everything off, solder a test wire where you need it to be, grab your probe on the wire end, ensure there isn’t a short circuit and then switch on the power. Alternatively, you can buy a couple of fine-pitch grabbers, expensive but useful, or a stand-off to maintain the probe in a precise position. But still don’t try to connect them to a powered board.—Robert Lacoste, CC25, 2013

High-Bandwidth Oscilloscope Probe

Keysight Technologies recently announced a new high-bandwidth, low-noise oscilloscope probe, the N7020A, for making power integrity measurements to characterize DC power rails. The probe’s specs include:

  • low noise
  • large ± 24-V offset range
  • 50 kΩ DC input impedance
  • 2-GHz bandwidth for analyzing fast transients on their DC power-rails KeysightN7020A

According to Keysight’s product release, “The single-ended N7020A power-rail probe has a 1:1 attenuation ratio to maximize the signal-to-noise ratio of the power rail being observed by the oscilloscope. Comparable oscilloscope power integrity measurement solutions have up to 16× more noise than the Keysight solution. With its lower noise, the Keysight N7020A power-rail probe provides a more accurate view of the actual ripple and noise riding on DC power rails.”

 

The new N7020A power-rail probe starts at $2,650.

Source: Keysight Technologies 

WaveSurfer 3000 Oscilloscopes with MAUI

Teledyne LeCroy recently introduced the WaveSurfer 3000 series of oscilloscopes. The series features the MAUI advanced user interface, which “integrates a deep measurement toolset and multi-instrument capabilities into a cutting edge user experience centered on a large 10.1” touch screen,” the company stated in a release.

Source: Teledyne LeCroy

Source: Teledyne LeCroy

Essential characteristics, specs, and features include:

  • Bandwidths from 200 MHz to 500 MHz, with 10 Mpts/ch memory and up to 4 GS/s sample rate.
  • Multi-instrument capabilities such as waveform generation, protocol analysis, and logic analysis
  • 130,000 waveforms/second with waveform update, as well as waveform playback and WaveScan search/find
  • An advanced active probe
  • A comprehensive toolset featuring powerful math and measurement capabilities, sequence mode segmented memory, and LabNotebook

The WaveSurfer 3000 is available in four different models (200 MHz, two-channel to 500 MHz, four-channel) with prices ranging from $3,200 to $6,950.

Source: Teledyne LeCroy

One Professor and Two Orderly Labs

Professor Wolfgang Matthes has taught microcontroller design, computer architecture, and electronics (both digital and analog) at the University of Applied Sciences in Dortmund, Germany, since 1992. He has developed peripheral subsystems for mainframe computers and conducted research related to special-purpose and universal computer architectures for the past 25 years.

When asked to share a description and images of his workspace with Circuit Cellar, he stressed that there are two labs to consider: the one at the University of Applied Sciences and Arts and the other in his home basement.

Here is what he had to say about the two labs and their equipment:

In both labs, rather conventional equipment is used. My regular duties are essentially concerned  with basic student education and hands-on training. Obviously, one does not need top-notch equipment for such comparatively humble purposes.

Student workplaces in the Dortmund lab are equipped for basic training in analog electronics.

Student workplaces in the Dortmund lab are equipped for basic training in analog electronics.

In adjacent rooms at the Dortmund lab, students pursue their own projects, working with soldering irons, screwdrivers, drills,  and other tools. Hence, these rooms are  occasionally called the blacksmith’s shop. Here two such workplaces are shown.

In adjacent rooms at the Dortmund lab, students pursue their own projects, working with soldering irons, screwdrivers, drills, and other tools. Hence, these rooms are occasionally called “the blacksmith’s shop.” Two such workstations are shown.

Oscilloscopes, function generators, multimeters, and power supplies are of an intermediate price range. I am fond of analog scopes, because they don’t lie. I wonder why neither well-established suppliers nor entrepreneurs see a business opportunity in offering quality analog scopes, something that could be likened to Rolex watches or Leica analog cameras.

The orderly lab at home is shown here.

The orderly lab in Matthes’s home is shown here.

Matthes prefers to build his  projects so that they are mechanically sturdy. So his lab is equipped appropriately.

Matthes prefers to build mechanically sturdy projects. So his lab is appropriately equipped.

Matthes, whose research interests include advanced computer architecture and embedded systems design, pursues a variety of projects in his workspace. He describes some of what goes on in his lab:

The projects comprise microcontroller hardware and software, analog and digital circuitry, and personal computers.

Personal computer projects are concerned with embedded systems, hardware add-ons, interfaces, and equipment for troubleshooting. For writing software, I prefer PowerBASIC. Those compilers generate executables, which run efficiently and show a small footprint. Besides, they allow for directly accessing the Windows API and switching to Assembler coding, if necessary.

Microcontroller software is done in Assembler and, if required, in C or BASIC (BASCOM). As the programming language of the toughest of the tough, Assembler comes second after wire [i.e., the soldering iron].

My research interests are directed at computer architecture, instruction sets, hardware, and interfaces between hardware and software. To pursue appropriate projects, programming at the machine level is mandatory. In student education, introductory courses begin with the basics of computer architecture and machine-level programming. However, Assembler programming is only taught at a level that is deemed necessary to understand the inner workings of the machine and to write small time-critical routines. The more sophisticated application programming is usually done in C.

Real work is shown here at the digital analog computer—bring-up and debugging of the master controller board. Each of the six microcontrollers is connected to a general-purpose human-interface module.

A digital analog computer in Matthes’s home lab works on master controller board bring-up and debugging. Each of the six microcontrollers is connected to a general-purpose human-interface module.

Additional photos of Matthes’s workspace and his embedded electronics and micrcontroller projects are available at his new website.

 

 

 

User-Extensible FDA for Real-Time Oscilloscopes

Keysight Technologies recently announced the availability of a frequency domain analysis (FDA) option, a user-extensible spectrum frequency domain analysis application solution for real-time oscilloscopes.

Source: Keysight Technologies

Source: Keysight Technologies

The FDA option extends the capabilities of Keysight Infiniium and InfiniiVision Series oscilloscopes by enabling you to acquire live signals from the oscilloscope and visualize them in the frequency domain, as well as make key frequency domain measurements.

Option N8832A-001 includes the application, the application source code for user extensibility, and MATLAB software. These tools enable you to extend an application’s capabilities to meet their current and future testing needs.

With the FDA application, you can address a variety of FDA challenges such as:

  • Power spectral density (PSD) and spectrogram visualization
  • Frequency domain measurements in an application including relevant peaks in the PSD and measurements such as occupied bandwidth, SNR, total harmonic distortion (THD ), spurious free dynamic range (SFDR), and frequency error
  • Oscilloscope configuration through the application to allow for repeatable instrument configuration and measurements; optionally includes additional SCPI commands for more advanced instrument setup
  • Insertion of additional custom signal processing commands prior to frequency domain visualization, as needed, for more advanced analysis insight
  • Live or post-acquisition analysis of time-domain data in MATLAB software

Source: Keysight Technologies

Measuring Jitter (EE Tip #132)

Jitter is one of the parameters you should consider when designing a project, especially when it involves planning a high-speed digital system. Moreover, jitter investigation—performed either manually or with the help of proper measurement tools—can provide you with a thorough analysis of your product.

There are at least two ways to measure jitter: cycle-to-cycle and time interval error (TIE).

WHAT IS JITTER?
The following is the generic definition offered by The International Telecommunication Union (ITU) in its G.810 recommendation. “Jitter (timing): The short-term variations of the significant instants of a timing signal from their ideal positions in time (where short-term implies that these variations are of frequency greater than or equal to 10 Hz).”

First, jitter refers to timing signals (e.g., a clock or a digital control signal that must be time-correlated to a given clock). Then you only consider “significant instants” of these signals (i.e., signal-useful transitions from one logical state to the other). These events are supposed to happen at a specific time. Jitter is the difference between this expected time and the actual time when the event occurs (see Figure 1).

Figure 1—Jitter includes all phenomena that result in an unwanted shift in timing of some digital signal transitions in comparison to a supposedly “perfect” signal.

Figure 1—Jitter includes all phenomena that result in an unwanted shift in timing of some digital signal transitions in comparison to a supposedly “perfect” signal.

Last, jitter concerns only short-term variations, meaning fast variations as compared to the signal frequency (in contrast, very slow variations, lower than 10 Hz, are called “wander”).

Clock jitter, for example, is a big concern for A/D conversions. Read my article on fast ADCs (“Playing with High-Speed ADCs,” Circuit Cellar 259, 2012) and you will discover that jitter could quickly jeopardize your expensive, high-end ADC’s signal-to-noise ratio.

CYCLE-TO-CYCLE JITTER
Assume you have a digital signal with transitions that should stay within preset time limits (which are usually calculated based on the receiver’s signal period and timing diagrams, such as setup duration and so forth). You are wondering if it is suffering from any excessive jitter. How do you measure the jitter? First, think about what you actually want to measure: Do you have a single signal (e.g., a clock) that could have jitter in its timing transitions as compared to absolute time? Or, do you have a digital signal that must be time-correlated to an accessible clock that is supposed to be perfect? The measurement methods will be different. For simplicity, I will assume the first scenario: You have a clock signal with rising edges that are supposed to be perfectly stable, and you want to double check it.

