The Influence of Capacitance in The Emitter Follower (Part II)
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The document analyzes the influence of capacitance in an emitter follower circuit. It presents analytical calculations for both DC and AC analyses. For the DC analysis, it calculates the Thevenin voltage, emitter voltage, and emitter current. For the AC analysis, it calculates various resistances, currents, and output voltage. Simulation results are presented and show differences ranging from 18-98% when compared to the analytical calculations. Increasing the capacitance decreases the frequency-dependent effects in the circuit.
![Electronusa Mechanical System [Research Center for Electronic and Mechanical]
Influence of Capacitance in The Emitter Follower (Part II)
Umar Sidik.BEng.MSc*
Director of Engineering
Electronusa Mechanical System
*umar.sidik@engineer.com
1. Introduction
Commonly, capacitor is used to pass the ac signal in the circuit. Furthermore, the characteristics of ac
signal in the circuit are influenced by capacitor. Theoretically, the capacitance of capacitor will
influence the time of charge and discharge, where the bigger capacitance requires longer time in
charge and discharge. In addition, this study uses the metalized ceramic plate capacitor for analysis.
2. Analytical Work
We have two analyzes consisting of:
a. Analysis of dc
b. Analysis of ac
2.1 Analysis of dc
(a) (b)
Figure 1. (a). The circuit of emitter follower
(b). The equivalent circuit in 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
Actually, in this circuit ்ܸு ൌ ܸ , so ܸ ൌ 3.55ܸ.
1|Page](https://image.slidesharecdn.com/05-theinfluenceofcapacitanceintheemitterfollowerpartii-130203214338-phpapp02/85/The-Influence-of-Capacitance-in-The-Emitter-Follower-Part-II-1-320.jpg)
![Electronusa Mechanical System [Research Center for Electronic and Mechanical]
The second step, we have to calculate ܸா :
ܸா ൌ ܸ െ ܸா
ܸா ൌ 3.55ܸ െ 0.7ܸ
ܸா ൌ 2.85ܸ
The third step, we have to calculate the ܫா :
ܸா
ܫா ൌ
ܴா
2.85ܸ
ܫா ൌ
150Ω
ܫா ൌ 19݉ܣ
2.2 Analysis of ac
(a) (b)
Figure 2. (a). The circuit of emitter follower with the internal resistance of emitter
