ECE 3110 - Full Lab Report 2

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BJT Common-Emitter Circuit Voltage Gain October 31, 2023 ECE 3110 – 003 Electrical Engineering Laboratory III ABSTRACT: This experiment is intended to show how altering the bias of the circuit and the resistor values inside it can alter the voltage gain of a C E bipolar transistor circuit. The function of the emitter bypass capacitor C E will also be demonstrated. Furthermore, it will be illustrated how the Q-point is determined by the base resistors and how the Q-point impacts the relationship between the input and output wave shapes.
INTRODUCTION: One common electronic circuit architecture for amplifying tiny signals is the common- emitter ( C E ) transistor amplifier. It is commonly applied for small-signal AC and DC amplification, and it makes use of a bipolar junction transistor (BJT). When there is no input signal for the transistor, the common-emitter circuit’s DC function includes setting a stable operating point or Q-point. The DC values of collector current ( I C ) and collector-emitter voltage ( V CE ) are determined by this Q-point. The transistor is kept in the active zone and prepared to amplify signals thanks to DC biasing. The C E amplifier also amplifies weak AC impulses and sends them to its base terminal. The transistor operates differently when the input signal is placed on the DC biasing point (Q-point). The ratio of the AC output voltage to the AC input voltage, or V O V I , determines the voltage gain of the C E amplifier. By modifying the DC biasing resistors, the Q-point can be changed, which in turn affects the transistor’s operating voltage and current ( I C and V CE ). On the transistor’s characteristic curves, if the Q-point is moved excessively to the left, the transistor may enter cutoff or saturation states, which would restrict linearity and signal amplification. To guarantee that the transistor runs in its active region and enables efficient signal amplification with ideal gain and linearity while preventing saturation or cutoff, the Q-point must be adjusted correctly. Changing the values of the emitter and collector resistors has an impact on the circuit’s voltage gain. A BJT’s collector current ( I C ) is determined by the transistor’s , temperature, and circuit components. However, selecting biasing resistors so that the quiescent (DC) collector current stays consistent, independent of transistor temperature, is necessary for successful amplifier design. The collector current and voltage gain are kept reasonably constant by choosing
the appropriate biasing network and resistors. The emitter resistor, RE, and the values of the bias resistors, R1 and R2, are the essential components that stabilize the circuit against variations in the transistor. The stability of the circuit in response to variations in the transistor’s is influenced by essential components, namely the emitter resistor ( R E ) and the bias resistors ( R 1 and R 2 ). To preserve the high gain of the common emitter ( C E ) circuit, a common practice is to bypass the emitter resistor with a sizable capacitor. The introduction of an emitter resistor diminishes the AC voltage gain at the AC component ( i C ) is obliged to pass through RE to reach ground. Consequently, RE hinders i C , and the negative feedback voltage across RE diminishes the AC gain. To counteract this undesirable AC response while retaining effective control over I C (collector current) and the stabilizing impact of RE, a capacitor is connected across RE to short-circuit the AC current ( i C ) around RE to ground. This capacitor, usually denoted as C E , is typically of substantial magnitude, such as 10 F or greater, facilitating the majority of the AC current to flow through RE to ground. I C still traverses through R E as the capacitor functions as an open circuit for DC, thereby maintaining the stabilizing effect of R E . The investigation in this laboratory will explore the impact of the absence of C E , revealing that the voltage gain is determined by the ratio of R L (total AC load resistance) to R E . OVERVIEW / BACKGROUND: Before conducting the lab, review the dc analysis methods for determining a common- emitter circuit’s Q-point and how changing the ratio between two base resistors ( R 1 and R 2 ) affects the load line’s motion and base voltage. As prelab, LTSpice simulations were
