LAB_REPORT_02_RAHMAN_40106588

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LABORATORY REPORT Electronics II Course: ELEC312 Lab Section: WL-X Experiment No.: 2 Date Performed: 2024 – 02– 14 Experiment Title: RC COUPLED CE AMPLIFIER Name: Rahman, Md Wasique ID No.: 40106588 I certify that this submission is my original work and meets the Faculty’s Expectations of Originality Signature: Date: 2024 – 03 – 06
Abstract This research paper explores the comprehensive design procedure for discrete amplifiers, delineating essential steps crucial for optimal performance. The process begins with meticulous circuit configuration selection tailored to specific application requisites, followed by meticulous DC design to establish biasing and ensure stability. Subsequent AC design endeavors aim to ascertain critical parameters such as gain and bandwidth, with a predominant focus on AC design while briefly acknowledging DC design nuances. For instance, in the context of a single-stage common- emitter amplifier, intricate self-biasing techniques leveraging resistors R1 and R2, alongside pivotal components like RC and RE, are instrumental for stability maintenance and gain preservation. Capacitors, notably coupling and bypass capacitors, play a pivotal role in mitigating DC current while safeguarding DC characteristics to prevent adverse effects on gain. Additionally, internal capacitances of the BJT are meticulously considered, impacting the amplifier's high-frequency performance profoundly. Through meticulous frequency response analysis, it's revealed that gain diminishes at low and high frequencies yet remains relatively constant within the midband. Crucially, bandwidth and gain-bandwidth product emerge as paramount metrics for assessing amplifier efficacy. Furthermore, the methodology elucidates the determination of upper and lower 3dB points utilizing equivalent circuits and time constants, accompanied by streamlined analysis techniques tailored for multistage amplifiers. Additionally, comprehensive specifications and pin connections for the P2N2222A BJT serve to enrich the understanding of amplifier design and implementation.
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Table of Contents Introduction .................................................................................................................................................................................................. 7 Procedure ..................................................................................................................................................................................................... 9 Results and Discussion ............................................................................................................................................................................... 10 ................................................................................................................................................................................................................... 11 Conclusion .................................................................................................................................................................................................. 33 References .................................................................................................................................................................................................. 35
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Introduction Objectives The main objective of this experiment is to provide a comprehensive understanding of capacitor coupled BJT amplifiers through the analysis of their frequency response characteristics, with a particular focus on the role of coupling and bypass capacitors at lower frequencies. Additionally, the investigation will explore the impact of junction capacitance on amplifier behavior, especially as frequencies increase. Capacitor coupling is a vital aspect of amplifier design, facilitating the transmission of AC signals while blocking DC components. Bypass capacitors further enhance performance by preserving DC biasing while allowing AC signals to pass through unhindered, thereby influencing the amplifier's gain and frequency response at lower frequencies. Junction capacitance, inherent to the transistor structure, becomes increasingly significant as frequencies rise, affecting the amplifier's performance in the higher frequency range. Through systematic observation and analysis, this experiment aims to provide participants with a comprehensive understanding of these key concepts, enriching their knowledge of amplifier design and operation. Theory The design process for discrete amplifiers necessitates strict adherence to a specific sequence of steps. Initially, meticulous attention is given to establishing an appropriate circuit configuration, setting the foundation for subsequent analyses. DC design follows suit, enabling visualization of biasing and stabilization parameters crucial for optimal amplifier performance. Subsequently, AC design is employed to delve deeper into key parameters such as amplifier gain and bandwidth, with a primary focus on this aspect in the current experiment. Illustrated in Figure 1 is a single-stage common emitter amplifier showcasing a BJT, wherein the biasing circuit integrates resistors R1 and R2, enabling the utilization of a single power supply via the self-biasing technique, strategically positioned between the base and collector. To ensure the maintenance of proper DC characteristics and stabilization of the amplifier, a bypass capacitor (CE) is strategically connected across RE, compensating for the potential reduction in gain induced by RE during AC
operation. Additionally, coupling capacitors (CC1 and CC2) are integrated to impede the flow of DC current within the amplifier stage. Noteworthy is the consideration of junction capacitances (Ccb/Cbe) of the BJT, despite being beyond direct control, as they exert a significant influence on circuit performance. The primary objective of the experiment is to assess the frequency response of the amplifier stage, with the overall gain determined by the function T.F = Vout/Vin = A(jw). Analysis reveals that amplifier gain diminishes at both low and high frequencies, remaining constant in the midband. As for Figure 2, it serves as a visual aid in comprehending the calculated frequency by delineating corresponding regions. Frequencies in the low-frequency domain indicate the presence of non-zero equivalent impedance attributed to coupling and bypass capacitors, while frequencies in the midband signify the disappearance of coupling and bypass effects, albeit with internal capacitances retaining relevance. Ultimately, frequencies in the high-frequency domain mark the initiation of the influence of internal capacitances on device performance. Figure 1. A schematic representation of a Coupling and bypass capacitors Figure 2. General frequency response of the amplifier
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Procedure The experiment involves constructing the circuit shown in figure 1 using specific components detailed in the provided table, including resistors R1, R2, RE, RC, RS, RL, and capacitors VCC, CC1, CC2, and CE. During assembly, a 3-legged transistor mount is utilized for the BJT. A DC measurement is conducted post-assembly to determine the operating point and β, which involves measuring IC, VCE, and IB. Subsequently, a sinusoidal signal is applied to the input, and its amplitude is adjusted to ensure a distortion-free output waveform, with emphasis on adjustment in the midband region, typically around 25mV (50mV peak-to- peak). A sketch illustrating the amplitude response as a function of input signal frequency is then created using semi-log graph paper, with frequency depicted on the horizontal axis (log scale) and amplitude in dB on the vertical axis (linear scale), with additional points plotted to capture significant changes in output while keeping the input constant. Steps 3 and 4 are repeated, this time using CC1=CC2=CE=22µF. Record all the data on an Excel file.
