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Archive for category Electronics Workbench

DDS Musings: Arithmetic with 32-bit Fixed Point Numbers

Spoiler alert: having spent a while trying to fit the DDS calculations into fixed-point numbers stuffed into a single 32 bit unsigned long value, it’s just a whole bunch of nope.

The basic problem, as alluded to earlier, comes from calculations on numbers near 32768.0 and 60000.0 Hz, which require at least 6 significant digits. Indeed, 0.1 Hz at 60 kHz works out to 1.7 ppm, so anything around 0.05 Hz requires seven digits.

The motivation for fixed-point arithmetic, as alluded to earlier, comes from the amount of program memory and RAM blotted up by the BigNumber arbitrary precision arithmetic library, which seems like a much bigger hammer than necessary for this problem.

So, we begin.

Because the basic tuning increment works out to 0.0291 Hz, you can’t adjust the output frequency in nice, clean 0.01 Hz clicks. That doesn’t matter, as long as you know the actual frequency with some accuracy.

Setting up the DDS requires calculations involving numbers near 125.000000 MHz and 2³², both of which sport nine or ten significant figures, depending on how fussy you are about calibrating the actual oscillator frequency and how you go about doing it. Based on a sample of one AD8950 DDS board, the 125 MHz oscillator runs 300 to 400 Hz below its nominal 125 MHz: about 3 ppm low, with a -2.3 Hz/°C tempco responding to a breath. It’s obviously not stable enough for precise calibration, but even 1 ppm = 125 Hz chunks seem awkwardly large.

Many of the doodles below explore various ways to fit integer values up to 125 MHz and fractions down to 0.0291 Hz/count into fixed point numbers with 24 integer bits + 8 fraction bits, perhaps squeezed a few bits either way. Fairly obviously, at least in retrospect, it can’t possibly work: 125×10⁶ requires 28 bits. Worse, 8 fraction bits yield steps of 0.0039, so you start with crappy resolution.

The DDS tuning word is about 2×10⁶ for outputs around 60 kHz, barely covered by 21 bits. You really need at least seven significant figures = 0.1 ppm for those computations, which means the 125 MHz / 2³² ratio must carry seven significant figures, which means eight decimal places: 0.02910383 and not a digit less.

En passant, it’s disturbing how many Arduino DDS libraries declare all their variables as double and move on as if the quantities were thereby encoded in 64 bit floating point numbers. Were that the case, I’d agree 125e6 / pow(2.0,32) actually meant something, but it ain’t so.

The original non-linear doodles, which, despite containing some values useful in later computations, probably aren’t worth your scrutiny:

AD9850 DDS Fixed-point Number Doodles - 1

AD9850 DDS Fixed-point Number Doodles – 1

AD9850 DDS Fixed-point Number Doodles - 2

AD9850 DDS Fixed-point Number Doodles – 2

AD9850 DDS Fixed-point Number Doodles - 3

AD9850 DDS Fixed-point Number Doodles – 3

AD9850 DDS Fixed-point Number Doodles - 4

AD9850 DDS Fixed-point Number Doodles – 4

AD9850 DDS Fixed-point Number Doodles - 5

AD9850 DDS Fixed-point Number Doodles – 5

AD9850 DDS Fixed-point Number Doodles - 6

AD9850 DDS Fixed-point Number Doodles – 6

AD9850 DDS Fixed-point Number Doodles - 7

AD9850 DDS Fixed-point Number Doodles – 7

AD9850 DDS Fixed-point Number Doodles - 8

AD9850 DDS Fixed-point Number Doodles – 8

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Beckman DM73 Circuitmate: RIP

I’d added Mad Phil’s trusty Circuitmate to the tool kit I carry along to Squidwrench:

Beckman DM73 - new ground clip

Beckman DM73 – new ground clip

Over the last few months it became increasingly erratic, eventually got to the point where slight pressure on the case would blank the display, and finally didn’t turn on at all. Yes, I replaced the batteries.

So I took it apart:

Beckman DM73 Circuitmate - case open

Beckman DM73 Circuitmate – case open

Nothing seemed particularly broken and, even after resoldering all the joints, it continued to not work at all:

Beckman DM73 Circuitmate - PCB

Beckman DM73 Circuitmate – PCB

If you want to try your hand at instrument rehabilitation, let me know.

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Generic AD8950 DDS Modules: Beware Swapped D7 and GND Pins!

