TRANSDUCERS 



e-m transducer interact so that the mechanical properties of the transducer 

 can be influenced by the nature of the electrical circuits driving it. 



MECHANICAL IMPEDANCE OF TRANSDUCERS 



The input impedance of an electrical instrument is a measure of the extent 

 to which the instrument disturbs the circuit under test. When measuring 

 voltage a high-impedance meter is needed; the measurement of current 

 requires a low-impedance instrument (see Chapters 32 and 43). Similarly, 

 the disturbance due to a transducer is assessed in terms of its mechanical 

 input impedance; whether this impedance should be low or high depends on 

 the nature of the quantity to be measured. A transducer measuring displace- 

 ment should require as little force as possible to deflect it, i.e. it must present 

 a 'low impedance'. A force-measuring transducer, on the other hand, 

 should be of high impedance, as it must 'give' as little as possible under the 

 influence of the applied force. Although the impedance of a transducer is 

 given directly by the input of its equivalent electrical circuit, the compliance 

 components usually predominate within the working range, and hence they 

 largely determine the impedance. 



Most m-e transducers produce an output dependent upon their displace- 

 ment; whether they are most suitable for measuring force or movement 

 depends on their impedance. A low-impedance transducer can be adapted 

 to measure force by putting a stiff spring across its input, thereby raising its 

 impedance, while a high-impedance transducer connected to a preparation 

 through a weak spring may be suitable for measuring movement. 



It is therefore not intended in this chapter to separate transducers 

 artificially into 'force' and 'displacement' types since these differ only in 

 their impedance; both fundamentally are sensitive to displacement. 



The characteristics of e-m transducers can similarly be described in terms 

 of their mechanical output impedance. A low-impedance device is one 

 producing constant force regardless of movement, while a high-impedance 

 device gives a displacement virtually independent of load. Most e-m trans- 

 ducers are fundamentally of low impedance, but if combined with a stiff" 

 spring can be made to present a high impedance. 



The transformation of a low impedance transducer into a high-impedance 

 one, and vice versa, by the use of a spring is not without its pitfaUs. To 

 demonstrate this, and to give further illustrations of mechanical circuit 

 analogies, the equivalent circuits of various transducer arrangements will be 

 considered. 



If a very high-impedance m-e transducer, such as might be suitable for 

 measuring force, is connected to a moving preparation through a weak 

 spring so as to measure the displacement of the preparation, the equivalent 

 circuit will be as in Figure 33.7. 



Here m, c are the masses and compliances of the short elements of length 

 of the spring; Q is the (very low) compliance of the transducer. At low 

 frequencies the effect of the masses becomes negligible and the circuit reduces 

 to the compliance of the spring as a whole in parallel with C^. However, 

 at high frequencies, the spring with its distributed mass and compliance 

 behaves like an electrical transmission Hne, with distributed inductance and 



478 



