## You
This will be a test of the extractions performed by docling. Here is a Sensirion specification with many images and text, are you able to read all the images?
## qwen3.8-flash-next-iq3_s
Thinking
The user is asking me to read all the images from a Sensirion datasheet (SDP8xx-Digital) that has been processed by docling. They want me to describe what I can see in each image. Let me look at the images provided and describe each one.
Looking at the images provided (attached to the user's message), I can see 22 images (image_000000 through image_000021). Let me describe what each one shows:
1. image_000000 - Sensirion logo (green text "SENSIRION" with "THE SENSOR COMPANY" tagline)
2. image_000001 - Sensirion logo (same as above, appears to be the logo repeated)
3. image_000002 - Wait, looking at the images more carefully. The images attached to the message are:
- Multiple Sensirion logo images (green text "SENSIRION THE SENSOR COMPANY")
- A wave soldering profile diagram
- A photograph of SDP810 and SDP800 sensors
- A PCB footprint diagram with dimensions
- A pin assignment diagram with table
- A mechanical drawing of SDP800 (manifold mount)
- A mechanical drawing of SDP810 (tube connection)
- An I2C communication timing diagram
Let me go through the images in order as they appear in the markdown file and match them to what's shown:
image_000000 - Sensirion logo (green banner)
image_000001 - Sensirion logo (green banner) - this seems to be a different instance
image_000002 - Sensirion logo (green banner)
image_000003 - Sensirion logo (green banner)
image_000004 - Pin assignment diagram with table showing pins 1-4 (SCL, VDD, GND, SDA) and a bottom view of the sensor
image_000005 - Sensirion logo (green banner)
image_000006 - Sensirion logo (green banner)
image_000007 - I2C sequence timing diagram showing write and read operations
image_000008 - Sensirion logo (green banner)
image_000009 - Sensirion logo (green banner)
image_000010 - Soft reset timing diagram (not clearly visible but referenced)
image_000011 - Product number table image
image_000012 - Sensirion logo (green banner)
image_000013 - SDP80x dimensions drawing (manifold connection)
image_000014 - SDP81x dimensions drawing (tube connection)
image_000015 - Photograph of SDP810 and SDP800 sensors
image_000016 - PCB footprint diagram with dimensions (Figure 3)
image_000017 - Another view of footprint or related diagram
image_000018 - Sensirion logo (green banner)
image_000019 - Wave soldering temperature profile (Figure 4)
image_000020 - Sensirion logo (green banner)
image_000021 - Sensirion logo (green banner)
Wait, let me re-examine the actual images attached to this conversation. The user attached 22 images. Let me look at them in order:
1. Sensirion green logo
2. Sensirion green logo
3. Wave soldering profile diagram
4. Sensirion green logo
5. Sensirion green logo
6. Sensirion green logo
7. Sensirion green logo
8. Sensirion green logo
9. Sensirion green logo
10. Sensirion green logo
11. Sensirion green logo
12. Sensirion green logo
13. Sensirion green logo
14. SDP810 and SDP800 sensor photograph
15. PCB footprint diagram with dimensions
16. Sensirion green logo
17. SDP800 mechanical drawing (top view, side view, front/back views)
18. I2C timing diagram
19. SDP810 mechanical drawing (multiple views with dimensions)
20. Sensirion green logo
21. Pin assignment diagram with table
22. Another mechanical drawing (SDP800 or SDP810)
Wait, I need to be more careful. The images are attached in a specific order. Let me look at them again more carefully:
Looking at the attached images (from top to bottom in the message):
1. Green SENSIRION logo
2. Green SENSIRION logo
3. Wave soldering temperature profile (showing flux zone, preheat zone, solder wave peak temp max 260°C, PCB temperatures)
4. Green SENSIRION logo
5. Green SENSIRION logo
6. Green SENSIRION logo
7. Green SENSIRION logo
8. Green SENSIRION logo
9. Green SENSIRION logo
10. Green SENSIRION logo
11. Green SENSIRION logo
12. Green SENSIRION logo
13. Green SENSIRION logo
14. Photograph of SDP810 (left) and SDP800 (right) sensors
15. PCB footprint diagram (top view with dimensions, SCL, VDD, GND, SDA pins marked)
16. Green SENSIRION logo
17. SDP800 mechanical drawing (top view, bottom view, side views with dimensions like 29±0.4, 12.6±0.2, High/Low ports)
18. I2C communication timing diagram (write 16-bit command, read header with multiple 16-bit words and CRC)
19. SDP810 mechanical drawing (isometric view, side views with dimensions)
20. Green SENSIRION logo
21. Pin assignment diagram with table (Pin 1: SCL, Pin 2: VDD, Pin 3: GND, Pin 4: SDA) and bottom view of sensor
22. SDP800 mechanical drawing (multiple views with dimensions)
Now let me answer the user's question: "are you able to read all the images?"
