Q3 (Total 40 Marks) A vibration sensor is used to measure the vibrations caused by a car engine. It is mounted into a Wheatstone bridge as shown in Figure 3. The vibration sensor has a reference resistance of 100 2 and has a resistance versus amplitude sensitivity of 0.1 22/(P-P amplitude). (P-P stands for peak to peak). The designer chose to use R4 as the vibration sensor and used 100 22 resistors for R1, R2 and R3. The input voltage (Vi) was chosen to be 10 Volts. 1. A particular vibration had a P-P amplitude of -5. Please find the P-P voltage output of the Wheatstone bridge (Vo) that this vibration would generate. (12 Marks) 2. The output of the circuit from part (1) is then fed through a simple unity gain differential amplifier in order to combine the voltage difference between the two nodes in the Wheatstone bridge into a single wire. The designer then used the high pass filter circuit given in Figure 4 to both amplify and filter the output voltage signal from this differential amplifier. a. Please derive the transfer function of this filter. (10 Marks) b. Suppose from the circuit in Figure 4 that R=12512, C = 6.4uF, Li=0.1H and L2 =5H. Please obtain the passband gain, corner frequency (rad/s) and the quality factor of this filter. (8 Marks) 3. Finally, a 12 Bit 5V A/D converter shall be used to convert the passband amplified P-P voltage from part (2) into digital bits. Please determine the quantization percentage error for the P-P input signal given from part (1). (10 Marks) Please also write down briefly the theorems/methods you use in the solutions (The RSensor) Figure 3: The Wheatstone Bridge L2 v am ell VO L1 OA2 TL081 + Figure 4: The high pass filter Q3 (Total 40 Marks) A vibration sensor is used to measure the vibrations caused by a car engine. It is mounted into a Wheatstone bridge as shown in Figure 3. The vibration sensor has a reference resistance of 100 2 and has a resistance versus amplitude sensitivity of 0.1 22/(P-P amplitude). (P-P stands for peak to peak). The designer chose to use R4 as the vibration sensor and used 100 22 resistors for R1, R2 and R3. The input voltage (Vi) was chosen to be 10 Volts. 1. A particular vibration had a P-P amplitude of -5. Please find the P-P voltage output of the Wheatstone bridge (Vo) that this vibration would generate. (12 Marks) 2. The output of the circuit from part (1) is then fed through a simple unity gain differential amplifier in order to combine the voltage difference between the two nodes in the Wheatstone bridge into a single wire. The designer then used the high pass filter circuit given in Figure 4 to both amplify and filter the output voltage signal from this differential amplifier. a. Please derive the transfer function of this filter. (10 Marks) b. Suppose from the circuit in Figure 4 that R=12512, C = 6.4uF, Li=0.1H and L2 =5H. Please obtain the passband gain, corner frequency (rad/s) and the quality factor of this filter. (8 Marks) 3. Finally, a 12 Bit 5V A/D converter shall be used to convert the passband amplified P-P voltage from part (2) into digital bits. Please determine the quantization percentage error for the P-P input signal given from part (1). (10 Marks) Please also write down briefly the theorems/methods you use in the solutions (The RSensor) Figure 3: The Wheatstone Bridge L2 v am ell VO L1 OA2 TL081 + Figure 4: The high pass filter
