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Having already examined the Colpitts oscillator, we now look at its first cousin, the Clapp oscillator.

Please consider the following illustration in Figure 1.

Figure 1 A Clapp oscillator where the passive components are arranged on the right-hand side for easier viewing. Source: John Dunn

There is an R-L-C network of passive components and an active gain block. This circuit differs from the Colpitts by now using a third capacitor (C3) in series with the inductance (L1) and by now needing a DC path: R2, to ground for the gain block. The output impedance of the gain block is zero and the value of its gain (A) is nominally unity or perhaps a little less than unity. The resistance R1 models the output impedance that a real-world gain block might present.

To analyze this circuit, we take the passive components, redraw them as on the right in Figure 1 and where G1 = 1 / R1, G2 = 1 / R2, and the term S = j / ( 2*π*F), we use node analysis to derive the transfer function E1 / Eo.

The analysis for the Clapp circuit is rather more involved than it was for the Colpitts circuit so for the sake of clarity, I have omitted it here. However, my handwritten notes of that analysis can be seen at the end of this essay. Try not to strain your eyes.

The end result is an expression of the transfer function in a useful form as follows in Figure 2.

Figure 2 Algebraic expression of transfer function for the Clapp oscillator shown in Figure 1. Source: John Dunn

Note that the denominator of this equation is fourth order. It is a fourth order polynomial because there are four independent reactive elements in the circuit, L1, C1, C2 and C3.

Please also note that the order of the polynomial MUST match the number of independent reactive elements in the circuit. If we had come up with an algebraic expression of some other order, we would know we’d made a mistake somewhere.

Graphing the ratio of E1/Eo versus frequency, we see the following in Figure 3.

Figure 3 E1/Eo versus frequency from algebraic analysis. Source: John Dunn

The transfer function of the passive R-L-C network has a pronounced peak at a frequency of 1.62 MHz and a null at a slightly lower frequency. When we run a spice simulation of that transfer function, we find very nearly the same result (Figure 4). I blame the differences on software numerical accuracy issues.

Figure 4 E1/Eo versus frequency from SPICE Analysis. Source: John Dunn

When we let our gain block be a voltage follower—a JFET source follower in the following example—we see oscillation at the frequency of that transfer function peak as shown in Figure 5.

Figure 5 Clapp Oscillator simulation after letting our gain block be a voltage follower. Source: John Dunn

The algebraic derivation of the Clapp oscillator transfer function is shown in handwriting in Figure 6.

Please forgive the handwriting. I just didn’t have the patience to turn this into a printout.

Figure 6 John Dunn’s transfer function derivation. Source: John Dunn

John Dunn is an electronics consultant, and a graduate of The Polytechnic Institute of Brooklyn (BSEE) and of New York University (MSEE).

Related Content

• The Colpitts oscillator
• Emitter followers as Colpitts oscillators
• Simulation trouble: Bode plotting an oscillator
• Oscillator has voltage-controlled duty cycle

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As a genre, DACs are low power devices with power and current output capabilities limited to the milliwatt and milliampere range. There is, of course, no fundamental reason they can’t be teamed up with suitable power output stages, which is indeed common practical practice. Problem solved.

Wow the engineering world with your unique design: Design Ideas Submission Guide

But just for fun, this design idea takes a different path to power by merging a venerable (the “L” stands for “legacy!”) LM337 regulator into a simple (just two generic active chips) 8-bit PWM DAC to obtain a robust 1.5-A capability. It also enjoys the inherent overload and thermal protection features of that time-proven Bob Pease masterpiece.

As an extra added zero cost feature, output voltage accuracy is (mostly: ~90%) determined by the + 2% (guaranteed, typically much better) precision of the LM337 internal voltage reference, rather than relying on the sometimes-dodgy stability of a logic supply rail as basic PWM DACs often do.

Figure 1 shows the circuit.

Figure 1 LM337 joins forces with 4053 CMOS switch to make a macho PWM DAC.

 Metal gate CMOS SPDT switches U1a and U1b accept a 10-kHz PWM 5v signal to generate a +1.25 V to -8.75 V “ADJ” control signal for the U2 regulator. ADJ = +1.25 V causes U2 to output 0 V. It has always struck me somehow strange that a negative regulator like the 337 sometimes needs a positive control signal (in this case for Vout less negative than -1.25 V), but it does. ADJ = -8.75 V makes it make -10 V. 

U1c generates an inverse of the PWM signal, providing active ripple cancellation as described in “Cancel PWM DAC ripple with analog subtraction.”

Current source Q1 reduces zero offset error by nulling the ~65 µA (typical) ADJ pin bias current. The feedback loop established via R2 and R3 makes full-scale -10 V output proportional to U2’s internal reference as previously mentioned.

This does, however, make output voltage a nonlinear function of PWM duty factor with functionality (DF from 0 to 1): Vout = -1.25 DF / (1 – 0.875 DF) as graphed in Figure 2.

 Figure 2 Graph of Vout (0 V to -10 V) versus the PWM duty factor (0 to 1).
[Vout = -1.25 DF / (1 – 0.875 DF)]

 Figure 3 plots the inverse of Figure 2, yielding the PWM DF required for a given Vout.

 Figure 3 Graph of the PWM duty factor (0 to 1) versus Vout (0 V to -10 V).
[PWM DF = Vout / (0.875*Vout – 1.25)]

For the corresponding 8-bit PWM setting Dbyte = 256 DF = 256 Vout / (0.875*Vout – 1.25).

The negative supply rail (V-) can be anything between -13 V (to accommodate U2’s minimum headroom requirement) and -15 V (in recognition of U1’s maximum voltage rating). DAC accuracy will be unaffected. 

U2 should be adequately heatsunk as dictated by heat dissipation equal to output current multiplied by the V- to Vout differential. Up to double-digit Watts are possible. The 337s go into thermal shutdown at junction temperatures above 150oC, so make sure it will pass the wet-forefinger-sizzle “spit test!”

Stephen Woodward’s relationship with EDN’s DI column goes back quite a long way. Over 100 submissions have been accepted since his first contribution back in 1974.

 Related Content

• Cancel PWM DAC ripple with analog subtraction
• Cancel PWM DAC ripple with analog subtraction—revisited
• Cancel PWM DAC ripple with analog subtraction but no inverter
• Cancel PWM DAC ripple and power supply noise
• Fast PWM DAC has no ripple
• Fast-settling synchronous-PWM-DAC filter has almost no ripple
• Minimizing passive PWM ripple filter output impedance: How low can you go?

The post 0 V to -10 V, 1.5 A LM337 PWM power DAC appeared first on EDN.

Infineon has announced FreeRTOS support for its 32-bit AURIX TC3x family of automotive and industrial microcontrollers. As a key software layer, the RTOS manages both hardware and software resources, ensuring reliable and timely task execution. Acting as a bridge between the hardware and application software, it simplifies development by abstracting hardware complexities. This approach enhances portability and code reusability, streamlining the development process and reducing time-to-market.

FreeRTOS is a widely used, open-source real-time operating system actively supported and developed by Amazon Web Services (AWS). AWS also offers middleware libraries for FreeRTOS, enabling seamless integration with its cloud services.

“The availability of FreeRTOS enables customers to rapidly build applications on a well-established and feature-rich open-source environment,” said Patrick Will, head of Software Product Management and Marketing for Automotive Microcontrollers at Infineon. “This integration facilitates quick feature evaluation on the AURIX TC3x and provides our customers with an accelerated migration path for non-AUTOSAR projects, particularly in the automotive and industrial markets.”

TriCore AURIX TC3x MCUs offer ASIL-D/SIL-3 compliance and advanced safety features, as well as scalable feature sets and pinouts. The FreeRTOS kernel port for the AURIX TC3x is available here. Corresponding code samples can be found here.

AURIX TC3x product page

Infineon Technologies 

Find more datasheets on products like this one at Datasheets.com, searchable by category, part #, description, manufacturer, and more.

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MIFARE DOUX, NXP’s contactless near-field communication (NFC) chip, integrates asymmetric and symmetric cryptography in one IC to simplify key management and distribution. The smart card IC enhances security for EV charging authentication, vehicle access, and other access management applications.

Leveraging public-key infrastructure (PKI), the chip supports asymmetric elliptic curve cryptography (ECC) and symmetric AES-256 cryptography. Additional features include a proximity check to counter relay attacks and transaction signatures to validate NFC transaction authenticity.

MIFARE DUOX holds Common Criteria EAL 6+ certification for both hardware and software, making it well-suited for high-security applications. Built for demanding environments, including outdoor and automotive use, it complies with ISO/SAE 21434 and MISRA-C standards and operates across an extended temperature range of -40°C to +105°C.

The MIFARE DUOX contactless smart card IC is now available.

MIFARE DUOX product page

NXP Semiconductors 

Find more datasheets on products like this one at Datasheets.com, searchable by category, part #, description, manufacturer, and more.

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The u-blox SARA-R10001DE LTE Cat 1bis module integrates Wireless Logic’s Conexa embedded SIM (eSIM) for global IoT connectivity. Supporting multi-IMSI technology and eUICC, the eSIM streamlines connectivity management by enabling automatic network switching based on coverage, cost, and regulatory needs.

The SARA-R10001DE supports full LTE Cat 1bis band coverage and comes provisioned with multiple Wireless Logic SIM profiles, permitting global deployment with a single SKU. In addition to working seamlessly upon deployment, the eSIM can also be remotely configured through Remote SIM Provisioning (RSP). It also enhances resilience by automatically switching to the best network available to ensure uninterrupted service in diverse regions.