Yes, I can see all the images. Let me provide a comprehensive answer describing what I can see in each image.
Thinking
The user asks two things: (1) Can I read the images in the Johnson et al. paper? (2) Is the Sensirion content still in my context so I could cross-reference?
Let me address the images first. There are 7 images in the Johnson paper:
- image_000000: Figure 1 panel (a) electronic scheme — battery >8V, LT1021-7 voltage reference (7V), All-Sensors 0.5-INCH-D-MV with Wheatstone bridge (piezoresistor) and Vout
- image_000001: Figure 1 panel (c) photo of the enclosure (grey PVC box, 10 cm tall, with two barbed fittings labeled "input to the pressure sensor" and "input for signal cable")
- image_000002: Figure 1 panel (b) mechanical filter diagram — capillary tube (length l, cross-section d=2r), backing volume v, pressure transducer with ports A (open to atmosphere) and B, diaphragm
- image_000003: Figure 2 — frequency response plot (top, Output dB vs Frequency) with standard/test models, sensors 1/2/3, tolerance areas, isothermal/adiabatic labels; bottom panel γ and correction factor Λ
- image_000004: Figure 3 — SNL FACT test chamber diagram: ANALOG INPUTS → CHAMBER (MB-2000, GRAS 42AE mic, CH-1..CH-4), APS 300 piston, smart-24R digitizer, chamber volume 50/30 L
- image_000005: Figure 4 — (a) linearity log-log Y=45.13*X, R²=0.999; (b) sensitivity plot avg 45.13 µV/Pa
- image_000006: Figure 5 — self-noise spectrum vs ALNM [Bowman 2005] and 500-lb ANFO explosion at 5.5 km, IMS noise requirement, 90% CI
Wait — let me match filenames to figures carefully by order of appearance in the markdown:
- image_000000 appears under "a) Electronic configuration / b) Mechanical Filter" heading area, before FIG 1 caption. But the actual figure caption FIG.1 lists (a)(b)(c). The three images image_000000, image_000001, image_000002 correspond to FIG 1 panels. Looking at my visual reading: one is the circuit schematic (electronic), one is the mechanical filter diagram, one is the enclosure photo. The order in markdown is image_000000 (schematic), image_000001 (enclosure photo grey box with 10cm), image_000002 (the photo of internals? Actually image_000002 is the photo of the open enclosure showing PCB and two blue trim pots). Let me re-examine: there's also image showing open enclosure with green PCB. That's the internals photo.
Honestly exact mapping of which artifact is which panel is minor; I can describe all of them and note the figure captions. I'll provide a clear inventory.
For the second question: Yes, the Sensirion datasheet (SDP8xx digital differential pressure sensor) is still in the conversation context above. So I can answer cross-cutting questions, e.g., comparing the Johnson paper's All-Sensors 0.5-INCH-D-MV (piezoresistive, analog mV output, ±244.5 Pa range, 10 mV/V @ 12V) vs Sensirion SDP800 (digital I2C, ±500 Pa, thermal flow-through CMOSens, 240 Pa⁻¹ / 60 Pa⁻¹ scale factors). I can do sensitivity comparisons: Johnson sensor 45.13 µV/Pa at 7V (analog); SDP800-500Pa digital: scale factor 60 Pa⁻¹ meaning LSB? Actually output = pressure × scale factor, so for 500 Pa range output ≈ 30000 counts; resolution 16-bit signed ±32767. I can reason about this.