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performed of the circuit in Figure 1, using the resistor values listed in Table 1, both with and without C E . Assume sinusoidal input VS = 0.02Vp-p at 1 kHz, the transistor is a 2N3904, and all capacitors are 22 F or greater. The simulated results were recorded in Table 1. Important formulas: A V = V O pp V S pp , which was used to determine the voltage gain. = I C I B V CE = V CO V EO I C ≈ I E = V EO R E V CE (max) = V CC I C ( max )= V CC R E + R C Table 1: List of Resistors for Prelab and Simulated Data With C E Without C E R C ( ) R E ( ) V OMin (mV) V OMax (mV) V OMin (mV) V OMax (mV) 3.9 k 1 k -915.3412 756.27914 -19.886941 20.218734 3.9 k 200 -265.35281 218.92653 -86.002651 89.18741 3.9 k 10 k -32.985416 25.446516 -1.894901 2.183624 1 k 1 k -422.890132 345.56552 -37.23240 39.28542 20 k 1 k -15.448301 446.70943 -7.287621 33.058711
Figure 1: Common-Emitter circuit with emitter bypass capacitor EXPERIMENTAL PROCEDURE and RESULTS: Equipment used: - 1 NPN Transistor, 2N3904 - Curve Tracer function on Waveforms - 1 Decade Resistance Box - NI-ELVIS workstation - Resistors (2.2k, 220, 16k) - Capacitors (22 F) - Lab Kits - AD2 Part 1 Procedures: During this part, the proper Q-point was established. Using the curve tracer, a Q-point closest to V CE = 2.5 and I C = 1 mA was determined which was V CE = 2.5096 and I C = 1.4256 mA. Additionally, I b = 0.01064 mA and V bE = 0.69988 and = 1.4256 0.01064 = 133.984. Figure 2 shows the screenshot of the determined Q-point on the transistor characteristics graph.
Figure 2: Screenshot of Q-point found on Waveforms Using Figure 3 as reference, the circuit was constructed with V CC = 5 V . The DMM was used to measure V CO and V EO and got a measurement of V CO = 3.115V and V EO = 0.184 V. V CE was determined as V CO V EO = 3.115 – 0.184 = 2.931 V and I C ≈ I E = V EO R E = 0.184 220 = 0.83636 mA. Figure 4 portrays the transistor characteristic with the determined Q- point using the DMM and drawn load line. . Figure 3: Common-Emitter Circuit for Q-point measurement
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Figure 4: Output Characteristic plot (hand drawn) with Q-point. Part 2 Procedures: This part of the lab was performed to determine the AC measurements and the voltage gain versus the collector resistor ( R C ) with and without the emitter bypass capacitor ( C E )). First, the circuit was constructed using Figure 5 as reference. Section 1 & 2 of Part 2 Procedures: V O and V S were measured with the oscilloscope. R C was replaced with the resistance decade box and set to 3.9 k . Again, the oscilloscope was used to measure V O , which was the same as the previous step. V O was continuously measured while R C was varied from 1 k to 20 k and V S was determined to be 20.292 mV. The V O measurements, output wave shape, and voltage gain was recorded into Table 2. Voltage gain was determined by A V = 255.041 20.292 = 12.5685 and was repeated for each measurement. Once the data was collected, the emitter bypass capacitor, C E , was removed and the same procedures were repeated. The data was recorded in Table 2.
Figure 5: The Common Emitter Circuit with added capacitors and input signal VS provided by the function generator and the voltage divider, RS1 and RS2. Table 2: V O vs R C R C () With C E Without C E V O pp Output shape A V V O pp Output shape A V 1k 255.041 sine 12.569 88.426 sine 4.358 2.2k 546.671 sine 26.940 190.282 sine 9.476 6.8k - clipped - - clipped - 10k - clipped - - clipped - 15k - clipped - - clipped - 20k - clipped - - clipped - Figure 6: R C = ¿ 1k , R E = 220, with C E
Figure 7: R C = ¿ 6.8 k , R E = 220, with C E Figure 8: R C = ¿ 20 k , R E = 220, with C E Figure 9: R C = ¿ 1k , R E = 220, without C E
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Figure 10: R C = ¿ 6.8k , R E = 220, without C E Figure 11: R C = ¿ 20k , R E = 220 , without C E 1000 2200 6800 10000 15000 20000 0 5 10 15 20 25 30 Plot 1: RC vs Av with CE RC () Av (voltage Gain) (V) Figure 12: Plot of R C vs A V with C E
1000 2200 6800 10000 15000 20000 0 1 2 3 4 5 6 7 8 9 10 Plot 2: RC vs Av without CE RC ( Av (voltage Gain) (V) Figure 13: Plot of R C vs A V without C E Table 2’s findings demonstrate that, as predicted, the signal at the collector terminal in the table and graphs above with C E present is stronger than it is in the absence of C E . This is due to the fact that when C E is present in the circuit, the resistor R E is bypassed. For the values of R C shown in the table, distortion displayed as clipping occurs very early on because the Q-point value is no longer centered along the DC load line. Section 3 & 4 of Part 2 Procedures: R C was set to 3.9k using a fixed resistor instead of a resistance decade box and the emitter bypass capacitor, C E , was connected using Figure 5 as reference. R E was replaced with the resistance decade box and set to 1 k . V O was measured using the oscilloscope with ranging R E values from 100 to 10k. V S was measured to be 20.292 mV. The determined data was recorded in Table 3. After the data was collected, the emitter bypass capacitor, C E , was removed and repeated the steps with data recorded in the table.
