Converting PBR 260 Logarithmic Pressure Signal on S7-1500

Converting a Pfeiffer Vacuum PBR 260 Logarithmic Pressure Signal on a Siemens S7-1500 with TIA Portal V18

A common commissioning problem in vacuum process skids is a linear scaled reading of several hundred hPa while a calibrated reference instrument reports a few pascals. The root cause is almost always a sensor output curve that is logarithmic rather than linear. The Pfeiffer Vacuum PBR 260 combination gauge (Pirani + cold cathode / Bayard-Alpert hybrid) is one of the most frequently used vacuum transducers with a non-linear 0 V to 10 V output where every 0.75 V represents one decade of pressure. Engineers who treat that 0 V to 10 V window as a straight line and apply the standard Siemens y = mx + b scaling will compute a near-atmospheric value (e.g. 683 hPa) for a signal that physically corresponds to a few pascals. This article walks through the topology, the math, the TIA Portal V18 implementation in SCL, the data type pitfalls, and a verification procedure that resolves the issue end-to-end.

1. Problem Statement

The reported symptom: a process line uses a Pfeiffer Vacuum PBR 260 to measure the forevacuum pressure between a rotary vane pump and a downstream control valve. The PBR 260 is wired into a Beckhoff KL 3062 analog input terminal that is itself mounted on a BK 3120 K-bus coupler. The BK 3120 exposes the process data to a Siemens S7-1500 CPU 1516-3 over PROFINET. The PLC was programmed to convert the 0 V to 10 V signal linearly to a 0 hPa to 1000 hPa pressure range using a standard SCALE or manual y = mx + b block. The scaled value displays approximately 683 hPa, while a calibrated handheld reference instrument connected directly to the same gauge reports 19 Pa (0.19 hPa). The discrepancy is roughly three and a half decades, which immediately points to a logarithmic sensor being interpreted as a linear one.

The supervisor's instruction to switch to a logarithmic relationship is correct. The remaining task is to implement that logarithmic conversion in TIA Portal V18, choose the right data type for the raw Beckhoff input, validate the result against the reference instrument, and document the calibration offsets coming from the PBR 260 individual test certificate.

2. Hardware Topology and Signal Path

The signal chain for the application is shown schematically in the topology below. Each block introduces its own scaling, polarity, and resolution constraints that must be carried into the TIA Portal code.

Key points of the chain that drive the conversion code:

• PBR 260 output. Single-ended 0 V to 10 V signal, logarithmic, 0.75 V per decade, measurement range 5×10⁻⁹ hPa to 1000 hPa. Each unit ships with a calibration certificate giving the exact voltage at 1.0×10⁻⁴ hPa and 1.0×10⁻⁶ hPa. Use those numbers, not generic values.
• KL 3062 scaling. Beckhoff Bus Terminals in the KL/EL 3xxx series encode a 0 V to 10 V signal as a 16-bit unsigned value 0 to 32767 (0x7FFF) by default. The status byte (lowest bits) and the data word (upper 15 bits) follow the EtherCAT/Modbus convention, and the BK 3120 exposes a 16-bit process value to the PLC. The PLC therefore receives an INT with 0 to 32767 representing 0 V to 10 V, not the Siemens-native 0 to 27648 convention used on SIMATIC SM modules.
• BK 3120 transparency. The K-bus coupler is a passthrough for the KL 3062 process data; no additional scaling is applied. The PROFINET GSDML maps the analog input directly into the slot configured in the device configuration.
• S7-1500 input tag. A symbol such as "KL3062_AI1_Raw" of type INT receives the Beckhoff value. Type choice matters: INT spans -32768 to 32767, so a raw value of 32767 is the positive full scale. For a guaranteed-positive vacuum signal, the recommended type is UINT (0 to 65535) or DINT if you intend to preserve headroom for future signal conditioning.

3. PBR 260 Sensor Output Characteristics

The PBR 260 is a wide-range combination gauge. The Pirani section covers the rough and medium vacuum range, and the cold-cathode (inverted magnetron) section extends the range to UHV. The manufacturer specifies a single logarithmic characteristic across the operating range, which is what allows one signal wire to represent ten decades of pressure.

The relationship between voltage U (in volts) and pressure p (in hPa) is:

log₁₀(p / p₀) = (U − U₀) / 0.75

p = p₀ · 10^{(U − U₀) / 0.75}

where p₀ and U₀ are the pressure and voltage at a chosen reference point on the certificate. A common reference is p₀ = 1×10⁻⁴ hPa at U₀ = 7.5 V, but the certificate values must take priority.

4. Root Cause Analysis

Three independent mistakes tend to converge on a reading like 683 hPa when the true value is 19 Pa. Identifying each one explicitly makes the fix straightforward.

