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## Piezoresistive pressure sensor design circuit with temperature compensation

Published on Jan 20 2011

Abstract: A basic principle of temperature compensation method, the solution of the micro pressure sensor Warming problems; a practical detail the overall compensation circuitry, and analysis derived from the theoretical formula, given the overall sensor sensitivity and temperature coefficient of zero in contrast to the situation before and after compensation.
Keywords: Piezoresistive sensor; temperature measurement; overall temperature compensation
I. Introduction
With the development of integrated circuits and semiconductor technology, there have been piezoresistive effect of semiconductor materials for the principle of force-sensitive sensors made of semiconductor, of which silicon piezoresistive pressure sensors due to small size, high performance, low-cost advantages are a wide range of applications. But the use of diffusion technology is easy to form the bridge resistance changes with temperature, and the piezoresistive element piezoresistive coefficients have large negative temperature coefficient, which can lead to resistance and temperature coefficient of resistance of dispersion, resulting in thermal sensitivity drift of the pressure sensor and drift [1]. To this end, a design of a piezoresistive pressure sensor for the overall temperature compensation circuit, which has compensated high precision, stable performance, easy adjustment, the application can achieve satisfactory results.
Second, the error sources
As the temperature sensitive semiconductor material, the four piezoresistive pressure sensor for the detection of resistance have received more Wheatstone bridge, which has two working modes constant current and constant voltage. Assuming the semiconductor strain gauge resistance Rt of the temperature coefficient a, the temperature coefficient of sensitivity of K ß, increase the voltage of the sensor Vin, the resistance value changes with the temperature sensitivity of expression are:
RT = R0 (1 + aT) (1); KT = K0 (1 + ßT)
(2)
The sensor output is [2]: Vout = (R/R0) Vin = K0 (1 + ßT) eVin (3)
Where, R0-reference temperature of the sensor resistance value (initial value); R-stress-induced change in resistance;
K0-base temperature sensitivity; e-strain coefficient.
This type known, the amount of pressure change with temperature and ß change with temperature the same, with a large negative temperature coefficient, temperature coefficient of -0.002 / ~ -0.003 /. Figure 1 shows the different doping concentrations of P-type silicon with temperature sensitivity coefficient of the curve [3]. The figure, from a to e of the curve corresponding to increasing doping concentration. The figure shows, P-type strain resistance, either lightly doped or heavily doped, the sensitivity coefficients increase with temperature gradually decreases. As a result of resistance strain gauges can not be matched, and the temperature coefficient of resistance strain gauges in the 0.3% / or so, will result in zero drift voltage.

Third, the temperature compensation principle and circuit design
1, the zero drift compensation
Four piezoresistive pressure sensor for the detection of resistance have received more form of Wheatstone bridge, the principle shown in Figure 2 (a) below. From the Wheatstone bridge principle we can see that the output voltage is zero:
Vout =

(4)
The room temperature should enable R2R4-R1R3 = 0 [3], zero-bit output to 0. When the outside temperature T, the bridge output to zero:
Vout ‘=

(5)
If R2TR4T-R1TR3T> 0, then the drift is positive; if R2TR4T-R1TR3T <0, then the drift is negative. Therefore, the key to adjust the zero drift is to change the size of R2TR4T or R1TR3T. Method is used on the series resistance R1 or Rm in parallel with resistor R3 Rn, respectively, as shown in Figure 2 (b), 2 (c) below, adjust Rm, Rn resistance size, can achieve the purpose of regulating the output of zero . Rm and Rn the resistance obtained by the following formula.
(1) Find the value of series resistance Rm
Principle by the bridge, then Figure 2 (b) the output voltage is: Vout ‘= U

(6)
By R1 ‘= R1 + Rm and let Vout’ = 0, substituting into (1), the calculation yields:
Rm = R4

(2) Find the value of parallel resistance Rn management in Figure 2 (c) in
Vout ‘= U
(7)
By R3 ‘=

And Vout ‘= 0, according to (6), we have:
Rn =

2, the sensitivity temperature compensation
Warming way by the whole circuit to compensate for temperature drift of sensitivity to design the circuit shown in Figure 3. The figure, A1 and A2 form the differential amplifier, the output of the sensor signal into a differential voltage, then the A4 as a differential input single ended output amplifier, the voltage difference between the output signal into an electrical signal to ground. Because of the sensitivity drift of the sensor output voltage has a negative temperature coefficient, then use the transistor base – emitter voltage Vbe to offset the negative temperature characteristics of it. Meanwhile, on A4 negative feedback resistor in parallel with positive temperature coefficient thermistor RT, the gain is used to achieve better temperature characteristics of sensitivity to make up the bridge part of the purpose of negative temperature characteristics.

3, the overall performance of the design
Since the zero compensation, the actual sensor output Vout is generally not zero for the 0V, does not meet the R2R4 = R1R3 assumptions, it takes the processing circuit in Figure 3, the A4 is access to a complement input phase zero resistance, it Zero drift can be together and make it up. Adjust the size of VP3 to change its resistance so that the output voltage follower A4 by the reverse-side input to the A5, you can eliminate the impact of zero drift. Due to the current flowing through the VP3 is not constant, so the voltage conversion in many cases is not constant, it must control access to integrated operational amplifier A3, to enhance the stability of the sensor performance.