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Electronusa Mechanical System

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Electronusa Mechanical System

This document discusses impedance matching in audio signal processing. It presents an analytical analysis and simulation of a circuit that uses an emitter-follower configuration to provide impedance matching between an input and output. The analytical work derives expressions for various circuit parameters in both DC and AC analysis. The simulation results show good agreement with the analytical work but with some differences, likely due to approximations made in the analytical derivations. Percent differences between the analytical and simulation results are provided.

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Electronusa Mechanical System [Research Center for Electronic and Mechanical] 1 | P a g e The Impedance Matching in The Audio Signal Processing Umar Sidik.BEng.MSc* Director of Engineering Electronusa Mechanical System (CTRONICS) *umar.sidik@engineer.com 1. Introduction Commonly, impedance is obstruction to transfer energy in the electronic circuit. Therefore, the impedance matching is required to achieve the maximum power transfer. Furthermore, the impedance matching equalizes the source impedance and load impedance. In other hand, the emitter-follower (common-collector) provides the impedance matching delivered from the base (input) to the emitter (output). The emitter-follower has high input resistance and low output resistance. In the emitter-follower, the input resistance depends on the load resistance, while the output resistance depends on the source resistance. In addition, this study implements the radial electrolytic capacitor 470݊‫ܨ‬ 63ܸ⁄ . 2. Analytical Work In this study, ܴଵ and ܴଶ form the Thevenin voltage, while ‫ܥ‬ଵ and ‫ܥ‬ଶ deliver ac signal as ‫ݒ‬௜௡ and ‫ݒ‬௢௨௧(figure 1). (a) (b) Figure 1. (a). The concept of circuit analyzed in the study (b). The equivalent circuit 2.1 Analysis of dc First step, we have to calculate the Thevenin’s voltage in figure 1: ்ܸு ൌ ܴଶ ܴଵ ൅ ܴଶ ൈ ܸ஼஼ For this circuit, ܸ஼஼ is 5ܸ, then: ்ܸு ൌ 24݇Ω 10݇Ω ൅ 24݇Ω ൈ 5ܸ ்ܸு 24݇Ω 34݇Ω ൈ 5ܸ ்ܸு ൌ ሺ0.71ሻ ൈ 5ܸ ்ܸு ൌ 3.55ܸ
Electronusa Mechanical System [Research Center for Electronic and Mechanical] 2 | P a g e Actually, in this circuit ்ܸு ൌ ܸ஻, so ܸ஻ ൌ 3.55ܸ. The second step, we have to calculate ܸா: ܸா ൌ ܸ஻ െ ܸ஻ா ܸா ൌ 3.55ܸ െ 0.7ܸ ܸா ൌ 2.85ܸ The third step, we have to calculate ‫ܫ‬ா: ‫ܫ‬ா ൌ ܸா ܴா ‫ܫ‬ா ൌ 2.85ܸ 150Ω ‫ܫ‬ா ൌ 19݉‫ܣ‬ 2.2 Analysis of ac In the analysis of ac, we involve the capacitor to pass the ac signal and we also involve the internal resistance of emitter known as ‫ݎ‬௘ (figure 2). (a) (b) Figure 2. (a). The ac circuit (b). The equivalent circuit for ac analysis The first step, we have to calculate ‫ݎ‬௘ in the figure 2: ‫ݎ‬௘ ൌ 25݉‫ݒ‬ ‫ܫ‬ா ‫ݎ‬௘ ൌ 25ܸ݉ 19݉‫ܣ‬ ‫ݎ‬௘ ൌ 1.32Ω The second step, we have to calculate ‫ݎ‬௜௡ሺ௕௔௦௘ሻ: ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺߚ ൅ 1ሻ൫ሺܴଷ ൅ ܴସሻԡ‫ݎ‬௘൯ ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ200 ൅ 1ሻ൫ሺ150Ω ൅ 8.2Ωሻԡ1.32Ω൯
Electronusa Mechanical System [Research Center for Electronic and Mechanical] 3 | P a g e ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ201ሻ൫ሺ158.2Ωሻԡ1.32Ω൯ ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ201ሻ ൬ 1 158.2Ω ൅ 1 1.32Ω ൰ ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ201ሻ ൬ 1.32 208.824Ω ൅ 158.2 208.824Ω ൰ ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ201ሻ ൬ 159.52 208.824Ω ൰ ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ201ሻሺ0.764Ωሻ ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ 153.564Ω The third step is to calculate ݅௕: ݅௕ ൌ ‫ݒ‬௜௡ ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ݅௕ ൌ 1ܸ݉ 153.564Ω ݅௕ ൌ 0.0065݉‫ܣ‬ ݅௕ ൌ 6.5ߤ‫ܣ‬ The fourth step is to calculate ݅௖: ݅௖ ൌ ߚ݅௕ ݅௖ ൌ ሺ200ሻሺ0.0065݉‫ܣ‬ሻ ݅௖ ൌ 1.3݉‫ܣ‬ The last step is to calculate ‫ݒ‬௢௨௧: ‫ݒ‬௢௨௧ ൌ ݅௖‫ݎ‬௢௨௧ ‫ݒ‬௢௨௧ ൌ ሺ1.3݉‫ܣ‬ሻሺ0.764Ωሻ ‫ݒ‬௢௨௧ ൌ 0.9932ܸ݉ ‫ݒ‬௢௨௧ ൌ 993.2ߤܸ 3. Simulation Work The simulation work can be classified into the dc analysis and the ac analysis. 3.1 Analysis of dc In the simulation, ்ܸு is 3ܸ (figure 3), while in the analytical work ்ܸு is 3.55ܸ. The different of the analytical work and the simulation work is: ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ்ܸுሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ்ܸுሺ௦௜௠௨௟௔௧௜௢௡ሻ ்ܸுሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 3.55ܸ െ 3ܸ 3.55ܸ ൈ 100%