(b). The equivalent circuit in ac
The first step, we have to calculate ݎ in figure 2:
25ܸ݉
ݎ ൌ
ܫா
25݉ݒ
ݎ ൌ
19݉ܣ
ݎ ൌ 1.32Ω
The second step, we have to calculate ݎሺ௦ሻ :
ݎሺ௦ሻ ൌ ሺߚ 1ሻ൫ሺܴଷ ܴସ ሻԡݎ ൯
ݎሺ௦ሻ ൌ ሺ200 1ሻ൫ሺ15݇Ω 8.2Ωሻԡ1.32Ω൯
ݎሺ௦ሻ ൌ ሺ201ሻ൫ሺ15,000Ω 8.2Ωሻԡ1.32Ω൯
ݎሺ௦ሻ ൌ ሺ201ሻሺ15,008.2Ωԡ1.32Ωሻ
2|Page](https://image.slidesharecdn.com/05-theinfluenceofcapacitanceintheemitterfollowerpartii-130203214338-phpapp02/85/The-Influence-of-Capacitance-in-The-Emitter-Follower-Part-II-2-320.jpg)
![Electronusa Mechanical System [Research Center for Electronic and Mechanical]
1 1
ݎሺ௦ሻ ൌ ሺ201ሻ ൬ ൰
15,008.2Ω 1.32Ω
1.32 15,008.2
ݎሺ௦ሻ ൌ ሺ201ሻ ൬ ൰
19,810.824Ω 19,810.824Ω
15,009.52
ݎሺ௦ሻ ൌ ሺ201ሻ ൬ ൰
19,810.824Ω
19,810.824Ω
ݎሺ௦ሻ ൌ ሺ201ሻ ൬ ൰
15,009.52
ݎሺ௦ሻ ൌ ሺ201ሻሺ1.32Ωሻ
ݎሺ௦ሻ ൌ 265.3Ω
The third step is to calculate ݅ :
ݒ
݅ ൌ
ݎሺ௦ሻ
1ܸ݉
݅ ൌ
265.3Ω
݅ ൌ 3.77݉ܣ
The fourth step is to calculate ݅ :
݅ ൌ ߚ݅
݅ ൌ ሺ200ሻሺ3.77݉ܣሻ
݅ ൌ 754݉ܣ
The last step is to calculate ݒ௨௧ :
ݒ௨௧ ൌ ݅ ݎ௨௧
ݒ௨௧ ൌ ሺ754݉ܣሻሺ1.32Ωሻ
ݒ௨௧ ൌ 995.1 ܸ݉
3|Page](https://image.slidesharecdn.com/05-theinfluenceofcapacitanceintheemitterfollowerpartii-130203214338-phpapp02/85/The-Influence-of-Capacitance-in-The-Emitter-Follower-Part-II-3-320.jpg)
![Electronusa Mechanical System [Research Center for Electronic and Mechanical]
3. Simulation Work
The simulation work classified into the analysis of dc and the analysis of ac.
3.1 Analysis of dc
Figure 3. ்ܸு in simulation
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:
்ܸுሺ௬௧ሻ െ ்ܸுሺ௦௨௧ሻ
ሺ%ሻௗ ൌ ൈ 100%
்ܸுሺ௬௧ሻ
3.55ܸ െ 3ܸ
ሺ%ሻௗ ൌ ൈ 100%
3.55ܸ
0.55ܸ
ሺ%ሻௗ ൌ ൈ 100%
3ܸ
ሺ%ሻௗ ൌ 18.33%
Figure 4. ܸா in 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:
ܸாሺ௬௧ሻ െ ܸாሺ௦௨௧ሻ
ሺ%ሻௗ ൌ ൈ 100%
ܸாሺ௬௧ሻ
2.85ܸ െ 2.25ܸ
ሺ%ሻௗ ൌ ൈ 100%
2.85ܸ
4|Page](https://image.slidesharecdn.com/05-theinfluenceofcapacitanceintheemitterfollowerpartii-130203214338-phpapp02/85/The-Influence-of-Capacitance-in-The-Emitter-Follower-Part-II-4-320.jpg)
![Electronusa Mechanical System [Research Center for Electronic and Mechanical]
0.6ܸ
ሺ%ሻௗ ൌ ൈ 100%
2.85ܸ
ሺ%ሻௗ ൌ 21.05%
Figure 5. ܫா in simulation
In the simulation ܫா is 15݉ ,ܣwhile in the analytical work ܫா is 19݉ .ܣThe difference is:
ܫாሺ௬௧ሻ െ ܫாሺ௦௨௧ሻ
ሺ%ሻௗ ൌ ൈ 100%
ܫாሺ௬௧ሻ
19݉ ܣെ 15݉ܣ