My first suggestion is to connect this clock to your best oscilloscope’s input, trigger the oscilloscope on the clock’s rising edge, adjust the time base to get a full period on the screen, and measure the clock edge’s time dispersion of the transition just following the trigger. This method will provide a measurement of the so-called cycle-to-cycle jitter (see Figure 2).

Figure 2—Cycle-to-cycle is the easiest way to measure jitter. You can simply trigger your oscilloscope on a signal transition and measure the dispersion of the following transition’s time.

Figure 2—Cycle-to-cycle is the easiest way to measure jitter. You can simply trigger your oscilloscope on a signal transition and measure the dispersion of the following transition’s time.

If you have a dual time base or a digital oscilloscope with zoom features, you could enlarge the time zone around the clock edge you are interested in for more accurate measurements. I used an old Philips PM5786B pulse generator from my lab to perform the test. I configured the pulse generator to generate a 6.6-MHz square signal and connected it to my Teledyne LeCroy WaveRunner 610Zi oscilloscope. I admit this is high-end equipment (1-GHz bandwidth, 20-GSPS sampling rate and an impressive 32-M word memory when using only two of its four channels), but it enabled me to demonstrate some other interesting things about jitter. I could have used an analog oscilloscope to perform the same measurement, as long as the oscilloscope provided enough bandwidth and a dual time base (e.g., an old Tektronix 7904 oscilloscope or something similar). Nevertheless, the result is shown in Figure 3.

Figure 3—This is the result of a cycle-to-cycle jitter measurement of the PM5786A pulse generator. The bottom curve is a zoom of the rising front just following the trigger. The cycle-to-cycle jitter is the horizontal span of this transition over time, here measured at about 620 ps.

Figure 3—This is the result of a cycle-to-cycle jitter measurement of the PM5786A pulse generator. The bottom curve is a zoom of the rising front just following the trigger. The cycle-to-cycle jitter is the horizontal span of this transition over time, here measured at about 620 ps.

This signal generator’s cycle-to-cycle jitter is clearly visible. I measured it around 620 ps. That’s not much, but it can’t be ignored as compared to the signal’s period, which is 151 ns (i.e., 1/6.6 MHz). In fact, 620 ps is ±0.2% of the clock period. Caution: When you are performing this type of measurement, double check the oscilloscope’s intrinsic jitter as you are measuring the sum of the jitter of the clock and the jitter of the oscilloscope. Here, the latter is far smaller.

TIME INTERVAL ERROR
Cycle-to-cycle is not the only way to measure jitter. In fact, this method is not the one stated by the definition of jitter I presented earlier. Cycle-to-cycle jitter is a measurement of the timing variation from one signal cycle to the next one, not between the signal and its “ideal” version. The jitter measurement closest to that definition is called time interval error (TIE). As its name suggests, this is a measure of a signal’s transitions actual time, as compared to its expected time (see Figure 4).

Figure 4—Time interval error (TIE) is another way to measure jitter. Here, the actual transitions are compared to a reference clock, which is supposed to be “perfect,” providing the TIE. This reference can be either another physical signal or it can be generated using a PLL. The measured signal’s accumulated plot, triggered by the reference clock, also provides the so-called eye diagram.

Figure 4—Time interval error (TIE) is another way to measure jitter. Here, the actual transitions are compared to a reference clock, which is supposed to be “perfect,” providing the TIE. This reference can be either another physical signal or it can be generated using a PLL. The measured signal’s accumulated plot, triggered by the reference clock, also provides the so-called eye diagram.

It’s difficult to know these expected times. If you are lucky, you could have a reference clock elsewhere on your circuit, which would supposedly be “perfect.” In that case, you could use this reference as a trigger source, connect the signal to be measured on the oscilloscope’s input channel, and measure its variation from trigger event to trigger event. This would give you a TIE measurement.

But how do you proceed if you don’t have anything other than your signal to be measured? With my previous example, I wanted to measure the jitter of a lab signal generator’s output, which isn’t correlated to any accessible reference clock. In that case, you could still measure a TIE, but first you would have to generate a “perfect” clock. How can this be accomplished? Generating an “ideal” clock, synchronized with a signal, is a perfect job for a phase-locked loop (PLL). The technique is explained my article, “Are You Locked? A PLL Primer” (Circuit Cellar 209, 2007.) You could design a PLL to lock on your signal frequency and it could be as stable as you want (provided you are willing to pay the expense).

Moreover, this PLL’s bandwidth (which is the bandwidth of its feedback filter) would give you an easy way to zoom in on your jitter of interest. For example, if the PLL bandwidth is 100 Hz, the PLL loop will capture any phase variation slower than 100 Hz. Therefore, you can measure the jitter components faster than this limit. This PLL (often called a carrier recovery circuit) can be either an actual hardware circuit or a software-based implementation.

So, there are at least two ways to measure jitter: Cycle-to-cycle and TIE. (As you may have anticipated, many other measurements exist, but I will limit myself to these two for simplicity.) Are these measurement methods related? Yes, of course, but the relationship is not immediate. If the TIE is not null but remains constant, the cycle-to-cycle jitter is null.  Similarly, if the cycle-to-cycle jitter is constant but not null, the TIE will increase over time. In fact, the TIE is closely linked to the mathematical integral over time of the cycle-to-cycle jitter, but this is a little more complex, as the jitter’s frequency range must be limited.

Editor’s Note: This is an excerpt from an article written by Robert Lacoste, “Analyzing a Case of the Jitters: Tips for Preventing Digital Design Issues,” Circuit Cellar 273, 2013.

A Shed Packed with Projects and EMF Test Equipment

David Bellerose, a retired electronic equipment repairman for the New York State Thruway, has had a variety of careers that have honed the DIY skills he employs in his Lady Lake, FL, workspace.

Bellerose has been a US Navy aviation electronics technician and a computer repairman. “I also ran my own computer/electronic and steel/metal welding fabrication businesses, so I have many talents under my belt,” he says.

Bellerose’s Protostation, purchased on eBay, is on top shelf (left). He designed the setup on the right, which includes a voltmeter, a power supply, and transistor-transistor logic (TTL) oscillators. A second protoboard unit is on the middle shelf (left). On the right are various Intersil ICM7216D frequency-counter units and DDS-based signal generator units from eBay. The bottom shelf is used for protoboard storage.

Bellerose’s Protostation, purchased on eBay, is on top shelf (left). He designed the setup on the right, which includes a voltmeter, a power supply, and transistor-transistor logic (TTL) oscillators. A second protoboard unit is on the middle shelf (left). On the right are various Intersil ICM7216D frequency-counter units and DDS-based signal generator units from eBay. The bottom shelf is used for protoboard storage.

Bellerose’s project interests include model rockets, video security, solar panels, and computer systems. “My present project involves Intersil ICM7216D-based frequency counter modules to companion with various frequency generator modules, which I am also designing for a frequency range of 1 Hz to 12 GHz,” he says.

His workspace is an 8′-by-15′ shed lined with shelves and foldable tables. He describes how he tries to make the best use of the space available:

“My main bench is a 4′-by-6’ table with a 2’-by-6’ table to hold my storage drawers. A center rack holds my prototype units—one bought on eBay and two others I designed and built myself. My Tektronix 200-MHz oscilloscope bought on eBay sits on the main rack on the left, along with a video monitor. On the right is my laptop, a Heathkit oscilloscope from eBay, a 2.4-GHz frequency counter and more storage units. All the units are labeled.

“I try to keep all projects on paper and computer with plenty of storage space. My network-attached storage (NAS) totals about 23 terabytes of space.

“I get almost all of my test equipment from eBay along with parts that I can’t get from my distributors, such as the ICM7216D chips, which are obsolete. I try to cover the full EMF spectrum with my test equipment, so I have photometers, EMF testers, lasers, etc.”

The main workbench has a 4′-by-6′ center rack and parts storage units on the left and right. The main bench includes an OWON 25-MHz oscilloscope, storage drawers for lithium-ion (Li-on) batteries (center), voltage converter modules, various project modules on right, a Dremel drill press, and a PC monitor.

The main workbench has a 4′-by-6′ center rack and parts storage units on the left and right. The main bench includes an OWON 25-MHz oscilloscope, storage drawers for lithium-ion (Li-on) batteries (center), voltage converter modules, various project modules on the right, a Dremel drill press, and a PC monitor.

Photo 3: This full-room view shows the main bench (center), storage racks (left), and an auxiliary folding bench to work on large repairs. The area on right includes network-attached storage (NAS) storage and two PCs with a range extender and 24-port network switch.

Photo 3: This full-room view shows the main bench (center), storage racks (left), and an auxiliary folding bench to work on large repairs. The area on right includes network-attached storage (NAS) and two PCs with a range extender and 24-port network switch.

Photo 4: Various versions of Bellerose’s present project are shown. The plug-in units are for eight-digit displays. They are based on the 28-pin Intersil ICM 7216D chip with a 10-MHz time base oscillator, a 74HC132 input buffer, and a 74HC390 prescaler to bring the range to 60 MHz. The units’ eight-digit displays vary from  1″ to 0.56″ and 0.36″.

Various versions of Bellerose’s present project are shown. The plug-in units are for eight-digit displays. They are based on the 28-pin Intersil ICM 7216D chip with a 10-MHz time base oscillator, a 74HC132 input buffer, and a 74HC390 prescaler to bring the range to 60 MHz. The units’ eight-digit displays vary from 1″ to 0.56″ and 0.36″.