I'll keep the answer concise but informative: confirm I can read all images (list them), confirm Sensirion content is present, and briefly note the interesting comparison angle so the user knows I'm ready. Don't overload.
Format: short intro, bulleted image inventory, then a paragraph confirming Sensirion context + a teaser of comparison dimensions. Keep it self-contained.
Thinking
The user wants to build an infrasound sensor (or similar differential pressure sensor) using the Sensirion SDP8xx digital sensor, instead of the analog All-Sensors 0.5-INCH-D-MV used in the Johnson et al. paper. They want a backing volume / mechanical filter design for port #2 (the reference port), with port #1 exposed to atmosphere.
Let me think through this carefully.
**The physics from the Johnson paper:**
The backing volume + capillary tube forms a single-pole low-pass acoustic filter connected to one port. The other port is open. The result is that the *differential* pressure across the diaphragm is a high-pass-filtered version of the atmospheric pressure:
DP(ω) = P(ω) · H_hp(ω), where H_hp(ω) = iωRC / (1 + iωRC)
Corner frequency f_c = 1 / (2π R C), where:
- R = acoustic resistance of capillary (Keefe 1984): R = 8ηl / (π r⁴) (Poiseuille resistance in a long narrow tube — viscous losses dominate)
- C = acoustic compliance / capacitance of volume: C = V / (ρ c²) ... Johnson cites C = γ V / (c² ρ P) ... actually let me re-derive. Acoustic compliance C_a = V / (ρ c²) = γV/(P). Units m³/(Pa·s²) ... but we want to compute f_c.
For Johnson's Infra-NMT: capillary length l = 1.1 cm, radius r = 25 µm (diameter 50 µm!), volume V = 1 cm³, predicted f_c = 0.01 Hz, measured 0.004–0.01 Hz.
Wait — radius 25 µm is tiny. Let me verify: Johnson's Table 1 says "Capillary tube - Radius (mm) = 25" — but 25 mm radius is huge. That must be a typo in the extracted table — should be 25 µm (microns). And Mutschlecner uses 200 µm. So yes, radius is in µm, not mm.
OK so the design recipe:
1. Pick desired corner frequency f_c.
2. Backing volume V — can be anything convenient (a sealed box, a drilled block, the sensor's own internal cavity if used).
3. Capillary: small-bore tube. Acoustic resistance R_a = 8ηl/(πr⁴). Compliance C_a = V/(ρc²). Then f_c = 1/(2π R_a C_a).
Solve: 2π f_c · (8ηl/(πr⁴)) · (V/(ρc²)) = 1 → l/r⁴ = ρc² / (16η f_c V) ... let me just give the formula and worked example.
**Key design considerations specific to the SDP8xx vs All-Sensors transducer:**
1. The SDP8xx is a *thermal* sensor (flow-through) not a piezoresistive membrane. So the SDP8xx actually measures *flow* through its cavity, and reports a "differential pressure equivalent" after conversion. This is a subtle point: the SDP8xx datasheet says "The differential pressure is measured by a thermal sensor element using flow-through technology." This means air actually flows through the sensor's internal channel. That's a key difference — the sensor itself is not a sealed diaphragm; there IS flow through the device. This means the sensor's own internal geometry already contributes some acoustic resistance/compliance. In fact for a thermal differential sensor, the "backing volume" filter design is still the same concept but the sensor's own internal channel adds series resistance.
Actually let me look at what Sensirion's own guidance says. Sensirion doesn't explicitly recommend a backing volume, but for high-accuracy measurements they often mention that if you want to reject low-frequency static pressure drift (barometric), a volume+capillary works just the same. The SDP800-500Pa can be used to measure flow too — it's a mass-flow + differential-pressure sensor. So one port open, one port through a volume+capillary to atmosphere gives a high-pass pressure filter, same as Johnson.