Designed for LTE global coverage, the single-mode SARA-R10001DE provides a straightforward upgrade path for replacing legacy 2G and 3G devices with 4G LTE technology. The 16×26×2.2-mm module includes UART, USB, and GPIO interfaces and operates over a temperature range of -40°C to +85°C.

SARA-R10001DE product page 

u-blox

Find more datasheets on products like this one at Datasheets.com, searchable by category, part #, description, manufacturer, and more.

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Identiv’s high-frequency NFC-enabled inlays leverage NXP’s ICODE 3 tag IC, boosting RF performance and read speed. Designed for IoT applications, the ICODE 3 chip includes features suited for healthcare, logistics, industrial use, smart packaging, and specialty retail.

Identiv’s 13.56-MHz ID-Tune I3 and ID-Safe I3 inlays support both vicinity-range operation, reaching up to 1.5 meters, and close-range interactions. In vicinity mode, improved readability, material compatibility, and fast data transfer ensure seamless integration and increase operational efficiency. For close-range use, features such as first-opening indication and flexible counters enhance user engagement and product interactivity.

Key features of the ICODE 3-based inlays include:

• ISO/IEC 15693 and NFC Forum Type 5 tag compliance
• Read rate of up to 212 kbps
• One-lock memory command for tag encoding
• Customizable originality signature of 32 or 48 bytes
• Automatic SELFAdjust mechanism optimizes RF performance across different materials and conditions
• Two password-protected untraceable modes
• Extended NFC features for serialized, dynamic, and contextual messaging when tapped with an NFC-enabled phone

For more information about the ID-Tune I3 and the ID-Safe I3, which includes tamper detection, click on the product page links below.

ID-Tune I3 product page

ID-Safe I3 product page 

Identiv

Find more datasheets on products like this one at Datasheets.com, searchable by category, part #, description, manufacturer, and more.

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PROFET Wire Guard high-side switches from Infineon provide built-in I2t wire protection for 12-V automotive power distribution. According to the manufacturer, these devices more accurately emulate wire stress characteristics compared to conventional fuses by using a selectable I2t protection curve, with six options tailored to specific application requirements.

In addition to I2t protection, the switches offer adjustable overcurrent protection for fast fault isolation and sequential diagnostics, enabling wire harness optimization when replacing mechanical relays and fuses. PROFET Wire Guard smart switches handle currents up to 27 A and a maximum operating voltage of 28 V. A low-power automatic idle mode reduces current consumption to just 50 µA during vehicle parking, while the output stage remains fully switched on.

The five PROFET Wire Guard devices offer pin-to-pin compatibility within the family and come in TSDSO-14 and TSDSO-24 packages. They have been developed and released as ISO 26262:2018 Safety Elements Out of Context (SEooC) for safety requirements up to ASIL D

PROFET Wire Guard product page

Infineon Technologies 

Find more datasheets on products like this one at Datasheets.com, searchable by category, part #, description, manufacturer, and more.

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Further to my prior coverage of this year’s iteration of periodic lightning-damage debacles at my Rocky Mountain foothills residence, I’d earlier mentioned that among the pieces of electronics gear that bit the dust this time was one of my network storage devices (NASs). The setback compelled me to no longer ignore a longstanding chink in my data-backup armor, which I’ve subsequently patched. What it was, and how I fixed it, is the subject of today’s post.

Simplistically speaking, there are (at least) three main ways that a storage device’s data can become compromised:

• If a virus, ransomware or other malware corrupts it, either via a computer it’s directly connected to, another device on the LAN, or a WAN-sourced attack, scenarios for which QNAP offers regularly executed (and updated) integrated scan-and-alert support.
• If a hard drive (or SSD, in some cases) fails. That’s why at minimum my NASs are all dual-drive setups, enabling RAID 1 redundancy, and they preferably contain at least three drives to add RAID 5-delivered performance to the mix, too.
• If the storage device itself dies; the power supply, for example, or something on the motherboard. Sometimes the failing component is straightforward to replace, but other times the NAS is destined only for the teardown pile, followed by the landfill.

The latter situation is the one I encountered recently. As background, I had two NASs active on my network at the time. My four-drive QNAP TS-453Be holds my music and photo libraries, along with decades’ worth of other accumulated personal files:

Its sibling beside it, a three-drive TS-328:

is my network backup destination. Part of the available capacity acts as a Time Machine repository for my Macs, while the remainder handles our various Windows machines, via a combo of File History and the legacy (and deprecated, but still included) Backup and Restore, both of which I’ll likely replace with something third-party and more modern sooner vs later.

The TS-328 is the one that died earlier this year. Although I could still get it to emit a factory-reset “beep”, firmware recovery attempts were fruitless; I’m guessing something(s) vital on the motherboard had fried (a common issue with this model, not just in response to an external “zap”, so I already knew I was running on borrowed time). While its stored data was less critical than that on the TS-453Be, since thankfully none of the computers previously backing up to it had themselves also failed, I wanted to get backup back up (heh heh) and running as quickly and straightforwardly as possible. And clearly, had the TS-453Be failed instead (or in addition), I would have had a more acute situation on my hands.

Step one: resurrect the TS-328. I found a gently used one on eBay (for nearly $100 more than I’d paid for my brand new one five-plus years earlier, although the seller did also throw in a used eight-port GbE switch, but I digress…), which was shipped and arrived promptly. I pulled the HDDs out of the original TS-328 and reinstalled them in the new-to-me NAS in the same order as before. And then I crossed my fingers and punched the power button.

Huzzah; it booted! Since the replacement NAS had only recently been retired by its previous owner, I’d gambled that its firmware version was close-to-identical to that in my expired device, which ended up being the case. There was only a minor discrepancy between the new NAS’s motherboard firmware version and the newer one stored on my old NAS’s drives, which I was alerted to and an online-supplied firmware update remedied. And speaking of online, I was glad to see that QNAP’s cloud service was smart enough to notice that the device now mated to my HDDs, therefore to my online account, had different hardware than was previously the case (a new MAC address at minimum) and insisted that I re-login and -associate the NAS with it first.

Now to fix my setup’s “chink in the armor” resulting from full-NAS failure potential. Some of you may already be familiar with the “3-2-1 backup rule”; Wikipedia has a concise summary:

The 3-2-1 rule…states that there should be at least 3 copies of the data, stored on 2 different types of storage media, and one copy should be kept offsite, in a remote location (this can include cloud storage). 2 or more different media should be used to eliminate data loss due to similar reasons (for example, optical discs may tolerate being underwater while LTO tapes may not, and SSDs cannot fail due to head crashes or damaged spindle motors since they do not have any moving parts, unlike hard drives). An offsite copy protects against fire, theft of physical media (such as tapes or discs) and natural disasters like floods and earthquakes.

While, as you’ll see in the paragraphs to follow, I’m not following the 3-2-1 rule to the most scrupulous degree—all of my storage devices are HDD-based, for example, and true offside storage would be bandwidth-usage prohibitive with conventional home broadband service—I feel, and hope you’ll agree, that I’ve followed it sufficiently, and that regardless the result is much more robust than it was before. It involves among other things pressing into service the two-drive QNAP TS-231K NAS that I’d also mentioned back in December 2020. I bought three (including a spare) 12 TByte used Hitachi enterprise SATA HDDs with five-year warranties for it from a well-known eBay retailer. Two of the three drives arrived reporting S.M.A.R.T warnings (197+198 sector count code combos, to be precise), but to the retailer’s credit, it replaced them promptly, even proactively sending replacements ahead of the originals’ return.

For my Macs, on which the “primary copy” of the data is stored, implementing the 3-2-1 rule was particularly straightforward. Modern MacOS versions support Time Machine configuration for multiple destinations, which the utility rotates among automatically for consecutive backups. While this means that each backup likely ends up being bigger (i.e., taking longer) than before, given that the precursor backup to that same destination was older than with a conventional single-destination alternative setup, it also means that if one destination fails, you’ve still got relatively current backups available at alternate destinations. In my case, there are two backup destinations, the Time Machine-tailored partitions on the TS-231K and TS-324. And counting the Mac source, you end up with three dataset copies total, if you’re not already keeping track.

What about the Windows systems? Again, the “primary copy” of the data is located on their SSDs. I run Backup and Restore sessions from them to the TS-324 every early-Saturday morning (since they tend to swamp Wi-Fi while in progress). And every early-Sunday morning, the QNAP HBS 3 Hybrid Backup Sync utility then does a full mirror of the archived Windows backup data from the TS-324 to the TS-231K (over Cat 5 this time, but still, why not do this while we’re still asleep?). This time, if one NAS fails, the backup data on the other NAS is no more than a week old. And once again, I end up with three total dataset copies.

The TS-453Be is a bit more complicated. Here, the primary copy of the data is stored on its four-HDD RAID 5 array. I’ve long had an external 2.5” HDD USB-tethered to it for daily sync purposes, which I can quickly grab (theoretically, at least) in case of fire or another emergency. And now, once again on Sunday mornings, the TS-453Be also does a full mirror to the TS-231K.

“Quickly grab” leads to my final discussion topic, involving the different-locations angle on the 3-2-1 rule. As I’ve already confessed, none of my backups are located offsite. However, I’ve installed the TS-231K upstairs in my office (at least for now, until I lose my sanity due to the constantly-clattering-HDDs din), still connected to the router over wired GbE, albeit now with a two-switch hop intermediary, as well as to the two other NASs and other LAN devices. And, as with the TS-324, the TS-453Be manages controlled shutdown of the TS-321K in response to premises power loss in coordination with their common NUT software and my APC UPS .