Photo 5: This is a smaller version of Bellerose’s project with a 0.36″ display mounted over an ICM chip with 74hc132 and 74hc390 chips and 5-V regulators. Bellerose is still working on the final PCB layout. “With regulators, I can use a 9-V adapter,” he says.  “Otherwise, I use 5 V for increased sensitivity. I use monolithic microwave (MMIC) amplifiers (MSA-0486) for input.”

This is a smaller version of Bellerose’s project with a 0.36″ display mounted over an ICM chip with 74HC132 and 74HC390 chips and 5-V regulators. Bellerose is still working on the final PCB layout. “With regulators, I can use a 9-V adapter,” he says. “Otherwise, I use 5 V for increased sensitivity. I use monolithic microwave (MMIC) amplifiers (MSA-0486) for input.”

 

 

A Workspace for “Engineering Magic”

Brandsma_workspace2

Photo 1—Brandsma describes his workspace as his “little corner where the engineering magic happens.”

Sjoerd Brandsma, an R&D manager at CycloMedia, enjoys designing with cameras, GPS receivers, and transceivers. His creates his projects in a small workspace in Kerkwijk, The Netherlands (see Photo 1). He also designs in his garage, where he uses a mill and a lathe for some small and medium metal work (see Photo 2).

Brandsma_lathe_mill

Photo 2—Brandsma uses this Weiler lathe for metal work.

The Weiler lathe has served me and the previous owners for many years, but is still healthy and precise. The black and red mill does an acceptable job and is still on my list to be converted to a computer numerical control (CNC) machine.

Brandsma described some of his projects.

Brandsma_cool_projects

Photo 3—Some of Brandsma’s projects include an mbed-based camera project (left), a camera with an 8-bit parallel databus interface (center), and an MP3 player that uses a decoder chip that is connected to an mbed module (right).

I built a COMedia C328 UART camera with a 100° lens placed on a 360° servomotor (see Photo 3, left).  Both are connected to an mbed module. When the system starts, the camera takes a full-circle picture every 90°. The four images are stored on an SD card and can be stitched into a panoramic image. I built this project for the NXP mbed design challenge 2010 but never finished the project because the initial idea involved doing some stitching on the mbed module itself. This seemed to be a bit too complicated due to memory limitations.

I built this project built around a 16-MB framebuffer for the Aptina MT9D131 camera (see Photo 3, center). This camera has an 8-bit parallel databus interface that operates on 6 to 80 MHz. This is way too fast for most microcontrollers (e.g., Arduino, Atmel AVR, Microchip Technology PIC, etc.). With this framebuffer, it’s possible to capture still images and store/process the image data at a later point.

This project involves an MP3 player that uses a VLSI VS1053 decoder chip that is connected to an mbed module (see Photo 3, right). The great thing about the mbed platform is that there’s plenty of library code available. This is also the case for the VS1053. With that, it’s a piece of cake to build your own MP3 player. The green button is a Skip button. But beware! If you press that button it will play a song you don’t like and you cannot skip that song.

He continued by describing his test equipment.

Brandma_test_equipment

Photo 4—Brandsma’s test equipment collection includes a Tektronix TDS220 oscilloscope (top), a Total Phase Beagle protocol analyzer (second from top), a Seeed Technology Open Workbench Logic Sniffer (second from bottom), and a Cypress Semiconductor CY7C68013A USB microcontroller (bottom).

Most of the time, I’ll use my good old Tektronix TDS220 oscilloscope. It still works fine for the basic stuff I’m doing (see Photo 4, top). The Total Phase Beagle I2C/SPI protocol analyzer Beagle/SPI is a great tool to monitor and analyze I2C/SPI traffic (see Photo 4, second from top).

The red PCB is a Seeed Technology 16-channel Open Workbench Logic Sniffer (see Photo 4, second from bottom). This is actually a really cool low-budget open-source USB logic analyzer that’s quite handy once in a while when I need to analyze some data bus issues.

The board on the bottom is a Cypress CY7C68013A USB microcontroller high-speed USB peripheral controller that can be used as an eight-channel logic analyzer or as any other high-speed data-capture device (see Photo 4, bottom). It’s still on my “to-do” list to connect it to the Aptina MT9D131 camera and do some video streaming.

Brandsma believes that “books tell a lot about a person.” Photo 5 shows some books he uses when designing and or programming his projects.

Brandsma_books

Photo 5—A few of Brandsma’s “go-to” books are shown.

The technical difficulty of the books differs a lot. Electronica echt niet moeilijk (Electronics Made Easy) is an entry-level book that helped me understand the basics of electronics. On the other hand, the books about operating systems and the C++ programming language are certainly of a different level.

An article about Brandsma’s Sun Chaser GPS Reference Station is scheduled to appear in Circuit Cellar’s June issue.

Traveling With a “Portable Workspace”

As a freelance engineer, Raul Alvarez spends a lot of time on the go. He says the last four or five years he has been traveling due to work and family reasons, therefore he never stays in one place long enough to set up a proper workspace. “Whenever I need to move again, I just pack whatever I can: boards, modules, components, cables, and so forth, and then I’m good to go,” he explains.

Raul_Alvarez_Workspace _Photo_1

Alvarez sits at his “current” workstation.

He continued by saying:

In my case, there’s not much of a workspace to show because my workspace is whichever desk I have at hand in a given location. My tools are all the tools that I can fit into my traveling backpack, along with my software tools that are installed in my laptop.

Because in my personal projects I mostly work with microcontroller boards, modular components, and firmware, until now I think it didn’t bother me not having more fancy (and useful) tools such as a bench oscilloscope, a logic analyzer, or a spectrum analyzer. I just try to work with whatever I have at hand because, well, I don’t have much choice.

Given my circumstances, probably the most useful tools I have for debugging embedded hardware and firmware are a good-old UART port, a multimeter, and a bunch of LEDs. For the UART interface I use a Future Technology Devices International FT232-based UART-to-USB interface board and Tera Term serial terminal software.

Currently, I’m working mostly with Microchip Technology PIC and ARM microcontrollers. So for my PIC projects my tiny Microchip Technology PICkit 3 Programmer/Debugger usually saves the day.

Regarding ARM, I generally use some of the new low-cost ARM development boards that include programming/debugging interfaces. I carry an LPC1769 LPCXpresso board, an mbed board, three STMicroelectronics Discovery boards (Cortex-M0, Cortex-M3, and Cortex-M4), my STMicroelectronics STM32 Primer2, three Texas Instruments LaunchPads (the MSP430, the Piccolo, and the Stellaris), and the following Linux boards: two BeagleBoard.org BeagleBones (the gray one and a BeagleBone Black), a Cubieboard, an Odroid-X2, and a Raspberry Pi Model B.

Additionally, I always carry an Arduino UNO, a Digilent chipKIT Max 32 Arduino-compatible board (which I mostly use with MPLAB X IDE and “regular” C language), and a self-made Parallax Propeller microcontroller board. I also have a Wi-Fi 3G TP-LINK TL-WR703N mini router flashed   with OpenWRT that enables me to experiment with Wi-Fi and Ethernet and to tinker with their embedded Linux environment. It also provides me Internet access with the use of a 3G modem.

Raul_Alvarez_Workspace _Photo_2

Not a bad set up for someone on the go. Alvarez’s “portable workstation” includes ICs, resistors, and capacitors, among other things. He says his most useful tools are a UART port, a multimeter, and some LEDs.

In three or four small boxes I carry a lot of sensors, modules, ICs, resistors, capacitors, crystals, jumper cables, breadboard strips, and some DC-DC converter/regulator boards for supplying power to my circuits. I also carry a small video camera for shooting my video tutorials, which I publish from time to time at my website (www.raulalvarez.net). I have installed in my laptop TechSmith’s Camtasia for screen capture and Sony Vegas for editing the final video and audio.

Some IDEs that I have currently installed in my laptop are: LPCXpresso, Texas Instruments’s Code Composer Studio, IAR EW for Renesas RL78 and 8051, Ride7, Keil uVision for ARM, MPLAB X, and the Arduino IDE, among others. For PC coding I have installed Eclipse, MS Visual Studio, GNAT Programming Studio (I like to tinker with Ada from time to time), QT Creator, Python IDLE, MATLAB, and Octave. For schematics and PCB design I mostly use CadSoft’s EAGLE, ExpressPCB, DesignSpark PCB, and sometimes KiCad.

Traveling with my portable rig isn’t particularly pleasant for me. I always get delayed at security and customs checkpoints in airports. I get questioned a lot especially about my circuit boards and prototypes and I almost always have to buy a new set of screwdrivers after arriving at my destination. Luckily for me, my nomad lifestyle is about to come to an end soon and finally I will be able to settle down in my hometown in Cochabamba, Bolivia. The first two things I’m planning to do are to buy a really big workbench and a decent digital oscilloscope.

Alvarez’s article “The Home Energy Gateway: Remotely Control and Monitor Household Devices” appeared in Circuit Cellar’s February issue. For more information about Alvarez, visit his website or follow him on Twitter @RaulAlvarezT.

Evaluating Oscilloscopes (Part 4)

In this final installment of my four-part mini-series about selecting an oscilloscope, I’ll look at triggering, waveform generators, and clock synchronization, and I’ll wrap up with a series summary.

