1. © G. Washington, 2002 1 Seismic Transducers A seismic transducer consists of two basic components: i.Spring – Mass – Damper Element ii.Displacement Transducer (MS Fig 4.77) (Note: x o = x i – x M )

2. © G. Washington, 2002 2 Seismic Transducers – Acceleration Sensor Let’s explore the dynamic response of the spring-mass-damper element alone. Noting the sign conventions in Fig. 4.77, we have, from Newton’s second law for the motion of mass M, x M : (Where x M = x i – x o ) (A classic 2 nd Order System) We define (again) With the result

3. © G. Washington, 2002 3 Seismic Transducer – Acceleration (cont). Let’s associate the following: Input is object acceleration Output is relative displacement of M and object Static Sensitivity (sec 2 ) Classic 2 nd Order System

4. © G. Washington, 2002 4 Seismic Accelerometer – Freq. Responce

5. © G. Washington, 2002 5 Seismic Accelerometer – Freq Response (cont) Question: Over what range of frequencies can we actually use a seismic accelerometer? Answer: To be most useful we desire a “flat” frequency response and a “linear” phase shift. In other words, we need i.  SIG <<  n ii.  ~ 0.4 – 0.6 But recall that

6. © G. Washington, 2002 6 Seismic Accelerator – “Readout” The previous discussion ignored the response of the displacement sensor used to measure x o !! We need to consider this! RECALL System 1 q i,1  System 2 q i,2  q o,1  q o,2

7. © G. Washington, 2002 7 Seismic Accelerometer i. Resistive Potentiometer Readout

8. © G. Washington, 2002 8 Seismic Accelerometer ii. Piezo Readout “Usable” range depends upon damping

9. © G. Washington, 2002 9 Seismic Displacement How about a seismic displacement transducer? (We’ll let you do this one as homework).

10. © G. Washington, 2002 10 Capacitance Transducers Consider a basic parallel plate capacitor, with C = Capacitance (pF) A = Plate Area (in 2 ) x = Plate Separation (in) If either x or A are changed, then C will change!!

11. © G. Washington, 2002 11 Basic Capacitance Transducer Geometries Linear MotionRotational Motion Typical Capacitance Values

12. © G. Washington, 2002 12 Capacitance Transducers – Signal Conversion Capacitance is not easy to measure directly. We need to convert “signal” to current or voltage. a. AC Voltage Approach We apply a constant amplitude AC voltage, V ex, at  =  ex This will result in a variable amplitude AC current at  ex Let’s Work This Out! Note: This approach is most useful for transducers in which x i modifiers A (the plate Area) Why??

13. © G. Washington, 2002 13 Capacitance Transducers – Signal Conversion b. AC Current Approach We apply a constant amplitude AC current, i ex, at  =  ex This will result in a variable amplitude AC Voltage at  ex, e o Let’s Work This Out! Note: This approach is most useful for transducers in which x i modifiers the gap (x). Why??

14. © G. Washington, 2002 14 Signal Conversion – AM Modulation Of course in either of the last two cases, the actual signal is AM modulated (Carrier Frequency =  ex MS Fig 4-37c

15. © G. Washington, 2002 15 Signal Recovery – Current Measurement A good approach to convert current to voltage is to use an Operational Amplifier as shown below i ai ~ 0 i f + i x = 0

16. © G. Washington, 2002 16 Op Amp Current – Voltage Conversion (Output voltage  1/C x )

17. © G. Washington, 2002 17 One Final Note This configuration is best for transducers in which gap is varied. (because C x  1/x so that e o varies linearly with x i ) Alternatively, we can exchange the positions of C f and C x, giving Best for transducers in which Area is varied. (because C x  A so that e o again varies linearly with x i )