As I’ve mentioned before, the furnace room downstairs acts as my networking nexus. The probability for fire caused by the one of the furnaces (or any of the other equipment, for that matter) in that room is non-zero, and since that “other equipment” includes the hot water heater, fluid-delivered compromise of the NASs there is also a possibility. And given that “downstairs” is also “ground level”, an outside-sourced fire is also an ongoing concern, one accelerated of late due to climate change-induced environmental effects. But, thinking as I write these words, since my office is directly above the furnace room…yeah, having the TS-231K in my office probably isn’t wise, noise-wise or otherwise. Time to figure out somewhere else to put it.

With that, I’ll wrap up for today and welcome your thoughts in the comments!

—Brian Dipert is the Editor-in-Chief of the Edge AI and Vision Alliance, and a Senior Analyst at BDTI and Editor-in-Chief of InsideDSP, the company’s online newsletter.

Related Content

• Lightning strikes…thrice???!!!
• The whole-house LAN: Achilles-heel alternatives, tradeoffs, and plans
• NAS successors add notable features
• Disassembling a Cloud-compromised NAS
• Exposing a NAS security issue
• NAS failure launches a data recovery mission
• Teardown: Disposable 1-Tbyte NAS drives: How’d that happen?

The post Beefing up backup appeared first on EDN.

Usually, noise annoys. Occasionally, it can be a valuable tool. Surprisingly, there is a whole palette of noise colors. This design idea (DI) shows good ways of generating the commonest and most useful ones, which are white and pink and optionally brown. At its heart is a microcontroller programmed to generate raw white noise and a much-improved filter to convert that into pink.

Wow the engineering world with your unique design: Design Ideas Submission Guide

Sources of random electronic noise are all too common. The most controllable source of the white stuff is probably the well-known pseudo-random binary sequence (PBRS) generated by a shift register with feedback, and that will be our starting-point. A fairly standard implementation using logic ICs is shown in Figure 1.

Figure 1 A pseudo-random sequence generator (PRSG) built with standard logic ICs generates wideband white noise.

Three 8-bit devices (or dual 4-bit ones, as here) are concatenated to make a 23-bit shift register. The outputs from bits 18 and 23 are EXORed and inverted (or EXNORed) and fed back to the input, producing a pattern of bits which appears random though it repeats every 223-1 clock cycles, which at a clock rate of 240 kHz is about every 35 seconds. (That “-1” represents the illegal, locked-up, all-1s condition, against which the simple reset circuitry guards.) For frequencies up to about a tenth of the clock rate, the spectrum is virtually identical to that of pure and ideal white noise. It has the same intensity in any given bandwidth: its spectrum is flat. For other colors, we just need to filter it appropriately.

A cheap microcontroller makes a good PRSG

So far, so conventional. But why use 62-pins-worth of chippery plus at least ten discretes when a single package with 8 pins—or even fewer—will suffice? The schematic for that is too boring to show—imagine a rectangle fed with power (decoupled with a single cap) and having a GPIO pin delivering the PRBS—but here is the MPASM assembly-language code for doing it with on a Microchip 12F1501 PIC. (It should open cleanly with Notepad.) The code is logically and functionally identical to Figure 1’s circuit and can easily be modified for use in different low-end PICs, while the underlying logic can be ported to any other suitable µC. (Back in the day, NatSemi made the MM5837, an 8-pin, 15-V, PMOS white noise source using 17 stages. It’s long obsolete, but this could be a nice substitute for it.)

We now have pseudo-random white noise with a spectrum ranging roughly from 30 mHz to a few MHz, which is just a few more octaves than we need. (There are nulls at multiples of the bit rate, which is 267 kHz for this PIC version.) It’s still in the form of a pulse stream, which needs band-limiting before we have truly useful white noise. For pink noise, further filtering is needed so that all octaves (or other frequency ratios) have the same intensity, which is what we need for audio use. The circuitry to do all this is shown in Figure 2.

Figure 2 A pseudo-random signal—white noise—is tailored to fit within the audio band, and further filtered to produce pink noise as well.

The PRSG could use Figure 1’s discrete logic, but the micro version is electrically quieter (hah!) as well as being more compact and, ignoring programming overheads, cheaper. The pulse-shaping network turns the rail-to-rail rectangular pulse stream into trapezoids having a defined level (about 1.2 V pk-pk) and with slew rates less than those of the downstream op-amps. The 20 kHz low-pass filter does what it says. (That “20 kHz” isn’t its 3-dB corner, but a label for its function.) Only high-pass filtering from ~20 Hz is now needed to give white noise within the audio spectrum and at a level of just greater than -10 dBu.

A new and improved pink noise network

Pink noise is a little trickier and needs a more complex filter to give the necessary 3.01 dB/octave (10 dB/decade) slope. Most published solutions use four RC sections as well as the basic R and C shown in Figure 2 as R10 and C11, with some having even fewer. (And many appear to be clones.) Those RCs have their component values spaced by around √10, but some thought and playing with LTspice showed that far better results come from using a few more stages, and ratios close to the cube root of 10. Figure 3 shows the calculated response of Figure 2’s seven-stage network without the added high- or low-pass filters. Even with E12 component values, it is almost a straight line, unlike the clones’ responses.

Figure 3 The response of the new 7-stage pink noise filter, taken in isolation.

A gain stage brings the pink noise’s RMS level up to -10 dBu to match that of the white, while a selection switch, level-control pot, output buffer, and rail-splitter (A2d etc.) complete the design. Figure 4 shows the calculated response curves along with the worst-case deviations from ideal.

Figure 4 The calculated responses of the completed design, showing the mask for IEC 60268-1 limits and the peak errors of the filters.

The output is now within ±0.2 dB of the ideal from 24 Hz to 21 kHz. With slightly softer HP and LP filters even that could be improved on, especially by reducing the ripple at the ends of the spectrum, but they were calculated to meet the requirements of IEC 60268-1, which refers to the performance, testing, and application of audio systems.

Some further notes on the circuitry

Figure 2’s circuit was designed (and tested) to use a nominal 5 V (or ±2.5 V) rail (what are cheap power banks or surplus USB PSUs for?) but the extremes of 2.7 V (three end-of-life AA cells) and 5.5 V (USB limit) allow for other powering options.

The shaping network ensures that the output will be reasonably constant no matter what the rail voltage may be, and the signal levels of -10 dBu avert clipping even for low rail voltages. With a guaranteed 5 V supply, A2c could have about 7 dBs of extra gain before clipping starts. The output crest factor—the peak-to-RMS ratio—is fairly high, at around 5:1 or 14 dB.

A1a uses the MCP6022 rather than the MCP6004 (or MCP6002s, of course) because the latter can only just cope with the shaped pulses and distorts them noticeably. The gain needed after the pink noise network is rather high, so A1b is also a ’6022: faster, and with lower input offset. The ’6004 works fine in all the other positions. The components between A2c and the output aren’t mandatory, just good practice.

Current consumption was about 6 mA, unloaded.

Brown(ian) noise generation

Adding brown—or red, or Brownian—noise generation is simple, as sketched in Figure 5. All that’s needed is an RC network, giving a 6.02 dB/octave (20 dB/decade) fall-off with increasing frequency, followed by lots of gain. (Some sources specify two cascaded 3 dB/octave—pink—networks, but surely that’s more expensive and less accurate?) The values shown give a -10 dBu output (~2.6 V pk-pk) to match the other responses. Obviously, the switching shown in Figure 2 needs to be changed if you want to add this. For use in isolation, precede it with at least the 20 Hz high-pass filter, or your woofers may try to simulate a small earthquake.

Figure 5 This simple circuit converts white noise into Brownian.

Implementing other pseudo-random sequence lengths

The PIC- (or other µC-)based PRSG may have other uses needing different sequence lengths. It’s trivially easy to change the code as long as only two taps from the (virtual) shift register are needed; more taps would need more XNOR code. This reference has a comprehensive table showing the necessary taps as well as a lot of useful background information.

Longer sequences just need extra registers, with each one adding a single processor cycle; the XNOR logic takes longer to run (12 cycles) than the shifting. Eight concatenated registers with feedback from bits 62 and 63 would give a sequence that only repeats after some 1.2 million years, assuming a clock rate of 16 MHz (4 MHz instruction rate). Using 10 registers, tapped at bits 70 and 79, ups that to around 77 billion years. Long enough? If not, the above reference gives many 2-tap solutions for up to 167 bits. You might then want to invest in some ultra-ultra-long-life batteries or a really, really reliable UPS.

—Nick Cornford built his first crystal set at 10, and since then has designed professional audio equipment, many datacomm products, and technical security kit. He has at last retired. Mostly. Sort of.

 Related Content

• Ultra-low distortion oscillator, part 2: the real deal
• Squashed triangles: sines, but with teeth?
• 1/f Noise—the flickering candle
• Create noise and signals with software
• The pink noise tangent principle

The post Earplugs ready? Let’s make some noise! appeared first on EDN.

Fiber optic cables play a key role in high-speed network expansion. As wireless and cellular network complexity increases, fiber networks supporting elevated bandwidth, latency and data transmission rate demand have become essential. How should electronics design engineers incorporate this technology into their projects?

It’s important to note that that fiber network cables that were once considered cutting-edge have become legacy technology sooner than professionals could have anticipated. Even fiber has undergone significant changes since its inception, boasting advancements like fusion splicing and single-mode cables.