4.1 Linear assumption on a log sensor. The original code used a single y = mx + b block with m = 100 hPa / V and b = 0 hPa. That is valid only for sensors with a linear transfer function (most strain-gauge and piezoresistive pressure transducers). The PBR 260 is fundamentally not linear, so the math must use the exponential form shown in §5.

4.2 Wrong data type for the Beckhoff raw word. Beckhoff delivers the analog value as a 16-bit unsigned word where 0x8000 is the high bit of the status byte, and 0x7FFF is the positive full scale. Siemens S7-1500 INT is signed (-32768 to 32767). If the value is read as INT and the top status bit happens to be set, the result will be negative even though the signal is perfectly healthy. The first debugging step is to swap INT for UINT (or WORD with manual mask) and observe whether the raw value lives in the upper half of the range, as expected for a mid-vacuum signal.

4.3 Missing calibration certificate offsets. A new PBR 260 ships with a printed test certificate that records the actual output voltage at two or three reference pressures (typically 1×10⁻⁴, 1×10⁻⁶, and 1×10⁻² hPa). The generic 0.75 V/decade slope is a typcial value; the certificate value is the real one. If you are off by 0.1 V at the reference, you introduce a 0.1 / 0.75 ≈ 0.13 decade error, i.e. a 35% multiplicative error in pressure.

5. Mathematical Model for Logarithmic Conversion

The conversion is a two-step process. Step 1 is a standard linear conversion from the raw 16-bit word to a voltage. Step 2 is the exponential that reconstructs the pressure from the voltage.

Step 1: Raw to voltage.

U = (Raw / 32767) · 10 V

Use 32767 (not 27648) because the Beckhoff terminal uses the full 15-bit magnitude range. If the BK 3120 has been configured in TIA Portal to present a 0 to 27648 scaled value to match Siemens SM-module convention, use 27648 instead. Confirm by reading the GSDML module description.

Step 2: Voltage to pressure.

p (hPa) = 10^{(U − U₀) / 0.75 + log₁₀(p₀)}

Combining both steps in a single expression using the raw word Raw:

p = 10^{( (Raw / 32767) · 10 − U₀ ) / 0.75 + log₁₀(p₀)}

Worked example with the values from the case. Suppose the raw word is 21200 (about 65% of full scale, which corresponds to ~6.47 V) and the certificate reference is U₀ = 7.5 V at p₀ = 1×10⁻⁴ hPa:

U = (21200 / 32767) · 10 = 6.469 V

exponent = (6.469 − 7.5) / 0.75 + log₁₀(1×10⁻⁴) = −1.374 + (−4) = −5.374

p = 10^−5.374 ≈ 4.22×10⁻⁶ hPa = 4.22×10⁻⁴ Pa

That result is in the deep vacuum range, which is consistent with a healthy forevacuum between a rotary vane pump and a throttling valve. The previous linear block would have produced:

p_lin = (21200 / 32767) · 1000 = 647 hPa

i.e. ~647 hPa - close to the 683 hPa reported by the operator. The error is the entire logarithmic gap between the two interpretations.

6. TIA Portal V18 Implementation

The conversion is implemented as a re-usable function block (FB) called PBR260_Scale. Inputs are the raw word, the calibration reference voltage, the calibration reference pressure, and the slope (0.75 V/decade default). The output is the pressure in hPa as a 64-bit LREAL to preserve dynamic range. A second output converts the value to the engineering unit you display in the HMI (hPa, mbar, Pa, or Torr).

6.1 Block interface.

6.2 SCL source of the function block.

FUNCTION_BLOCK "PBR260_Scale"
{ S7_Optimized_Access := 'TRUE' }
VERSION : 0.1
   VAR_INPUT
      RawValue            : UINT;     // 0..32767 from KL 3062
      RawFullScale        : REAL := 32767.0;
      VoltageFullScale    : REAL := 10.0;
      Slope_V_per_Decade  : REAL := 0.75;  // 0.75 V / decade for PBR 260
      U_ref               : REAL := 7.5;    // V at reference pressure
      P_ref_hPa           : REAL := 1.0E-4;// hPa at reference pressure
      MinValidRaw         : UINT  := 100;  // discard near-zero wire-break noise
   END_VAR

   VAR_OUTPUT
      Pressure_hPa        : LREAL;
      Pressure_Eng        : LREAL;
      EngUnit             : INT;   // 0=hPa, 1=mbar, 2=Pa, 3=Torr
      Valid               : BOOL;
   END_VAR

   VAR
      U                   : LREAL;
      Decades             : LREAL;
      Log10Pref           : LREAL;
   END_VAR

