Smart Sensor Systems

Solutions to Problems

Chapter 2

Solution to Problem 2.1

(a) What is the shape and magnitude of the amplifier output voltage V₀?

Figure 1(a) shows an equivalent circuit diagram of the front-end amplifier, including the cable capacitances, where C_p1 = C_p2 = 100 pF. Capacitor C_p1 charges the excitation voltage source. However, because of the low impedance (zero ohm), this has no effect on the voltage across the sensor capacitor C_s. With respect to C_p2 it can be noted that, with an ideal amplifier, the amplifier input voltage equals 0 V. Because this voltage equals the voltage over C_p2, the current through C_p2 equals zero. Therefore, the current I_i (Figure 1(a)) equals

where s represents the Laplace operator. The output voltage V₀ equals

Equation (2) shows that the amplifier with its feedback circuitry has a real amplification factor, which equals C_s/C_f = 1/5. Therefore, the output voltage is a square-wave voltage with a peak-to-peak value of 2 V.

(b) What is the shape and magnitude of the amplifier output voltage V₀ for this modified circuit configuration?

Figure 1(b) shows the equivalent circuit diagram of the front-end amplifier, including the parasitic capacitor. The input voltage over the capacitors C_s and C_p2 is equal to V_exc. Therefore, the current I_i amounts to

and

Figure ...