Compare this picture:

AD9850 DDS Module - swapped GND D7 pins

AD9850 DDS Module – swapped GND D7 pins

… with any of the doc for the generic AD8950/51 DDS modules you’ll find out on the Interwebs. This snippet from the seller’s schematic will suffice:

AD9850 module schematic - cropped

AD9850 module schematic – cropped

Here’s a closer look at the 2×7 header in the upper left corner:

 

AD9850 module schematic - J5 detail

AD9850 module schematic – J5 detail

Don’t blame me for the blur, the schematic is a JPG.

Compared it with the board in hand:

AD9850 DDS Module - swapped GND D7 pins - detail

AD9850 DDS Module – swapped GND D7 pins – detail

Yup, the D7 and GND pins are reversed.

Some careful probing showed the silkscreen is correct: the pins are, in fact, correctly labeled.

Should you be laying out a PCB in the expectation of using any DDS module from the lowest-price supplier, remember this high truth: Hell hath no fury like that of an unjustified assumption.

Fortunately, I’m hand-wiring the circuit and caught it prior to the smoke test.

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AD8310 Log Amp Module: Video Bandwidth Rolloff

The part I didn’t understand turned out to be the bandwidth of the final output stage = “video bandwidth”, which defaults to 25 MHz. After fixing the input circuitry, a 25 MHz VBW let the output track a 60 kHz input signal just fine:

AD8310 - modified - 60 kHz 1Vpp

AD8310 – modified – 60 kHz 1Vpp

Adding a 56 nF cap across the C6 terminals (just above the AD8310) lowered the VBW to about 1 kHz:

AD8310 Log Amp module - VBW rolloff cap

AD8310 Log Amp module – VBW rolloff cap

Which flattened that sucker right out:

AD8310 - 1 kHz VBW cap - 60 kHz 1.394 V

AD8310 – 1 kHz VBW cap – 60 kHz 1.394 V

The ripple for an absurdly high amplitude 32 kHz signal amounts to 36 mV:

AD8310 - 1 kHz VBW cap - 32 kHz - VBW ripple

AD8310 – 1 kHz VBW cap – 32 kHz – VBW ripple

Firing the tracking generator into the input with a frequency sweep from 100 kHz to 250 MHz shows the low end looks much better:

AD8310 - 1 kHz VBW cap - 100 kHz 250 MHz - 0 dB atten

AD8310 – 1 kHz VBW cap – 100 kHz 250 MHz – 0 dB atten

There’s a slight droop across the sweep that might amount to 50 mV = 2 dB, which I’m inclined to not worry about in this context.

Applying the attenuators once again produces a scale factor of 23.5 mV/dB across 30 dB of RF, but this time the 60 kHz output makes sense, too.

Using the typical output curve from AN-691, that 2.0 V output corresponds to -13 dBm, which sounds about right for the tracking generator (which might really be -10 dBm).

I must calibrate the log amp output to find the actual intercept point (nominally -95 dBm, but could range from -86 to -102) at 60 kHz. The intercept is the extrapolated RF input producing 0 V out, which then acts as an offset for the voltage-to-dBm calculation; you start by finding the slope of the voltage vs. dBm line at some convenient power levels, then solve for dBm with V=0.

So a cheap AD8310 Log Amp module from eBay can work in the LF band, after you rearrange the input circuitry and tweak the chip’s filters. At least now I have a better understanding of what’s going on …

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AD8310 Log Amp Module: Corrected Input Circuit

After puzzling over the AD8310 Log Amp module’s peculiar frequency response, I hacked up the front end circuitry to match the data sheet’s recommended layout:

AD8310 Log Amp module - revised

AD8310 Log Amp module – revised

Given the intended LF crystal-measurement application, a hulking 51 Ω metal film resistor sprawled across the ground plane will work just fine. All three ceramic caps measure a bit under 1 µF; I intended to solder the input caps atop the existing 10 nF caps, but that didn’t work out well at all.

I should harvest the InLo SMA connector to prevent anyone from mistaking it for an actual input.

With that in place, the log amp output makes more sense:

AD8310 - modified - 100 kHz 150 MHz - 0 dB atten

AD8310 – modified – 100 kHz 150 MHz – 0 dB atten

That trace tops out at 150 MHz, not the previous 500 MHz, but now the response is flat all the way out. The log amp generates plenty of hash when the tracking generator isn’t producing a valid signal.