ሺ%ሻௗ ൌ ൈ 100%
19݉ܣ
4݉ܣ
ሺ%ሻௗ ൌ ൈ 100%
19݉ܣ
ሺ%ሻௗ ൌ 21.05%
5|Page](https://image.slidesharecdn.com/05-theinfluenceofcapacitanceintheemitterfollowerpartii-130203214338-phpapp02/85/The-Influence-of-Capacitance-in-The-Emitter-Follower-Part-II-5-320.jpg)
![Electronusa Mechanical System [Research Center for Electronic and Mechanical]
3.2 Analysis of ac
(a) (b) (c)
(e) (f) (g)
Figure 6. ݅ in different the circuit’s capacitance
(a). ܥൌ 1݊ܨ (b). ܥൌ 10݊ܨ (c). ܥൌ 22݊ܨ
(d). ܥൌ 1.8ܨ (e). ܥൌ 120ܨ (f). ܥൌ 820ܨ
In the simulation, ݅ is 0.07݉ ,ܣwhile in the analytical ݅ is 3.77݉ .ܣthe difference is:
݅ሺ௬௧ሻ െ ݅ሺ௦௨௧ሻ
ሺ%ሻௗ ൌ ൈ 100%
݅ሺ௬௧ሻ
3.77݉ ܣെ 0.07݉ܣ
ሺ%ሻௗ ൌ ൈ 100%
3.77݉ܣ
3.70݉ܣ
ሺ%ሻௗ ൌ ൈ 100%
3.77݉ܣ
ሺ%ሻௗ ൌ 98.14%
6|Page](https://image.slidesharecdn.com/05-theinfluenceofcapacitanceintheemitterfollowerpartii-130203214338-phpapp02/85/The-Influence-of-Capacitance-in-The-Emitter-Follower-Part-II-6-320.jpg)
![Electronusa Mechanical System [Research Center for Electronic and Mechanical]
(a) (b) (c)
(d) (e) (f)
Figure 7. ݅ in different the circuit’s capacitance
(a). ܥൌ 1݊ܨ (b). ܥൌ 10݊ܨ (c). ܥൌ 22݊ܨ
(d). ܥൌ 1.8ܨ (e). ܥൌ 120ܨ (f). ܥൌ 820ܨ
In the simulation, ݅ is 15݉ ,ܣwhile in the analytical ݅ is 754݉ .ܣthe difference is:
݅ሺ௬௧ሻ െ ݅ሺ௦௨௧ሻ
ሺ%ሻௗ ൌ ൈ 100%
݅ሺ௬௧ሻ
754݉ ܣെ 15݉ܣ
ሺ%ሻௗ ൌ ൈ 100%
754݉ܣ
739݉ܣ
ሺ%ሻௗ ൌ ൈ 100%
754݉ܣ
ሺ%ሻௗ ൌ 98.01%
7|Page](https://image.slidesharecdn.com/05-theinfluenceofcapacitanceintheemitterfollowerpartii-130203214338-phpapp02/85/The-Influence-of-Capacitance-in-The-Emitter-Follower-Part-II-7-320.jpg)
![Electronusa Mechanical System [Research Center for Electronic and Mechanical]
(a) (b) (c)
(d) (e) (f)
Figure 8. ݒ௨௧ in different the circuit’s capacitance
(a). ܥൌ 1݊ܨ (b). ܥൌ 10݊ܨ (c). ܥൌ 22݊ܨ
(d). ܥൌ 1.8ܨ (e). ܥൌ 120ܨ (f). ܥൌ 820ܨ
In the simulation, ݒ௨௧ is 0ܸ݉, while in the analytical ݒ௨௧ is 995.1ܸ݉. the difference is:
ݒ௨௧ሺ௬௧ሻ െ ݒ௨௧ሺ௦௨௧ሻ
ሺ%ሻௗ ൌ ൈ 100%
ݒ௨௧ሺ௬௧ሻ
995.1ܸ݉ െ 0ܸ݉
ሺ%ሻௗ ൌ ൈ 100%
995.1ܸ݉
995.1ܸ݉
ሺ%ሻௗ ൌ ൈ 100%
995.1ܸ݉
ሺ%ሻௗ ൌ 100%
8|Page](https://image.slidesharecdn.com/05-theinfluenceofcapacitanceintheemitterfollowerpartii-130203214338-phpapp02/85/The-Influence-of-Capacitance-in-The-Emitter-Follower-Part-II-8-320.jpg)
