handbook of modern sensors

5.1 Input Characteristics of Interface Circuits 153
source, which would be connected in parallel with the sensor output impedance. Both
representations are equivalent to one another, so we will use voltage. Accounting for
both impedances, the circuit input voltage, V in , is represented as
Z in
V in = E . (5.4)
Z in + Z out
In any particular case, an equivalent circuit of a sensor should be defined. This helps to
analyze the frequency response and the phase lag of the sensor–interface combination.
For instance, a capacitive detector may be modeled as pure capacitance connected in
parallel with the input impedance. Another example is a piezoelectric sensor which
can be represented by a very high resistance (on the order of 10 11 ) shunted by a
capacitance (in the order of 10 pF).
To illustrate the importance of the input impedance characteristics, let us consider
a purely resistive sensor connected to the input impedance as shown in Fig. 5.2A. The
circuit’s input voltage as a function of frequency, f , can be expressed by
V =
E
√1 + (f/f c ) 2 , (5.5)
where f c = (2πRC) −1 is the corner frequency, (i.e., the frequency where the amplitude
drops by 3 dB). If we assume that a 1% accuracy in the amplitude detection is
required, then we can calculate the maximum stimulus frequency that can be processed
by the circuit:
f max ≈ 0.14f c , (5.6)
or f c ≈ 7f max ; that is, the impedance must be selected in such a way as to assure a
sufficiently high corner frequency. For example, if the stimulus’ highest frequency is
100 Hz, the corner frequency must be selected to be at least at 700 Hz. In practice,
f c is selected even higher, because of the additional frequency limitations in the
subsequent circuits.
One should not overlook a speed response of the front stage of the interface
circuit. Operational amplifiers, which are the most often used building blocks of
interface circuits, usually have limited frequency bandwidths. There are the so-called
programmable operational amplifiers which allow the user to control (to program) the
bias current and, therefore, the first stage frequency response. The higher the current,
the faster would be the response.
Figure 5.3 is a more detailed equivalent circuit of the input properties of a passive
electronic interface circuit 1 , (e.g., an amplifier or an A/D converter). The circuit is
characterized by the input impedance Z in and several generators. They represent
voltages and currents which are generated by the circuit itself. These signals are
spurious and may pose substantial problems if not handled properly. All of these
signals are temperature dependent.
The voltage e 0 is called the input offset voltage. If the input terminals of the circuit
are shorted together, that voltage would simulate a presence of an input dc signal
1 Here, the word passive means that the circuit does not generate any excitation signal.