SlideShare a Scribd company logo

Electronusa Mechanical System

Electronusa Mechanical System, profile picture
Electronusa Mechanical System

This 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, dc voltage, and currents. The simulation matches these values reasonably well, with differences generally under 25%. For ac signals, the simulation shows currents increasing with frequency as expected. Overall, the document compares analytical and simulated analyses of a circuit to understand impedance matching.

TechnologyBusiness
1 of 10
Download to read offline
1
2
3
4
5
6
7
8
9
10
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 3.3μ‫ܨ‬ 50ܸ⁄ . 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 െ 0.11ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0.00011݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.29989݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 99.99% For 100Hz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 1.41ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0.00141݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.29859݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 99.89% For 1kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 14.3ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0.0143݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.2857݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 98.9% For 10kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 73.2ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0.0732݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.2268݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100%
Electronusa Mechanical System [Research Center for Electronic and Mechanical] 8 | P a g e ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 94.369% For 16kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 79.7ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0.0797݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.2203݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 93.869% (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 െ 0.01ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.19ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 99.99%
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 െ 0.62ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 982.58ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 98.93% For 100Hz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 8.10ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 985.10ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 99.184% For 1kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 80.1ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 913.10ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 58.719% For 10kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 410ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 583.20ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 58.719% For 16kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 446ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 547.20ߤܸ 993.2ߤܸ ൈ 100%
Electronusa Mechanical System [Research Center for Electronic and Mechanical] 10 | P a g e ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 55.095% 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

More Related Content

PDF
Electronusa Mechanical System
Electronusa Mechanical System
 
PDF
Electronusa Mechanical System
Electronusa Mechanical System
 
PDF
Electronusa Mechanical System
Electronusa Mechanical System
 
PDF
Electronusa Mechanical System
Electronusa Mechanical System
 
PDF
Electronusa Mechanical System
Electronusa Mechanical System
 
PDF
Electronusa Mechanical System
Electronusa Mechanical System
 
PDF
Electronusa Mechanical System
Electronusa Mechanical System
 
PDF
Electronusa Mechanical System
Electronusa Mechanical System
 
Electronusa Mechanical System
Electronusa Mechanical System
 
Electronusa Mechanical System
Electronusa Mechanical System
 
Electronusa Mechanical System
Electronusa Mechanical System
 
Electronusa Mechanical System
Electronusa Mechanical System
 
Electronusa Mechanical System
Electronusa Mechanical System
 
Electronusa Mechanical System
Electronusa Mechanical System
 
Electronusa Mechanical System
Electronusa Mechanical System
 
Electronusa Mechanical System
Electronusa Mechanical System
 

What's hot (18)

PDF
Electronusa Mechanical System
Electronusa Mechanical System
 
PDF
Electronusa Mechanical System
Electronusa Mechanical System
 
PDF
Electronusa Mechanical System
Electronusa Mechanical System
 
PDF
Electronusa Mechanical System
Electronusa Mechanical System
 
PDF
Electronusa Mechanical System
Electronusa Mechanical System
 
PDF
Electronusa Mechanical System
Electronusa Mechanical System
 
PDF
Electronusa Mechanical System
Electronusa Mechanical System
 
PDF
Electronusa Mechanical System
Electronusa Mechanical System
 
PDF
Electronusa Mechanical System
Electronusa Mechanical System
 
PDF
Electronusa Mechanica System
Electronusa Mechanical System
 
PDF
Risk assessment of a hydroelectric dam with parallel
eSAT Publishing House
 
PDF
17.pmsm speed sensor less direct torque control based on ekf
Mouli Reddy
 
PDF
HYPERCHAOS SYNCHRONIZATION USING GBM
aciijournal
 
PDF
Risk assessment of a hydroelectric dam with parallel redundant turbine
eSAT Journals
 
PDF
Suspension state space controller design-lqr
Minhhau Tran
 
PDF
Control system compensator lag lead
Nilesh Bhaskarrao Bahadure
 
PDF
ADAPTIVE STABILIZATION AND SYNCHRONIZATION OF HYPERCHAOTIC QI SYSTEM
cseij
 
PDF
Iaetsd position control of servo systems using pid
Iaetsd Iaetsd
 
Electronusa Mechanical System
Electronusa Mechanical System
 
Electronusa Mechanical System
Electronusa Mechanical System
 
Electronusa Mechanical System
Electronusa Mechanical System
 
Electronusa Mechanical System
Electronusa Mechanical System
 
Electronusa Mechanical System
Electronusa Mechanical System
 
Electronusa Mechanical System
Electronusa Mechanical System
 
Electronusa Mechanical System
Electronusa Mechanical System
 
Electronusa Mechanical System
Electronusa Mechanical System
 
Electronusa Mechanical System
Electronusa Mechanical System
 
Electronusa Mechanica System
Electronusa Mechanical System
 
Risk assessment of a hydroelectric dam with parallel
eSAT Publishing House
 
17.pmsm speed sensor less direct torque control based on ekf
Mouli Reddy
 
HYPERCHAOS SYNCHRONIZATION USING GBM
aciijournal
 
Risk assessment of a hydroelectric dam with parallel redundant turbine
eSAT Journals
 
