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The impedance Matching in The Audio Signal Processing (Part IV)

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Electronusa Mechanical System

The document discusses impedance matching in audio signal processing. It analyzes a circuit both analytically and through simulation. The analytical work calculates values like Thevenin voltage (3.55V), emitter voltage (2.85V), and emitter current (19mA) for DC analysis. It also calculates values for AC analysis like input resistance (153.564Ω), input current (6.5μA), and output current (1.3mA). The simulation matches these analytical values closely but with small differences, such as Thevenin voltage of 3V instead of 3.55V. The document compares analytical and simulation results to within 18-21% difference.

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Electronusa Mechanical System [Research Center for Electronic and Mechanical] 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 100ߤ‫. ܸ52⁄ ܨ‬ 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 ்ܸு ൌ ൈ 5ܸ 10݇Ω ൅ 24݇Ω 24݇Ω ்ܸு ൈ 5ܸ 34݇Ω ்ܸு ൌ ሺ0.71ሻ ൈ 5ܸ ்ܸு ൌ 3.55ܸ 1|Page
Electronusa Mechanical System [Research Center for Electronic and Mechanical] 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 ൌ ܴா 2.85ܸ ‫ܫ‬ா ൌ 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: 25݉‫ݒ‬ ‫ݎ‬௘ ൌ ‫ܫ‬ா 25ܸ݉ ‫ݎ‬௘ ൌ 19݉‫ܣ‬ ‫ݎ‬௘ ൌ 1.32Ω The second step, we have to calculate ‫ݎ‬௜௡ሺ௕௔௦௘ሻ : ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺߚ ൅ 1ሻ൫ሺܴଷ ൅ ܴସ ሻԡ‫ݎ‬௘ ൯ ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ200 ൅ 1ሻ൫ሺ150Ω ൅ 8.2Ωሻԡ1.32Ω൯ 2|Page
Electronusa Mechanical System [Research Center for Electronic and Mechanical] ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ201ሻ൫ሺ158.2Ωሻԡ1.32Ω൯ 1 1 ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ201ሻ ൬ ൅ ൰ 158.2Ω 1.32Ω 1.32 158.2 ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ201ሻ ൬ ൅ ൰ 208.824Ω 208.824Ω 159.52 ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ201ሻ ൬ ൰ 208.824Ω ‫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௔௡௔௟௬௧௜௖௔௟ሻ െ ்ܸுሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ்ܸுሺ௔௡௔௟௬௧௜௖௔௟ሻ 3.55ܸ െ 3ܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 3.55ܸ 3|Page
Electronusa Mechanical System [Research Center for Electronic and Mechanical] 0.55ܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 3.55ܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 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௔௡௔௟௬௧௜௖௔௟ሻ െ ܸாሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ܸாሺ௔௡௔௟௬௧௜௖௔௟ሻ 2.85ܸ െ 2.25ܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 2.85ܸ 0.6ܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 2.85ܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 21.05% Figure 4. ܸா in the simulation In the simulation, ‫ܫ‬ா is 15݉‫( ܣ‬figure 5), while in the analytical work ‫ܫ‬ா is 19݉‫ .ܣ‬The difference is: ‫ܫ‬ாሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ܫ‬ாሺ௦௜௠௨௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ‫ܫ‬ாሺ௔௡௔௟௬௧௜௖௔௟ሻ 19݉‫ ܣ‬െ 15݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 19݉‫ܣ‬ 4݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 19݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 21.05% 4|Page
Electronusa Mechanical System [Research Center for Electronic and Mechanical] Figure 5. ‫ܫ‬ா in the simulation 3.2 Analysis of ac In the analytical ݅௕ is 6.5ߤ‫ܣ݉5600.0( ܣ‬ሻ, while in the simulation ݅௕ is 0.07݉‫( ܣ‬figure 6). The difference is: ݅௕ሺ௦௜௠௨௟௔௧௜௢௡ሻ െ ݅௕ሺ௔௡௔௟௬௧௜௖௔௟ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ݅௕ሺ௦௜௠௨௟௔௧௜௢௡ሻ 0.07݉‫ ܣ‬െ 0.0065݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 0.07݉‫ܣ‬ 0.0635 ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 0.07 ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 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 5|Page