Electronusa Mechanical System [Research Center for Electronic and Mechanical] 4 | P a g e ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 0.55ܸ 3.55ܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 18.33% Figure 3. ்ܸு in the simulation In the simulation, ܸா is 2.25ܸ (figure 4), while in the analytical work ܸா is 2.85ܸ. The different of the analytical work and the simulation work is: ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ܸாሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ܸாሺ௦௜௠௨௟௔௧௜௢௡ሻ ܸாሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 2.85ܸ െ 2.25ܸ 2.85ܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 0.6ܸ 2.85ܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 21.05% Figure 4. ܸா in the simulation In the simulation, ‫ܫ‬ா is 15݉‫ܣ‬ (figure 5), while in the analytical work ‫ܫ‬ா is 19݉‫.ܣ‬ The difference is: ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ܫ‬ாሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ܫ‬ாሺ௦௜௠௨௔௧௜௢௡ሻ ‫ܫ‬ாሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 19݉‫ܣ‬ െ 15݉‫ܣ‬ 19݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 4݉‫ܣ‬ 19݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 21.05%
Electronusa Mechanical System [Research Center for Electronic and Mechanical] 5 | P a g e Figure 5. ‫ܫ‬ா in the simulation 3.2 Analysis of ac In the analytical ݅௕ is 6.5ߤ‫ܣ‬ (0.0065݉‫ܣ‬ሻ, while in the simulation ݅௕ is 0.07݉‫ܣ‬ (figure 6). The difference is: ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௕ሺ௦௜௠௨௟௔௧௜௢௡ሻ െ ݅௕ሺ௔௡௔௟௬௧௜௖௔௟ሻ ݅௕ሺ௦௜௠௨௟௔௧௜௢௡ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 0.07݉‫ܣ‬ െ 0.0065݉‫ܣ‬ 0.07݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 0.0635 0.07 ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 90.71% (a) (b) (c) (d) (e) Figure 6. (a). ݅௕ in the simulation at 1Hz (b). ݅௕ in the simulation at 10Hz (c). ݅௕ in the simulation at 100Hz (d). ݅௕ in the simulation at 1kHz (e). ݅௕ in the simulation at 10kHz
Electronusa Mechanical System [Research Center for Electronic and Mechanical] 6 | P a g e In the simulation, ݅௖ is 14.9݉‫ܣ‬ (figure 7), while in the analytical ݅௖ is 1.3݉‫.ܣ‬ The difference is: ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௖ሺ௦௜௠௨௟௔௧௜௢௡ሻ െ ݅௖ሺ௔௡௔௟௬௧௜௖௔௟ሻ ݅௖ሺ௦௜௠௨௟௔௧௜௢௡ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 14.9݉‫ܣ‬ െ 1.3݉‫ܣ‬ 14.9݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 13.6݉‫ܣ‬ 14.9݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 91.275% (a) (b) (c) (d) (e) Figure 7. (a). ݅௖ in the simulation at 1Hz (b). ݅௖ in the simulation at 10Hz (c). ݅௖ in the simulation at 100Hz (d). ݅௖ in the simulation at 1kHz (e). ݅௖ in the simulation at 10kHz In the simulation, ݅௢௨௧ is 0ߤ‫ܣ‬ at 1Hz, is 0ߤ‫ܣ‬ at 10Hz, is 0.05ߤ‫ܣ‬ at 100Hz, is 0.94ߤ‫ܣ‬ at 1kHz, 9.61ߤ‫ܣ‬ at 10kHz, and 15.2ߤ‫ܣ‬ at 16kHz (figure 8). The difference is: For 1Hz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0݉‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 100%
Electronusa Mechanical System [Research Center for Electronic and Mechanical] 7 | P a g e For 10Hz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 100% For 100Hz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0.17ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0.00017݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.29983݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 99.987% For 1kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 2.02ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0.00202݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.29798݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 99.884% For 10kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 20.1ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3000݉‫ܣ‬ െ 0.0201݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.2799݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100%