Results and Discussion For the measurement of the I c , I B and V CE , the data table the circuit and the data table are found below: Figure 3. Drawing if the circuit used to measure Ic, Ib and Vce Table 1. Data table for the experimental values of Ic, Ib and Vce I c I B V CE 0.8400 mA 0.1400 mA 7.1918 V
Figure 4. The built circuit for the first part of the experiment using a breadboard. Figure 5. The experimental value of Ib using a digital multimeter.
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Figure 6. The experimental value of Ic using a digital multimeter. Figure 7. The experimental value of Vce using a digital multimeter.
The data recorded for Vin≈50 mV pk-to-pk, f=100 kHz and CC1=CC2=CE=0.1 µF are found in the following table: Table 2. The data table of the gain and Vout for for Vin≈50 mV pk-to-pk, f=100 kHz and CC1=CC2=CE=0.1 µF. The gain is calculated by the following equation: 20log ( V out V ¿ )
1 10 100 1000 10000 0 5 10 15 20 25 30 35 The graphical plot of the gain as a function of the frequency for Vin≈50 mV pk- to-pk and CC1=CC2=CE=0.1 µF Frequency (KHz) Gain (dB) Figure 8. The graphical plot of the gain as a function of the frequency for Vin≈50 mV pk-to-pk and CC1=CC2=CE=0.1 µF. Figure 9. The built circuit for the second part of the experiment using a breadboard and the measurement of the Vout using an oscilloscope.
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The data recorded for Vin≈50 mV pk-to-pk, f=100 kHz and CC1=CC2=CE=22 µF are found in the following table: Table 3. The data table of the gain and Vout for for Vin≈50 mV pk-to-pk, f=100 kHz and CC1=CC2=CE=22 µF. 0.01 0.1 1 10 100 1000 0 5 10 15 20 25 30 35 The graphical plot of the gain as a function of the frequency for Vin≈50 mV pk-to-pk and CC1=CC2=CE=22 µF Frequency (KHz) Gain (dB) Figure 10. The graphical plot of the gain as a function of the frequency for Vin≈50 mV pk-to-pk and CC1=CC2=CE=22 µF.
We can note the narrow range of frequencies within the midband in this scenario. Specifically, the low frequency spans from 1kHz to 60kHz, the midband covers the range from 60kHz to 100kHz, and the high frequency extends from 100kHz to 1150kHz. Likewise, the subsequent phase of the experiment utilized coupling capacitors of 22 𝜇𝐹 . A graph depicting the amplitude response against frequency is provided below. It's evident that with increased capacitance, the midband shifts towards lower frequencies, reaching 1 kHz in this instance. Similarly, in this experiment, the high-frequency range spans from 60 kHz to 945 kHz. To find the theoretical values to compare with the experimental ones for each different circuits, an online circuit simulator software ( Circuit Simulator Applet (falstad.com) ) was used. The simulations for the circuits are shown in the figures below:
Figure 11. Simulation of the circuit used to measure Ic, Ib and Vce β Theo = i c i b = 802.517 μA 8.025 μA = 10 β exp = i c i b = 0.8400 mA 0.1400 mA = 6 % Error β = | Experimentalvalue − Theoreticalvalue Theoreticalvalue | ∗ 100 = | 6 − 10 10 | ∗ 100 = 40% % Error V CE = | Experimental value − Theoretical value Theoretical value | ∗ 100 = | 7.418 V − 7.419 V 7.419 V | ∗ 100 = 0.013%
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Figure 12. Simulation of the circuit for Vin≈50 mV pk-to-pk and CC1=CC2=CE=0.1 µF. TheoreticalGainfor f = 1 kHz = 20log V out V ¿ = 20log ( 0.104 V 0.05 V ) = 6.36 dB % Error Gain = | Experimentalvalue − Theoreticalvalue Theoreticalvalue | ∗ 100 = | 6.62 dB − 6.36 dB 6.36 dB | ∗ 100 = 4.09%
Figure 13. Simulation of the circuit for Vin≈50 mV pk-to-pk and CC1=CC2=CE=22 µF. TheoreticalGainfor f = 1 kHz = 20log V out V ¿ = 20log ( 2 0.05 V ) = 32.04 dB % Error Gain = | Experimentalvalue − Theoreticalvalue Theoreticalvalue | ∗ 100 = | 28.85 dB − 32.04 dB 32.04 dB | ∗ 100 = 9.96%
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1. What is the maximum allowable ac output swing in step 3? The AC output should not exceed 1.46 V, as any value beyond this threshold leads to a noticeable decrease in performance.
