Experiment 1 - Part 1

Q1: What does the calibration equation pdiff(V)=aV+b represent?

This is a linear equation that relates the output voltage V of the Kulite sensor to the differential pressure pdiff applied during calibration.

• The slope a represents how much pressure changes per volt.

• The intercept b is the offset when V=0, meaning the sensor reads a small pressure even with zero voltage due to zero-point shift.

Q2: Why do we assume a linear relationship between voltage and pressure?

Kulite sensors use piezoresistive elements arranged in a Wheatstone bridge.

• Within the sensor’s operating range, the membrane deformation is small and the resulting strain causes a proportional resistance change.

• This leads to a linear voltage response to applied pressure.

• The very high R2=0.9999993 confirms that linearity is a valid assumption.

Q3: What is the meaning of the coefficient of determination R²? Why is it important here?

R2 tells us how well the linear model fits the calibration data.

• R2=1 means a perfect fit.

• Our result of R²=0.9999993 means the data almost perfectly follows the linear trend.

• This confirms the sensor behaves very predictably over the tested range.

Q4: What is zero-point shift and how did you calculate it? Why does zero-point shift occur?

Zero-point shift is the offset voltage the sensor gives when the differential pressure is zero. It's calculated as:

V0=−b/a

• In our case, it was about −0.0061 V, meaning the sensor doesn't output exactly 0 V when no pressure is applied.

• It can happen due to:

  • Small manufacturing imbalances in the Wheatstone bridge,

  • Mechanical stress during mounting,

  • Temperature gradients affecting the piezoresistors,

  • Aging of materials or electronics.

Q6: How do you compensate for zero-point drift during experiments?

We use two methods:

1. Re-zeroing before each session: Record the voltage at pdiff=0p_{\text{diff}} = 0pdiff​=0, then subtract it from future measurements.

2. Periodic checks: During long experiments, we repeat this zeroing process and track how the offset changes over time.

Q7: Why do we add ambient pressure to the differential pressure?

The Kulite sensor measures differential pressure.
To get absolute pressure, we add the ambient pressure measured separately:

pabs=pdiff+pamb

This gives us the actual total pressure at the measurement point, which is useful for comparing with theoretical models.

Q8: How do you know your calibration is valid and trustworthy?

• The linear fit is visually well-aligned with the measured data.

• The coefficient R^2 is extremely close to 1.

• Residuals (difference between measured and fitted values) are small and random — no systematic error pattern.

Q9: Your linear model assumes constant slope a. Under what conditions could this assumption break down?

The assumption of constant slope could break down if:

• The sensor is used outside its calibrated pressure range, where the membrane deformation becomes nonlinear.

• There are temperature variations that affect the piezoresistive properties of the silicon.

• The power supply to the bridge fluctuates, changing the sensitivity.

• Hysteresis occurs in the membrane due to mechanical fatigue or overpressure.
  These factors would lead to a nonlinear voltage–pressure relationship, and a linear fit would no longer be accurate.

Q10: Why is it better to calculate absolute pressure using pabs​=pdiff​+pamb​ rather than using an absolute pressure sensor directly?

Using a differential sensor plus a separate ambient pressure measurement:

• Allows higher precision and faster response at the measurement point, because differential Kulite sensors can be made smaller and more responsive.

• Reduces sensor cost and complexity — absolute pressure sensors with high bandwidth are more expensive and less compact.

• Enables modular calibration, where the ambient pressure source (like a Vaisala transmitter) can be shared across sensors.
  However, care must be taken to ensure that the ambient pressure reference is accurate and synchronized.

Q11: What would be the effect on your calibration curve if the ambient pressure was not measured accurately?

If pamb​ is incorrect:

• The entire absolute pressure calibration curve shifts vertically by that error.

• The slope (sensitivity) remains unaffected.

• This leads to systematic error in all pressure measurements, even though the differential readings are still valid.
  This highlights the importance of using a precise and calibrated ambient pressure measurement device.

Q12: If the sensor shows a perfect R^2, can you still have an inaccurate calibration?

Yes. A high R^2 only indicates that the data fits the chosen model well, but it doesn’t guarantee that:

• The calibration was done over the correct pressure range

• The sensor is properly zeroed

• The voltages were measured accurately (e.g., no noise, correct scaling)

• The pressure values applied during calibration were truly known

So, even a perfect linear fit can still produce inaccurate results if the system setup, assumptions, or reference measurements are flawed.

Q13: If your zero-point offset drifts slowly over time, what physical effects might cause this?

Zero-point drift can be caused by:

• Temperature changes affecting the silicon resistors’ base resistance.

• Mechanical creep in the mounting or bonding materials applying stress on the membrane.

• Electronic aging in the signal conditioning circuit (e.g., op-amps or A/D converters).

• Hose relaxation or leakage in pneumatic connections (if applicable).
  To minimize this, re-zeroing and thermal compensation are commonly used.

Q14: In your calibration graph (Figure 3.1), the calibration curve doesn't pass exactly through 0 V. Why is that physically acceptable?

That’s because the sensor exhibits a zero-point offset — a small output voltage even when the applied pressure is zero.
This is common in real sensors due to:

• Slight imbalances in the Wheatstone bridge.

• Built-in strain in the membrane or mounting.

• Minor thermal or electronic offsets.

This does not affect the measurement accuracy as long as:

• The offset is measured and accounted for.

• The sensor operates within the calibrated linear range.

Q15: How would you verify whether the zero-point drift is due to temperature changes or sensor fatigue?

You could:

• Perform a controlled thermal test, where the ambient temperature is varied while keeping the pressure constant. If offset drifts with temperature, it’s thermal.

• Perform long-term tests at constant temperature and pressure. If drift appears over time, it may be due to sensor fatigue, bonding creep, or electronics.

• Use multiple sensors under identical conditions — if they all drift similarly with temperature, the cause is likely thermal.
  Additionally, plotting V_0​ over time and correlating with T would help identify trends.

What's the problem with conventional pneumatic pressure measurement?

They use long hoses or tubes to connect the pressure port to the pressure sensor.

❌ Why is that bad?

• The air inside the hose acts like a spring/damper system.

• This acts like a low-pass filter:

  • Low frequencies pass through just fine.

  • But high-frequency pressure fluctuations get damped or delayed.

  • You lose details about fast pressure changes (like blade passing or shock waves).

How do Kulite sensors solve this?

Kulite sensors are very small and can be mounted directly at the measurement point (flush with the surface or inside a probe).

Their silicon membrane is very stiff and small → it has a natural frequency > 150 kHz.

This means they can accurately measure very fast pressure changes, like:

• Shock waves in a shock tube

• Blade passing in compressors (often in the kHz range)