Electronusa Mechanical System [Research Center for Electronic and Mechanical] 8 | P a g e ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 98.45% For 16kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 30.8ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3000݉‫ܣ‬ െ 0.0308݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.2692݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 97.63% (a) (b) (c) (d) (e) (f) Figure 8. (a). ݅௢௨௧ in the simulation at 1Hz (b). ݅௢௨௧ in the simulation at 10Hz (c). ݅௢௨௧ in the simulation at 100Hz (d). ݅௢௨௧ in the simulation at 1kHz (e). ݅௢௨௧ in the simulation at 10kHz (f). ݅௢௨௧ in the simulation at 16kHz In the simulation, ‫ݒ‬௢௨௧ is 0ߤܸ at 1Hz, is 0ߤܸ at 10Hz, is 0.32ߤܸ at 100Hz, is 5.36ߤܸ at 1kHz, is 53.8ߤܸ at 10kHz, and 85.3ߤܸ at 16kHz (figure 9). The difference is: For 1Hz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 0ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 100%
Electronusa Mechanical System [Research Center for Electronic and Mechanical] 9 | P a g e For 10Hz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 0.01ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.19ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 99.99% For 100Hz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 0.97ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 992.23ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 99.90% For 1kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 11.5ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 981.7ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 98.84% For 10kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 112ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 881.2ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 88.723% For 16kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 173ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 820.2ߤܸ 993.2ߤܸ ൈ 100%
Electronusa Mechanical System [Research Center for Electronic and Mechanical] 10 | P a g e ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 82.581% In this study, the simulation shows that the ݅௢௨௧ and ‫ݒ‬௢௨௧ became stable started at 1 kHz. (a) (b) (c) (d) (e) (f) Figure 9. (a). ‫ݒ‬௢௨௧ in the simulation at 1Hz (b). ‫ݒ‬௢௨௧ in the simulation at 10Hz (c). ‫ݒ‬௢௨௧ in the simulation at 100Hz (d). ‫ݒ‬௢௨௧ in the simulation at 1kHz (e). ‫ݒ‬௢௨௧ in the simulation at 10kHz (f). ‫ݒ‬௢௨௧ in the simulation at 16kHz

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Electronusa Mechanical System

  • 1. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 1 | P a g e The Impedance Matching in The Audio Signal Processing Umar Sidik.BEng.MSc* Director of Engineering Electronusa Mechanical System (CTRONICS) *umar.sidik@engineer.com 1. Introduction Commonly, impedance is obstruction to transfer energy in the electronic circuit. Therefore, the impedance matching is required to achieve the maximum power transfer. Furthermore, the impedance matching equalizes the source impedance and load impedance. In other hand, the emitter-follower (common-collector) provides the impedance matching delivered from the base (input) to the emitter (output). The emitter-follower has high input resistance and low output resistance. In the emitter-follower, the input resistance depends on the load resistance, while the output resistance depends on the source resistance. In addition, this study implements the radial electrolytic capacitor 470݊‫ܨ‬ 63ܸ⁄ . 2. Analytical Work In this study, ܴଵ and ܴଶ form the Thevenin voltage, while ‫ܥ‬ଵ and ‫ܥ‬ଶ deliver ac signal as ‫ݒ‬௜௡ and ‫ݒ‬௢௨௧(figure 1). (a) (b) Figure 1. (a). The concept of circuit analyzed in the study (b). The equivalent circuit 2.1 Analysis of dc First step, we have to calculate the Thevenin’s voltage in figure 1: ்ܸு ൌ ܴଶ ܴଵ ൅ ܴଶ ൈ ܸ஼஼ For this circuit, ܸ஼஼ is 5ܸ, then: ்ܸு ൌ 24݇Ω 10݇Ω ൅ 24݇Ω ൈ 5ܸ ்ܸு 24݇Ω 34݇Ω ൈ 5ܸ ்ܸு ൌ ሺ0.71ሻ ൈ 5ܸ ்ܸு ൌ 3.55ܸ