Suspension state space controller design-lqr
Minhhau Tran
 
Control system compensator lag lead
Nilesh Bhaskarrao Bahadure
 
ADAPTIVE STABILIZATION AND SYNCHRONIZATION OF HYPERCHAOTIC QI SYSTEM
cseij
 
Iaetsd position control of servo systems using pid
Iaetsd Iaetsd
 
Ad

Viewers also liked (16)

PDF
Método científico
cristheyllymontenegroneyra
 
PDF
Metodocientifico.
k92148
 
DOCX
mi empresa dml style
escorpio988615959
 
DOCX
Praktikum Genetika - Alel Ganda
widya veronica
 
PDF
myclever™ Agency - 'Paid Social: Your Backstage Pass to the Biggest Gig In Town'
Myclever Agency
 
PDF
Duc.metodocientifico
Marbel96
 
PDF
Formularios
Arqui Tecto Papudo
 
DOCX
Historias de biblioteca, teatro infantil
productora
 
PDF
Manual tc6
Arqui Tecto Papudo
 
PPTX
La revolucion digital
Sylvain Loubradou
 
DOC
Formulario te1
Arqui Tecto Papudo
 
PPT
Leyes sociales
Arqui Tecto Papudo
 
PPTX
Resistencia en educacion fisica
henorpesa
 
PDF
Método científico
docentecis
 
DOCX
PROYECTO CREAR COLEGIO PRIVADO
Sara García
 
PDF
Economics Tutor in Singapore
H1 Economics Tuition
 
Método científico
cristheyllymontenegroneyra
 
Metodocientifico.
k92148
 
mi empresa dml style
escorpio988615959
 
Praktikum Genetika - Alel Ganda
widya veronica
 
myclever™ Agency - 'Paid Social: Your Backstage Pass to the Biggest Gig In Town'
Myclever Agency
 
Duc.metodocientifico
Marbel96
 
Formularios
Arqui Tecto Papudo
 
Historias de biblioteca, teatro infantil
productora
 
Manual tc6
Arqui Tecto Papudo
 
La revolucion digital
Sylvain Loubradou
 
Formulario te1
Arqui Tecto Papudo
 
Leyes sociales
Arqui Tecto Papudo
 
Resistencia en educacion fisica
henorpesa
 
Método científico
docentecis
 
PROYECTO CREAR COLEGIO PRIVADO
Sara García
 
Economics Tutor in Singapore
H1 Economics Tuition
 
Ad

Similar to Electronusa Mechanical System (19)

DOCX
Tennessee State University College of Engineering, Tec.docx
mehek4
 
DOCX
EEE 117L Network Analysis Laboratory Lab 1 1
EvonCanales257
 
PDF
Loren k. schwappach ee331 - lab 4
Loren Schwappach
 
PDF
Network_theory_by_alaxander_and_sadiku.pdf
parameshwar7
 
PDF
Tutorial simulations-elec 380
Moez Ansary
 
PPT
Microwaves_hafta................... 1.ppt
ibrahimmohamed381587
 
PDF
Electronics and Communication Engineering : Analog circuits, THE GATE ACADEMY
klirantga
 
PDF
Circuit Analysis With Devices Theory And Practice 3rd Edition Allan H Robbins
vljrstraox398
 
PDF
Active filters
faisal_18
 
PPT
Topic 2b ac_circuits_analysis
Gabriel O'Brien
 
PPTX
pulse and digital circuits-pulse and digital circuits
SundarSrinivasKuchib1
 
PDF
Filters DAC and ADC
Rendy Ardiwinata
 
PDF
Analog for all_preview
Anand Udupa
 
PDF
Analog for all_preview
SahyogeeTech
 
PDF
Electric Circuits : AC Fundamentals Part 1
nimmichandran4
 
PDF
Design and implementation of cyclo converter for high frequency applications
cuashok07
 