The Influence of Capacitance in The Emitter Follower (Part II)
- 1. Electronusa Mechanical System [Research Center for Electronic and Mechanical] Influence of Capacitance in The Emitter Follower (Part II) Umar Sidik.BEng.MSc* Director of Engineering Electronusa Mechanical System *umar.sidik@engineer.com 1. Introduction Commonly, capacitor is used to pass the ac signal in the circuit. Furthermore, the characteristics of ac signal in the circuit are influenced by capacitor. Theoretically, the capacitance of capacitor will influence the time of charge and discharge, where the bigger capacitance requires longer time in charge and discharge. In addition, this study uses the metalized ceramic plate capacitor for analysis. 2. Analytical Work We have two analyzes consisting of: a. Analysis of dc b. Analysis of ac 2.1 Analysis of dc (a) (b) Figure 1. (a). The circuit of emitter follower (b). The equivalent circuit in 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 Actually, in this circuit ்ܸு ൌ ܸ , so ܸ ൌ 3.55ܸ. 1|Page
- 2. Electronusa Mechanical System [Research Center for Electronic and Mechanical] The second step, we have to calculate ܸா : ܸா ൌ ܸ െ ܸா ܸா ൌ 3.55ܸ െ 0.7ܸ ܸா ൌ 2.85ܸ The third step, we have to calculate the ܫா : ܸா ܫா ൌ ܴா 2.85ܸ ܫா ൌ 150Ω ܫா ൌ 19݉ܣ 2.2 Analysis of ac (a) (b) Figure 2. (a). The circuit of emitter follower with the internal resistance of emitter (b). The equivalent circuit in ac The first step, we have to calculate ݎ in figure 2: 25ܸ݉ ݎ ൌ ܫா 25݉ݒ ݎ ൌ 19݉ܣ ݎ ൌ 1.32Ω The second step, we have to calculate ݎሺ௦ሻ : ݎሺ௦ሻ ൌ ሺߚ 1ሻ൫ሺܴଷ ܴସ ሻԡݎ ൯ ݎሺ௦ሻ ൌ ሺ200 1ሻ൫ሺ15݇Ω 8.2Ωሻԡ1.32Ω൯ ݎሺ௦ሻ ൌ ሺ201ሻ൫ሺ15,000Ω 8.2Ωሻԡ1.32Ω൯ ݎሺ௦ሻ ൌ ሺ201ሻሺ15,008.2Ωԡ1.32Ωሻ 2|Page
- 3. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 1 1 ݎሺ௦ሻ ൌ ሺ201ሻ ൬ ൰ 15,008.2Ω 1.32Ω 1.32 15,008.2 ݎሺ௦ሻ ൌ ሺ201ሻ ൬ ൰ 19,810.824Ω 19,810.824Ω 15,009.52 ݎሺ௦ሻ ൌ ሺ201ሻ ൬ ൰ 19,810.824Ω 19,810.824Ω ݎሺ௦ሻ ൌ ሺ201ሻ ൬ ൰ 15,009.52 ݎሺ௦ሻ ൌ ሺ201ሻሺ1.32Ωሻ ݎሺ௦ሻ ൌ 265.3Ω The third step is to calculate ݅ : ݒ ݅ ൌ ݎሺ௦ሻ 1ܸ݉ ݅ ൌ 265.3Ω ݅ ൌ 3.77݉ܣ The fourth step is to calculate ݅ : ݅ ൌ ߚ݅ ݅ ൌ ሺ200ሻሺ3.77݉ܣሻ ݅ ൌ 754݉ܣ The last step is to calculate ݒ௨௧ : ݒ௨௧ ൌ ݅ ݎ௨௧ ݒ௨௧ ൌ ሺ754݉ܣሻሺ1.32Ωሻ ݒ௨௧ ൌ 995.1 ܸ݉ 3|Page