BEGIN
   // Default to invalid output
   Valid := FALSE;
   Pressure_hPa := 0.0;
   Pressure_Eng := 0.0;

   // Range check
   IF RawValue < MinValidRaw OR RawValue > RawFullScale THEN
      RETURN;   // leave Valid = FALSE, Pressure = 0
   END_IF;

   // 1) Raw word to voltage
   U := (UINT_TO_LREAL(RawValue) / RawFullScale) * VoltageFullScale;

   // 2) Voltage to decades from the reference
   Decades  := (U - U_ref) / Slope_V_per_Decade;
   Log10Pref := LN(P_ref_hPa) / LN(10.0);   // log10 of the reference pressure

   // 3) Pressure via 10^x
   Pressure_hPa := EXP(Decades * LN(10.0)) * P_ref_hPa;

   // 4) Engineering unit conversion (1 hPa = 1 mbar; 1 Torr = 1.333224 hPa)
   EngUnit := 0;
   Pressure_Eng := Pressure_hPa;
   IF Pressure_Eng < 1.0E-3 THEN
      // Switch to Pa for readability in deep vacuum
      Pressure_Eng := Pressure_hPa * 100.0;
      EngUnit := 2;
   END_IF;

   Valid := TRUE;
END_FUNCTION_BLOCK

6.3 Why LREAL and not REAL. The pressure can span 12 decades (5×10⁻⁹ hPa to 1000 hPa). A 32-bit REAL provides roughly 7 decimal digits of mantissa. At the low end of the range, the resolution is therefore ~1 part in 10⁷, which is marginal when the value is 1×10⁻⁸ hPa. LREAL doubles the mantissa to ~15 digits, which keeps the smallest representable pressure value well below the noise floor of the gauge. LREAL is supported by the S7-1500 CPU family natively and adds no execution time penalty on a 1516.

6.4 Where to call the FB. Place a single instance DB in the cyclic OB (OB1 or OB30 if you are using a time-driven OB for slower vacuum loops). For a 100 ms loop, a 1516-3 with the EXP and LN instructions runs in well under 100 µs. The instance DB is added to the watch table and forced via the certificate reference for commissioning.

6.5 LAD/FBD alternative. If your team standardises on ladder, the equivalent uses the EXPT block to compute b^e with b = 10.0 and e = the calculated exponent, followed by a MUL_R for the reference pressure. The math instructions for the intermediate steps are SUB, DIV, and MUL only. SCL is recommended for readability and to allow the engineering-unit switch to be coded inline.

7. Data Type and Resolution Considerations

Data type choice affects both the correctness of the conversion and the cleanliness of the HMI display.

The UINT selection is the single most impactful change in many cases. The original INT-based tag in the case may have been reading 21200 (positive full scale) but could flip to a negative value if the status bits from the Beckhoff terminal occupy the high bit. Always start debugging by switching the raw tag to UINT and verifying the live value with the watch table.

Resolution-wise, a 15-bit Beckhoff value over a 0 V to 10 V range gives a per-LSB voltage step of 10 / 32767 ≈ 305 µV. Converted to decades, that step is 0.305 mV / 0.75 V ≈ 4.1×10⁻⁴ decades, or about 0.1% multiplicative. That is more than adequate for process control; the bottleneck is sensor noise, not ADC resolution.

8. Alternative Approaches

For sites that prefer to keep all the math out of SCL, three alternative implementations are supported by TIA Portal V18.

8.1 Normalise, then use a graph block. The voltage-to-pressure curve can be linearised with a piecewise linear approximation. Insert 10 to 20 breakpoints (for example, 0 V → 5×10⁻⁹ hPa, 1 V → 1×10⁻⁷ hPa, ..., 9 V → 100 hPa, 10 V → 1000 hPa) and let the TIA Portal graph block interpolate. The graph block lives under "Math functions" and supports up to 50 breakpoints. The breakpoints are populated from the certificate and can be edited at runtime through an HMI page for fine tuning without re-downloading the PLC.

8.2 Polynomial approximation of the log curve. A 4th-order polynomial of the form log₁₀(p) = a₀ + a₁U + a₂U² + a₃U³ + a₄U⁴ reproduces the 0.75 V/decade line within ~1% over the useful range. Coefficients are derived by least-squares fit in a spreadsheet. The polynomial runs entirely on MUL/ADD instructions and avoids the slower EXP and LN calls. The trade-off is that the polynomial must be regenerated if the calibration reference changes.

8.3 Lookup table with floating-point interpolation. For deep-vacuum applications where every millisecond of cycle time matters, a 256-entry lookup table from 0 V to 10 V can be generated offline and indexed by the top 8 bits of the raw value. The lower 7 bits provide linear interpolation. The result is sub-microsecond execution on a 1516-3 with zero transcendental functions in the path. The memory cost is ~2 KB of LREAL constants, which is negligible on a 1516.

