of Microprocessors

DIGITAL-TO-ANALOG AND ANALOG-TO-DIGITAL CONVERSION 405
pass section, impedance converters are normally used for active elliptical filters.
An impedance converter is an active circuit that in effect converts one type of
passive component, such as a capacitor, to another type, such as an inductor,
by means of phase shifting. A gyrator, for example, does just that; connect a
capacitor across its ourput terminals and its input terminals have the
frequency-phase characteristic of an equivalent inductor. A negative impedance
converter shift things just 90° instead of 180° and thus can make a resistor act
like an inductor in a suitably designed circuit. While these circuits are
interesting to study, their theory is beyond the scope of this discussion.
The negative impedance converter (NIC) is very easy to apply to the L­
Celliptical filter circuits given earlier, however. Figure 12-26A shows the
series resonant form of a seventh-order elliptical filter adapted to a NIC active
circuit. In effect, the phase of everything has been shifted 90° so every
inductor becomes a resistor, every resistor becomes a capacitor, and every
capacitor becomes a "frequency-dependent negative resistor" implemented
with a negative impedance converter and two capacitors. Fig. 12-26B shows
the same circuit with "practical" element values included. These were
calculated for a lO-kHz cutoff from the Table 12-2 entries for a seventhorder,
0.28/60-dB filter. First, an impedance scale factor is determined using
Z = 1/6.283FC, where F is the cutoff frequency and C is a convenient
capacitor value in farads. For best results, choose C so that Z is in the 5K to
20K range. For this example, 2,200 pF gave an impedance scale factor of
7,235. Values for the remaining components are simply the impedance scale
factor times the corresponding element values from the filter table. Figure
12-26C shows the actual active filter circuit. Most of the resistor values are
simply copied from the element values in Fig. 12-26B. The two 499K
resistors are included to provide a path for the amplifier bias current and also
give the circuit accurate response down to de. The 4.99K resistors in the
negative impedance converters merely need to be matched; their actual value
does not affect the response.
One of the big advantages of this circuit is that all of the capacitors are
the same value! Ofcourse, the resistors turn out to be strange values, but it is
much easier to find precision resistors with strange values than capacitors. In
practice, the circuit impedance is usually adjusted so that the capacitors are
some standard value (such as 2,200 pF here) which is easy to get. One would
typically purchase several dozen 5% capacitors of this value and select those
that fall within 1% of 2,200 pF for use. One pitfall of this circuit is that at
certain frequencies, the output swings of the NIC op-amps will be three times
the input signal amplitude. Thus, the input signal amplitude should be
restricted to 3 V peak to avoid severe distortion. Also, there is a 6 dB
passband loss that is made up for somewhere, usually in the output amplifier.
Amplifier noise is not much of a problem because the NICs don't tend to
amplify noise at the resonant peaks. Note that the bias current for amplifiers
AI, A3, and A5 plus that of the output amplifier passes through the two