My previous posts have included Part 1, which discusses probes and physical characteristics of stand-alone vs. PC-based oscilloscopes; Part 2, which examines core specifications such as bandwidth, sample rate, and ADC resolution; and Part 3, which focuses on software. My posts are more a “collection of notes” based on my own research rather than a completely thorough guide. But I hope they are useful and cover some points you might not have otherwise considered before choosing an oscilloscope.

This is a screenshot from Colin O'Flynn's YouTube video "Using PicoScope AWG for Testing Serial Data Limits."

This is a screenshot from Colin O’Flynn’s YouTube video “Using PicoScope AWG for Testing Serial Data Limits.”

Topic 1: Triggering Methods
Triggering your oscilloscope properly can make a huge difference in being able to capture useful waveforms. The most basic triggering method is just a “rising” or “falling” edge, which almost everyone is (or should be) familiar with.

Whether you need a more advanced trigger method will depend greatly on your usage scenario and a bit on other details of your oscilloscope. If you have a very long buffer length or ability to rapid-fire record a number of waveforms, you might be able to live with a simple trigger since you can easily throw away data that isn’t what you are looking for. If your oscilloscope has a more limited buffer length, you’ll need to trigger on the exact moment of interest.

Before I detail some of the other methods, I want to mention that you can sometimes use external instruments for triggering. For example, you might have a logic analyzer with an extremely advanced triggering mechanism.  If that logic analyzer has a “trigger out,” you can trigger the oscilloscope from your logic analyzer.

On to the trigger methods! There are a number of them related to finding “odd” pulses: for example, finding glitches shorter or wider than some length or finding a pulse that is lower than the regular height (called a “runt pulse”). By knowing your scope triggers and having a bit of creativity, you can perform some more advanced troubleshooting. For example, when troubleshooting an embedded microcontroller, you can have it toggle an I/O pin when a task runs. Using a trigger to detect a “pulse dropout,” you can trigger your oscilloscope when the system crashes—thus trying to see if the problem is a power supply glitch, for example.

If you are dealing with digital systems, be on the lookout for triggers that can function on serial protocols. For example, the Rigol Technologies stand-alone units have this ability, although you’ll also need an add-on to decode the protocols! In fact, most of the serious stand-alone oscilloscopes seem to have this ability (e.g., those from Agilent, Tektronix, and Teledyne LeCroy); you may just need to pay extra to enable it.

Topic 2: External Trigger Input
Most oscilloscopes also have an “external trigger input.”  This external input doesn’t display on the screen but can be used for triggering. Specifically, this means your trigger channel doesn’t count against your “ADC channels.” So if you need the full sample rate on one channel but want to trigger on another, you can use the “ext in” as the trigger.
Oscilloscopes that include this feature on the front panel make it slightly easier to use; otherwise, you’re reaching around behind the instrument to find the trigger input.

Topic 3: Arbitrary Waveform Generator
This isn’t strictly an oscilloscope-related function, but since enough oscilloscopes include some sort of function generator it’s worth mentioning. This may be a standard “signal generator,” which can generate waveforms such as sine, square, triangle, etc. A more advanced feature, called an arbitrary waveform generator (AWG), enables you to generate any waveform you want.

I previously had a (now very old) TiePie engineering HS801 that included an AWG function. The control software made it easy to generate sine, square, triangle, and a few other waveforms. But the only method of generating an arbitrary waveform was to load a file you created in another application, which meant I almost never used the “arbitrary” portion of the AWG. The lesson here is that if you are going to invest in an AWG, make sure the software is reasonable to use.

The AWG may have a few different specifications; look for the maximum analog bandwidth along with the sample rate. Be careful of outlandish claims: a 200 MS/s digital to analog converter (DAC) could hypothetically have a 100-MHz analog bandwidth, but the signal would be almost useless. You could only generate some sort of sine wave at that frequency, which would probably be full of harmonics. Even if you generated a lower-frequency sine wave (e.g., 10 MHz), it would likely contain a fair amount of harmonics since the DAC’s output filter has a roll-off at such a high frequency.

Better systems will have a low-pass analog filter to reduce harmonics, with the DAC’s sample rate being several times higher than the output filter roll-off. The Pico Technology PicoScope 6403D oscilloscope I’m using can generate a 20-MHz signal but has a 200 MS/s sample rate on the DAC. Similarly, the TiePie engineering HS5-530 has a 30-MHz signal bandwidth, and similarly uses a 240 MS/s sample rate. A sample rate of around five to 10 times the analog bandwidth seems about standard.

Having the AWG integrated into the oscilloscope opens up a few useful features. When implementing a serial protocol decoder, you may want to know what happens if the baud rate is slightly off from the expected rate. You can quickly perform this test by recording a serial data packet on the oscilloscope, copying it to the AWG, and adjusting the AWG sample rate to slightly raise or lower the baud rate. I illustrate this in the following video.


Topic 4: Clock Synchronization

One final issue of interest: In certain applications, you may need to synchronize the sample rate to an external device. Oscilloscopes will often have two features for doing this. One will output a clock from the oscilloscope, the other will allow you to feed an external clock into the oscilloscope.

The obvious application is synchronizing a capture between multiple oscilloscopes. You can, however, use this for any application where you wish to use a synchronous capture methodology. For example, if you wish to use the oscilloscope as part of a software-defined radio (SDR), you may want to ensure the sampling happens synchronous to a recovered clock.

The input frequency of this clock is typically 10 MHz, although some devices enable you to select between several allowed frequencies. If the source of this clock is anything besides another instrument, you may have to do some clock conditioning to convert it into one of the valid clock source ranges.

Summary and Closing Comments
That’s it! Over the past four weeks I’ve tried to raise a number of issues to consider when selecting an oscilloscope. As previously mentioned, the examples were often PicoScope-heavy simply because it is the oscilloscope I own. But all the topics have been relevant to any other oscilloscope you may have.

You can check out my YouTube playlist dealing with oscilloscope selection and review.  Some topics might suggest further questions to ask.

I’ve probably overlooked a few issues, but I can’t cover every possible oscilloscope and option. When selecting a device, my final piece of advice is to download the user manual and study it carefully, especially for features you find most important. Although the datasheet may gloss over some details, the user manual will typically address the limitations you’ll run into, such as FFT length or the memory depths you can configure.

Author’s note: Every reasonable effort has been made to ensure example specifications are accurate. There may, however, be errors or omissions in this article. Please confirm all referenced specifications with the device vendor.

Evaluating Oscilloscopes (Part 3)

In Part 3 of my series on selecting an oscilloscope, I look at the software running the oscilloscope and details such as remote control, fast Fourier transform (FFT) features, digital decoding, and buffer types.

Two weeks ago, I covered the differences between PC-based and stand-alone oscilloscopes and discussed the physical probe characteristics. Last week I discussed the “core” specifications: analog bandwidth, sample rate, and analog-to-digital converter (ADC) resolution. Next week, I will look into a few remaining features such as external trigger and clock synchronization, and I will summarize all the material I’ve covered.

Topic 1: Memory Depth
The digital oscilloscope works by sampling an ADC and then stores these samples somewhere. Thus an important consideration will be how many samples it can actually store. This especially becomes apparent at higher sample rates—at 5 gigasamples per second (GS/s), for example, even 1 million samples (i.e., 1 megasample or 1 MS) means 200 µs of data. If you are looking at very low-cost oscilloscopes, be aware that many of them have very small buffers. Searching on eBay, you can find an oscilloscope such as the Hantek DSO5202P, which has a 1 GS/s sample rate and costs only $400. The record length is only 24 kilosamples (KS) however, which would be 24 µs of data. You can find even smaller buffers:  the Tektronix TDS2000C series has only a 2,500-sample (2.5 KS) buffer length. If you only want to look around the trigger signal, you can live with a small buffer. Unfortunately, when it comes to troubleshooting you rarely have a perfect trigger, and you may need to do a fair amount of “exploration.”  A small buffer means the somewhat frustrating experience of trying to capture the signal of interest within your tiny window of opportunity.

Even if the buffer space is advertised as being huge, you may not be able to easily access the entire space. The Pico Technology PicoScope PS6403D advertises a 1-GS buffer space, one of the largest available. With the PC-based software you can configure a number of parameters; however, it always seems to limit the sample buffer to about 500 MS.  I do admit it’s fairly impressive that this still works at the 5 GS/s sample rate, since that suggests a memory bandwidth of 40 Gb/s! Using the segmented buffer (discussed later in this article) enables use of the full sample memory, but it cannot record a full continuous 1 GS trace, which you might expect based on the sales pitch.

Topic 2: FFT Length
Oscilloscope advertisements often allude to their ability to perform in a “spectrum analyzer” mode. In reality, what the oscilloscope is doing is performing an FFT of the measured signal. One critical difference is that a spectrum analyzer typically has a “center frequency” and you are able to measure a certain bandwidth amount to either side of that center frequency. By sweeping the center frequency, you can get a graph of the power present in the frequency system over a very wide range.