For most vacuum skids, the SCL EXP/LN implementation in §6 is the right balance between clarity, maintainability, and execution time. The other approaches are worth considering only when there is a CPU bottleneck or when the calibration is regularly changed at runtime.

9. Verification Procedure and Acceptance Test

Before the new code is released to production, run a structured verification against a calibrated reference. The procedure below produces a pass/fail decision per decade.

1. Connect a calibrated reference gauge (Pfeiffer Vacuum CMR 361/362/363/364, Inficon CDG045, or MKS Baratron 627B) to the same chamber port as the PBR 260. The reference must be traceable to NIST or PTB.
2. Bring the chamber to atmospheric pressure (1.0×10³ hPa) and wait for both gauges to stabilise. Record the raw word from the KL 3062 and the reference pressure. Expected: raw word near 32767, pressure within ±25% of the reference.
3. Step the chamber down in roughly 1-decade increments using a leak valve or a controlled pump-down: 1×10², 1×10¹, 1×10⁰, 1×10⁻¹, 1×10⁻², 1×10⁻³, 1×10⁻⁴, 1×10⁻⁵, 1×10⁻⁶, 1×10⁻⁷ hPa. Allow at least 60 s of dwell at each point for the cold-cathode section to settle.
4. At each point, log the raw word, the calculated pressure, and the reference pressure. The acceptance criterion is |log₁₀(p_calc) - log₁₀(p_ref)| ≤ 0.10 (i.e. the calculated value is within ±25% of the reference). Loosen the criterion to 0.15 if the chamber cannot hold a stable pressure.
5. Plot the log-log deviation chart. A straight horizontal line at zero indicates a correct calibration. A slope indicates that the certificate slope is wrong; an offset indicates that the certificate reference voltage is wrong.
6. Repeat with the chamber heated and at process temperature if the production cycle sees thermal excursions. The Pirani section is temperature-sensitive; the certificate is valid only at the temperature printed on it.

10. Troubleshooting Matrix

The matrix below captures the typical failure modes seen during commissioning of a PBR 260 on a Beckhoff front-end feeding a Siemens S7-1500. Use it as a triage checklist before changing code.

11. Edge Cases and Field Caveats

Cold-cathode ignition delay. When the chamber crosses into the high-vacuum range (typically below 1×10⁻⁵ hPa), the cold-cathode section of the PBR 260 needs 1 to 30 seconds to ignite. During that window the gauge may report a static value that is artificially high. The PLC code should treat the transition with hysteresis: only switch from "using Pirani" to "using cold cathode" after the value has been within one decade of the cold-cathode range for at least 10 seconds. The PBR 260 implements this internally and exposes a status flag; the PLC should still respect the flag rather than relying on the raw value alone.

Atmospheric pressure operation. The PBR 260 is rated to 1000 hPa. Operating it at 1500 hPa (overpressure) will not damage the gauge but will produce a saturated output near 10 V. The PLC should clamp the pressure to the certificate maximum rather than compute a value above 1000 hPa.

Temperature dependence of the Pirani section. The Pirani part of the PBR 260 is temperature-dependent at the ±10% level between 0 °C and 50 °C. The certificate is valid at one specific temperature (typically 25 °C). For installations where the gauge sits at a different temperature, apply a correction factor or use the Pfeiffer Vacuum TPR 280 (which has a built-in temperature sensor and a corrected output).

EMC considerations. The 0 V to 10 V signal from a PBR 260 is low-energy and susceptible to conducted noise. The KL 3062 input impedance is high (>100 kΩ), so even a few microamps of leakage current can introduce a measurable offset. Use a shielded twisted pair (e.g. Belden 8761 or Lapp ETHERLINE), ground the shield at the PLC cabinet end only, and keep the cable at least 20 cm away from variable-frequency drive output cables and 24 VDC power harnesses.

Calibration interval. Pfeiffer Vacuum recommends re-calibration of the PBR 260 every 12 months in production service, or sooner if the gauge has been exposed to a venting event or a corrosive process. The certificate value drifts by typically ±0.1 V per year on the reference point, which translates to a 0.13-decade pressure drift. Track the certificate date in the PLC's data log and trigger a maintenance work order when the interval is exceeded.

Replacement without re-commissioning. A spare PBR 260 should not be swapped in without re-entering the certificate values into the FB inputs. A common field failure is to swap a gauge, leave the certificate values from the previous unit loaded, and ship a process that reads correctly at one point and incorrectly everywhere else. Add a gauge serial-number tag in the HMI and force the operator to confirm the certificate before the new gauge is enabled.

12. FAQ