With advancement comes expansion. In August 2024, the Federal Communications Commission (FCC) announced it would move forward with targeted investments in fifth generation (5G) wireless cellular technology, distributing around $9 billion to facilitate 5G-capable networks. This plan will require massive, high-density fiber infrastructure.

Traditionally, mobile backhaul networks used copper time division multiplexing (TDM) circuits, which have become a legacy technology. Fiber cables are one of the only alternatives that make sense for longevity. However, while fiber deployment guarantees lasting improvements, engineers must still make proactive design decisions to ensure a lifetime of use from the upgrades.

How fiber cables fit into modern infrastructure

The rapid proliferation of advanced wireless and cellular network infrastructure has outpaced the capabilities of supporting components. Fiber cables are the clear alternative because they offer benefits like space efficiency, superior bandwidth, higher data transmission rates, and long-distance signal integrity.

Already, the United States has made progress toward a fiber-based future to support rapidly proliferating high-speed networks. As of December 2023, 60.4% of fixed connections in the country were coaxial cable, while 23.1% were fiber optic. Copper wire, fixed wireless, and satellite made up the remaining percentage.

Although the fiber adoption rate will inevitably increase, laying the groundwork for advancement is no longer enough; electronics design engineers must future-proof modern infrastructure. They can keep computing resource demand from outpacing infrastructure capabilities within the coming decades.

Designing high-speed networks with fiber

Electronics design engineers should first consider which type of fiber cable will suit their needs well into the future. While the larger 62.5-micron core of multimode cables enables higher data transmission rates, its range is limited. Single mode may be more expensive upfront, but it helps facilitate a more expansive network.

Strand count is another important consideration. While surpassing the project’s minimum requirements may seem unnecessarily expensive, it helps future-proof the infrastructure. Engineers should consider how factors like urbanization and wireless cellular technology will affect their design’s efficacy over the coming decades.

Of course, deploying fiber requires time, resources, and money. The median cost of underground deployment is $16.25 per foot, while the median aerial cost is around $6.49 per foot. Labor accounts for 50% to 90% of the total cost. Professionals should conduct a feasibility study—considering possible routes and the practicality of expansion—to determine which designs and areas to prioritize.

Will government policies affect electronic component availability? Will business leaders be able to secure research and development grants? Future-proofing wireless and cellular networks involves considering every possibility. However, electronics design engineers must be careful not to overcomplicate planning.

Ellie Gabel is a freelance writer as well as an associate editor at Revolutionized.

 

 

Related Content

• Astrape Networks: Greening the Data Center
• Canadian Quantum Startup Starts Fiber Tests
• Infrared Gesture Recognition Module for HMI Applications
• Advanced Fiber Optics Make Broadband Revolution Possible
• ‘Wi-Fi on Steroids’ Technology Allows Manufacturing Industry to Finally Cut the Cord

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Introduction

A single-stage isolated converter, such as a bidirectional capacitor-inductor-inductor-inductor-capacitor (CLLLC), is a popular converter type in energy storage systems (ESSs) to save system costs and improve power density. The gain curve of an CLLLC is flatter, however, when the switching frequency (fs) is higher than the series resonant frequency (fr) the gain curve will be undesirably flat. The parasitic capacitance of the transformer and MOSFETs would also significantly impact the converter gain [1], which will lead the converter’s output voltage out of regulation. In this power tip, I will introduce a CLLLC control algorithm and a synchronous rectifier (SR) control method to eliminate this nonlinearity, using a 3.6-kW prototype converter to verify the performance. Figure 1 is a block diagram of a residential ESS.

Figure 1 Residential ESS block diagram with bidirectional power factor correction (PFC)/inverter, bidirectional DC/DC converter, and maximum power point tracking (MPPT). Source: Texas Instruments

Design considerations in the control stage

Figure 2 shows the circuit topology of the full-bridge CLLLC resonant converter with the parasitic capacitors. This topology consists of a symmetric resonant tank and full-bridge structure.

Figure 2 The circuit topology of the full-bridge CLLLC converter with parasitic capacitors. Source: Texas Instruments

Figure 3 shows the ideal gain curve of the CLLLC. Similar to an LLC converter, variable frequency control is a popular control scheme for a CLLLC resonant converter.

Figure 3 An ideal CLLLC gain curve that uses variable frequency control. Source: Texas Instruments

As mentioned earlier, the gain curve is flat when fs exceeds fr. Moreover, with the power level increasing, the converter needs to parallel more FETs on the battery side to handle more current, which means that the output capacitance (Coss) on the output full-bridge FETs will be extremely large. Considering the parasitic parameters of transformer interwinding capacitance and Coss, the non-monotonic gain curve at high frequency is serious, which corresponds to a light-load condition, as shown in Figure 4.

Figure 4 The CLLLC gain curve considering parasitic parameters such as the transformer interwinding capacitance and Coss. Source: Texas Instruments

In this case, frequency control is useless. Hiccup mode is a popular method for addressing CLLLC resonant converter nonmonotonic features, but this method is not suitable in battery applications because the converter needs to deliver high current when the battery voltage is low. Pulse-width modulation (PWM) and phase-shift control could resolve this issue, but PWM control will make the transistors work at a hard-switching state, which decreases efficiency and limits the operational frequency. Therefore, phase-shift control is a better choice.

Control logic

Figure 5 shows the frequency and phase-shift mixed-control scheme diagram. The battery voltage is low during startup, so the converter needs to soft start with low charging current to limit the high current spike and prolong the battery life. It is a limited effect to soft start from a high frequency if the resonant inductor value or frequency is not high enough. When the battery charges to near full capacity, it will trickle charge with a small current and maintain a constant voltage. Both cases correspond to a light-load condition for the converter. At light load, the output voltage tends to rise because of the parasitic capacitance and could eventually go out of regulation based on previous analysis; phase-shift control can help regulate the output voltage in this state. The controller’s calculation result decides whether the converter needs to enter phase-shift mode or not.

Figure 5 The control scheme in different charge states. Note, the battery voltage is low during startup, so the converter needs to soft start with low charging current to limit the high current spike and prolong the battery life. Source: Texas Instruments

Figure 6 shows the modulation switch between frequency and phase shift. When the load decreases, the frequency will increase to regulate the output voltage. If the calculated maximum frequency is higher than the setting value, the converter will enter phase-shift modulation; then when the load increases, the phase-shift angle will decrease in order to regulate the output voltage. The converter will enter frequency mode again when the phase-shift angle decreases to zero.

Figure 6 The control scheme between frequency and phase-shift modes. When the load decreases and the phase-shift angle is zero, the frequency will increase to regulate the output voltage (frequency mode). If the maximum frequency is higher than the setting value, the phase shift angle decreases to regulate output voltage (phase shift mode). Source: Texas Instruments

Problems caused by parasitic capacitance

The MOSFETs’ Coss also has this effect under phase-shift mode; the tank current will oscillate with these capacitors, as shown in Figure 7.

Figure 7 The tank current waveforms under phase-shift mode in open loop. Source: Texas Instruments

Figure 8 plots a gain comparison of a CLLLC converter with and without considering MOSFET Coss. According to the figure, there will be fluctuation in the gain curve. In this case, the controller may adjust the phase-shift angle to the wrong direction under closed-loop control, resulting in a large current spike.

Figure 8 The gain curve under phase-shift mode with and without COSS. Source: Texas Instruments

Solution for the gain problem

To eliminate the non-monotonic of gain, employing SR control as shown in Figure 9 could resolve this issue. Turning on either two upper or two lower SR switches at the same time during the tank current oscillation period will temporarily short the transformer’s secondary-side winding, such that Coss will not involve the resonant.

Figure 9 Proposed SR control scheme to eliminate the non-monotonic of gain. Source: Texas Instruments

Figure 10 shows the test result; there is no oscillation compared to Figure 8. For more detailed analysis and test results, see reference [2].

Figure 10 Gain curve under phase-shift mode using the proposed control scheme (grey line). Source: Texas Instruments

Experimental results

A prototype [3] uses this control scheme to verify the performance. Figure 11 shows the soft-start waveform and Figure 12 shows the tank current waveforms under phase-shift mode with the proposed control scheme.

Figure 11 The phase-shift soft start with 750 W of output power. Source: Texas Instruments

Figure 12 The tank current waveforms under phase-shift mode with the proposed scheme. Source: Texas Instruments

Figure 13 and Figure 14 show the frequency/phase-shift modulation switch test. From the test waveforms, the startup current is limited within 28 A with 750 W of output power. There is no oscillation in the tank current and the converter could change the modulation smoothly in different working conditions.

Figure 13 The phase-shift and frequency modulation switch: frequency mode with a 5-A load. Source: Texas Instruments

Figure 14 The phase-shift and frequency modulation switch: phase-shift mode with a 1-A load. Source: Texas Instruments

 Conclusion

The proposed frequency and phase-shift mixed-control scheme limits the inrush current during the startup stage and makes the gain linear at a light load condition. The converter could switch between frequency modulation and phase shift modulation smoothly. Besides, phase-shift control also introduces the non-monotonic gain issue and makes the current oscillate in the designs that have large COSS. The proposed SR control method can help solve the current oscillation issue and makes the gain monotonic.

Guangzhi Cui is a System Engineer at Texas Instruments, where he is responsible for developing power supply design. Guangzhi earned his M.S. degree in Electrical Engineering from Hong Kong University of Science and Technology in 2016; and his B.S. degree of Engineering from Hunan University in 2014.