PDF
Circuit Analysis With Multisim David Bezlpez Flix E Guerrerocastro
asirenaquibv
 
DOCX
Assignment 1 Description Marks out of Wtg() Due date .docx
fredharris32
 
PPTX
Analogue electronics lec (1)
Dr. Abeer Kamal
 
Tennessee State University College of Engineering, Tec.docx
mehek4
 
EEE 117L Network Analysis Laboratory Lab 1 1
EvonCanales257
 
Loren k. schwappach ee331 - lab 4
Loren Schwappach
 
Network_theory_by_alaxander_and_sadiku.pdf
parameshwar7
 
Tutorial simulations-elec 380
Moez Ansary
 
Microwaves_hafta................... 1.ppt
ibrahimmohamed381587
 
Electronics and Communication Engineering : Analog circuits, THE GATE ACADEMY
klirantga
 
Circuit Analysis With Devices Theory And Practice 3rd Edition Allan H Robbins
vljrstraox398
 
Active filters
faisal_18
 
Topic 2b ac_circuits_analysis
Gabriel O'Brien
 
pulse and digital circuits-pulse and digital circuits
SundarSrinivasKuchib1
 
Filters DAC and ADC
Rendy Ardiwinata
 
Analog for all_preview
Anand Udupa
 
Analog for all_preview
SahyogeeTech
 
Electric Circuits : AC Fundamentals Part 1
nimmichandran4
 
Design and implementation of cyclo converter for high frequency applications
cuashok07
 
Circuit Analysis With Multisim David Bezlpez Flix E Guerrerocastro
asirenaquibv
 
Assignment 1 Description Marks out of Wtg() Due date .docx
fredharris32
 
Analogue electronics lec (1)
Dr. Abeer Kamal
 

More from Electronusa Mechanical System (12)

PDF
Fluid Contaminant Control as Essential Technique to Implement Proactive Maint...
Electronusa Mechanical System
 
PDF
Electronusa Mechanical System
Electronusa Mechanical System
 
PDF
Electronusa Mechanical System
Electronusa Mechanical System
 
PDF
15. the impedance matching in the audio signal processing (part x)
Electronusa Mechanical System
 
PDF
14. the impedance matching in the audio signal processing (part ix)
Electronusa Mechanical System
 
PDF
13. the impedance matching in the audio signal processing (part viii)
Electronusa Mechanical System
 
PDF
12. the impedance matching in the audio signal processing (part vii)
Electronusa Mechanical System
 
PDF
11. the impedance matching in the audio signal processing (part vi)
Electronusa Mechanical System
 
PDF
10. the impedance matching in the audio signal processing (part v)
Electronusa Mechanical System
 
PDF
The impedance Matching in The Audio Signal Processing (Part IV)
Electronusa Mechanical System
 
PDF
The Impedance Matching in The Audio Signal Processing (Part III)
Electronusa Mechanical System
 
PDF
The Impedance Matching in The Audio Signal Processing
Electronusa Mechanical System
 
Fluid Contaminant Control as Essential Technique to Implement Proactive Maint...
Electronusa Mechanical System
 
Electronusa Mechanical System
Electronusa Mechanical System
 
Electronusa Mechanical System
Electronusa Mechanical System
 
15. the impedance matching in the audio signal processing (part x)
Electronusa Mechanical System
 
14. the impedance matching in the audio signal processing (part ix)
Electronusa Mechanical System
 
13. the impedance matching in the audio signal processing (part viii)
Electronusa Mechanical System
 
12. the impedance matching in the audio signal processing (part vii)
Electronusa Mechanical System
 
11. the impedance matching in the audio signal processing (part vi)
Electronusa Mechanical System
 
10. the impedance matching in the audio signal processing (part v)
Electronusa Mechanical System
 
The impedance Matching in The Audio Signal Processing (Part IV)
Electronusa Mechanical System
 
The Impedance Matching in The Audio Signal Processing (Part III)
Electronusa Mechanical System
 
The Impedance Matching in The Audio Signal Processing
Electronusa Mechanical System
 

Recently uploaded (20)

PPT
Module 1.ppt Iot fundamentals and Architecture
nanditha7766
 
PDF
ENT215_Completing-a-large-scale-migration-and-modernization-with-AWS.pdf
ssuser28425f
 
PPTX
The various Industrial Revolutions .pptx
bandileshozi3
 
PDF
Enhancing emotion recognition model for a student engagement use case through...
IAESIJAI
 