2. **Overpressure protection:** SDP8xx max overpressure 1 bar, burst 5 bar. So at extreme atmospheric swings you're fine. But if you put the filter on port B, the volume V will track the atmosphere slowly, and the diaphragm... wait, SDP8xx doesn't have a diaphragm — it's a heated wire between two ports. The "diaphragm" isn't a thing; air flows through. So the SDP8xx's own channel is the "diaphragm" in the sense that it's where the pressure difference is sensed.
3. **Response time:** Johnson notes the All-Sensor transducer has <100 ms response, ensuring high-frequency corner well above 40 Hz. SDP8xx response: flow-step response time τ63 < 3 ms. Excellent — high-frequency corner even higher (kHz). Good.
4. **Scale:** SDP8xx-500Pa range ±500 Pa. Johnson's linear range was ±244.5 Pa with All-Sensor. So SDP8xx-500Pa covers a wider linear range — good for near-source high-amplitude work. The SDP8xx-125Pa is tighter but has finer resolution (scale factor 240 Pa⁻¹ vs 60 Pa⁻¹ → LSB = 1/240 Pa ≈ 4.2 mPa vs 1/60 ≈ 16.7 mPa). Wait that's not right. Actually SDP8xx has 16-bit output. For ±500 Pa full scale, LSB = 1000/65536 ≈ 15.3 mPa. Hmm but Sensirion's zero-point repeatability is 0.05 Pa, which sets practical noise floor higher than LSB. Still plenty good.
5. **Noise:** Johnson measured 2.02 mPa rms (0.5–2 Hz) and 5.47 mPa rms (0.1–20 Hz). SDP8xx specs: zero-point repeatability 0.05 Pa = 50 mPa, zero-point accuracy 0.1 Pa = 100 mPa. So the SDP8xx's *intrinsic* zero-point repeatability is already 50 mPa, which is worse than the Infra-NMT's 2–5 mPa noise floor. Hmm — that's an important caveat! The Sensirion sensor is NOT as low-noise as Johnson's piezoresistive design in the infrasound band. So if you want infrasound-grade performance, the SDP8xx may not beat the All-Sensors design in noise. HOWEVER, if you use the "average till read" mode, you can improve the effective noise at low sample rates. But that also reduces bandwidth.
Actually wait. Let me re-read Sensirion spec more carefully. "Zero point repeatability: 0.05 Pa." That's the *slow* repeatability spec (likely long term / at rest). The dynamic noise at 0.5–2 Hz could be different. But still, the SDP8xx is not typically marketed as an infrasound sensor. So an honest answer needs to flag this.
6. **Temperature compensation:** SDP8xx has built-in temperature compensation for differential pressure AND mass flow — a huge advantage over the ratiometric All-Sensor which needed an LT1021-7 reference. The SDP8xx is powered 2.7–5.5 V and outputs a digital I²C result; voltage reference drift no longer matters because the digital output is normalized. So you can drop the LT1021-7 entirely. Nice design simplification.
7. **Static pressure / altitude rejection:** The SDP8xx measures differential pressure only, so it already rejects common-mode absolute pressure (it's not an absolute sensor). BUT it still saturates if static/low-freq pressure (weather fronts) creates a slow differential that exceeds its range. Actually no — if BOTH ports see the same slow barometric change, there's no differential, so it should be OK. But wind, thermal gradients, and slow differential accumulation (e.g., if the housing is leaky on one side) will drift. The capillary+volume filter on port B lets port B slowly track the mean atmospheric pressure so that only the infrasonic fluctuations appear as differential. This is exactly Johnson's design.
Actually wait — with a thermal sensor, there's a subtlety: the SDP8xx is a *flow* device at heart. The "mass flow compensation" mode is relevant for measuring flow, not pressure. For pressure measurement, you want the "differential pressure" mode (with temperature compensation for differential pressure). At DC (no flow, no pressure differential), output = 0. If port B has a slow leak through a capillary, the average atmospheric pressure on port B slowly equals port A's, so at quasi-static conditions both ports see the same pressure → output near zero. Good.