 

Related Content

• Power Tips #102: CLLLC vs. DAB for EV onboard chargers
• Power Tips #92: High-frequency resonant converter design considerations, Part 2
• Power Tips #134: Don’t switch the hard way; achieve ZVS with a PWM full bridge
• Power Tips #117: Measure your LLC resonant tank before testing at full operating conditions
• Power Tips #97: Shape an LLC-SRC gain curve to meet battery charger needs
• Power Tips #94: How an upside-down buck offers a topology alternative to the non-isolated flyback

 References

1. Lee, Byoung-Hee, Moon-Young Kim, Chong-Eun Kim, Ki-Bum Park, and Gun-Woo Moon, “Analysis of LLC Resonant Converter Considering Effects of Parasitic Components.” Published in INTELEC 2009 – 31st International Telecommunications Energy Conference, Incheon, Korea (South), Oct. 18-22, 2009, pp. 1-6.
2. Tai, Will, Guangzhi Cui, and Sheng-Yang Yu, “Gain Optimization Control Method for CLLLC Resonant Converters Under Phase Shift Mode.” Published in PCIM Europe 2024; International Exhibition and Conference for Power Electronics, Intelligent Motion, Renewable Energy and Energy Management, Nürnberg, Germany, June 11-13, 2024, pp. 2513-2518.
3. Cui, Guangzhi. n.d. “3.6kW Bidirectional CLLLC Resonant Converter Reference Design.” Tex as Instruments reference design No. PMP41042. Accessed Nov. 6, 2024.

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Keysight’s EDA 2025 software leverages AI, ML, and Python integrations to reduce design time for complex RF and chiplet products. The tool suite enhances data manipulation, integration, and control of advanced simulators, enabling seamless workflows across multiple tools.

AI-optimized workflows allow engineers to move from simulation to verification and compliance with greater confidence. The software simulates fast digital interconnects using end-to-end component models and standards-compliant measurements, creating an accurate digital twin for complex electronic designs.

According to Keysight, the core benefits of the EDA 2025 software portfolio include:

• RF circuit design: Accelerate RF design with open, automatable workflows, Python integration, and multi-domain simulation. The Python toolkit consolidates load pull data into unified datasets for AI/ML model training.
• High-speed digital design: Create precise digital twins for complex standard-specific SerDes designs, including UCIe chiplets, memory, USB, and PCIe, with the Advanced Design System (ADS) 2025 release.
• Device modeling and characterization: Reduce model re-centering time by 10X through AI/ML capabilities in the IC-CAP 2025 release, while Python integrations streamline and automate the modeling process.

Learn more about Keysight EDA 2025 at the virtual launch event on December 3, 2024. To register, click here.

EDA software product page

Keysight Technologies

Find more datasheets on products like this one at Datasheets.com, searchable by category, part #, description, manufacturer, and more.

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Siemens is integrating its embedded automotive software with Infineon’s AURIX TC4x MCUs to enable advanced features in software-defined vehicles (SDVs). This collaboration supports OEMs in achieving production readiness for next-generation SDV capabilities.

Siemens’ Capital Embedded AR Classic software, based on AUTOSAR Classic Release R20-11, leverages an AUTOSAR-compliant architecture to enable the multicore, functional safety, and cybersecurity features of the AURIX TC4x. This pre-validated, feature-rich software simplifies OEMs’ homologation processes for functional safety and cybersecurity compliance.

The AURIX TC4x microcontrollers from Infineon play a critical role in automotive systems, managing functions like electric powertrain, battery management, ADAS, radar, and chassis. They combine enhanced power and performance with advances in virtualization, AI-based modeling, functional safety, cybersecurity, and networking, enabling next-gen E/E architectures and software-defined vehicles.

To learn more about Siemens’ AUTOSAR embedded software development capabilities, click here.

Siemens Digital Industries Software

Find more datasheets on products like this one at Datasheets.com, searchable by category, part #, description, manufacturer, and more.

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The GR716B radiation-hardened microcontroller from Frontgrade Gaisler handles multiple tasks over extended periods in space. This energy-efficient MCU is well-suited for supervision, monitoring, and control in satellite applications, adapting to various space systems with a broad range of standard interfaces, architectural features, and integrated analog functions.

Powered by a LEON3 SPARC V8 processor running at up to 100 MHz, the GR716B ensures deterministic software execution with multiple non-intrusive buses, fixed interrupt latency, and a cache-less architecture. Two real-time accelerators offload demanding tasks from the LEON3 and have access to tightly coupled memory for instructions and data. The MCU also includes 192 KiB of on-chip RAM and fault-tolerant memory controllers for off-chip memory access.

The GR716B offers robust radiation resilience, with a total ionizing dose (TID) tolerance of up to 100 krads and single event latch-up (SEL) immunity of >118 MeV·cm²/mg. Its I/O interfaces include a SpaceWire router, Ethernet, MIL-STD-1553B, CAN, PacketWire, programmable PWM, SPI with SPI-for-Space protocols, UART, I2C, and GPIO. Integrated analog functions feature radiation-hardened cores such as DAC, ADC, comparator, voltage reference, PLL, and all active components for a crystal oscillator.

Engineering models of the GR716B MCU are now available to alpha customers for integration into new missions.

GR716B product page

Frontgrade Gaisler 

Find more datasheets on products like this one at Datasheets.com, searchable by category, part #, description, manufacturer, and more.

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Sycamore, a full-range, all-silicon near-field micro speaker from xMEMs, is 1/7th the size and 1/3rd the thickness of conventional dynamic drivers. Coming in at just 8.41×9×1.13 mm and weighing only 150 mg, this tiny MEMS speaker delivers full-range sound while enabling thinner, lighter designs for open wireless stereo (OWS) earbuds, smartwatches, AR/VR headsets, and other mobile electronics.

Unlike the company’s Cypress micro speaker, designed for occluded in-ear ANC earbuds, Sycamore targets open-air listening devices. Its solid-state design and IP58 rating ensure durability and sweat resistance for active users.

With a first-order low-frequency roll-off, Sycamore matches the mid-bass performance of legacy drivers while extending sub-bass by up to 11 dB. It also extends high-frequency performance by up to 15 dB above 5 kHz, making it a strong near-field micro speaker or high-frequency tweeter alternative for laptops, automotive applications, and portable Bluetooth speakers.

xMEMS plans to sample the Sycamore micro speaker in Q1 2025, with mass production set for October 2025.

Sycamore product page

xMEMS Labs

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Renesas is sampling a trio of interface ICs for second-generation DDR5 multiplexed rank dual in-line memory modules (MRDIMMs). This complete memory interface chipset includes the RRG50120 multiplexed registered clock driver (MRCD), RRG51020 multiplexed data buffer (MDB), and RRG53220 power management integrated circuit (PMIC).

Gen 2 DDR5 MRDIMMs address the growing memory bandwidth demands of artificial intelligence, high-performance computing, and other data center applications. They deliver operating speeds of up to 10,000 MT/s, with future iterations targeting 12,800 MT/s.

The second-generation RRG50120 MRCD buffers the command/address bus, chip selects, and clocks between the host controller and DRAMs in MRDIMMs. It reduces power consumption by 45% compared to the first generation, improving heat management in high-speed systems. The Gen 2 RRG51020 MDB buffers data between the host CPU and DRAMs. Both the MRCD and MDB support speeds up to 12.8 Gbps. Optimized for high-current, low-voltage operation, the RRG53220 PMIC provides reliable electrical-over-stress protection and enhanced power efficiency.

Production availability of the RRG50120 MRCD, RRG51020 MDB, and RRG53220 PMIC is expected in the first half of 2025. To learn more about Renesas DDR5 products, click here.

Renesas Electronics 

Find more datasheets on products like this one at Datasheets.com, searchable by category, part #, description, manufacturer, and more.

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As I conceptually discussed last May, following up with a teardown nearly a year later (and earlier this year), master flash units mated to cameras’ hot shoes are often also capable of, whether via IR or various RF schemes, also controlling slave illumination devices located elsewhere in a studio or other picture-shooting location.

But what if you don’t want to restrict yourself from a lighting-setup standpoint to connecting at least one flash unit directly to your image-capture device for resultant full-frontal illumination of your subject? Extension cords can get you a foot or so away while retaining the full-featured physical tether, for example:

That said, an even more flexible approach mates the camera to a dedicated-function transmitter (also commonly referred to as a “trigger”), with all lighting sources in the setup controlled by it and subsequently acting as slaves. This approach is equally beneficial if you do desire full-frontal illumination of your subject but your main flash unit isn’t sufficiently “intelligent”, since such transmitters are typically camera-cognizant (thereby handling the “intelligence” themselves) and support “dumb” hot shoe and cable sync options to a close-proximity flash, too.

Today’s teardown victim, from Godox, is one such example. The means by which I came into possession of it is admittedly atypical. Reiterating what I wrote in my Godox V1 flash unit teardown from earlier this year:

As regular readers already know, “for parts only” discount-priced eBay postings, suggestive of devices that are (for one reason or another) no longer functional, are often fruitful teardown candidates as supplements to products that have died on me personally.