- 4. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 3. Simulation Work The simulation work classified into the analysis of dc and the analysis of ac. 3.1 Analysis of dc Figure 3. ்ܸு in simulation 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: ்ܸுሺ௬௧ሻ െ ்ܸுሺ௦௨௧ሻ ሺ%ሻௗ ൌ ൈ 100% ்ܸுሺ௬௧ሻ 3.55ܸ െ 3ܸ ሺ%ሻௗ ൌ ൈ 100% 3.55ܸ 0.55ܸ ሺ%ሻௗ ൌ ൈ 100% 3ܸ ሺ%ሻௗ ൌ 18.33% Figure 4. ܸா in 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: ܸாሺ௬௧ሻ െ ܸாሺ௦௨௧ሻ ሺ%ሻௗ ൌ ൈ 100% ܸாሺ௬௧ሻ 2.85ܸ െ 2.25ܸ ሺ%ሻௗ ൌ ൈ 100% 2.85ܸ 4|Page
- 5. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 0.6ܸ ሺ%ሻௗ ൌ ൈ 100% 2.85ܸ ሺ%ሻௗ ൌ 21.05% Figure 5. ܫா in simulation In the simulation ܫா is 15݉ ,ܣwhile in the analytical work ܫா is 19݉ .ܣThe difference is: ܫாሺ௬௧ሻ െ ܫாሺ௦௨௧ሻ ሺ%ሻௗ ൌ ൈ 100% ܫாሺ௬௧ሻ 19݉ ܣെ 15݉ܣ ሺ%ሻௗ ൌ ൈ 100% 19݉ܣ 4݉ܣ ሺ%ሻௗ ൌ ൈ 100% 19݉ܣ ሺ%ሻௗ ൌ 21.05% 5|Page
- 6. Electronusa Mechanical System [Research Center for Electronic and Mechanical] 3.2 Analysis of ac (a) (b) (c) (e) (f) (g) Figure 6. ݅ in different the circuit’s capacitance (a). ܥൌ 1݊ܨ (b). ܥൌ 10݊ܨ (c). ܥൌ 22݊ܨ (d). ܥൌ 1.8ܨ (e). ܥൌ 120ܨ (f). ܥൌ 820ܨ In the simulation, ݅ is 0.07݉ ,ܣwhile in the analytical ݅ is 3.77݉ .ܣthe difference is: ݅ሺ௬௧ሻ െ ݅ሺ௦௨௧ሻ ሺ%ሻௗ ൌ ൈ 100% ݅ሺ௬௧ሻ 3.77݉ ܣെ 0.07݉ܣ ሺ%ሻௗ ൌ ൈ 100% 3.77݉ܣ 3.70݉ܣ ሺ%ሻௗ ൌ ൈ 100% 3.77݉ܣ ሺ%ሻௗ ൌ 98.14% 6|Page
- 7. Electronusa Mechanical System [Research Center for Electronic and Mechanical] (a) (b) (c) (d) (e) (f) Figure 7. ݅ in different the circuit’s capacitance (a). ܥൌ 1݊ܨ (b). ܥൌ 10݊ܨ (c). ܥൌ 22݊ܨ (d). ܥൌ 1.8ܨ (e). ܥൌ 120ܨ (f). ܥൌ 820ܨ In the simulation, ݅ is 15݉ ,ܣwhile in the analytical ݅ is 754݉ .ܣthe difference is: ݅ሺ௬௧ሻ െ ݅ሺ௦௨௧ሻ ሺ%ሻௗ ൌ ൈ 100% ݅ሺ௬௧ሻ 754݉ ܣെ 15݉ܣ ሺ%ሻௗ ൌ ൈ 100% 754݉ܣ 739݉ܣ ሺ%ሻௗ ൌ ൈ 100% 754݉ܣ ሺ%ሻௗ ൌ 98.01% 7|Page
- 8. Electronusa Mechanical System [Research Center for Electronic and Mechanical] (a) (b) (c) (d) (e) (f) Figure 8. ݒ௨௧ in different the circuit’s capacitance (a). ܥൌ 1݊ܨ (b). ܥൌ 10݊ܨ (c). ܥൌ 22݊ܨ (d). ܥൌ 1.8ܨ (e). ܥൌ 120ܨ (f). ܥൌ 820ܨ In the simulation, ݒ௨௧ is 0ܸ݉, while in the analytical ݒ௨௧ is 995.1ܸ݉. the difference is: ݒ௨௧ሺ௬௧ሻ െ ݒ௨௧ሺ௦௨௧ሻ ሺ%ሻௗ ൌ ൈ 100% ݒ௨௧ሺ௬௧ሻ 995.1ܸ݉ െ 0ܸ݉ ሺ%ሻௗ ൌ ൈ 100% 995.1ܸ݉ 995.1ܸ݉ ሺ%ሻௗ ൌ ൈ 100% 995.1ܸ݉ ሺ%ሻௗ ൌ 100% 8|Page