Readout technique

• Wheatstone-bridge configuration
  To convert the resistance change to a voltage signal
  

• Equally positioned resistors form opposite arms of the bridge
• Under applied pressure, the left and right output nodes of the bridge deviate from their zero-pressure voltage with opposite signs
• Bridge output voltage:
  

• Change of bridge output voltage:
  

• Simplified expression can be used
  
  • If all resistors due to their dimensioning have the same resistance, R₀ for the unloaded case
  • If the absolute value of all resistance changes is equal to dR

Numerical example

• Membrane sensor with the configuration corresponding to the figure
• Piezoresistance coefficients of silicon as in the preceding table
• Resistors R₁ and R₃ compared to R₂ and R₄ experience stresses rotated 90o
• Longitudinal stress on R₁ and R₃ is the transverse stress at R₂ and R₄ and vice versa
• Change of resistances

• Supposing that unloaded values of all resistances are the same and equal to R₀, we can write:

where a₁ and a₂ represent the product of the effective piezoresistive coefficient and the stress.

• Bridge output voltage:

• Optimally large output without a large nonlinearity
  since a₁ and a₂ are typically small, and differ from each other by only 10%
• Advantages of Wheatstone-bridge
  • Converts the resistance change directly to a voltage signal
  • Output voltage is independent of the absolute value of the piezoresistors
    is determined by the relative resistance change and the bridge voltage
  • In the ideal case, the total resistance of bridge is independent of pressure since the resistance changes cancel one another
  • In the case of a perfectly balanced bridge, temperature influences and other common-mode effects are compensated by an equal variation of all piezoresistors

More details

Related reading

Middelhoek, S., Audet, S. A., Silicon sensors, Academic Press, 1989.

Rufer L.,  La modelisation des microsystemes electromecaniques. in Mir, S. (Ed.), Conception des microsystemes sur silicium.
                Traite EGEM, Hermes Science Publications, pages 101-128, 2002.

Rufer L., Les microsystemes electromecaniques. in Mir, S. (Ed.), Les applications des microsystemes sur silicium.
                Traite EGEM, Hermes Science Publications, pages 19-64, 2002.

Senturia S. D., Microsystem Design, Kluwer Academic Publishers, 2001