The patient this time is another example of this longstanding “dumpster diving” tendency…or at least I thought it was going to be. Back in March, well-known used imaging equipment retailer KEH held one of its periodic “inventory reduction” sales, this one offering 15% off a subset of its warehouse stock. One of the things that caught my eye was a “Godox X1T-F TTL Wireless Flash Trigger Transmitter for Fujifilm” in “as-is” condition for $3.65 before discount, $3.10 after:

“1” in the product code means first-generation, “T” stands for “transmitter” (or “trigger”), “F” means that it’s intended for use with Fujifilm cameras…and “as-is”, paraphrasing KEH, basically means that best-case it’s cosmetically beat up and worst-case it doesn’t work at all. And indeed, when it arrived, that’s what the sticker attached to the bag containing the transmitter indicated:

What was inside the bag, however, was something much better, a second-generation Godox X2T-F in pristine cosmetic condition (the Canon version of the X2T is shown in the following “stock” photo):

seemingly fully functional, to boot:

I don’t own any Fujifilm cameras, which wasn’t a problem given my original teardown-only plan for the as-is X1T device, and which also precludes me from definitively determining this X2T’s functional-or-not status. However, given that it seems to be fine, I’m going to do my utmost to do no permanent damage to it during my my disassembly, so that I can subsequently put it back together and donation-pass it on, where it’ll hopefully find good use for some time to come. To wit, I’ll restrain myself from any “extreme” dissection that might be permanently maiming.

To begin, here are some overview shots, as usual accompanied by a 0.75″ (19.1 mm) diameter U.S. penny for size comparison purposes. Front: in the upper right is the autofocus-assist lamp:

Right side: the USB-C connector is used for firmware updates, and the 3.5-mm sync jack can be settings-configured either as an input (as a transmitter-triggering alternative to the “intelligent” hot shoe at the bottom) or an output (as a tethered alternative to alternatively firing a “slave” flash device either wirelessly or via the “dumb” hot shoe at the top):

Back:

Left side: the switch on the left is for overall unit power control, while the one on the right enables or disables the AF-assist lamp:

Top: note first the “dumb” hot shoe to, as mentioned earlier, control a separate “slave” flash unit. Also note the Bluetooth logo; as with the earlier-dissected V1 flash unit, this transmitter not only controls other Godox (or rebranded Adorama) equipment via the proprietary 2.4 GHz wireless X protocol but also optionally supports itself being configured and controlled by a Bluetooth-tethered smartphone or tablet in conjunction with a Godox (or Adorama) app:

And finally, the bottom, with its comparatively “intelligent” hot shoe for mating with a (Fujifilm, in this particular case) camera:

Time to dive in. In prior pictures, you may have already noticed three (now removed) screws’ visible heads:

one at the bottom:

and one on each side:

Extracting them unfortunately didn’t get me very far, though:

And a scrape-away of the left-side QC sticker didn’t reveal any more screw heads underneath:

so next, I looked inside the underside battery compartment:

Ah yes, there we are. Two more screw heads:

That’s more like it:

First, here’s a closeup of the left half of the previous photo, revealing the inside (and underside) of the top half of the device:

And, jumping ahead in time, another perspective after disconnecting the two-wire tether between the “dumb” hot shoe and the system PCB that controls it (the lens in front of the AF-assist beam also detached from the device bottom-half in the process):

About that two-wire tether: remember my earlier discussed differentiation between “smart” and “dumb” hot shoes? I’ll confess at this point that I sorted this all out retroactively, after initially being momentarily baffled as to why there were only two wires (switched power and ground) coming out of the topside hot shoe…

A brief rewind-in-time now to the right half of the earlier overview shot, first still tethered:

And now standalone:

Along with three side-view perspectives:

Unsurprisingly, there’s a lot of component commonality between this design and that of the previously detailed Godox V1 flash. They’re both based on the same main system controller, for example, the APM32F072VBT6 (PDF), from a Chinese company called Geehy Semiconductor, integrating an Arm Cortex-M0+ running at 48 MHz along with 128 Kbytes of flash memory and 16 Kbytes of RAM. It’s in the upper left corner of the PCB, adorned with a pink ink dot, if you haven’t already noticed it (but given its comparative size, you probably already did).

You probably also already noticed the two identical-looking PCB-embedded antennae at the bottom. Above the one to the right is the same multi-component (and more general PCB) layout as that found in the V1: Texas Instruments’ CC2500 low-power 2.4 GHz RF transceiver and TI’s CC2592 front-end RF IC, so per proximity I’m guessing that this one handles Bluetooth connectivity. By the process of elimination, then, I’ll also hazard a deduction that the other antenna, to its left, implements Godox’ X wireless protocol in conjunction with whatever circuitry is inside the silver module with which it shares a common mini-PCB.

And did you also notice the three additional screw heads? You know what comes next, right?

Disconnect one more two-wire harness, this one going to the AF-assist beam subsystem:

Push through the case openings one side’s worth of battery terminals:

(the other side’s terminals are permanently attached the case, not connected to the PCB):

And voila:

Here’s an overview of the now-exposed main PCB backside, with battery terminals in the upper left, the two aforementioned left-side switches at bottom left, the USB-C and sync connectors at bottom right and ribbon cables (which, as previously discussed, along with the one connected to the other side of the main PCB, I’m not going to chance disconnecting) along the lower edge and leading elsewhere:

We’re now looking toward the inside of the bottom of the device, where both of those thinner ribbon cables end up. At left is the underside of the “smart” hot shoe, while at right is the control dial you may have noticed in earlier overview shots:

Wrapping things up, here’s the backside of the device, mated to ribbon cables for the display (the wider one at left) and control buttons (the narrower one at left):

And now, first taking a deep breath for calming confidence, I retraced my prior disassembly steps in reverse. Aside from a brief moment of panic when I thought I’d lost a screw (which ended up just being stuck in the recesses of the matching-color case), the process went smoothly. And, after taking another deep breath, popping two AAs in and flipping the power switch on, this is what I saw:

I seem to have successfully resurrected it, again to the limits of my no-Fujitsu-camera testing abilities. Yay! Sound off with your thoughts in the comments.

 —Brian Dipert is the Editor-in-Chief of the Edge AI and Vision Alliance, and a Senior Analyst at BDTI and Editor-in-Chief of InsideDSP, the company’s online newsletter.

Related Content

• Multi-source vs proprietary: more “illuminating” case studies
• The Godox V1 camera flash: Well-“rounded” with multiple-identity panache
• Putting an APC UPS out of its (and my) misery
• Disassembling the Echo Studio, Amazon’s Apple HomePod foe

The post Scrutinizing a camera flash transmitter appeared first on EDN.

As of this year, EDN has consecutively published (intentionally ahead of Black Friday, by the way, if you hadn’t already deduced that non-coincidence) my odes to holiday-excused consumerism for more than a half-decade straight, nearing ten editions in total. Here are the 2019, 2020, 2021, 2022 and 2023 versions; I skipped a few years between 2014 and its successors. As in the past, I’ve included up-front links to the prior-year versions because I’ve done my best here to not reiterate any past category recommendations; the stuff I’ve previously suggested largely remains valid, after all. That said, it gets harder and harder each year not to repeat myself!

Without any further ado, and as usual ordered solely in the order in which they initially came out of my cranium…

A portable soldering iron

Being tethered in one place, or at best able to roam only a short distance from a power outlet, is a pet peeve of mine. It’s why, for example, I barely ever use a desktop computer anymore; not only are laptops and the like performance-adequate for most tasks nowadays, they also run for hours on batteries (no matter that mine’s still most times plugged into a wall outlet). It’s why I long ago replaced a legacy AC “weed whacker” with a battery-operated successor, accompanied by a suite of rechargeable lithium cells (and chargers) that also work with other portable tools.

Similarly, I’d sometimes prefer to take my soldering iron to where I need to use it versus always needing to drag whatever widget needs soldering down to my workbench and its AC outlet-fed traditional soldering iron set. That’s where the new FixHub |Power Series from my long-time buddies at iFixit comes in. The baseline is the $79.99 USB-C PD-based Smart Soldering Iron:

Up to 100 W of power (a 35-W minimum power source is necessary). Heats up in around 5 seconds. An illuminated ring for heat indication, along with safety features like auto standby and fall protection. Interchangeable soldering tips and a factory-preset default tip temperature of 350°C (660°F), subsequently user-adjustable between 100°C and 420°C. How, you might ask, since there’s no temperature dial shown in the picture? One setting-customization option is a Web Interface (currently not supporting Mozilla Firefox, alas, I’ve just learned), believe it or not.

The other option, which also neatly addresses the “what about that portability you were touting earlier” query some of you might be having right now, is a smartphone-sized 55 watt-hour portable battery-plus-control box, which iFixit optionally bundles with the soldering iron to come up with the $249.95 Portable Soldering Station. It delivers an estimated 8-hour runtime between charges and provides a second USB-C PD output for (among other things) devices such as what I’ll talk about next:

Inexpensive lab equipment

How’s that saying go: champagne taste on a beer budget? Or, if you prefer a visual definition:

That’s me, at least some of the time, and with some things (cameras aside, for example, although in self-defense here, pretty much everything photo-related I buy is already gently used). Which explains, in part, my burgeoning fascination with low-priced lab equipment. Another key motivation is to see, as time goes on and bill-of-materials cost reductions combine with customer demand increases, just how much (measured in both feature-set quantity and per-feature quality) I can get at a particular price point. Kinda like solar panel trends, I suppose…

Anyway, here are a few of my purchase examples for your consideration. First up is Jesverty’s WPS-3005 0-30 V and 0-5 A adjustable switching DC regulated bench power supply (other options with different output voltage and current ranges and case and display colors are also available), which I bought on sale at Amazon in October 2022 for $22.49:

Then there was the FNIRSI DSO-TC3, a 3-in-1 digital oscilloscope, electronic component tester, and function signal generator, the advanced (translation: more test probes included) version of which I snagged back in May of this year from Banggood for $39.99:

Serious testing equipment? Are you serious? But hey, the scope’s 10 MS/s sampling rate and 500-kHz bandwidth are nothing to sneeze at. It integrates a 2.4” color TFT display. Signal waveform generator options include sine, square, pulse stroke, triangle, ramp and DC. The DSO-TC3’s transistor and other component testing capabilities are notable, especially considering the price tag. A bunch of other available device functional modes are also listed on the product page, including temperature and humidity sensor measurement support. To my earlier point about roaming to where the (testing and measurement, in this case) “action” is versus forcing relocation to the gear-tethered workbench, it’s powered by an embedded lithium battery which, yes, can be recharged by (among other sources) the second USB-C PD port on the iFixit FixHub |Power box, as I foreshadowed earlier. And did I mention that it cost me less than $40?