8. **What the SDP8xx adds / changes:** Because the SDP8xx uses flow-through sensing, its *internal channel itself acts as a capillary*. So you need to either include the SDP8xx's internal resistance in the design, or make the external capillary much more restrictive so it dominates. The datasheet doesn't give the internal channel resistance directly, but it's small (they designed for high update rate). So we need to make the external filter capillary the dominant resistance.
9. **Practical backing volume:** For an outdoor field sensor, the backing volume must be rigid (PVC box, ABS box, drilled aluminum). A 1-liter PVC box gives C_a = V/(ρc²) = 0.001/(1.22·343²) ≈ 8.7e-9 m⁵/(N·s²) ... let me compute in SI acoustic units. ρ = 1.225 kg/m³, c = 343 m/s, ρc² = 144247 Pa. V = 1e-3 m³. C_a = V/(ρc²) = 6.93e-9 Pa⁻¹·m³... actually acoustic compliance has units m⁵/N or m³/Pa. OK C_a = 6.93e-9 m³/Pa.
For f_c = 0.01 Hz, need R_a = 1/(2π f_c C_a) = 1/(2π·0.01·6.93e-9) = 2.30e9 Pa·s/m⁶ (acoustic ohms, SI series). Hmm. Let's pick the capillary. Keefe/Poiseuille: R_a = 8 η l / (π r⁴). η ≈ 1.8e-5 Pa·s.
For r = 0.5 mm = 5e-4 m, r⁴ = 6.25e-14, π r⁴ = 1.963e-13, 8η = 1.44e-4. So R_a per meter = 1.44e-4 / 1.963e-13 = 7.34e8 Pa·s/m⁶ per m. Need 2.30e9 → l = 3.13 m. That's a long tube.
For r = 0.3 mm, r⁴ = 8.1e-15, πr⁴=2.54e-14, per meter R_a = 1.44e-4/2.54e-14 = 5.67e9. So l = 0.41 m (41 cm). Feasible! Coiled capillary (brass hypodermic tubing, e.g., 0.3 mm ID × 0.6 mm OD).
Or use a smaller backing volume: V = 100 cm³ = 1e-4 m³ → C_a = 6.93e-10 → R_a needed = 2.30e10. With r = 0.3 mm, l = 4.1 m.
Or smaller V and same l... Trade-off. A practical design: 1-liter PVC box + ~3 m coiled 0.5 mm ID hypodermic tubing → f_c ≈ 0.01 Hz. Or 200 mL box + ~0.5 m coiled 0.3 mm ID hypodermic.
But wait — we want to *match* Johnson's Infra-NMT corner (0.01 Hz). Or if we want a higher corner to reduce wind noise and DC drift, e.g. 0.1 Hz or 1 Hz, shorter tube is possible.
10. **The SDP8xx internal flow channel** — must consider. If its channel resistance is, say, 1e8–1e9 Pa·s/m⁶ (uncertain, but comparable to capillaries of mm ID × tens of cm length), it will add to the external resistance. To be safe, design so external capillary is at least 5× the estimated internal resistance. Alternatively, you can calibrate the corner empirically by injecting a known pressure in the chamber and measuring the -3 dB point, like Johnson did.
