handbook of modern sensors

164 5 Interface Electronic Circuits
When converting currents from such sensors as piezoelectrics and pyroelectrics,
the resistor R b (R in Fig. 5.10B) may be required on the order of tens or even hundreds
of gigohms. In many cases, resistors of such high values may be not available or
impractical to use due to poor environmental stability. A high-ohmic resistor can be
simulated by a circuit known as a resistance multiplier. It is implemented by adding
a positive feedback around the amplifier. Figure 5.12B shows that R 1 and R 3 form a
resistive divider. Due to a high open-loop gain of the OPAM, voltages at noninverting
and inverting inputs are almost equal to one another: V + ≈ V − . As a result, voltage,
V 2 , at the divider is
R 3 R 3
V 2 = V − ≈ V + , (5.15)
R 1 + R 3 R 1 + R 3
and current through the resistor is defined through the voltage drop:
I b = V
R b
= V + − V 2
R b
= V +
R b
R 1
R 1 + R 3
. (5.16)
From this equation, the input voltage can be found as a function of the input current
and the resistive network:
(
V + = I b R b 1 + R )
3
. (5.17)
R 1
It is seen that the resistor R b is multiplied by a factor of (1 + R 3 /R 1 ). For example, if
the highest resistor you may consider is 10 M, by selecting the multiplication factor
of, say, 5, you get a virtual resistance of 50 M. Resistance multiplication, although
being a powerful trick, should be used with caution. Specifically, noise, bias current,
and offset voltage are all also multiplied by the same factor (1 + R 3 /R 1 ), which may
be undesirable in some applications. Further, because the network forms a positive
feedback, it may cause circuit instability. Therefore, in practical circuits, resistance
multiplication should be limited to a factor of 10.
5.3 Excitation Circuits
External power is required for the operation of active sensors. Examples are temperature
sensors [thermistors and resistive temperature detectors (RTDs)], pressure
sensors (piezoresistive and capacitive), and displacement (electromagnetic and optical).
The power may be delivered to a sensor in different forms. It can be a constant
voltage, constant current, or sinusoidal or pulsing currents. It may even be delivered
in the form of light or ionizing radiation. The name for that external power is an excitation
signal. In many cases, stability and precision of the excitation signal directly
relates to the sensor’s accuracy and stability. Hence, it is imperative to generate the
signal with such accuracy that the overall performance of the sensing system is not
degraded. In the following subsections, we review several electronic circuits which
feed sensors with appropriate excitation signals.