Understanding Logarithmic Output in High Vacuum Measurement

Introduction

High-vacuum measurement spans many orders of magnitude—from 10⁻⁷ Torr in ultra-clean chambers to 10⁻³ Torr during process gas introduction. A linear voltage output would compress most of the useful range into a few millivolts at the low-pressure end, making precise control impossible. The Poseidon Scientific VG-SM225 Cold Cathode Vacuum Gauge therefore uses a logarithmic 0–10 V analog output with a fixed slope of 1.33 V per decade. This scaling matches the exponential nature of vacuum pressure, delivering uniform resolution across six decades and simplifying integration with PLCs, SCADA systems, and data loggers.

As the product manager who designed the VG-SM225 alongside its companion VG-SP205 Pirani Vacuum Transmitter, I created this guide to help engineers and procurement teams understand why logarithmic output is essential, how to interpret the signal, and how to integrate it seamlessly into automated coating, semiconductor, and analytical systems. The principles here follow decades of vacuum metrology best practices and are implemented in every VG-SM225 shipped from our facility.

Why Vacuum Pressure Uses a Logarithmic Scale

Vacuum pressure is inherently exponential. A change from 10⁻³ Torr to 10⁻⁴ Torr represents a tenfold drop in gas density, while the same absolute change at 10⁻⁶ Torr is only a 1 % relative shift. Linear scaling would allocate equal voltage steps to vastly different physical effects, sacrificing resolution where it matters most—at the lowest pressures critical for contamination control and nucleation uniformity.

A logarithmic scale compresses these decades into equal voltage increments. For the VG-SM225 the output voltage \( V_{\text{out}} \) relates to pressure \( P \) (in Torr) by:

P (Torr) = 10^((V_out - 7.75) / 1.33)

This formula is factory-calibrated for air and remains accurate across common process gases with published correction factors. The result is uniform sensitivity: every 1.33 V change equals exactly one decade of pressure, regardless of absolute value. Engineers see the same voltage resolution at 10⁻⁷ Torr as at 10⁻³ Torr, making PID tuning, trending, and alarm setpoints straightforward and repeatable.

1.33 V per Decade – Practical Example

Consider a typical PVD process chamber. At base pressure the VG-SM225 outputs 2.0 V (≈1 × 10⁻⁷ Torr). When process argon is introduced and pressure rises to 5 × 10⁻³ Torr, the output reaches ≈8.0 V. The voltage change is 6 V—corresponding to four full decades (10⁻⁷ to 10⁻³ Torr).

Using the formula:

P = 10^((8.0 - 7.75) / 1.33) ≈ 10^(0.25 / 1.33) ≈ 10^0.188 ≈ 1.54 × 10−3 Torr

(Actual value is adjusted by the controller for the exact operating point.) This linear-in-log relationship means a simple PLC scaling block or LabVIEW VI can convert voltage directly to pressure on a log axis without lookup tables or piecewise linearization. The same scaling works across the entire 2.0–9.6 V effective range, giving engineers consistent resolution for charting, alarming, and closed-loop control.

Why Linear Output Fails in High Vacuum

A hypothetical linear 0–10 V output scaled 0–10⁻³ Torr would allocate only 0.01 V (10 mV) to the entire 10⁻⁶–10⁻⁷ Torr decade—well below the noise floor of most PLC analog inputs. Small voltage fluctuations of 20–50 mV (common from EMI or grounding issues) would appear as massive pressure swings, triggering false interlocks or masking real leaks.

Linear scaling also wastes dynamic range. At higher pressures the signal would saturate early, leaving the low-pressure regime with almost no resolution. The VG-SM225 logarithmic output avoids these problems entirely: every decade receives equal voltage span, noise is proportionally distributed, and the full 0–10 V range is used efficiently. This is why cold-cathode gauges have used logarithmic scaling for decades in research and production tools.

Data Interpretation Tips

Interpreting the VG-SM225 output is simple once the logarithmic relationship is understood:

• 2.0 V = 10⁻⁷ Torr (lower limit)
• 3.33 V ≈ 10⁻⁶ Torr
• 4.66 V ≈ 10⁻⁵ Torr
• 5.99 V ≈ 10⁻⁴ Torr
• 7.32 V ≈ 10⁻³ Torr (upper practical limit)
• Values 9.6 V indicate error or over-range; the red status LED flashes.

Always reference the exact formula for your firmware version (printed on the label or available in the manual). For trending, plot voltage on a linear axis with a secondary log-pressure axis or use the direct exponential conversion in your HMI. When comparing against a reference gauge, convert both to the same engineering units first. Gas correction factors (argon ≈0.7× air, helium ≈1.4× air) can be applied in software or selected via the optional RS232 interface on paired systems.

Integration into PLC and Automation Systems

The logarithmic output integrates directly with any modern controller:

1. Wire the 0–10 V signal to a differential analog input module (recommended) or single-ended with proper grounding.
2. In the PLC scaling block, apply the formula: Pressure = 10^((V_in – 7.75) / 1.33). Most platforms (Siemens, Allen-Bradley, Beckhoff) have native LOG10 and POW functions.
3. Add a simple first-order digital filter (τ = 0.5–2 s) to smooth residual EMI without losing process response.
4. Use the status line or voltage threshold (<2 V) for fault detection and interlocks.
5. For hybrid systems, combine with the VG-SP205 Pirani (RS232) and implement automatic crossover logic at 10⁻³ Torr for continuous coverage from atmosphere to high vacuum.

Sample function blocks and LabVIEW VIs are available on the product page. The low output impedance (<20 Ω) and built-in filtering make the signal robust even in electrically noisy production environments.

Application Example: Reactive Sputtering Coater

A production optical-coating line required stable base-pressure confirmation below 5 × 10⁻⁷ Torr before introducing argon to 5 mTorr. The previous linear-output gauge produced noisy readings at the low end, causing erratic plasma ignition and thickness variation >±5 %.

Replacing it with the VG-SM225 gave a clean 2.1 V signal at 8 × 10⁻⁷ Torr. The PLC converted voltage directly to pressure and held the chamber at target with ±2 % stability. The logarithmic scaling allowed a single alarm threshold (3.0 V = 10⁻⁶ Torr) to protect the entire high-vacuum phase. Yield improved 18 %, false trips disappeared, and calibration interval extended to 12 months. The same gauge now runs on six identical tools with one spare-parts kit.

Conclusion

The logarithmic output of the VG-SM225 Cold Cathode Vacuum Gauge solves the fundamental problem of measuring pressure across many decades: it delivers uniform resolution, simplifies scaling, and rejects noise proportionally. By understanding the 1.33 V/decade relationship, applying the simple conversion formula, and following basic integration practices, engineers achieve clean, actionable pressure data for the most demanding high-vacuum processes.

Ready to upgrade your coating or analytical system with reliable logarithmic high-vacuum measurement? Our applications team offers free technical reviews, sample PLC code, custom calibration curves, and rapid quotations. Contact us today for a no-obligation consultation—simply visit the product page or reply to this article.

VG-SM225 Cold Cathode Vacuum Gauge – Logarithmic 0–10 V Output
VG-SP205 Pirani Vacuum Transmitter – Roughing Companion for Full-Range Coverage

At Poseidon Scientific we design vacuum instrumentation that engineers trust—delivering the clean signals, easy integration, and long-term stability your high-vacuum processes demand.