Electronusa Mechanical System
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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 is then compared to the analytical work. For dc analysis, the Thevenin voltage and dc voltage match within 18-21%. For ac analysis, the input and output currents match the analytical work within 91%. This analysis helps verify the circuit design through both mathematical and simulated approaches.
![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 4.7ߤܨ 50ܸ⁄ .
2. Analytical Work
In this study, ܴଵ and ܴଶ form the Thevenin voltage, while ܥଵ and ܥଶ deliver ac signal as ݒ and
ݒ௨௧(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](https://image.slidesharecdn.com/32-theimpedancematchingintheaudiosignalprocessingpartxxvii-130509140555-phpapp02/85/Electronusa-Mechanical-System-1-320.jpg)
![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 ݎሺ௦ሻ:
ݎሺ௦ሻ ൌ ሺߚ 1ሻ൫ሺܴଷ ܴସሻԡݎ൯
ݎሺ௦ሻ ൌ ሺ200 1ሻ൫ሺ150Ω 8.2Ωሻԡ1.32Ω൯](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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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 4.7ߤܨ 50ܸ⁄ . 2. Analytical Work In this study, ܴଵ and ܴଶ form the Thevenin voltage, while ܥଵ and ܥଶ deliver ac signal as ݒ and ݒ௨௧(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 ݎሺ௦ሻ: ݎሺ௦ሻ ൌ ሺߚ 1ሻ൫ሺܴଷ ܴସሻԡݎ൯ ݎሺ௦ሻ ൌ ሺ200 1ሻ൫ሺ150Ω 8.2Ωሻԡ1.32Ω൯
- 3. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 3 | P a g e ݎሺ௦ሻ ൌ ሺ201ሻ൫ሺ158.2Ωሻԡ1.32Ω൯ ݎሺ௦ሻ ൌ ሺ201ሻ ൬ 1 158.2Ω 1 1.32Ω ൰ ݎሺ௦ሻ ൌ ሺ201ሻ ൬ 1.32 208.824Ω 158.2 208.824Ω ൰ ݎሺ௦ሻ ൌ ሺ201ሻ ൬ 159.52 208.824Ω ൰ ݎሺ௦ሻ ൌ ሺ201ሻሺ0.764Ωሻ ݎሺ௦ሻ ൌ 153.564Ω The third step is to calculate ݅: ݅ ൌ ݒ ݎሺ௦ሻ ݅ ൌ 1ܸ݉ 153.564Ω ݅ ൌ 0.0065݉ܣ ݅ ൌ 6.5ߤܣ The fourth step is to calculate ݅: ݅ ൌ ߚ݅ ݅ ൌ ሺ200ሻሺ0.0065݉ܣሻ ݅ ൌ 1.3݉ܣ The last step is to calculate ݒ௨௧: ݒ௨௧ ൌ ݅ݎ௨௧ ݒ௨௧ ൌ ሺ1.3݉ܣሻሺ0.764Ωሻ ݒ௨௧ ൌ 0.9932ܸ݉ ݒ௨௧ ൌ 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 ൌ ்ܸுሺ௬௧ሻ െ ்ܸுሺ௦௨௧ሻ ்ܸுሺ௬௧ሻ ൈ 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 ൌ ܸாሺ௬௧ሻ െ ܸாሺ௦௨௧ሻ ܸாሺ௬௧ሻ ൈ 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 ൌ ܫாሺ௬௧ሻ െ ܫாሺ௦௨௧ሻ ܫாሺ௬௧ሻ ൈ 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 ൌ ݅ሺ௦௨௧ሻ െ ݅ሺ௬௧ሻ ݅ሺ௦௨௧ሻ ൈ 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 ൌ ݅ሺ௦௨௧ሻ െ ݅ሺ௬௧ሻ ݅ሺ௦௨௧ሻ ൈ 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 ൌ ݅௨௧ሺ௬௧ሻ െ ݅௨௧ሺ௦௨௧ሻ ݅௨௧ሺ௬௧ሻ ൈ 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 ൌ ݅௨௧ሺ௬௧ሻ െ ݅௨௧ሺ௦௨௧ሻ ݅௨௧ሺ௬௧ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 1.3݉ܣ െ 0.18ߤܣ 1.3݉ܣ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 1.30000݉ܣ െ 0.00018݉ܣ 1.3000݉ܣ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 1.29982݉ܣ 1.3000݉ܣ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 99.986% For 100Hz, ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ ݅௨௧ሺ௬௧ሻ െ ݅௨௧ሺ௦௨௧ሻ ݅௨௧ሺ௬௧ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 1.3݉ܣ െ 2.02ߤܣ 1.3݉ܣ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 1.300݉ܣ െ 0.00202݉ܣ 1.3000݉ܣ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 1.29798݉ܣ 1.3000݉ܣ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 