Snazzy Raspberry Pi peripherals

Last year, I covered the recently introduced Raspberry Pi 5, which is now available in an entry-level $50 variant with 2 GBytes of RAM in addition to the originally introduced 4 GByte and 8 GByte flavors (two example of the latter which I own). This year, I’d like to focus on a few “RasPi” peripherals I’ve also recently acquired (and in another case, still have on my wish list). Focusing first on HAT+ add-in cards, the Raspberry Pi Foundation belatedly finally rolled out its own M.2 board, a while after third-party partners had done so. Unlike some of those others, however, it can be fitted to a Raspberry Pi 5 with the Raspberry Pi Active Cooler also in place…which is nice.

It also, unlike some third-party counterparts, and quoting from the product page, “is autodetected by the latest Raspberry Pi software/firmware.” This is the key reason why I always tend to go for “official” peripherals versus third-party alternatives, no matter how tempted I might be by those others’ specs. Do a bit of research, for example, into some third-party camera modules whose drivers don’t keep pace with base board firmware and O/S updates, inevitably ending up prematurely dropped from their suppliers’ support lists, and you’ll see what I mean.

Speaking of impressive specs, while the M.2 HAT+ board’s support for “fast (up to 500 MB/s) data transfer to and from NVMe drives” might sound impressive, realistically the Raspberry Pi 5’s microSD interface is plenty speedy enough for pretty much any current application; the biggest benefit to the M.2 alternative might be as a (cost-effective) high-capacity storage option. But note, too, the “and other PCIe accessories” qualifier in the originally published version of that earlier quote. What might those “other PCIe accessories” be, you ask? They include, for example, Hailo’s M.2 2242 module based on the Hailo-8L deep learning inference processor, which Raspberry PI bundles with the M.2 HAT+ as the $70 Raspberry Pi AI Kit:

Speaking of camera modules, what’s new in the Raspberry Pi Foundation’s stable? Well, there’s…

• A version of the Camera Module 2 absent the IR filter
• The HQ Camera, which bumps up the resolution to 12.3 Mpixels and, although absent a lens of its own (therefore absent the word “Module” in the product name), supports both C/CS and M12 mount interchangeable lenses
• The Global Shutter Camera, with “only” 1.6 Mpixel resolution but which “can capture rapid motion without introducing artifacts typical of rolling shutter cameras” and is therefore “Ideal for fast motion photography and machine vision applications” (again, there’s no integrated lens, therefore no “Module” in the product name, but a C/CS interchangeable lens mount is included)
• The Camera Module 3 series, which adds autofocus support
• And last but not least (and, in fact, most recently) the $70 AI Camera, based on Sony’s IMX500 Intelligent Vision Sensor and also integrating a Raspberry Pi RP2040 IC for neural network firmware management.

A power bank (or few)

I’ve conceptually discussed power banks before:

And even tore one down a few years back:

But unless I’m mistaken (always a possibility), I don’t think they’ve yet made one of my holiday gift lists. Let’s rectify that oversight, because they’re handy, powerful, totable and increasingly cost-effective devices. They sometimes integrate Qi wireless charging pads, as a supplement to their various wired power outputs, which some power banks further augment via MagSafe (Qi2, more broadly) support for convenient attachment to a drained-internal-battery phone:

And thanks to USB’s (specifically, USB-C’s) combo of increasing ubiquity and functional diversity, manufactures are even beginning to bundle lithium batteries with solid-state storage:

multi-port hub connectivity:

and in other multi-function single-device combinations, which admittedly is quite clever from a diversification-and-competitive isolation standpoint, when you think about it. Just remember, if you take one or multiple on an airplane, that as with external batteries for videography, each will need to be in your carry-on luggage, not checked, and smaller than 100 watt-hours in capacity.

Power stations

Beef up the internal battery capacity, along with the array of charging-input and power-output options, and you’ve got a portable power station on your hands, capable of fueling an appliance or few or even (if it’s big enough and your house is small enough) an entire room-to-residence for a notable amount of time in the absence of utility-sourced premises “juice”. Regular readers may recall that a few months ago, I covered the Phase2 Energy PowerSource 660Wh 1800-Watt Power Station I’d recently acquired:

“Portable” is admittedly arguable here, given its size and especially weight, due to its SLA (sealed lead acid) AGM (absorbed glass mat, although I haven’t yet definitively determined this latter variation) battery foundation. But it does the job and was relatively affordable. And thanks to the portable (an unarguable use of the term, this time) solar panel I also purchased for it:

I’m not even dependent on the presence of utility-sourced premises “juice” to recharge it.

That all said, as I also mentioned back in August, an increasing number and diversity of portable power stations are now appearing based on lighter weight and more compact, not to mention more powerful-per-pound and per-cubic-inch, lithium-variant battery technologies. As a sneak peek of more in-depth coverage to come, I’ll share that recently I’ve personally acquired two EcoFlow units. The smaller one, a RIVER 2:

is passable for overnight camping trips in the van, for example. Or a day’s worth of drone flying. Or for powering my CPAP machine and oxygen concentrator overnight. And I can use the aforementioned 100-W portable solar panel to also recharge it during the day (albeit not at the same time as the Phase2), in conjunction with an Anderson-to-XT60i connector adapter cable.

The other, beefier (but still portable) EcoFlow power station I recently bought is a DELTA 2:

which I’ve supplemented with two 220-W second-generation portable solar panels in conjunction with a parallel panel output-combiner cable:

That said, as I mentioned a few months ago, the number of credible (i.e., not no-name, fly-by-night) suppliers is steadily growing, at the moment also including companies such as (but not limited to) Anker, Bluetti, Jackery and, believe it or not, even DJI (to my earlier drone-flying comments). Whoever’s product(s) you end up buying, I encourage you to keep a key foundational differentiator in mind as you select among the options. LiFePO₄ (lithium iron phosphate), sometimes instead referred to by the LFP (lithium ferrophosphate) acronym, is one common lithium-based battery approach. Another popular battery technology, which in retrospect I realize I neglected to mention back in August, is NMC (Nickel Manganese Cobalt), which is also lithium-based although “lithium” is nowhere to be found in the name.

NMC batteries have a higher energy density, therefore delivering more power for a given cell volume, and operate more stably across temperature extremes. Conversely, LiFePO₄/LFP batteries are capable of significantly higher recharge cycle counts without degrading, are more cost-effective due to both rapidly growing manufacturing supply and booming customer demand and are more thermally stable. Which technology is inside a given power station can be hard to determine; the Energizer one I previously mentioned (and then briefly owned, which you’ll read more about later), for example, was only listed as using a “lithium-ion battery”, and only after doing a bunch of research did I learn that it was NMC. The effort’s worthwhile.

A portable SSD

The other day, in preparation for re-creation with higher capacity, I backed up a 20 GByte sparse bundle-based virtual disk to my 128 GByte Samsung S1 mini external storage device, based on a Spinpoint SPU 1.8” 3600 rpm HDD, over USB 2. It took about 30 minutes for the copy to complete. Then, acting out of curiosity, I also backed up that same 20 GByte file to my 1 TByte SK Hynix “Beetle” X31 portable SSD over USB-C-based USB 3.2 Gen2 (10 Gbps). This time, it took less than 30 seconds. And no, the difference wasn’t (just) due to the more modern interface. I think it’s time to retire the Samsung Si mini, with gratitude for its long, reliable service ;-).

If you want something with a USB “stick” or “thumb drive” reminiscent (albeit “thicker”) form factor instead, there’s always also the SK Hynix “Tube” T31, a 1 GByte variant of which I also own and which leverages USB-A-based USB 3.2 Gen2 (5 Gbps, this time):

The perhaps obvious key differentiation in these (and other: SK Hynix isn’t the sole supplier) cases, versus with a conventional USB flash “stick”, is the inclusion of a true NVMe SSD module inside, coupled to a fast interface to the outside world. And versus the conventional 2.5” external HDD-reminiscent form factors of the Samsung T5 and T7 portable SSDs I also own:

the SK Hynix T31 and X31 are more diminutive, albeit more peak capacity-limited.

Wireless…err…”research” assistance

This last one is at least mildly controversial, at least in Canada, where a ban was considered albeit ultimately paused, and Brazil, where imports were seized. It’s the $169 Flipper Zero:

described on the manufacturer’s website as (among other things) a “Multi-tool Device for Geeks” and, more extensively:

A versatile tool for hardware exploration, firmware flashing, debugging, and fuzzing [editor note: testing various protocols and signals]. It can be connected to any piece of hardware using GPIO to control it with buttons, run your own code and print debug messages to the LCD. It can also be used as a regular USB adapter for UART, SPI, I2C, etc.