  • 2. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 2 | P a g e Actually, in this circuit ்ܸு ൌ ܸ஻, so ܸ஻ ൌ 3.55ܸ. The second step, we have to calculate ܸா: ܸா ൌ ܸ஻ െ ܸ஻ா ܸா ൌ 3.55ܸ െ 0.7ܸ ܸா ൌ 2.85ܸ The third step, we have to calculate ‫ܫ‬ா: ‫ܫ‬ா ൌ ܸா ܴா ‫ܫ‬ா ൌ 2.85ܸ 150Ω ‫ܫ‬ா ൌ 19݉‫ܣ‬ 2.2 Analysis of ac In the analysis of ac, we involve the capacitor to pass the ac signal and we also involve the internal resistance of emitter known as ‫ݎ‬௘ (figure 2). (a) (b) Figure 2. (a). The ac circuit (b). The equivalent circuit for ac analysis The first step, we have to calculate ‫ݎ‬௘ in the figure 2: ‫ݎ‬௘ ൌ 25݉‫ݒ‬ ‫ܫ‬ா ‫ݎ‬௘ ൌ 25ܸ݉ 19݉‫ܣ‬ ‫ݎ‬௘ ൌ 1.32Ω The second step, we have to calculate ‫ݎ‬௜௡ሺ௕௔௦௘ሻ: ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺߚ ൅ 1ሻ൫ሺܴଷ ൅ ܴସሻԡ‫ݎ‬௘൯ ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ200 ൅ 1ሻ൫ሺ150Ω ൅ 8.2Ωሻԡ1.32Ω൯
  • 3. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 3 | P a g e ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ201ሻ൫ሺ158.2Ωሻԡ1.32Ω൯ ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ201ሻ ൬ 1 158.2Ω ൅ 1 1.32Ω ൰ ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ201ሻ ൬ 1.32 208.824Ω ൅ 158.2 208.824Ω ൰ ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ201ሻ ൬ 159.52 208.824Ω ൰ ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ201ሻሺ0.764Ωሻ ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ 153.564Ω The third step is to calculate ݅௕: ݅௕ ൌ ‫ݒ‬௜௡ ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ݅௕ ൌ 1ܸ݉ 153.564Ω ݅௕ ൌ 0.0065݉‫ܣ‬ ݅௕ ൌ 6.5ߤ‫ܣ‬ The fourth step is to calculate ݅௖: ݅௖ ൌ ߚ݅௕ ݅௖ ൌ ሺ200ሻሺ0.0065݉‫ܣ‬ሻ ݅௖ ൌ 1.3݉‫ܣ‬ The last step is to calculate ‫ݒ‬௢௨௧: ‫ݒ‬௢௨௧ ൌ ݅௖‫ݎ‬௢௨௧ ‫ݒ‬௢௨௧ ൌ ሺ1.3݉‫ܣ‬ሻሺ0.764Ωሻ ‫ݒ‬௢௨௧ ൌ 0.9932ܸ݉ ‫ݒ‬௢௨௧ ൌ 993.2ߤܸ 3. Simulation Work The simulation work can be classified into the dc analysis and the ac analysis. 3.1 Analysis of dc In the simulation, ்ܸு is 3ܸ (figure 3), while in the analytical work ்ܸு is 3.55ܸ. The different of the analytical work and the simulation work is: ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ்ܸுሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ்ܸுሺ௦௜௠௨௟௔௧௜௢௡ሻ ்ܸுሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 3.55ܸ െ 3ܸ 3.55ܸ ൈ 100%
  • 4. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 4 | P a g e ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 0.55ܸ 3.55ܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 18.33% Figure 3. ்ܸு in the simulation In the simulation, ܸா is 2.25ܸ (figure 4), while in the analytical work ܸா is 2.85ܸ. The different of the analytical work and the simulation work is: ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ܸாሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ܸாሺ௦௜௠௨௟௔௧௜௢௡ሻ ܸாሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 2.85ܸ െ 2.25ܸ 2.85ܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 0.6ܸ 2.85ܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 21.05% Figure 4. ܸா in the simulation In the simulation, ‫ܫ‬ா is 15݉‫ܣ‬ (figure 5), while in the analytical work ‫ܫ‬ா is 19݉‫.ܣ‬ The difference is: ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ܫ‬ாሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ܫ‬ாሺ௦௜௠௨௔௧௜௢௡ሻ ‫ܫ‬ாሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 19݉‫ܣ‬ െ 15݉‫ܣ‬ 19݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 4݉‫ܣ‬ 19݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 21.05%
  • 5. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 5 | P a g e Figure 5. ‫ܫ‬ா in the simulation 3.2 Analysis of ac In the analytical ݅௕ is 6.5ߤ‫ܣ‬ (0.0065݉‫ܣ‬ሻ, while in the simulation ݅௕ is 0.07݉‫ܣ‬ (figure 6). The difference is: ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௕ሺ௦௜௠௨௟௔௧௜௢௡ሻ െ ݅௕ሺ௔௡௔௟௬௧௜௖௔௟ሻ ݅௕ሺ௦௜௠௨௟௔௧௜௢௡ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 0.07݉‫ܣ‬ െ 0.0065݉‫ܣ‬ 0.07݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 0.0635 0.07 ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 90.71% (a) (b) (c) (d) (e) Figure 6. (a). ݅௕ in the simulation at 1Hz (b). ݅௕ in the simulation at 10Hz (c). ݅௕ in the simulation at 100Hz (d). ݅௕ in the simulation at 1kHz (e). ݅௕ in the simulation at 10kHz