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2. What is the figure of merit of the amplifier? The figure of merit of an amplifier serves as a comprehensive evaluation tool, gauging its efficiency in meeting specific objectives. This metric considers various crucial factors, including gain, bandwidth, input and output impedance, distortion, noise, and power consumption, thus offering a holistic assessment of its performance. The choice of a particular figure of merit depends on the amplifier's intended application and the desired outcomes. For example, in audio amplifiers, metrics such as signal-to-noise ratio (SNR) or total harmonic distortion (THD) are frequently utilized, whereas in RF amplifiers, parameters like gain-bandwidth product or power efficiency may take precedence, aligning with the operational demands of the system. G B≡ A M ( ωH − ωL ) A M = the average of themidband amplituderesponse ( gain ) ωH = the valueof the high 3 dB point ωL = the value of thelow 3 dB point For the circuit using the 0.1 𝜇𝐹 -> G B≡ 23.48 ( 100 kHz − 60 kHz ) = 939.20 For the circuit using the 22 𝜇𝐹 -> G B≡ 21.52 ( 945 kHz − 60 kHz ) = 19054.20
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3. Discuss the influence of the bypass, coupling, internal, and stray capacitances on the frequency response. A bypass capacitor serves as a pathway for AC signals to be redirected to ground, effectively neutralizing their adverse effects, and maintaining the integrity of DC characteristics, resulting in a smoother DC signal output. Coupling capacitors are instrumental in blocking the flow of DC current through the amplifier circuit, ensuring that only the desired AC signals are transmitted. In the context of bipolar junction transistors (BJTs), internal or junction capacitance naturally exists between the base and collector. While this capacitance cannot be altered, it's crucial to recognize its influence on circuit behavior, particularly at higher frequencies. Furthermore, stray capacitance, which arises between various electronic components within a circuit, poses a challenge as it's unintended. This stray capacitance can detrimentally impact circuit performance and needs to be carefully considered during circuit design and implementation.
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4. What is the purpose of capacitor’s CC1 and CC2? These capacitors are employed to impede the passage of direct current (DC) into and out of the amplifier stage, ensuring that only alternating current (AC) signals are allowed to pass through.
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5. In Fig.1 (a) CE = 0.1 µF. This value is changed to 22 µF in step 5. Based on your theoretical knowledge, how do you expect the lower 3 dB to change when CE is increased to 22 µF? The graphs displayed in the figures above provide a clear illustration of the results. As the capacitance increases, a distinct alteration in the midband's frequency range becomes evident, characterized by a decrease in both the initial and final frequencies. Furthermore, this increase in capacitance correlates with a concurrent rise in the signal's amplitude.
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6. Does CE have any effect on upper 3 dB point? The CE capacitor acts as a bypass, preserving the upper or high 3dB point of the system without any changes. However, it does affect the lower or low 3dB point, indicating its impact on the bandwidth characteristics of the system.
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Conclusion In summary, this experiment aimed to provide a comprehensive understanding of capacitor coupled BJT amplifiers, focusing on their frequency response characteristics and the influence of coupling and bypass capacitors at lower frequencies, as well as the impact of junction capacitance on amplifier behavior at higher frequencies. Capacitor coupling plays a crucial role in amplifier design, allowing AC signals to pass while blocking DC components, while bypass capacitors further enhance performance by preserving DC biasing. Junction capacitance, inherent to the transistor structure, becomes increasingly significant as frequencies rise. Through systematic observation and analysis, participants gained insights into these key concepts, enriching their knowledge of amplifier design and operation. The design process for discrete amplifiers involves establishing an appropriate circuit configuration, followed by DC and AC design phases. The experiment successfully assessed the frequency response of the amplifier stage, revealing changes in gain at different frequency ranges. The experiment provided valuable hands-on experience and theoretical understanding, contributing to a deeper appreciation of amplifier functionality and design principles. Overall, the successful completion of this experiment was confirmed during the demonstration to the lab instructor, effectively achieving the lab's objectives as the experimental values determined were very close to the theoretical values calculated (most analysis having close to 10% error).
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References 1) Sedra, A.S., Smith, K.C., Carusone, T.C., Gaudet, V., Microelectronic Circuits, Oxford University Press: 8th edition, © 2020 2) Alexander, C. K., & Sadiku, M. N. O. (2007). Fundamentals of electric circuits. Boston: McGraw-Hill Higher Education. 3) Shiyu Q., Laboratory Manual, ECE Electronics II, ELEC 312, Winter 2024.
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