Electronusa Mechanical System [Research Center for Electronic and Mechanical] In the simulation, ݅௖ is 14.9݉‫( ܣ‬figure 7), while in the analytical ݅௖ is 1.3݉‫ .ܣ‬The difference is: ݅௖ሺ௦௜௠௨௟௔௧௜௢௡ሻ െ ݅௖ሺ௔௡௔௟௬௧௜௖௔௟ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ݅௖ሺ௦௜௠௨௟௔௧௜௢௡ሻ 14.9݉‫ ܣ‬െ 1.3݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 14.9݉‫ܣ‬ 13.6݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 14.9݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 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 0.54ߤ‫ ܣ‬at 1Hz, is 4.38ߤ‫ ܣ‬at 10Hz, is 38.9ߤ‫ ܣ‬at 100Hz, is 83.2ߤ‫ ܣ‬at 1kHz, 84.8ߤ‫ ܣ‬at 10kHz, and 84.8ߤ‫ ܣ‬at 16kHz (figure 8). The difference is: For 1Hz, ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 1.3݉‫ ܣ‬െ 0.54ߤ‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3݉‫ܣ‬ 1.3000݉‫ ܣ‬െ 0.00054݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ 1.29945݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 99.957% 6|Page
Electronusa Mechanical System [Research Center for Electronic and Mechanical] For 10Hz, ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 1.3݉‫ ܣ‬െ 4.38ߤ‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3݉‫ܣ‬ 1.3000݉‫ ܣ‬െ 0.00438݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ 1.29562݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 99.66% For 100Hz, ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 1.3݉‫ ܣ‬െ 38.9ߤ‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3݉‫ܣ‬ 1.3000݉‫ ܣ‬െ 0.0389݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ 1.2611݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 97.007% For 1kHz, ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 1.3݉‫ ܣ‬െ 83.2ߤ‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3݉‫ܣ‬ 1.3000݉‫ ܣ‬െ 0.08327݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ 1.21673݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 93.595% For 10kHz, ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 1.3݉‫ ܣ‬െ 84.8ߤ‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3݉‫ܣ‬ 1.3000݉‫ ܣ‬െ 0.0848݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ 1.2152݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ 7|Page
Electronusa Mechanical System [Research Center for Electronic and Mechanical] ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 93.47% For 16kHz, ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 1.3݉‫ ܣ‬െ 84.8ߤ‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3݉‫ܣ‬ 1.3000݉‫ ܣ‬െ 0.0848݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ 1.2152݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 93.47% (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 2.97ߤܸ at 1Hz, is 24.6ߤܸ at 10Hz, is 218ߤܸ at 100Hz, is 466ߤܸ at 1kHz, is 475ߤܸ at 10kHz, and 475ߤܸ at 16kHz (figure 9). The difference is: For 1Hz, ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 993.2ߤܸ െ 2.97ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ 980.23ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 98.69% 8|Page
Electronusa Mechanical System [Research Center for Electronic and Mechanical] For 10Hz, ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 993.2ߤܸ െ 24.6ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ 968.6ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 97.52% For 100Hz, ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 993.2ߤܸ െ 218ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ 775.2ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 78.05% For 1kHz, ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 993.2ߤܸ െ 466ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ 527.2ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 53.08% For 10kHz, ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 993.2ߤܸ െ 475ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ 518.2ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 52.1747% For 16kHz, ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 993.2ߤܸ െ 475ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ 518.2ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ 9|Page
Electronusa Mechanical System [Research Center for Electronic and Mechanical] ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 52.1747% 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 10 | P a g e