Using the oscilloscope’s FFT mode, there is no such thing as the center frequency. Instead you are always measuring from 0 Hz up to some limit, which is usually user-adjustable. The limit is, at most, half the oscilloscope’s sample rate but may be further limited by the oscilloscope’s analog bandwidth. Now here is the trick—the oscilloscope will specify a certain “FFT length,” which is how many points are used in calculating the FFT. This will also define the number of “bins” (i.e., horizontal frequency resolution) in the output graph. Certain benchtop oscilloscopes may have very limited FFT lengths, such as those containing only 2,048 points.  This may seem fine for viewing the entire spectrum from 0–100 MHz. But what if you want to zoom in on the 95–98 MHz range? Since the oscilloscope is actually calculating the FFT from 0 Hz, it will have only ~60 points it can display in that range. It suddenly becomes apparent why you want very long FFT lengths—it allows you to zoom in and still obtain accurate results. You can set the oscilloscope sample rate down to zoom in on frequencies around 0 Hz. So, for example, if you want to accurately do some measurements at 1–10 kHz, it’s not a big issue since you can set a low enough sample rate so that the 2,048 points are distributed between 0–20 kHz or similar. And when you zoom in you’ve got lots of detail.

In addition to the improved horizontal detail, longer FFT lengths push down the noise floor.  If you do wish to use the oscilloscope for frequency analysis, having a long FFT length can be a huge asset. This is shown in Figure 1, which compares an FFT taken using a magnetic field probe of a microcontroller board. Here I’ve zoomed in on a portion of the spectrum, with the left FFT having 2,048 points, the right FFT having 131,072 points.

Figure 1: When zooming in on a portion of the fast Fourier transform (FFT), having a larger number of points for the original calculation becomes a huge asset. Also, notice the lower noise floor for the figure on the right, calculated with 131,072 points, compared to the 2,048 used for the figure on the left.

Figure 1: When zooming in on a portion of the fast Fourier transform (FFT), having a larger number of points for the original calculation becomes a huge asset. Also, notice the lower noise floor for the figure on the right, calculated with 131,072 points, compared to the 2,048 used for the figure on the left.

A note on selecting a unit: The very low-cost oscilloscopes with small data buffers will obviously use a very small FFT length. But specifications for some of the larger memory depth oscilloscopes, such as the Rigol Technologies DS2000, DS4000, and DS6000 models, show they use smaller FFT lengths.  These models use only 2,048 points, according to a document posted on Rigol’s website, despite their large memory (131 MS).  PC-based oscilloscopes seem to be the best, as they can perform the FFT on a powerful desktop PC, rather than requiring it be done in an embedded digital signal processor (DSP) or field-programmable gate array (FPGA). For example, the PicoScope 6403D allows the FFT length to be up to 1,048,576 points.

Topic 3: Segmented Buffer
A feature I consider almost a “must-have” is a segmented buffer. This means you can configure the oscilloscope to trigger on a certain event, and it will record a number of waveforms of a certain length. For glitches that occur only occasionally (which is, 90% of the time, why you are troubleshooting in the first place), this can speed up your ability to find details of what the system is doing during a glitch.

Figure 2 shows an example of the segmented buffer viewer on the PicoScope software, where the number of buffers can be configured up to 10,000. Similar features exist in the Rigol DS4000 and DS6000, which call each segment a “frame” and can record up to 200,000 frames! Once you have a number of segments/frames, you can either manually flip through looking for the glitch, or use features such as mask limit testing to highlight segments/frames that differ from the “usual.”

Figure 2

Figure 2: Segmented buffers allow you to capture a number of traces and then flip through them looking for some specific feature. Using mask-based testing will also speed this up, since you can quickly find “odd man out”-type waveforms.

Certain oscilloscopes might make the segmented buffer an add-on. For example, only certain Agilent Technologies 3000 X-Series models contain segmented buffers by default; others in that same family require you to purchase this feature for an extra $800! Of course, always review any promotional offers—Agilent has recently advertised that it will enable all features on that oscilloscope model for the price of a single option.

Topic 4: Remote Control/Streaming
One more advanced feature is controlling the oscilloscope from your computer. If you wish to use the oscilloscope in applications beyond electronics troubleshooting, you should seriously consider the features different oscilloscopes provide.

PC-based oscilloscopes tend to have a considerable advantage here, as they are typically designed to interface to the computer. It seems most PC-based oscilloscopes from popular suppliers come with nice application programming interfaces (APIs) for most languages: I’ve found examples in C, C#, C++, MATLAB, Python, LabVIEW, and Delphi for most PC-based oscilloscopes. Some of the “no-name” PC-based oscilloscopes you find on eBay do not have an API, so always check closely for your specific device.

Most of the stand-alone oscilloscopes also have a method of sending commands, typically using a standard such as the Virtual Instrument Software Architecture (VISA). However, I’ve found these stand-alone oscilloscopes seem to have a considerably slower interface compared to a PC-based oscilloscope. Presumably for the PC-based oscilloscope, this interface is critical to overall performance, whereas for the stand-alone it’s simply an “add-on” feature. This isn’t a sure thing, of course—for example, see the PC interface for the Teledyne LeCroy oscilloscope, as described in a company blog post. It looks to give you access to features similar to those of PC-based oscilloscopes (multiple windows, etc.).

Beyond just controlling the oscilloscope, another interesting feature is streaming mode. In streaming mode data is not downloaded to an internal buffer on the oscilloscope. Instead it streams directly over the PC interface (typically USB or Ethernet). This feature is considerably more complex to work with than simple PC-based control, as achieving fast streams via USB is not trivial. However, using streaming mode opens up many interesting features. For example, you could use your oscilloscope as part of a software defined radio (SDR). If you wish to use such a feature, be sure to carefully read the specification sheets for the streaming mode limitations.

Topic 5: Decoding Serial Protocols
Decoding of serial protocols is another useful feature. If you have a digital logic analyzer, it will almost certainly include the ability to decode serial protocols. But it can be helpful to have this feature in the oscilloscope as well. If you are chasing down an occasional parity error, you can use the oscilloscope’s analog display to see if the issue is simply a weak or noisy signal.

While most oscilloscopes seem to support this feature, many require you to pay for it. Typically PC-based oscilloscopes will include it for free, but stand-alone oscilloscopes require you to purchase it. For example, this feature costs $500 for the Rigol Technologies DS4000 series, $800 for the Agilent Technologies 3000X, and $1,100 for the Tektronix DPO/MSO3000 series. Depending on the vendor, it may include multiple protocols or only one. But if you wish to enable all available protocols, it could cost more than your oscilloscope! It would typically be cheaper to purchase a PC-based logic analyzer than it would be to buy the software module for your oscilloscope.

This is one of the major reasons I prefer PC-based oscilloscopes: There tends to be no additional cost for extra features! Without the decoding you can look at the signal and see if it “looks” noisy, but having the decoding built-in means you can easily point to the specific moment when the error occurs. I’ve got some examples of such serial decoding in my video below.

Topic 6: Software Features
I’ve already mentioned it a few times in passing, but you should always check to see what software features are actually included. You may be surprised to find out some features require payment—even some models adding the FFT or other “advanced math” features require payment of a substantial fee.

There is hope on the horizon for getting access to all features in stand-alone oscilloscopes at a reasonable cost. As I mentioned earlier, Agilent Technologies recently announced it would be providing access to all software features for the cost of one module in the X-2000, X-3000, and X-4000 series. Once this goes into effect, it means that it’s really just $500–$1,500 for decoding of all serial protocols and all math features, depending on your oscilloscope. They sell this as saving you up to $16,500. (Which to me just shows how insanely expensive all these software add-ons really are!) With luck, other vendors will follow suit, and perhaps even finally include these software options in the selling price.

If you’re looking at PC-based oscilloscopes, you’ll often be allowed to download the software and play with it, even if you don’t have an instrument. This can give you an idea of how “polished” the user interface is. Considering how long you’ll spend inside this user interface, it’s good to know about it!

Closing Comments
This week I covered a number of features revolving around the software running the oscilloscope. Next week I’ll be looking into a few remaining features such as external trigger and clock synchronization, which will round out this guide.

Author’s note: Every reasonable effort has been made to ensure example specifications are accurate. There may, however, be errors or omissions in this article. Please confirm all referenced specifications with the device vendor.

Evaluating Oscilloscopes (Part 2)

This is Part 2 of my mini-series on selecting an oscilloscope. Rather than a completely thorough guide, it’s more a “collection of notes” based on my own research. But I hope you find it useful, and it might cover a few areas you hadn’t considered.

Last week I mentioned the differences between PC-based and stand-alone oscilloscopes and discussed the physical probe’s characteristics. This week I’ll be discussing the “core” specifications: analog bandwidth, sample rate, and analog-to-digital converter (ADC) resolution.

Topic 1: Analog Bandwidth
Many useful articles online discuss the analog oscilloscope bandwidth, so I won’t dedicate too much time to it. Briefly, the analog bandwidth is typically measured as the “half-power” or -3 dB point, as shown in Figure 1. Half the power means 1/√2 of the voltage. Assume you put a 10-MHz, 1-V sine wave into your 100-MHz bandwidth oscilloscope. You expect to see a 1-V sine wave on the oscilloscope. As you increase the frequency of the sine wave, you would instead expect to see around 0.707 V when you pass a 100-MHz sine wave. If you want to see this in action, watch my video in which I sweep the input frequency to an oscilloscope through the -3 dB point.

Figure 1: The bandwidth refers to the "half-power" or -3 dB  point. If we drove a sine wave of constant amplitude and increasing frequency into the probe, the -3 dB point would be when the amplitude measured in the scope was 0.707 times the initial amplitude.

Figure 1: The bandwidth refers to the “half-power” or -3 dB point. If we drive a sine wave of constant amplitude and increasing frequency into the probe, the -3 dB point would be when the amplitude measured in the scope is 0.707 times the initial amplitude.

