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handbook of modern sensors

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174 5 Interface Electronic Circuits<br />

5.3.4 Drivers<br />

As opposed to current generators, voltage drivers must produce output voltages which,<br />

over broad ranges <strong>of</strong> the loads and operating frequencies, are independent <strong>of</strong> the output<br />

currents. Sometimes, the drivers are called hard-voltage sources. Usually, when the<br />

sensor which has to be driven is purely resistive, a driver can be a simple output stage<br />

which can deliver sufficient current. However, when the load contains capacitances<br />

or inductances (i.e., the load is reactive), the output stage becomes a more complex<br />

device.<br />

In many instances, when the load is purely resistive, there still can be some<br />

capacitance associated with it. This may happen when the load is connected though<br />

lengthy wires or coaxial cables. A coaxial cable behaves as a capacitor connected<br />

from its central conductor to its shield if the length <strong>of</strong> the cable is less than one-fourth<br />

<strong>of</strong> the wavelength in the cable at the frequency <strong>of</strong> interest f . For a coaxial cable, this<br />

maximum length is given by<br />

L ≤ 0.0165 c f , (5.23)<br />

where c is the velocity <strong>of</strong> light in a coaxial cable dielectric.<br />

For instance, if f = 100 kHz, L ≤ 0.0165(3 × 10 8 /10 5 ) = 49.5; that is, a cable<br />

less than 49.5 m (162.4 ft) long will behave as a capacitor connected in parallel with<br />

the load (Fig. 5.22A). For an R6-58A/U cable, the capacitance is 95 pF/m. This capacitance<br />

must be considered for two reasons: the speed and stability <strong>of</strong> the circuits.<br />

The instability results from the phase shift produced by the output resistance <strong>of</strong> the<br />

driver R 0 and the loading capacitance C L :<br />

ϕ = arctan(2πf R 0 C L ). (5.24)<br />

For instance, for R 0 = 100 and C L = 1000 pF, at f = 1 MHz, the phase shift ϕ ≈ 32 ◦ .<br />

This shift significantly reduces the phase margin in a feedback network which may<br />

cause a substantial degradation <strong>of</strong> the response and a reduced ability to drive capacitive<br />

loads. The instability may be either overall, when an entire system oscillates, or<br />

localized when the driver alone becomes unstable. The local instabilities <strong>of</strong>ten can be<br />

(A)<br />

(B)<br />

Fig. 5.22. Driving a capacitive load: (A) a load capacitor is coupled to the driver’s input through<br />

a feedback; (B) decoupling <strong>of</strong> a capacitive load.

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