TRANSDUCERS 



From the results of Chapter 3 it is clear that the transducer-amplifier 

 combination will reproduce faithfully sinusoidal variations of stress only if 

 they occur at a sufficiently high frequency, and that transient variations will 

 be accurately delineated only if they occur rapidly enough. Graph 9 shows 

 the steady-state behaviour of a piezo-electric transducer; the transient 

 response will be similar to Graph 7. 



Typical piezo-electric transducers may have capacitances of 100-2,000 pF; 

 accurate reproduction of frequencies down to a few c/s will thus involve an 

 amplifier with an input resistance of many megohms. A cathode follower 

 (Chapter 11) using if necessary an electrometer valve (Chapter 24) provides 

 a suitable high input-resistance first stage for this amplifier. 



Two piezo-electric materials are suitable for biological transducers: 

 Rochelle salt and barium titanate. Rochelle salt is usually assembled into a 

 double slab (or 'bimorph') and the applied stress may be in the form of a 

 torque ('twister' bimorph) or a flexure ('bender' bimorph). Bimorphs are 

 used extensively in gramophone pick-ups; the insert cartridge from such a 

 pick-up forms a convenient transducer, stress being applied to the needle 

 through a tension wire. As a transducer such a device has a high mechanical 

 impedance and behaves like a stiff spring of compliance about 10~^ cm per 

 dyne (10 {x per g wt). As mentioned on page 478, such a transducer is 

 immediately applicable to the measurement of force, but has to be connected 

 through a light spring when used to measure displacement. Typical gramo- 

 phone pick-up cartridges have a capacity of 500 pF, and give an output 

 voltage of a few mV per dyne, i.e. several volts for a force of 1 g wt. 



Barium titanate bars are in common use as accelerometers in vibration 

 detection. Here the stress in the material is generated by inertial forces as 

 the transducer is subjected to acceleration. Some of these accelerometers 

 are usable as transducers if a tension wire is attached to an appropriate 

 point. A typical barium titanate transducer, used in tension, has a compliance 

 of about 10~^° cm per dyne (1 /< per kg wt). This high impedance makes it 

 immediately applicable to the measurement of force. An output of the order 

 of 20 [jN per dyne (20 mV per g wt) can be obtained in this way. 



All piezo-electric transducers reach an upper frequency limit when their 

 mechanical resonant frequency is approached. This frequency is determined 

 by the compliance of the transducer, in combination with the effective mass 

 of its moving parts plus the mass of the preparation and attachments. With 

 reasonable care resonant frequencies of many kc/s can be achieved. 



In biological research piezo-electric transducers are likely to be of the 

 greatest value for the measurement of rapidly changing forces, such as the 

 contraction of fast muscles. Here the fact that the response does not extend 

 down to zero frequency is little disadvantage, while the small size, high upper 

 frequency limit, large output and low compliance can be particularly useful. 



Two typical piezo-electric transducers are shown in Figure 33.10. 



Ekctrodynamic transducers 



The principle of all electrodynamic transducers is as follows. The mechani- 

 cal input is arranged to vary the magnetic field through a coil ; this variation 

 induces a voltage in the coil. The voltage is proportional to the rate of 



482 