Table 3: V O vs. R C R E () With C E Without C E V O pp Output shape A V V O pp Output shape A V 100 711.976 sine 35.087 390.311 sine 19.923 220 557.031 sine 27.451 190.349 sine 9.380 470 457.914 sine 22.566 91.743 sine 4.521 1k 365.122 sine 17.993 44.508 sine 2.193 4.7k 134.561 sine 6.631 12.224 sine 0.602 6.8k 99.901 sine 4.923 9.991 sine 0.492 10k 73.073 sine 3.601 6.553 sine 0.323 Figure 14: R C = ¿ 2.2k , R E = 220 , with C E Figure 15: R C = ¿ 2.2k , R E = 1k , with C E
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Figure 16: R C = ¿ 2.2k , R E = 6.8k , with C E Figure 17: R C = ¿ 2.2k , R E = 220 , without C E Figure 18: R C = ¿ 2.2k , R E = 1k , without C E
Figure 19: R C = ¿ 2.2k , R E = 6.8k , without C E 100 220 470 1000 4700 6800 10000 0 5 10 15 20 25 30 35 40 Plot 3: RE vs Av with CE RE () Av (Voltage Gain) (V) Figure 20: Plot of R E vs A V with C E
100 220 470 1000 4700 6800 10000 0 5 10 15 20 25 Plot 4: RE vs Av without CE RE () Av (Voltage Gain) (V) Figure 21: Plot of R E vs A V without C E Higher voltage gains are associated with lower values for R E , as Table 3 above illustrates because C E bypasses the R E resistor, which increases the voltage gain. Lower voltage gain results from increasing the resistance of R E , both with and without C E . Final section of Part 2 Procedures: R E was set to 1k and C E was connected. The input signal frequency was varied from 10 Hz to 50 kHz and the oscilloscope was used to see how the magnitude of the output signal varied. The results were recorded into Table 4. Table 4: Frequency Response of V O pp and Voltage Gain, A V Frequency (Hz) 10 100 1k 10k 25k 50k V O pp 59.215 108.321 360.965 538.212 538.435 540.794 A V 2.918 5.338 17.789 26.523 26.534 26.651 Changes to the frequency appear to make large changes to the voltage gain up until 10 kHz. From that point forward the voltage gain remains steady. This indicates that this range falls at the midrange frequency level, where the voltage gain remains at a steady level. The coupling capacitor, C 2 , has high reactance at lower frequencies which means only a small part of the
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signal will be output and it can’t be effectively bypass R E , which means increased resistance and a lower voltage gain as it does when C E is not present in the circuit. Post Lab Questions: 1. In certain instances, the findings of the comparison between the simulations of the circuits and the experimental data were extremely similar, but not always. This could be the result of variances in different physical components or human mistake in the experiment or simulation. 2. When C E is present in the circuit, the resistor R E is bypassed, resulting in a greater voltage gain. Without the bypass capacitor, C E , there is more resistance on the output voltage and therefore resulting in a lower voltage gain. CONCLUSION: As anticipated, the introduction of the C E capacitor resulted in an amplified output voltage. This amplification occurred as a consequence of bypassing the R E resistor. Elevations in the R C resistor’s resistance contributed to higher voltage gains, reaching a point of distortion manifested as clipping at 6.8 k . Conversely, increases in the R E resistor led to reduced voltage gains for the same reason observed without the bypass capacitor ( C E ). This reduction is attributed to the heightened resistance affecting the output voltage. Additionally, the frequency of the input signal significantly influences the voltage gain, as it impacts the reactance of the coupling capacitor C 2 .