The 60 kHz response looks different:

AD8310 - modified - 60 kHz 1Vpp

AD8310 – modified – 60 kHz 1Vpp

So it’s really the log amp response to the absolute value of the sine wave (or, more accurately, to the sine wave re-zeroed around Vcc/2), with minimum output at the input’s zero crossings. At 500 mV/div, the log amp says the input varies by 42 dB = 1000 mV/(24 mV/dB), which might actually be about right for a zero-crossing (or zero-approaching absolute value of a) signal; logarithms don’t deal well with zeros.

The AD8310 datasheet  and AN-691 suggest the 2.5 V output corresponds to +10 dBm = 12.5 Vrms input, which flat-out isn’t the case. However, the actual 500 mVpeak = 350 mVrms input is 2.5 mW = +4 dBm, so maybe it’s within spitting distance of being right.

AN-691 recommends 10 µF input caps for “low frequency” use, showing results down to 20 Hz; 1 µF seems to get the circuit close enough to the goal for use near 60 kHz.

It also recommends a cap on the BFIN pin (pin 6) to reduce the output stage bandwidth = “video bandwidth” and improve the overall accuracy, which remains to be done. The datasheet suggests rolling VBW off at 1/10 the minimum input frequency, which would be around 3 kHz for use with 32.768 kHz crystals. The equation, with reference to the internal 3 kΩ bias resistor:

CFILT = 1/(2π 3 kΩ VBW) – 2.1 pF = 18 nF

For a bit more margin, 1 kHz would require 56-ish nF.

The PCB has a convenient pair of pads labeled C6 for that capacitor. This may require protracted rummaging in the SMD capacitor stash.

Rolling off the VBW should reduce the hash on the 100 kHz end of the frequency sweep and filter the 60 kHz response down to pretty much a DC level.

Applying the 10 dB and 20 dB SMA attenuators to the input from the tracking generator and recording the log amp output voltage produces this useful table:

AD8310 Log Amp - mods and log response

AD8310 Log Amp – mods and log response

With the terminating resistor on the correct side of the input caps, the log amp seems to be working the way it should, with an output varying a bit under the nominal 24-ish mV/dB over a 30 dB range.

We need caps! Lots of caps!

A quick search with the obvious keywords suggests nobody else has noticed how these modules work over a reasonable bandwidth. Maybe I’m the first person to use them in the LF band?

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Kindle Fire Power Button: Some Things Don’t Last

Once again, the single moving part on my first-generation Kindle Fire stopped working. As before, the switch contacts accumulated enough fuzz & contamination to prevent any current flow, but this time the (soft) solder joints attaching the switch body to the PCB failed:

Kindle Fire power switch - failed anchor

Kindle Fire power switch – failed anchor

My joint cleaning & fluxing wasn’t up to contemporary standards, as shown by the obviously un-fused footprints left in the upper pads:

Kindle Fire power switch - failed anchor joints

Kindle Fire power switch – failed anchor joints

The switch frame seems to be unplated steel, which shouldn’t be an excuse.

So I dismantled the switch, cleaned the contacts and tactile bump plate, put it all back together, and did a much better job of surface preparation:

Kindle Fire power switch - rebuilt - right anchor

Kindle Fire power switch – rebuilt – right anchor

The other joint:

Kindle Fire power switch - rebuilt - left anchor

Kindle Fire power switch – rebuilt – left anchor

And, for completeness, the switch leads:

Kindle Fire power switch - rebuilt - switch pads

Kindle Fire power switch – rebuilt – switch pads

I don’t like the way the joint on the right looks, either, but we’ll see how long the whole affair holds together.

This may be the last time I can repair the Kindle, as a bypass cap came loose while I was working on the PCB, the screen has been accumulating dust at an increasing pace, and several latches securing the back of the case have cracked.

Methinks it’s getting on time for a new pocketable memory device; if only Pixel XL phablets had a bigger screen and didn’t cost night onto a kilobuck.

 

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AD8310 Log Amp Module: LF Response

The label atop a generic AD8310 Log Amp module seemed unambiguous:

AD8310 Log Amp module - overview

AD8310 Log Amp module – overview

Firing the HP 8591 tracking generator into the InHi SMA, terminating InLo (not shown above, for reasons you’ll see below), connecting the Out SMA to the scope’s Trace 1, and the spectrum analyzer’s sweep output to Trace 2 produced an oddity:

AD8310 Log Amp - 100 kHz 500 MHz

AD8310 Log Amp – 100 kHz 500 MHz

The upward-sloping ramp (lower trace) shows the HP 8591’s horizontal sweep, with the tracking generator tuning from 100 kHz to 500 MHz during the 20 ms sweep. The log amp output (upper trace) drops more-or-less linearly with increasing frequency, which seems odd. The tracking generator signal should be pretty much level and the log amp’s output should be more-or-less flat.