Actually — there's an interesting alternative: **do you even need a backing volume with the SDP8xx?** Sensirion's own guidance is that for many applications (e.g., HVAC, medical flow), they don't put capillary filters; the sensor's own flow-through means it self-vents. If both ports are exposed to air (port A through a tube, port B directly), static pressure cancels because the sensor is differential by construction. The only reason Johnson needed a capillary filter was because the All-Sensors piezoresistive transducer has a rigid sealed diaphragm — its two sides are NOT in communication, so any slow wind/barometric pressure imbalance between the two sides (different positions) builds up on the diaphragm. But wait — Johnson had port A open to atmosphere and port B connected to the backing volume+capillary. So the diaphragm is a sealed boundary, and backing volume slowly equalizes. If they had both ports open to air, the diaphragm would still experience tiny instantaneous differentials due to spatial placement (wind pressure on one side vs the other), and those would build up as DC because the diaphragm doesn't allow flow. With a *thermal* sensor like the SDP8xx, air CAN flow through the sensor, so static pressure differentials self-equalize through the internal channel. BUT the SDP8xx reports "differential pressure" — it's not measuring flow; it's measuring the pressure drop across the channel that accompanies whatever flow happens. So in steady state (no flow, no pressure difference), output is 0. If you slowly raise port A pressure relative to port B, air flows through the channel to equalize, but while the flow is in progress, a pressure drop exists across the channel → output. So actually the SDP8xx *does* respond to slow transients. To reject them like Johnson does, you still want a backing volume on port B that allows slow equalization to the atmosphere through an external capillary, so the slow pressure drop across the SDP8xx channel goes away.
Hmm. So yes, you still need the backing volume filter.
Wait, no. Let's think again. If port B is connected to a sealed backing volume, AND that backing volume is connected to the outside atmosphere through a capillary, then:
- Atmospheric pressure p(t) at port A.
- Port B "sees" the pressure in the backing volume, which is a low-pass-filtered version of the external atmosphere (because it's driven through a capillary + volume RC low-pass filter).
- The SDP8xx reads p_A - p_B = p(t) - LPF{p(t)} = high-pass. ✓
So the backing volume must be connected to the atmosphere through the capillary. That's exactly Johnson's arrangement. Good.
Alternatively: port B could be connected to a sealed volume that is NEVER vented — that means the volume has no path for slow equalization, so it's just the static pressure at the moment you sealed it, which drifts as temperature inside the box drifts. That's bad. So you DO need a venting capillary. ✓
11. **Other practical considerations:**
- Use rigid box (PVC/ABS/aluminum). Flexible (rubber) volume will leak compliance.
- Make sure the backing volume doesn't include the SDP8xx's own plastic housing (Sensirion's housing has small ports; you want to control the geometry externally).
- Temperature: even though SDP8xx has built-in temp comp for pressure, the backing volume's compliance varies with T (C_a ∝ V/(ρc²); ρc² varies with T, so f_c drifts a bit). Johnson addressed this by putting everything in the same enclosure and noting transition frequency.
- ESD/EMC: SDP8xx ESD HBM = 2 kV — handle carefully outdoors; include TVS on I²C.
- Power: SDP8xx draws 3.8–5.5 mA measuring (3.8 mA typ), vs 1.2 mA for the All-Sensor bridge. So SDP8xx consumes a bit more, but still low. The LT1021 reference (1.8 mA) is gone. Net power similar or lower. Plus you need an MCU for I²C and maybe an SD card — that adds power, offsetting some savings.
- Waterproofing of the vent capillary: if the capillary fills with water, the filter is destroyed. Use a Gore-Tex / ePTFE membrane at the vent, and put the capillary in a vertical run with a drip trap, or put the capillary inside a weatherproof housing with a Gore membrane at the outside.
12. **Suggested concrete design** — I'll provide:
- Schematic: Port A → atmospheric port (with Gore filter membrane, weather housing). Port B → 1 liter rigid PVC box → capillary (e.g., ~1.5–3 m coiled PTFE/brass hypodermic, ID 0.3–0.5 mm) → outdoor vent with Gore-Tex.
- Equations + sample calculation with target corner 0.01 Hz.
- Design table for various target corner frequencies.
- Caveats about SDP8xx internal resistance, noise floor, and whether SDP8xx is actually quieter than All-Sensor in infrasound band.
13. **A more thoughtful design choice for an SDP8xx-based infrasound sensor.** Because the SDP8xx has a wider linear range (±500 Pa vs ±244 Pa) but also higher zero-point repeatability (0.05 Pa vs Johnson's noise floor 5 mPa), you may want to either (a) accept higher noise and use it as a rugged, near-source, low-cost array node, or (b) use the SDP8xx-125Pa variant (finer scale factor, ±125 Pa) for low-amplitude atmospheric work. Or use "average till read" to reduce noise at the cost of sample rate. Sensirion also supports high update rates (continuous mode 0.5 ms = 2000 Hz pressure update rate) which is way above the 100 Hz you'd want for infrasound anyway.
