11.1: Theory Overview

Last updated
Save as PDF

Page ID: 26030

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

In order to span the range of audible tones with accuracy, low distortion, and reasonable volume levels, loudspeaker systems are typically comprised of two or more transducers, each designed to cover only a portion of the frequency spectrum. As the spectrum is broken up into multiple segments, a circuit is needed to “steer” the proper signals to the appropriate transducers. Failure to do so may result in distortion or damage to the transducers. As inductors and capacitors exhibit a reactance that is a function of frequency, they are ideal candidates for this job. In this exercise, a simple two-way crossover is examined. It has one output for the high frequency transducer (tweeter) and for the low frequency transducer (woofer). In order to reduce the size of the components in this exercise, the impedance has been scaled upward by a factor of nearly 100. In place of the transducers, two resistive loads are used. This has the added advantage of not producing any sound in the lab! While real-world crossovers tend to be more complex than the one in this exercise, it will suffice to show the basic operation.