My oscilloscope tops out at 150 MHz. The displayed RF is down by 3 dB = 0.6 div at 1.5 division = 190 MHz into the sweep:

AD8310 Log Amp - 100 kHz 500 MHz - RF 50 ohm term

AD8310 Log Amp – 100 kHz 500 MHz – RF 50 ohm term

However, the RF looks pretty much flat up to 125 MHz and it’s still visible beyond 400 MHz, so I think the tracking generator is doing what it’s supposed to. If the RF were decreasing, then the trace would look different, methinks.

The response to a 60 kHz sine wave doesn’t look quite right:

AD8310 Log Amp - 60 kHz 1 Vpk

AD8310 Log Amp – 60 kHz 1 Vpk

Eyeballometrically, it might be a log response to the absolute value of the derivative: kinda flat on the ups-and-downs, kinda zero-ish at the tops-and-bottoms. Or maybe it’s the log response to a phase-shifted version of the input, with the lows corresponding to the zero crossings.

Documentation for the circuit seems nonexistent, because eBay. Fortunately, one can pop the top to reveal the straightforward PCB layout:

AD8310 Log Amp module - uncovered

AD8310 Log Amp module – uncovered

A closer look:

AD8310 Log Amp module - PCB detail

AD8310 Log Amp module – PCB detail

A capacitance meter says input capacitors C5 and C7 are both 10 nF.

A sketch of the circuitry:

AD8310 Log Amp module - input circuit

AD8310 Log Amp module – input circuit

The datasheet puts the terminating resistor on the other side of the input caps, where it surely belongs:

AD8310 Datasheet - Basic Connections diagram

AD8310 Datasheet – Basic Connections diagram

 

Achtung: the solder blob just to the left of C7 grounds the signal pin on the InLo SMA. Don’t connect anything to InLo which might take offense at having its output shorted to ground; the SMA terminator I used had no effect whatsoever.

The AD8310 chip (assuming that’s what it really is) has a differential input resistance = 1 kΩ and capacitance = 1.4 pF in parallel with R3, the 52.3 Ω terminating resistor, making the net resistance just under 50 Ω.

At 60 kHz, the input caps have a reactance of 270 Ω apiece, which means the “terminating” resistor is maybe 10% of the mostly capacitive input impedance seen at the InHi connector. That means the AD8310 inputs see maybe 10% of the input signal.

In fact, if you regard those three parts as an RC high pass filter and merge the caps into a single 5 nF unit, it rolls off at 620 kHz = 1/(2π · 52 · 5 pF). Obviously, it’ll be a fine differentiator at 1/10 the breakpoint frequency.

A simulation shows it in action (clicky for more dots):

AD8310 Log Amp module - input circuit simulation

AD8310 Log Amp module – input circuit simulation

The two 1 MΩ resistors provide a balanced DC path-to-ground for R3 to keep the simulator happy.

The (+) input tends toward 0 dB as C5 tends toward a short, the (-) input tends toward ground as C7 does likewise, but their difference isn’t a constant value. Seeing as how a log amp should respond to small differences, methinks it’s hard at work.

The AD8310 data sheet says the scale factor is about 24 mV/dB between 10 MHz and 200 MHz, with no frequency dependence worth mentioning. Eyeballometrically, the output has a 240 mV = 10 dB straight-line decrease over the entire frequency range of that scope shot. It drops by 220 mV = 9.2 dB in the decade from 50 to 500 MHz, half of the 20 dB you’d expect from a first-order filter response.

The AD8310 has an internal 2 MHz high pass feedback loop to suppress low frequency input offset voltages. The doc recommends a 1 µF cap from OLFT to ground for frequencies down in the low audio range. One might solder the cap across the convenient pads labeled C8 below the chip.

Rearranging the input circuitry seems in order:

  • Move R3 outside C5 and C7, per the datasheet
  • Increase C5 and C7 to 1 µF -ish
  • Add 100nF – 1 µF bypass cap at C8

I have the uneasy feeling I’m overlooking something obvious …

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