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The impedance Matching in The Audio Signal Processing (Part IV)

  • 1. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 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 100ߤ‫. ܸ52⁄ ܨ‬ 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 ்ܸு ൌ ൈ 5ܸ 10݇Ω ൅ 24݇Ω 24݇Ω ்ܸு ൈ 5ܸ 34݇Ω ்ܸு ൌ ሺ0.71ሻ ൈ 5ܸ ்ܸு ൌ 3.55ܸ 1|Page
  • 2. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 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 ൌ ܴா 2.85ܸ ‫ܫ‬ா ൌ 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: 25݉‫ݒ‬ ‫ݎ‬௘ ൌ ‫ܫ‬ா 25ܸ݉ ‫ݎ‬௘ ൌ 19݉‫ܣ‬ ‫ݎ‬௘ ൌ 1.32Ω The second step, we have to calculate ‫ݎ‬௜௡ሺ௕௔௦௘ሻ : ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺߚ ൅ 1ሻ൫ሺܴଷ ൅ ܴସ ሻԡ‫ݎ‬௘ ൯ ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ200 ൅ 1ሻ൫ሺ150Ω ൅ 8.2Ωሻԡ1.32Ω൯ 2|Page
  • 3. Electronusa Mechanical System [Research Center for Electronic and Mechanical] ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ201ሻ൫ሺ158.2Ωሻԡ1.32Ω൯ 1 1 ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ201ሻ ൬ ൅ ൰ 158.2Ω 1.32Ω 1.32 158.2 ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ201ሻ ൬ ൅ ൰ 208.824Ω 208.824Ω 159.52 ‫ݎ‬௜௡ሺ௕௔௦௘ሻ ൌ ሺ201ሻ ൬ ൰ 208.824Ω ‫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௔௡௔௟௬௧௜௖௔௟ሻ െ ்ܸுሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ்ܸுሺ௔௡௔௟௬௧௜௖௔௟ሻ 3.55ܸ െ 3ܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 3.55ܸ 3|Page
  • 4. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 0.55ܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 3.55ܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 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௔௡௔௟௬௧௜௖௔௟ሻ െ ܸாሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ܸாሺ௔௡௔௟௬௧௜௖௔௟ሻ 2.85ܸ െ 2.25ܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 2.85ܸ 0.6ܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 2.85ܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 21.05% Figure 4. ܸா in the simulation In the simulation, ‫ܫ‬ா is 15݉‫( ܣ‬figure 5), while in the analytical work ‫ܫ‬ா is 19݉‫ .ܣ‬The difference is: ‫ܫ‬ாሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ܫ‬ாሺ௦௜௠௨௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ‫ܫ‬ாሺ௔௡௔௟௬௧௜௖௔௟ሻ 19݉‫ ܣ‬െ 15݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 19݉‫ܣ‬ 4݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 19݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 21.05% 4|Page
  • 5. Electronusa Mechanical System [Research Center for Electronic and Mechanical] Figure 5. ‫ܫ‬ா in the simulation 3.2 Analysis of ac In the analytical ݅௕ is 6.5ߤ‫ܣ݉5600.0( ܣ‬ሻ, while in the simulation ݅௕ is 0.07݉‫( ܣ‬figure 6). The difference is: ݅௕ሺ௦௜௠௨௟௔௧௜௢௡ሻ െ ݅௕ሺ௔௡௔௟௬௧௜௖௔௟ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ݅௕ሺ௦௜௠௨௟௔௧௜௢௡ሻ 0.07݉‫ ܣ‬െ 0.0065݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 0.07݉‫ܣ‬ 0.0635 ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 0.07 ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 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 5|Page
  • 6. Electronusa Mechanical System [Research Center for Electronic and Mechanical] In the simulation, ݅௖ is 14.9݉‫( ܣ‬figure 7), while in the analytical ݅௖ is 1.3݉‫ .ܣ‬The difference is: ݅௖ሺ௦௜௠௨௟௔௧௜௢௡ሻ െ ݅௖ሺ௔௡௔௟௬௧௜௖௔௟ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ݅௖ሺ௦௜௠௨௟௔௧௜௢௡ሻ 14.9݉‫ ܣ‬െ 1.3݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 14.9݉‫ܣ‬ 13.6݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 14.9݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 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 0.54ߤ‫ ܣ‬at 1Hz, is 4.38ߤ‫ ܣ‬at 10Hz, is 38.9ߤ‫ ܣ‬at 100Hz, is 83.2ߤ‫ ܣ‬at 1kHz, 84.8ߤ‫ ܣ‬at 10kHz, and 84.8ߤ‫ ܣ‬at 16kHz (figure 8). The difference is: For 1Hz, ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 1.3݉‫ ܣ‬െ 0.54ߤ‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3݉‫ܣ‬ 1.3000݉‫ ܣ‬െ 0.00054݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ 1.29945݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 99.957% 6|Page
  • 7. Electronusa Mechanical System [Research Center for Electronic and Mechanical] For 10Hz, ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 1.3݉‫ ܣ‬െ 4.38ߤ‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3݉‫ܣ‬ 1.3000݉‫ ܣ‬െ 0.00438݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ 1.29562݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 99.66% For 100Hz, ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 1.3݉‫ ܣ‬െ 38.9ߤ‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3݉‫ܣ‬ 1.3000݉‫ ܣ‬െ 0.0389݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ 1.2611݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 97.007% For 1kHz, ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 1.3݉‫ ܣ‬െ 83.2ߤ‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3݉‫ܣ‬ 1.3000݉‫ ܣ‬െ 0.08327݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ 1.21673݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 93.595% For 10kHz, ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 1.3݉‫ ܣ‬െ 84.8ߤ‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3݉‫ܣ‬ 1.3000݉‫ ܣ‬െ 0.0848݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ 1.2152݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ 7|Page
  • 8. Electronusa Mechanical System [Research Center for Electronic and Mechanical] ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 93.47% For 16kHz, ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 1.3݉‫ ܣ‬െ 84.8ߤ‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3݉‫ܣ‬ 1.3000݉‫ ܣ‬െ 0.0848݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ 1.2152݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 1.3000݉‫ܣ‬ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 93.47% (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 2.97ߤܸ at 1Hz, is 24.6ߤܸ at 10Hz, is 218ߤܸ at 100Hz, is 466ߤܸ at 1kHz, is 475ߤܸ at 10kHz, and 475ߤܸ at 16kHz (figure 9). The difference is: For 1Hz, ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 993.2ߤܸ െ 2.97ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ 980.23ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 98.69% 8|Page
  • 9. Electronusa Mechanical System [Research Center for Electronic and Mechanical] For 10Hz, ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 993.2ߤܸ െ 24.6ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ 968.6ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 97.52% For 100Hz, ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 993.2ߤܸ െ 218ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ 775.2ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 78.05% For 1kHz, ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 993.2ߤܸ െ 466ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ 527.2ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 53.08% For 10kHz, ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 993.2ߤܸ െ 475ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ 518.2ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 52.1747% For 16kHz, ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ 993.2ߤܸ െ 475ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ 518.2ߤܸ ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ ൈ 100% 993.2ߤܸ 9|Page
  • 10. Electronusa Mechanical System [Research Center for Electronic and Mechanical] ሺ%ሻ݂݂݀݅݁‫ ݁ܿ݊݁ݎ‬ൌ 52.1747% 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 10 | P a g e