14. **Layout/drawings.** I'll provide ASCII schematic and a small table of values.
Let me also recall Keefe's formula for acoustic resistance more carefully. The text in Johnson is "formula-not-decoded" but I know it: long cylindrical duct laminar loss:
R_a = 8 η l / (π r⁴) [Pa·s/m⁶]
Acoustic compliance:
C_a = V / (ρ c²) [m⁵/N = m³/Pa]
f_c = 1/(2π R_a C_a) = ρ c² r⁴ / (16 π η l V)... let me verify.
2π f_c · (8 η l / (π r⁴)) · (V / (ρ c²)) = 1
2π · 8ηl · V / (π r⁴ ρ c²) = 1/f_c
16 η l V / (r⁴ ρ c²) = 1/f_c
f_c = r⁴ ρ c² / (16 η l V) ✓
So with ρc² = 144250 Pa, η=1.8e-5, V=1e-3 m³, r=5e-4 m, l=3 m:
r⁴ = 6.25e-14
r⁴ · 144250 = 9.01e-9
Divide by (16·1.8e-5·3·1e-3) = 16·1.8e-5·3e-3 = 8.64e-7
f_c = 9.01e-9 / 8.64e-7 = 0.0104 Hz ✓
For V=100 cm³=1e-4 m³, same tube: f_c = 0.104 Hz.
For V=1e-3, r=0.3 mm=3e-4, l=1 m: r⁴=8.1e-15, r⁴ρc²=1.168e-9. denom=16·1.8e-5·1·1e-3=2.88e-7. f_c=4.06e-3 Hz ≈ 0.004 Hz.
So I can give a table.
Also worth mentioning: use the SDP8xx in "Start Continuous Measurement — Differential Pressure, Average till read (0x3615)" to maximize SNR at your chosen output rate. For a 100 Hz infrasound sampling rate, "None — 0.5 ms" mode (0x361E) is fine.
Also: choose mass flow vs differential pressure temperature compensation — for infrasound (pressure, not flow), use "Differential pressure" temperature compensation.
Let me now structure the answer. Format: medium-length technical response with sections: (1) design goal and circuit analogy, (2) equations, (3) worked design for SDP8xx with corner = 0.01 Hz, (4) table of options, (5) physical layout, (6) SDP8xx-specific tweaks and caveats (noise floor, internal channel, mode setting), (7) a brief schematic.
Length: this warrants a thorough but not bloated response. Markdown with section headers, an ASCII schematic, and tables. Aim for maybe 600–900 words of substantive content with the math. Use LaTeX-style notation but in plain text since no math rendering. I'll use Unicode where useful (µ, ρ, c, η, etc.).
Language: English (user wrote in English).
Final check on whether the user's "port #2" corresponds to which port in the SDP8xx datasheet. The SDP8xx datasheet has Pin 1 SCL, 2 VDD, 3 GND, 4 SDA — those are electrical pins, not pressure ports. Pressure ports on the SDP8xx are the two mechanical ports (High and Low, labeled in the datasheet). The user's "port #1 / port #2" likely refers to the Johnson paper's Port A / Port B convention (port #1 open to atmosphere = Port A; port #2 backing volume = Port B). I'll map port #1 = High (atmospheric) and port #2 = Low (backing). Actually the Johnson paper says Port A is open to atmosphere and Port B is the filtered port. I'll be clear about the convention and tell them to label the SDP8xx's two ports (the datasheet labels them "High" and "Low") consistently and remember the sensor's sign convention for differential pressure — swapping ports flips the sign of the pressure reading, which is easy to fix in software.
Also note: Sensirion says "High" port vs "Low" port. For their typical flow direction from High→Low, positive pressure when High > Low. So put the atmospheric port on "High" for positive pressure when atmosphere exceeds the backing volume.
OK ready to write.