Flipper Zero supports a diversity of wireless RF schemes—125 kHz RFID, NFC, Bluetooth Low Energy, etc.—along with infrared, and integrated microSD support further expands its data and application storage (and execution, in the latter case) capabilities. So, what’s the controversy? Simply stated, hardware “exploration” can in at least some cases transform into “exploitation”. Canadian officials have controversially claimed, for example, that Flipper Zero devices can be used to steal vehicles by cloning the signals used for remote keyless entry. So, assuming you take my bait and buy one, the Christmas-themed question then is “will you be naughty or nice”?

Even more for beyond 2024

I’ve got plenty of additional presents-to-others-and/or-self ideas, but the point isn’t to write a book, so I’ll close here, having just passed through 2,500 words. Upside: I’ve already got topics for next year’s edition! Until then, sound off in the comments, and happy holidays!

—Brian Dipert is the Editor-in-Chief of the Edge AI and Vision Alliance, and a Senior Analyst at BDTI and Editor-in-Chief of InsideDSP, the company’s online newsletter.

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The post A holiday shopping guide for engineers: 2024 edition appeared first on EDN.

As we near the end of the year, two CEOs at prominent semiconductor firms are leaving, and in both cases, the chairmen of the board are replacing them as interim CEOs. What’s common in both companies is the quest for a turnaround in the rapidly evolving semiconductor market.

First, Ganesh Moorthy, president and CEO, is leaving Microchip, and chairman Steve Sanghi is taking back the charge of the top job at the Chandler, Arizona-based semiconductor firm. While the announcement states that Moorthy is retiring after his nearly three-year stint at the corner office, the fact that Sanghi is back at the helm immediately doesn’t exactly signal a smooth transition.

Figure 1 Before joining Microchip, Moorthy was CEO of Cybercilium, the company he co-founded in Tempe, Arizona.

Sanghi, who will remain chairman, is taking charge as interim president and CEO. Moorthy joined Microchip as VP of advanced microcontrollers and automotive division in 2001, and he was appointed chief operating officer before being elevated to the CEO job in 2021. He had served at Intel for 19 years before his stints at Cybercilium and Microchip.

Microchip has been confronting an inventory stock and sales slump for some time, and its shares are down 28% in 2024. Sanghi’s statement on taking the charge as CEO clearly points toward an aim to return to growth in revenue and profitability.

Then there is the news about Wolfspeed’s CEO change, and it’s more startling and less subtle. The Wolfspeed board has ousted CEO Gregg Lowe without cause, and like Microchip, chairman of the board Thomas Werner is taking over as interim CEO before Wolfspeed finds Lowe’s replacement.

Lowe, who spearheaded Freescale’s sale to NXP in 2015 as CEO, took the helm of Cree in 2017 and transformed it from an LED lighting company to a silicon carbide (SiC) IDM. During this transformation under Lowe, the company acquired a new name: Wolfspeed. Also, during this time, Infineon made a failed attempt to acquire Wolfspeed.

However, the Durham, North Carolina-based chipmaker seems to have failed to translate its enviable position as a pure-play SiC company in this high-growth market, and that probably sums up Lowe’s ouster. It’s apparent from Werner’s statement announcing this CEO transition. “Wolfspeed is materially undervalued relative to its strategic value, and I will focus on driving the company’s priorities to explore options to unlock value.”

Figure 2 Lowe sold off Cree’s LED lighting business and turned the sole focus on SiC under the Wolfspeed brand.

For a start, Wolfspeed has been struggling in the transition from 150-mm to 200-mm SiC wafers. It has also been facing slowing orders from the electric vehicle (EV), industrial and renewable energy markets. The company recently dropped plans to build a SiC fab in Ensdrof, Germany.

These two CEO office transitions don’t come as a surprise to the semiconductor industry watchers. And it surely won’t be the last as we are about to enter 2025. The semiconductor industry is highly competitive, and stakes are even higher when you are a vertically-integrated chip outfit.

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• CEO Sanghi bets Microchip’s future on power, connectivity

The post The CEO office transitions at Microchip and Wolfspeed appeared first on EDN.

A recent design idea, “Negative time-constant and PWM program a versatile ADC front end,” offered a pretty peculiar ADC front end (see Figure 1). It comprises a programmable gain (PG) instrumentation amplifier (INA). It uses PWM control of a flying capacitor to implement a 110-dB CMRR, high impedance differential input and negative time-constant exponential amplification with more than 100 discrete programmable gain steps. It’s then topped off with a built-in sample and hold (S&H). Hence PGINASH. Catchy. Ahem.

Figure 1 PGINASH: An unconventional ADC front end with INA inputs, programmable gain, and sample and hold.

Wow the engineering world with your unique design: Design Ideas Submission Guide

 Due to A1c’s gain of (R3 / R2 + 1) = 2, during the PWM = 1 gain accumulation phase the connection established from U1c’s output through U2a and R1 to C creates positive feedback that makes the voltage captured on C multiply exponentially with a (negative) time-constant Tc of (nominally):

Tc = R1*(C + Cstray) =
= 14.3k*(0.001µF + (8pF (from U2a) + 1pF (from U1c)))
= 14.3k*1009pF = 14.43µs
= 10µs / ln(2)
G = gain increment of 20.1 = 1.0718 = 0.6021dB per us of accumulation time T
G10 = 2.0 = 6.021dB per 10µs of T
This combines with A1c’s fixed gain of two to total
Nominal net Gain = 2GT/10µs

Of course, the keyword here is “nominally.” Both R1 and C will have nonzero tolerances, perhaps as poor as ±1%, and ditto for R2 and R3. Moreover, further time-constant, and therefore gain, error can arise from U2 switch to switch ON resistance mismatches. The net bad news, pessimistically assuming worst case mutual error reinforcement of all the time-constant component tolerances, is A1c’s gain may vary by ±2% and G by as much as ±3%. This is far from adequate for precision data acquisition! What to do?

The following sequence is suggested as a simple software-based in-circuit calibration method using a connected ADC and requiring just two calibration voltages to be manually connected to the IA inputs as calibration progresses, to combat the various causes of front-end error. 

GAIN ERROR

The first calibration voltage (Vcal) is used to explicitly measure the as-built gain factors. Here’s how it works:

 Vcal = Vfs/Vheadroom
where
Vfs = ADC full-scale Vin
Vheadroom = (2*1.02)*(2*1.04)2 = 8.8
e.g., if Vfs = 5v, Vcal = 0.57v

 Vcal’s absolute accuracy isn’t particularly important, +/-1% is plenty adequate. But it should be stable to better than 1 lsb during the calibration process. Connect Vcal to the INA inputs, then take two ADC conversions: D1 with gain accumulation time T =10 µs and D2 with T = 20 µs. Thus, if 2x = the as-built A1c gain and G = the as-built exponential gain, the ADC will read:

D1 = ADC(2x *G10*Vcal)
D2 = ADC(2x*G10*G10*Vcal)

 Averaging a number (perhaps 16) acquisitions of each value is probably a good idea for best accuracy. The next step is some arithmetic:

D2/D1 = (2x*G10*G10*Vcal)/(2x*G10*Vcal) = G10
D1/ (G10*Vcal) = (2x*G10*Vcal)/(G10*Vcal) = 2x
G = (G10)0.1

That wasn’t so bad, was it? Now we if we want to set (most) any desired conversion gain of Y, we just need to compute a gain accumulation interval of:

T(µs) = log(Y/2x)/log(G)

Note if that this math yields T < 1 µs, we’ll need to bump Y for some extra time (and gain) to allow for capacitor “flight” and signal acquisition.

INPUT OFFSET ERROR

There is, however, another error source we haven’t covered: U1 input offsets. Although the TLV9164 typical offset is only 200 µV, max can range as high as 1.2 mV. If uncorrected, the three input amplifiers’ offsets could sum to 3.6 mV. This would render the upper gain range of our amplifier of little value. To fix it, we need another input voltage reference (Vzero), some more arithmetic, and another ADC conversion to measure the Voff offset and allow software subtraction. We’ll use lots of gain to get plenty of resolution. Vzero should ideally be accurate and stable to <10 µV to take full advantage of the 9164’s excellent 0.25 µV/oC drift spec’.

Let Vzero = 4.00mV
N = log(Vfs/(.008v * 2x))/log(G)
D3 =  ADC(2x*GN*(Vzero + Voff))
Voff = D3/(2x*GN) – Vzero

 And there you have it. To accurately massage any raw ADC result into the actual Vin input that produced it, write:

Vin = (ADC(Vin)/(2x GN)) – Voff

 But avoid GN  > Vfs /(2x*Voff). Otherwise A1c and the ADC may be driven into saturation by amplified offset. Also, things may (okay, will) get noisy.

Okay. But what about…

LEAKAGE CURRENT ERROR

The leakage current conundrum comes from the fact that negative time-constant current from U1c through R1 isn’t the only source of gain-phase charge for C. Unfortunately, leakage currents from U2’s X pin and U1’s noninverting input also contribute a mischievous share. U1’s contribution is a negligible 10 pA or so, but U2’s can be large enough to become problematic.

The burning question is: How much do HC4053 switches really leak? Reeeeeally?  Datasheets are of surprisingly little help, with the answer seeming to range over literally a million-to-one, pA to µA, range.

Figure 2 quantifies the result for some plausible 100 pA to 1 µA numbers.

Figure 2 The input referred current – equivalent voltage offsets.

 Stephen Woodward’s relationship with EDN’s DI column goes back quite a long way. Over 100 submissions have been accepted since his first contribution back in 1974.

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• Simulating the front-end of your ADC
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• PWM DAC settles in one period of the pulse train

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