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Use Kirchhoff's Laws and the characteristic equation for a transformer in the circuit below to prove Eq. 6.78.

Use Kirchhoff's Laws and the characteristic equation for a transformer in the circuit below to prove Eq. 6.78.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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1:0 ZMS 83 V ZEB F Figure 6.14. Equivalent circuit for a linear reciprocal transducer using impedance parameters. ZMs = ZMo(1 - k2) (6.78) where ZMs is defined as the short-circuit mechanical impedance, given by FIU when V is zero, and the electromechanical coupling constant ke is given by TEM ZEBZMO (6.79) Thus far, it seems we have manipulated a set of equations and then forced a circuit model to match themn. That is exactly what we have done! When we examine the linearization of nonlinear systems in the next chapter, we shall apply this formulation to the electrostatic transducer of this chapter, which will provide some intuition about the meaning of these symbols. In the mean time, this exercise provides good opportunity for practice in manipulating circuits that contain two-nort elements. 6.5 Use Kirchhoff's Laws and the characteristic equation for a transformer in the circuit below to prove Eq. 6.78. 1:0 ZMS ZEB 88 F2 V F ZMs = Zмо(1 - к) (6.78)
Transcribed Image Text:1:0 ZMS 83 V ZEB F Figure 6.14. Equivalent circuit for a linear reciprocal transducer using impedance parameters. ZMs = ZMo(1 - k2) (6.78) where ZMs is defined as the short-circuit mechanical impedance, given by FIU when V is zero, and the electromechanical coupling constant ke is given by TEM ZEBZMO (6.79) Thus far, it seems we have manipulated a set of equations and then forced a circuit model to match themn. That is exactly what we have done! When we examine the linearization of nonlinear systems in the next chapter, we shall apply this formulation to the electrostatic transducer of this chapter, which will provide some intuition about the meaning of these symbols. In the mean time, this exercise provides good opportunity for practice in manipulating circuits that contain two-nort elements. 6.5 Use Kirchhoff's Laws and the characteristic equation for a transformer in the circuit below to prove Eq. 6.78. 1:0 ZMS ZEB 88 F2 V F ZMs = Zмо(1 - к) (6.78)
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