Unfortunately, you are likely to be measuring square waves (e.g., in digital systems) and not sine waves. Square waves contain high-frequency components well beyond the fundamental frequency of the wave. For this reason the “rule of thumb”  is to select an oscilloscope with five times the analog bandwidth of the highest–frequency digital signal you would be measuring. Thus, a 66-MHz clock would require a 330-MHz bandwidth oscilloscope.

If you are interested in more details about bandwidth selection, I encourage you to see one of the many excellent guides. Adafruit has a blog post “Why Oscilloscope Bandwidth Matters” that offers more information, along with links to guides from Agilent Technologies and Tektronix.

If you want to play around yourself, I’ve got a Python script that applies analog filtering to a square wave and plots the results, available here. Figure 2 shows an example of a 50-MHz square wave with 50-MHz, 100-MHz, 250-MHz, and 500-MHz analog bandwidth.

Figure 2: This shows sampling a 50-MHz square wave with 50, 100, 250, and 500-MHz of analog bandwidth.

Figure 2: This shows sampling a 50-MHz square wave with 50, 100, 250, and 500 MHz of analog bandwidth.

Topic 2: Sample Rate
Beyond the analog bandwidth, oscilloscopes also prominently advertise the sample rate. Typically, this is in MS/s (megasamples per second) or GS/s (gigasamples per second). The advertised rate is nearly always the maximum if using a single channel. If you are using both channels on a two-channel oscilloscope that advertises 1 GS/s, typically the maximum rate is actually 500 MS/s for both channels.

So what rate do you need? If you are familiar with the Nyquist criterion, you might simply think you should have a sample rate two times the analog bandwidth. Unfortunately, we tend to work in the time domain (e.g., looking at the oscilloscope screen) and not the frequency domain. So you can’t simply apply that idea. Instead, it’s useful to have a considerably higher sample rate compared to analog bandwidth, say, a five times higher sample rate. To illustrate why, see Figure 3. It shows a 25.3-MHz square wave, which I’ve sampled with an oscilloscope with 50-MHz analog bandwidth. As you would expect, the signal rounds off considerably. However, if I only sample it at 100 MS/s, at first sight the signal is almost unrecognizable! Compare that with the 500 MS/s sample rate, which more clearly looks like a square wave (but rounded off due to analog bandwidth limitation).

Again, these figures both come from my Python script, so they are based purely on “theoretical” limits of sample rate. You can play around with sample rate and bandwidth to get an idea of how a signal might look.

Figure 3

Figure 3: This shows sampling a 25.3-MHz square wave at 100 MS/s results in a signal that looks considerably different than you might expect! Sampling at 500 MS/s results in a much more “proper” looking wave.

Topic 3: Equivalent Time Sampling
Certain oscilloscopes have an equivalent time sampling (ETS) mode, which advertises an insanely fast sample rate. For example, the PicoScope 6000 series, which has a 5 GS/s sample rate, can use ETS mode and achieve 200 GS/s on a single channel, or 50 GS/s on all channels.

The caveat is that this high sample rate is achieved by doing careful phase shifts of the A/D sampling clock to sample “in between” the regular intervals. This requires your input waveform be periodic and very stable, since the waveform will actually be “built up” over a longer time interval.

So what does this mean to you? Luckily, many actual waveforms are periodic, and you might find ETS mode very useful. For example, if you want to measure the phase shift in two clocks through a field-programmable gate array (FPGA), you can do this with ETS. At 50 GS/s, you would have 20 ps resolution on the measurement! In fact, that resolution is so high you could measure the phase difference due to a few centimeters difference in PCB trace.

To demonstrate this, I can show you a few videos. To start with, the simple video below shows moving the probes around while looking at the phase difference.

A more practical demonstration, available in the following video, measures the phase shift of two paths routed through an FPGA.

Finally, if you just want to see a sine wave using ETS you can check out the bandwdith demonstration  I referred to earlier in the this article. The video (see below) includes a portion using ETS mode.

 

Topic 4: ADC Resolution
A less prominently advertised feature of certain oscilloscopes is the ADC bit resolution in the front end. Briefly, the ADC resolution tells you how the analog waveform will get mapped to the digital domain. If you have an 8-bit ADC, this means you have 28 = 256 possible numbers the digital waveform can represent. Say you have a ±5 V range on the oscilloscope—a total span of 10 V. This means the ADC can resolve 10 V / 256 = 39.06 mV difference on the input voltage.

This should tell you one fact about digital oscilloscopes: You should always use the smallest possible range to get the finest granularity. That same 8-bit ADC on a ±1 V range would resolve 7.813 mV. However, what often happens is your signal contains multiple components—say, spiking to 7 V during a load switch, and then settling to 0.5 V. This precludes you from using the smaller range on the input, since you want to capture the amplitude of that 7-V spike.

If, however, you had a 12-bit ADC, that 10 V span (+5 V to -5 V) would be split into 212 = 4,096 numbers, meaning the resolution is now 2.551 mV.  If you had a 16-bit ADC, that 10-V range would give you 216 = 65,536 numbers, meaning you could resolve down to 0.1526 mV. Most of the time, you have to choose between a faster ADC with lower (typically 8-bit) resolution or a slower ADC with higher resolution. The only exception to this I’m aware of is the Pico Technology FlexRes 5000 series devices, which allow you to dynamically switch between 8/12/14/15/16 bits with varying changes to the number of channels and sample rate.

While the typical ADC resolution seems to be 8 bits for most scopes, there are higher-resolution models too. As mentioned, these devices are permanently in high-resolution mode, so you have to decide at purchasing time if you want a very high sample rate, or a very high resolution. For example, Cleverscope has always advertised higher resolutions, and their devices are available in 10, 12, or 14 bits. Cleverscope seems to sell the “digitizer” board separately, giving you some flexibility in upgrading to a higher-resolution ADC. TiePie engineering has devices available from 8–14 bits with various sample rate options. Besides the FlexRes device I mentioned, Pico Technology offers some fixed resolution devices in higher 14-bit resolution. Some of the larger manufacturers also have higher-resolution devices, for example Teledyne LeCroy has its High Resolution Oscilloscope (HRO), which is a fixed 12-bit device.

Note that many devices will advertise either an “effective” or “software enhanced” bit resolution higher than the actual ADC resolution. Be careful with this: software enhancement is done via filtering, and you need to be aware of the possible resulting changes to your measurement bandwidth. Two resources with more details on this mode include the ECN magazine article “How To Get More than 8 Bits from Your 8-bit Scope” and the Teledyne LeCroy application note “Enhanced Resolution.” Remember that a 12-bit, 100-MHz bandwidth oscilloscope is not the same as an 8-bit, 100-MHz bandwidth oscilloscope with resolution enhancement!

Using the oscilloscope’s fast Fourier transform (FFT) mode (normally advertised as the spectrum analyzer mode), we can see the difference a higher-resolution ADC makes. When looking at a waveform on the screen, you may think that you don’t care at all about 14-bit accuracy or something similar. However, if you plan to do measurements such as total harmonic distortion (THD), or otherwise need accurate information about frequency components, having high resolution may be extremely important to achieve a reasonable dynamic range.

As a theoretical example I’m using my script mentioned earlier, which will digitize a perfect sine wave and then display the frequency spectrum. The number of bits in the ADC (e.g., quantization) is adjustable, so the harmonic component is solely due to quantization error. This is shown in Figure 4. If you want to see a version of this using a real instrument, I conduct a similar demonstration in this video.

Certain applications may find the higher bit resolution a necessity. For example, if you are working in high-fidelity audio applications, you won’t be too worried about an extremely high sample rate, but you will need the high resolution.

Figure 4: In the frequency domain, the effect of limited quantization bits is much more apparent. Here a 10-MHz pure sine wave frequency spectrum is taken using a different number of bits during the quantization process.

Figure 4: In the frequency domain, the effect of limited quantization bits is much more apparent. Here a 10-MHz pure sine wave frequency spectrum is taken using a different number of bits during the quantization process. (CLICK TO ZOOM)

Coming Up
This week I’ve taken a look at some of the core specifications. I hope the questions to ask when purchasing an oscilloscope are becoming clearer! Next week, I’ll be looking at the software running the oscilloscope, and details such as remote control, FFT features, digital decoding, and buffer types. The fourth and final week will delve into a few remaining features such as external trigger and clock synchronization and will summarize all the material I’ve covered in this series.

Author’s note: Every reasonable effort has been made to ensure example specifications are accurate. There may, however, be errors or omissions in this article. Please confirm all referenced specifications with the device vendor.

An Organized Space for Programming, Writing, and Soldering

AndersonPhoto1

Photo 1—This is Anderson’s desk when he is not working on any project. “I store all my ‘gear’ in a big plastic bin with several smaller bins inside, which keeps the mess down. I have a few other smaller storage bins as well hidden here and there,” Anderson explained.

AndersonPhoto2

Photo 2—Here is Anderson’s area set up for soldering and running his oscilloscope. “I use a soldering mat to protect my desk surface,” he says. “The biggest issue I have is the power cords from different things getting in my way.”

Al Anderson’s den is the location for a variety of ongoing projects—from programming to writing to soldering. He uses several plastic bins to keep his equipment neatly organized.

Anderson is the IT Director for Salish Kootenai College, a small tribal college based in Pablo, MT. He described some of his workspace features via e-mail:

I work on many different projects. Lately I have been doing more programming. I am getting ready to write a book on the Xojo development system.

