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3.16 Circuit analysis of the acoustical circuit in Fig. 35.

Introduction and table of contents for postings 3.16a through 3.16g.

**Keywords:** circuit analysis, scattering, resonant, circulator

The string and acoustical circuits shown in the last two postings (Figs. 26, 35 and 36) can be analyzed conveniently with circuit analysis methods used in electrical engineering. In a string of postings starting with this one, we describe this analysis and graph the results. This analysis is done in a variety of ways to show the possibilities and also to cross check the results. In the posting 3.16a through 3.16g (also 3.18) we address the acoustical circuit in Fig. 35: we draw the equivalent circuit, analyze its response analytically, and then show the SPICE simulation of the circuit.

Fig. 40. A snap shot of the animation, Fig. 35, of the previous posting. |

The image above is a snapshot of Fig. 35 of the last posting. Incident waves are launched from the left, travel down the waveguide, through the circulator to the coupling hole of the resonator. There, the waves are reflected, travel back to the circulator, into the right waveguide, and finally to the absorber.

Analysis of this circuit is applicable to the many cases of one dimensional resonant wave scattering technology where the negative-going waves are easily separable from the incident waves. As pointed out in the last posting, it also applies to two and three dimensional cases where the angular distribution of the reflected waves is the same as the angular distribution of the waves radiated from the resonator mixing the two inseparably. This is the usual case in radar waves scattering off a large (compared with a wavelength) structure coated with a resonant layer or with LIDAR where extremely short wavelength light waves typically scatter off objects coated with molecules that act as resonant scatterers.

Table of contents "circuit analysis of acoustical circuits" (3.16, 3.16a through 3.16g ).

- 3.16 Introduction and table of contents
- 3.16a Electrical model of the acoustical circuit of Fig. 35
- 3.16b Looking at the resonator part of the circuit
- 3.16c Steady state response of the circuit
- 3.16d Transmission line resonators
- 3.16e Steady state response of a transmission line resonator via a Smith chart
- 3.16f Differential equation solution for transient response, SPICE simulation
- 3.16g Summary

All postings by author | previous: 3.15 Resonant scattering of waves - 1D | up: Contents | next: 3.16a Modeling the acoustic circuit with an electrical equivalent |