  • 6. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 6 | P a g e In the simulation, ݅௖ is 14.9݉‫ܣ‬ (figure 7), while in the analytical ݅௖ is 1.3݉‫.ܣ‬ The difference is: ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௖ሺ௦௜௠௨௟௔௧௜௢௡ሻ െ ݅௖ሺ௔௡௔௟௬௧௜௖௔௟ሻ ݅௖ሺ௦௜௠௨௟௔௧௜௢௡ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 14.9݉‫ܣ‬ െ 1.3݉‫ܣ‬ 14.9݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 13.6݉‫ܣ‬ 14.9݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 91.275% (a) (b) (c) (d) (e) Figure 7. (a). ݅௖ in the simulation at 1Hz (b). ݅௖ in the simulation at 10Hz (c). ݅௖ in the simulation at 100Hz (d). ݅௖ in the simulation at 1kHz (e). ݅௖ in the simulation at 10kHz In the simulation, ݅௢௨௧ is 0ߤ‫ܣ‬ at 1Hz, is 0ߤ‫ܣ‬ at 10Hz, is 0.05ߤ‫ܣ‬ at 100Hz, is 0.94ߤ‫ܣ‬ at 1kHz, 9.61ߤ‫ܣ‬ at 10kHz, and 15.2ߤ‫ܣ‬ at 16kHz (figure 8). The difference is: For 1Hz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0݉‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 100%
  • 7. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 7 | P a g e For 10Hz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 100% For 100Hz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0.17ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0.00017݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.29983݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 99.987% For 1kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 2.02ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0.00202݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.29798݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 99.884% For 10kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 20.1ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3000݉‫ܣ‬ െ 0.0201݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.2799݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100%
  • 8. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 8 | P a g e ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 98.45% For 16kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 30.8ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3000݉‫ܣ‬ െ 0.0308݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.2692݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 97.63% (a) (b) (c) (d) (e) (f) Figure 8. (a). ݅௢௨௧ in the simulation at 1Hz (b). ݅௢௨௧ in the simulation at 10Hz (c). ݅௢௨௧ in the simulation at 100Hz (d). ݅௢௨௧ in the simulation at 1kHz (e). ݅௢௨௧ in the simulation at 10kHz (f). ݅௢௨௧ in the simulation at 16kHz In the simulation, ‫ݒ‬௢௨௧ is 0ߤܸ at 1Hz, is 0ߤܸ at 10Hz, is 0.32ߤܸ at 100Hz, is 5.36ߤܸ at 1kHz, is 53.8ߤܸ at 10kHz, and 85.3ߤܸ at 16kHz (figure 9). The difference is: For 1Hz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 0ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 100%
  • 9. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 9 | P a g e For 10Hz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 0.01ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.19ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 99.99% For 100Hz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 0.97ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 992.23ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 99.90% For 1kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 11.5ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 981.7ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 98.84% For 10kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 112ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 881.2ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 88.723% For 16kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 173ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 820.2ߤܸ 993.2ߤܸ ൈ 100%
  • 10. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 10 | P a g e ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 82.581% In this study, the simulation shows that the ݅௢௨௧ and ‫ݒ‬௢௨௧ became stable started at 1 kHz. (a) (b) (c) (d) (e) (f) Figure 9. (a). ‫ݒ‬௢௨௧ in the simulation at 1Hz (b). ‫ݒ‬௢௨௧ in the simulation at 10Hz (c). ‫ݒ‬௢௨௧ in the simulation at 100Hz (d). ‫ݒ‬௢௨௧ in the simulation at 1kHz (e). ‫ݒ‬௢௨௧ in the simulation at 10kHz (f). ‫ݒ‬௢௨௧ in the simulation at 16kHz