Another project I have in the works is using a Raspberry Pi to control my hot tub. The hot tub is about 20 years old, and I want to have better control over what it is doing. Plus I want it to have several features. One feature is a wireless interface that would be accessible from inside the house. The other is a web control of the hot tub so I can turn it on when we are still driving back from skiing to soak my tired old bones.

I am also working on a home yard sprinkler system. I laid some of the pipe last fall and have been working on and off with the controller. This spring I will put in the sprinkler heads and rest of the pipe. I tend to like working with small controllers (e.g., the Raspberry Pi, BeagleBoard’s BeagleBone, and Arduino) and I have a lot of those boards in various states.

Anderson’s article about a Raspberry Pi-based monitoring device will appear in Circuit Cellar’s April issue. You can follow him on Twitter at @skcalanderson.

Evaluating Oscilloscopes (Part 1)

Recently, I was in the market for a new oscilloscope. There’s a good selection of devices for sale, but which should you choose? It’s clear from the ads that the “scope bandwidth” and “sample rate” are two important parameters. But are there other things hidden in the specification sheet you should take a look at?

I’ve compiled notes from my own oscilloscope-selection experience and wanted to share them with you. I’ll be pulling in specifications and examples from a few different oscilloscopes. Personally, I ended up selecting a PicoScope device, so I will be featuring it more prominently in my comparisons. But that’s simply because I don’t have a lab full of oscilloscopes to photograph! I don’t work for Pico Technology or have any affiliation with it, and will be attempting to pull in other manufacturers for this online series to provide some balance.

This “mini-series” will consist of four posts over four weeks. I won’t be discussing bandwidth and sample rate until next week. In this first post, I’ll cover some physical characteristics: stand-alone vs PC-based probe types and digital inputs. Next week I’ll discuss the “core” specifications, in particular the bandwidth, sample rate, and analog-to-digital converter resolution. The  third week will look at the software running the oscilloscope, and details such as remote control, fast Fourier transform (FFT) features, digital decoding, and buffer types. The final week will consider a few remaining features such as the external trigger and clock synchronization, and will summarize all the material I’ve covered.

I hope you find it useful!

Topic 1: Do You Want a PC-Based or Stand-Alone Instrument?
There are two fundamentally different types of instruments, and you’ll have to decide for yourself which you prefer. Many people like a stand-alone instrument, which you can place on your bench and probe your circuits to your heart’s content. You don’t need to have your computer nearby, and you have something solely dedicated to probing.

Figure 1: PC-based oscilloscopes make it easier to mount on a crowded bench. This PicoScope 6000 unit is velcroed to my desk, you can see the computer monitor to the upper left.

Photo 1: PC-based oscilloscopes make mounting easier on a crowded bench. This PicoScope 6000 unit is velcroed to my desk. You can see the computer monitor to the upper left.

The other option is a PC-based instrument, which today generally means it plugs in via USB. I’ve always preferred this type for a few reasons. The first is the minimal desk space needed. I can place an oscilloscope vertically and lose little space (see Photo 1). The second is I find it easier to interact with a standard keyboard and mouse, especially if you’re using more advanced features. In addition, you can easily save screenshots or data from the scope without having to transfer them using a USB key or something similar.

There are a few downsides to USB-based instruments. The most common complaint is probably the lack of knobs, although that’s fixable. In Photo 2, you can see a USB-based “knob board” I built, which pretends to be a USB key. Each turn of the knob sends a keystroke and, as long as your PC-based oscilloscope software lets you set custom keyboard shortcuts, can trigger features such as changing the input range or timebase. Most of the time, I still just use the regular PC interface, as I find it easier than knobs. If you’re interested in the design, you can find it on my blog Electronics & More.

Photo: A simple USB-based knob board uses mechanical encoders to control the USB scope via a physical panel.

Photo 2: A simple USB-based knob board uses mechanical encoders to control the USB scope via a physical panel.

Having a PC-based oscilloscope also means you can have a massive screen. A high-end oscilloscope will advertise a “large 12.1″ screen,” but you can purchase a 22″ screen for your computer for $200 or less.  If your PC-based oscilloscope software supports multiple “viewports,” you can more easily set up complex displays such as that in Figure 1.
Again this comes down to personal preference—personally, I like having the oscilloscope display as a window on my computer. You may wish to have a dedicated display separate from your other work, in which case consider a stand-alone device!

Figure 1: PC-based oscilloscopes make it easier for setting up windows in specific positions, due to a combination of much larger screen space and standard mouse/keyboard interaction.

Figure 1: PC-based oscilloscopes make it easier for setting up windows in specific positions, due to a combination of much larger screen space and standard mouse/keyboard interaction.

Topic 2: Where’s the Ground?
One common complaint with the PC-based oscilloscope is that the probe ground connects to USB ground. Thus, you need to ensure there isn’t a voltage difference between the ground of your device under test and the computer.

This is, in fact, a general limitation of most oscilloscopes, be they stand-alone or PC-based. If you check with an ohmmeter, you’ll generally find that the ”probe ground”  in fact connects to system Earth on stand-alone oscilloscopes. Or at least it did on the different Agilent units I tested. Thus the complaint is somewhat unfairly leveled at PC-based devices.

You can get oscilloscopes that have either “differential” or “isolated” inputs, which are designed to eliminate the problem of grounds shorting out between different inputs. They may also give you more measurement flexibility. For example, if you are trying to measure the voltage across a “high-side shunt resistor,” you can do this measurement differentially. The TiePie engineering  HS4 DIFF is one example of a device with this capability. Of course, you can purchase differential probes for any oscilloscope, which accomplish the same goal! Most manufactures make these differential probes (Agilent, Tektronix, Pico Technology, Rigol, etc.).

Topic 3: Input Types
Almost every scope will have either DC-coupled or AC-coupled inputs. You’ll likely want to compare the minimum/maximum voltage ranges the scope has. Don’t be too distracted by either the upper or lower limits unless you have very specific requirements. At the upper end, remember you will mostly be using the 10:1 probe, which means an oscilloscope with ±20 V input range becomes ±200 V with the 10:1 probe.

At the lower end, the noise is going to kill you. If your oscilloscope has a 1 mV/div range, for example, you’ll have to be extremely careful with noise. To probe very small signals, you’ll probably end up needing an active probe with amplification right at the measurement point. This can be something you build yourself, using a differential amplifier chip, for example, if you are attempting to measure current across a shunt.

Besides the actual measurement range, you’ll be interested in the “offset” range too. With the DC-input, most oscilloscopes can subtract a fixed voltage from the input. Thus you can measure a 1.2-V input on a 1-V maximum input range, as the oscilloscope is able to first subtract say 1 V from the signal. This is handy if you have a smaller signal riding on top of some fixed voltage.

Another input type you will encounter is the 50-Ω input. Normally, this means the oscilloscope can switch between AC, DC, and DC 50 input types. The DC 50 means the input is “terminated” with a 50-Ω impedance. This feature is typically found on oscilloscopes with higher analog bandwidth. For example, this allows you to measure a clock signal that is output on a SMA connector expecting a 50-Ω termination. In addition, the 50-Ω input allows you to simplify connection of other lab equipment to your oscilloscope. Want to use a low noise amplifier (LNA) to measure a very small signal? Not a problem, since you can properly terminate the output of that LNA.

If you end up needing DC 50 termination, you can buy “feed-through” terminators for about $15, which operate at up to 1-GHz bandwidth. You simply add those to the front of your oscilloscope to get 50-Ω terminated inputs.

Any given manufacturer will often have a range of inputs for different bandwidths and models. For example, the PicoScope 5000-series, which has up to 200-MHz bandwidth, has DC/AC high-impedance inputs. The 6000-series has DC/AC/DC 50 inputs for 500-MHz bandwidth and below. The 6000 series in 1,000 MHz bandwidth only has 50-Ω input impedance. Other manufacturers seem to follow a similar formula: the highest bandwidth device is 50-Ω input only, medium-bandwidth devices are DC/AC/DC 50, and lower-bandwidth devices will be DC/AC.

Topic 4: Probe Quality and Type
In day-to-day use, nothing will impact you more than the quality of your oscilloscope probe. This is your hands-on interaction with the oscilloscope.

Figure 4: A smaller spring-loaded probe tip is on the left,  and  a standard oscilloscope probe is on the right. Both  probes have removable tips, so if you damage the probe it’s easy to fix them. Not all probes have removable tips, however, meaning if the tip is damaged you may have to throw out the probe.

Photo 3: A smaller spring-loaded probe tip is on the left, and a standard oscilloscope probe is on the right. Both probes have removable tips, so if you damage the probe it’s easy to fix them. Not all probes have removable tips, however, meaning if the tip is damaged you may have to throw out the probe.

Most “standard” oscilloscope probes are of the type pictured to the right in Photo 3. They are normally switchable from 1:1 to 10:1 attenuation, where the 10:1 mode results in a 1/10 scaling of input voltage. It’s important to note that almost every oscilloscope probe has very limited bandwidth in 1:1 mode—often under 10 MHz. Whereas in 10:1 mode it might be 300 MHz! In addition, the 10:1 mode will load the circuit considerably less. Higher bandwidth probes will often only come in 10:1 mode. I assume the physical switch is too much hassle at higher frequencies!

