Page 44 - Analog Circuit Design Art, Science, and Personalities

Bernard Gordon

Now, consider another approach in which the characteristics of each of the indi-
vidual elements of the systems and their limitations are internalized by the designer.
With an understanding of the physics limiting the bandwidths of the crystal trans-
ducers, allow for the possibility that the crystals should not be cut to the transmission
frequency but to frequencies both well below and above that frequency.
Assume that the designer has not only a knowledge of the physics and therefore
the equivalent circuit of the mechanical transducer but also has a broad background
in the mathematics related to functions of a complex variable and an ability to com-
pute the transient response of a system characterized by a complex set of conjugate
poles. Further assume that the designer is intimately familiar with the responses of
conventional textbook filters, such as Butterworth maximally flat or Bessel maxi-
mally linear-phase filters, and recognizes that with the Butterworth the transient
response will ring too much and with the Bessel the economy of the system will be
inadequate due to the requirement for too many gain stages.
Now further suppose that the designer ‘‘fills” his head with many, many possible
other relevant factors and design possibilities, orders them in his head, thinks of
little else . . . and goes to sleep.
The designer then subconsciously conceives of making not a good flat-response,
amplitude-wise or linearity-wise, amplifier, but rather of making an amplifier which
on its own cannot do the job. In concert with the displaced poles of the crystal trans-
ducers, however, the modulator, amplifier, and transducers make up a system whose
transfer function, characterized by the concerted totality of the pole positions, pro-
vides a performance significantly better than any single part of the system could
have done individually. That is, the whole is better than the sum of its parts-see
Figure 5-3.

-_
---__ --_ Figure 5-3.

---__ -. Results of an
integrated system
design.

.. . .
xtal#2-’*.x ., *., ,.*, a, .,
1 I Modpiator
I
I
I
I
Relative
Lmplitude
pe‘.
Function I

Relative
hplitude
Overall

Envelope
Transient
Response

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