PDF
NewMind AI Weekly Chronicles - August'25-Week II
NewMind AI
 
PDF
Getting started with AI Agents and Multi-Agent Systems
Maxim Salnikov
 
PPTX
1. Introduction to Computer Programming.pptx
bonakiduza1024
 
PDF
project resource management chapter-09.pdf
ssuser00e6e21
 
PPTX
TLE Review Electricity (Electricity).pptx
JayPolicarpio2
 
PDF
WOOl fibre morphology and structure.pdf for textiles
Rajendrakumar868651
 
PPT
What is a Computer? Input Devices /output devices
GulJan8
 
PDF
Getting Started with Data Integration: FME Form 101
Safe Software
 
PDF
DASA ADMISSION 2024_FirstRound_FirstRank_LastRank.pdf
rameswartudu05
 
PDF
From MVP to Full-Scale Product A Startup’s Software Journey.pdf
KodekX
 
PPTX
Group 1 Presentation -Planning and Decision Making .pptx
MatthewLewis227954
 
PDF
Zenith AI: Advanced Artificial Intelligence
Biz Preneurs
 
PDF
2021 HotChips TSMC Packaging Technologies for Chiplets and 3D_0819 publish_pu...
KeXue5
 
PPTX
MicrosoftCybserSecurityReferenceArchitecture-April-2025.pptx
SilvioHayashi
 
PPTX
Programs and apps: productivity, graphics, security and other tools
4mqw9zch22
 
PDF
Architecture types and enterprise applications.pdf
ChristopherTHyatt
 
Module 1.ppt Iot fundamentals and Architecture
nanditha7766
 
ENT215_Completing-a-large-scale-migration-and-modernization-with-AWS.pdf
ssuser28425f
 
The various Industrial Revolutions .pptx
bandileshozi3
 
Enhancing emotion recognition model for a student engagement use case through...
IAESIJAI
 
NewMind AI Weekly Chronicles - August'25-Week II
NewMind AI
 
Getting started with AI Agents and Multi-Agent Systems
Maxim Salnikov
 
1. Introduction to Computer Programming.pptx
bonakiduza1024
 
project resource management chapter-09.pdf
ssuser00e6e21
 
TLE Review Electricity (Electricity).pptx
JayPolicarpio2
 
WOOl fibre morphology and structure.pdf for textiles
Rajendrakumar868651
 
What is a Computer? Input Devices /output devices
GulJan8
 
Getting Started with Data Integration: FME Form 101
Safe Software
 
DASA ADMISSION 2024_FirstRound_FirstRank_LastRank.pdf
rameswartudu05
 
From MVP to Full-Scale Product A Startup’s Software Journey.pdf
KodekX
 
Group 1 Presentation -Planning and Decision Making .pptx
MatthewLewis227954
 
Zenith AI: Advanced Artificial Intelligence
Biz Preneurs
 
2021 HotChips TSMC Packaging Technologies for Chiplets and 3D_0819 publish_pu...
KeXue5
 
MicrosoftCybserSecurityReferenceArchitecture-April-2025.pptx
SilvioHayashi
 
Programs and apps: productivity, graphics, security and other tools
4mqw9zch22
 
Architecture types and enterprise applications.pdf
ChristopherTHyatt
 

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 3.3μ‫ܨ‬ 50ܸ⁄ . 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 െ 0.11ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0.00011݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.29989݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 99.99% For 100Hz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 1.41ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0.00141݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.29859݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 99.89% For 1kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 14.3ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0.0143݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.2857݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 98.9% For 10kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 73.2ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0.0732݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.2268݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100%
  • 8. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 8 | P a g e ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 94.369% For 16kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ݅௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ݅௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 79.7ߤ‫ܣ‬ 1.3݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.3݉‫ܣ‬ െ 0.0797݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 1.2203݉‫ܣ‬ 1.3000݉‫ܣ‬ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 93.869% (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 െ 0.01ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.19ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 99.99%
  • 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 െ 0.62ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 982.58ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 98.93% For 100Hz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 8.10ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 985.10ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 99.184% For 1kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 80.1ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 913.10ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 58.719% For 10kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 410ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 583.20ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 58.719% For 16kHz, ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ െ ‫ݒ‬௢௨௧ሺ௦௜௠௨௟௔௧௜௢௡ሻ ‫ݒ‬௢௨௧ሺ௔௡௔௟௬௧௜௖௔௟ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 993.2ߤܸ െ 446ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 547.20ߤܸ 993.2ߤܸ ൈ 100%
  • 10. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 10 | P a g e ሺ%ሻ݂݂݀݅݁‫݁ܿ݊݁ݎ‬ ൌ 55.095% 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