Impedance Networks
The concept of impedance is central in classical electrical engineering. The simplest case is Ohm's Law for a resistor :
Thanks to the Laplace transform [449]2.15(or Fourier transform [451]), the concept of impedance easily extends to masses and springs as well. We need only allow impedances to be frequency-dependent. For example, the Laplace transform of Newton's yields, using the differentiation theorem for Laplace transforms [449],
The important benefit of this frequency-domain formulation of impedance is that it allows every interconnection of masses, springs, and dashpots (every RLC equivalent circuit) to be treated as a simple resistor network, parametrized by frequency.
As an example, Fig.1.11 gives the impedance diagram corresponding to the equivalent circuit in Fig.1.10. Viewing the circuit as a (frequency-dependent) resistor network, it is easy to write down, say, the Laplace transform of the force across the spring using the voltage divider formula:
Next Section:
Wave Digital Filters
Previous Section:
Equivalent Circuits