99.84% For 1kHz, ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ ݅௨௧ሺ௬௧ሻ െ ݅௨௧ሺ௦௨௧ሻ ݅௨௧ሺ௬௧ሻ ൈ 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% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 98.45% For 10kHz, ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ ݅௨௧ሺ௬௧ሻ െ ݅௨௧ሺ௦௨௧ሻ ݅௨௧ሺ௬௧ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 1.3݉ܣ െ 78.4ߤܣ 1.3݉ܣ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 1.3000݉ܣ െ 0.0784݉ܣ 1.3000݉ܣ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 1.2216݉ܣ 1.3000݉ܣ ൈ 100%
- 8. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 8 | P a g e ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 93.969% For 16kHz, ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ ݅௨௧ሺ௬௧ሻ െ ݅௨௧ሺ௦௨௧ሻ ݅௨௧ሺ௬௧ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 1.3݉ܣ െ 82.2ߤܣ 1.3݉ܣ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 1.3000݉ܣ െ 0.0822݉ܣ 1.3000݉ܣ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 1.2178݉ܣ 1.3000݉ܣ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 93.67% (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, ݒ௨௧ 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 ൌ ݒ௨௧ሺ௬௧ሻ െ ݒ௨௧ሺ௦௨௧ሻ ݒ௨௧ሺ௬௧ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 993.2ߤܸ െ 0.02ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 993.18ߤܸ 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 ൌ ݒ௨௧ሺ௬௧ሻ െ ݒ௨௧ሺ௦௨௧ሻ ݒ௨௧ሺ௬௧ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 993.2ߤܸ െ 1ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 992.3ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 99.909% For 100Hz, ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ ݒ௨௧ሺ௬௧ሻ െ ݒ௨௧ሺ௦௨௧ሻ ݒ௨௧ሺ௬௧ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 993.2ߤܸ െ 11.6ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 981.6ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 98.83% For 1kHz, ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ ݒ௨௧ሺ௬௧ሻ െ ݒ௨௧ሺ௦௨௧ሻ ݒ௨௧ሺ௬௧ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 993.2ߤܸ െ 112ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 881.2ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 88.72% For 10kHz, ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ ݒ௨௧ሺ௬௧ሻ െ ݒ௨௧ሺ௦௨௧ሻ ݒ௨௧ሺ௬௧ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 993.2ߤܸ െ 439ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 554.2ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 55.79% For 16kHz, ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ ݒ௨௧ሺ௬௧ሻ െ ݒ௨௧ሺ௦௨௧ሻ ݒ௨௧ሺ௬௧ሻ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 993.2ߤܸ െ 460ߤܸ 993.2ߤܸ ൈ 100% ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 533.2ߤܸ 993.2ߤܸ ൈ 100%
- 10. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 10 | P a g e ሺ%ሻ݂݂݀݅݁݁ܿ݊݁ݎ ൌ 53.68% In this study, the simulation shows that the ݅௨௧ and ݒ௨௧ became stable started at 1 kHz. (a) (b) (c) (d) (e) (f) Figure 9. (a). ݒ௨௧ in the simulation at 1Hz (b). ݒ௨௧ in the simulation at 10Hz (c). ݒ௨௧ in the simulation at 100Hz (d). ݒ௨௧ in the simulation at 1kHz (e). ݒ௨௧ in the simulation at 10kHz (f). ݒ௨௧ in the simulation at 16kHz