A first thing to check out is if the tip is removable. If you damage the tip, it can be useful to simply replace the tip rather than the entire probe. If you’re probing a PCB, it can be easy to catch a tip in a via, for example. Alternatively, certain probes might come with an adapter, which is designed for use in probing the PCB, rather than just the tip of the regular oscilloscope probe. The older Agilent 1160A probes come with such a tip.

One particular type of probe I really like has the spring-loaded tip shown to the left in Photo 3. This is a much smaller tip than “standard,” and the spring-loaded tip makes it much easier to get a good connection with solder joints. You can apply some pressure to break through the oxide layer, and the spring-loaded aspect keeps the tip right on the joint. In addition, you can even do things such as probe through the solder mask on a via. There are even plastic guard add-ons, which fit standard surface mount device (SMD) sizes (e.g., 1.27 mm, 1 mm, 0.8 mm, 0.5 mm) to probe TQFP/SOIC/TSSOP packages.

The particular probe I’m photographing comes with the PicoScope 6000 series, which is sold separately as part number TA150 (350-MHz bandwidth) or TA133 (500-MHz bandwidth). However, I’ve noticed that Agilent seems to also sell a probe that looks the same—under part number N287xA—right down to accessories. Similarly, Teledyne LeCroy also seems to sell this probe under the PP007 part number, and Rohde & Schwarz sells it under the RTM-ZP10 part number, also with the same accessories. Thus I suspect there is some upstream manufacturer! Depending on your supplier and options, prices range from $200-$400 for the probe if you want to pick it up separately.

Photo 5: The ground spring accessory can be used in a number of ways. If you're lucky, you can insert it into GND  vias on your PCB. If required, you can also solder a small section of wire to the spring.

Photo 4: The ground spring accessory can be used in a number of ways. If you’re lucky, you can insert it into GND vias on your PCB. If required, you can also solder a small section of wire to the spring.

Pomona Electronics sells a similar probe, part numbers 6491 through 6501 (the exact partnumber depending on bandwidth). The 150-MHz version (6493) is available for under $60 from Digi-Key, Mouser, and Newark element14, for example. This probe differs from the previous group of spring-loaded ones, but if you don’t need the higher bandwidth it may be a more reasonable purchase.

If you are dealing with a high-bandwidth probe, you may need to be concerned about the flatness of the frequency response. A probe may be sold with a 1G-Hz bandwidth, for example, which simply means the -3-dB point is at 1GHz. However, shoddy manufacturing may mean not having a very flat frequency response before that point, or not rolling off evenly after the -3-dB point.

When dealing with high bandwidth probes, the grounding will become a serious issue. The classic “alligator clip” probably won’t cut it anymore! The simplest accessory your probe is likely to come with is the spring adapter shown in Photo 4. There may be more advanced accessories available for grounding, too; check documentation for the probe itself. You can see an example of differences in grounding as part of my “probe review”  video.

Don’t be afraid to build your own accessories for the probe. Photo 5 shows a probe holder I built for a $15 adjustable arm. Details of the construction are here.

Here’s a simple 3-D probe holder you can build for $20 or less.

Photo 5: Here’s a simple 3-D probe holder you can build for $20 or less.

Topic 5: Digital Input?
The final item to consider is if you want digital inputs along with analog. This is, again, somewhat of a personal choice: You may wish to have a separate stand-alone digital analyzer, or you may wish to have it built into your oscilloscope.

I personally chose to have a stand-alone digital logic analyzer, which is a PC-based instrument. Digital logic analyzers are available at a fairly low cost from a variety of manufacturers (e.g., Saleae and Intronix). In my experience, the cost of purchasing a separate PC-based logic analyzer was considerably lower than the “incremental cost” of selecting an oscilloscope with logic analyzer capabilities compared to one without. When evaluating this yourself, be sure to look at features such as number of channels, maximum sample rate, buffer size, and what protocols can be decoded by the logic analyzer.

While integrated-device manufacturers claim you should buy a scope/analyzer in one unit to get perfect synchronization between digital and analog, remember many of these devices can output a trigger signal. So if your oscilloscope can output a trigger signal when it starts the analog capture, you can use this to capture the corresponding data on the digital logic analyzer (or vice versa).

Next Week: Core Specifications
This first week I covered physical details of the oscilloscope itself you might want to consider. Next week, I’ll look at the more ‘”core” specifications such as bandwidth, sample rate, and sample resolution.

Author’s note: Every reasonable effort has been made to ensure example specifications are accurate. There may, however, be errors or omissions in this article. Please confirm all referenced specifications with the device vendor.

 

Experimenting with Dielectric Absorption

Dielectric absorption occurs when a capacitor that has been charged for a long time briefly retains a small amount of voltage after a discharge.

“The capacitor will have this small amount of voltage even if an attempt was made to fully discharge it,” according to the website wiseGEEK. “This effect usually lasts a few seconds to a few minutes.”

While it’s certainly best for capacitors to have zero voltage after discharge, they often retain a small amount through dielectric absorption—a phenomenon caused by polarization of the capacitor’s insulating material, according to the website. This voltage (also called soakage) is totally independent of capacity.

At the very least, soakage can impair the function of a circuit. In large capacitor systems, it can be a serious safety hazard.

But soakage has been around a long time, at least since the invention of the first simple capacitor, the Leyden jar, in 1775. So columnist Robert Lacoste decided to have some “fun” with it in Circuit Cellar’s February issue, where he writes about several of his experiments in detecting and measuring dielectric absorption.

Curious? Then consider following his instructions for a basic experiment:

Go down to your cellar, or your electronic playing area, and find the following: one large electrolytic capacitor (e.g., 2,200 µF or anything close, the less expensive the better), one low-value discharge resistor (100 Ω or so), one DC power supply (around 10 V, but this is not critical), one basic oscilloscope, two switches, and a couple of wires. If you don’t have an oscilloscope on hand, don’t panic, you could also use a hand-held digital multimeter with a pencil and paper, since the phenomenon I am showing is quite slow. The only requirement is that your multimeter must have a high-input impedance (1 MΩ would be minimum, 10 MΩ is better).

Figure 1: The setup for experimenting with dielectric absorption doesn’t require more than a capacitor, a resistor, some wires and switches, and a voltage measuring instrument.

Figure 1: The setup for experimenting with dielectric absorption doesn’t require more than a capacitor, a resistor, some wires and switches, and a voltage measuring instrument.

Figure 1 shows the setup. Connect the oscilloscope (or multimeter) to the capacitor. Connect the power supply to the capacitor through the first switch (S1) and then connect the discharge resistor to the capacitor through the second switch (S2). Both switches should be initially open. Photo 1 shows you my simple test configuration.

Now turn on S1. The voltage across the capacitor quickly reaches the power supply voltage. There is nothing fancy here. Start the oscilloscope’s voltage recording using a slow time base of 10 s or so. If you are using a multimeter, use a pen and paper to note the measured voltage. Then, after 10 s, disconnect the power supply by opening S1. The voltage across the capacitor should stay roughly constant as the capacitor is loaded and the losses are reasonably low.

Photo 1: My test bench includes an Agilent Technologies DSO-X-3024A oscilloscope, which is oversized for such an experiment.

Photo 1: My test bench includes an Agilent Technologies DSO-X-3024A oscilloscope, which is oversized for such an experiment.

Now switch on S2 long enough to fully discharge the capacitor through the 100-Ω resistor. As a result of the discharge, the voltage across the capacitor’s terminals will quickly become very low. The required duration for a full discharge is a function of the capacitor and resistor values, but with the proposed values of 2,200 µF and 100 Ω, the calculation shows that it will be lower than 1 mV after 2 s. If you leave S2 closed for 10 s, you will ensure the capacitor is fully discharged, right?

Now the fun part. After those 10 s, switch off S2, open your eyes, and wait. The capacitor is now open circuited, at least if the voltmeter or oscilloscope input current can be neglected, so the capacitor voltage should stay close to zero. But you will soon discover that this voltage slowly increases over time with an exponential shape.

Photo 2 shows the plot I got using my Agilent Technologies DSO-X 3024A digital oscilloscope. With the capacitor I used, the voltage went up to about 120 mV in 2 min, as if the capacitor was reloaded through another voltage source. What is going on here? There aren’t any aliens involved. You have just discovered a phenomenon called dielectric absorption!

Photo 2: I used a 2,200-µF capacitor, a 100-Ω discharge resistor, and a 10-s discharge duration to obtain this oscilloscope plot. After 2 min the voltage reached 119 mV due to the dielectric absorption effect.

Photo 2: I used a 2,200-µF capacitor, a 100-Ω discharge resistor, and a 10-s discharge duration to obtain this oscilloscope plot. After 2 min the voltage reached 119 mV due to the dielectric absorption effect.

Nothing in Lacoste’s column about experimenting with dielectric absorption is shocking (and that’s a good thing when you’re dealing with “hidden” voltage). But the column is certainly informative.

To learn more about dielectric absorption, what causes it, how to detect it, and its potential effects on electrical systems, check out Lacoste’s column in the February issue. The issue is now available for download by members or single-issue purchase.

Lacoste highly recommends another resource for readers interested in the topic.

“Bob Pease’s Electronic Design article ‘What’s All This Soakage Stuff Anyhow?’ provides a complete analysis of this phenomenon,” Lacoste says. “In particular, Pease reminds us that the model for a capacitor with dielectric absorption effect is a big capacitor in parallel with several small capacitors in series with various large resistors.”