Solutions to Problems
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 Cp1 = Cp2 = 100 pF. Capacitor Cp1 charges the excitation voltage source. However, because of the low impedance (zero ohm), this has no effect on the voltage across the sensor capacitor Cs. With respect to Cp2 it can be noted that, with an ideal amplifier, the amplifier input voltage equals 0 V. Because this voltage equals the voltage over Cp2, the current through Cp2 equals zero. Therefore, the current Ii (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 Cs/Cf = 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 Cs and Cp2 is equal to Vexc. Therefore, the current Ii amounts to