Building A BJT Amplifier Engineering Essay

Building A BJT Amplifier Engineering Essay Students were required to research and design a BJT Amplifier. This amplifier was to be built in the laboratory and tested to verify specifications. Calculations for resistors and capacitors were done and theoretical values were obtained. The circuit was built using Multisim 7 and then simulated to obtain practical values for resistors and capacitors. This is called DC Analysis. When the circuit met the required specifications, building of the BJT Amplifier could begin. Testing of the BJT Amplifier was done using the Feedback FG601 Function Generator which provided an input and a Tektronix 2205 Oscilloscope which showed the output waveform. Also, the Fluke 177 Multi-meter was used when checking for quiescent voltages and currents. The voltage gain, maximum symmetrical swing and the lower cut-off frequency for the BJT Amplifier was tested. The results obtained during tested were compared with the simulated and theoretical results. Success of the BJT Amplifier can only be achieved when the tested values duplicate that of the given specifications. The report that follows records calculations performed, circuits designed and the results of the tests that was done on the BJT Amplifier. List of Abbreviations Voltage gain BJT Bipolar Junction Transistor Current gain Input Impedance Base current Collector current Current across resistor Current across resistor Current across the original emitter resistor Current across the new emitter resistor Current across the unbypassed resistor Resistor used in the potential divider Collector resistor Resistor used in the potential divider Original emitter resistor New emitter resistor (bypassed) Unbypassed resistor Load resistor Base emitter voltage Voltage across the collector and emitter Input voltage Output voltage Voltage across resistor Voltage across the collector resistor Voltage across resistor Voltage across the original emitter resistor Voltage across the new emitter resistor Voltage across the bypassed resistor Introduction It is known that transistors are widely used in electronic devices. This design project is ideal as it enables students to get practical experience in the designing of electrical devices. The practical and theoretical knowledge needed for this design project challenges students as they have to validate calculated values and explain why each process was done. Since the BJT Amplifier has to be designed theoretically, students will understand the limitations provided by the equipment. They will also grasp an appreciation of the simulated circuit model as it relates to the tests performed on the circuit. The theory from Electronics provided valuable knowledge in designing the BJT amplifier. Support was given from lectures based from Engineering Skills and Applications. The practical knowledge was covered in previous laboratory exercises which were designated to familiarizing students with the various equipments. Also, demonstrations were provided by the technicians on the use of the breadboard which is the core building block of the BJT amplifier. BACKGROUND INFORMATION Transistors are important components used in technological devices around the world. Computers, cell phones, and radios are some of the many devices that require transistors as part of their circuit. The transistor is a three terminal, solid state electronic device. In a three terminal device we can control electric current or voltage between two of the terminals by applying an electric current or voltage to the third terminal. This three terminal character of the transistor is what allows us to make an amplifier for electrical signals, like the one in our radio. (cited) The three terminals are the collector terminal, the base terminal and the emitter terminal. There are three possible configurations of a transistor; the common collector, common base and the common collector. In the common emitter amplifier configuration, the emitter terminal is common to both the input and output circuits. The current gain does not have any effect on the collector current , or the collector-emitter voltage . A quiescent point is the operating point of a device which when applied to a device, causes it to operate in a desired fashion. It also refers to the dc conditions of a circuit without an input signal. The Q-point is sometimes indicated on the output characteristics curves for a transistor amplifier. There are different biasing arrangements associated with transistor configurations. These include; simple bias, self stabilizing bias, and H-type bias. The simple bias circuit consists of a fixed bias resistor and a fixed load resistor. For this bias design, the transistor configuration being used is the common emitter. The dc current gain or beta, is the ratio of the dc collector current to the dc base current. This simple bias circuit is similar to the self bias circuit with one difference: the base resistor is returned to the transistor collector instead of the supply voltage. If the transistor used had a high current gain, then the collector voltage would fall. As is connected to the collector then the base current would be reduced to counter the effect. If the transistor had a low value of beta, then the collector voltage would rise. This in turn provides more base current for the transistor to conduct harder and stabilize the q-point. H-TYPE BIASING is the most widely used biasing scheme in general electronics. For a single stage amplifier this circuit offers the best resilience against changes in temperature and device characteristics. The disadvantage is that a couple of extra resistors are required, but this is outweighed by the advantage of excellent stability. The circuits below: The quiescent points are usually fixed for varying collector currents in H-type biasing. If increases, then this will result in an increase in . This increase in the emitter current will flow through the emitter resistor and from the equation V=IR, the voltage across the resistor will increase. This increase in voltage across the emitter resistor will reduce the effective base-emitter voltage resulting in an increase in the stability of the collector current. Also, this type of biasing introduces a potential divider situation, where resistors R1 and R2 fix the base potential of the transistor. With H-type bias, maximum symmetrical sw ing can be calculated. Design OBJECTIVES Various specifications for the design of the BJT Amplifier were given by the rubric. The specifications given are listed in the following; The Voltage Gain must be 50 The Lower Cut-off Frequency must be below 100Hz The BJT Amplifier must be capable of driving a 100KÃŽÂ © load A 15V supply voltage must be used as the source The output voltage must have maximum symmetrical swing A 2N3904 Transistor must be used CHOOSING CONFIGURATION The following transistor configuration comparison chart shows the different types of configurations; Common Emitter Common Base Common Collector (Sedra Smith, 2007) AMPLIFIER TYPE    COMMON BASE      COMMON EMITTER      COMMON EMITTER (Emitter Resistor)      COMMON COLLECTOR (Emitter Follower)   Ã‚  Ã‚   INPUT/OUTPUT PHASE RELATIONSHIP 0 ° 180 ° 180 ° 0 ° VOLTAGE GAIN HIGH MEDIUM MEDIUM LOW CURRENT GAIN LOW  Ã‚ ¡ MEDIUM MEDIUM  Ã‚ ¢ HIGH POWER GAIN LOW HIGH HIGH MEDIUM INPUT RESISTANCE LOW MEDIUM MEDIUM HIGH OUTPUT RESISTANCE HIGH MEDIUM MEDIUM LOW The common emitter transistor amplifier configuration was chosen and not the common base configuration as the common base configuration produces a voltage gain but generates no current gain between the input and the output signals. (Doug Gingrich, 1999) The following figure shows the general configuration of the common emitter transistor amplifier configuration; Figure 1: General configuration of the common emitter transistor amplifier configuration Methodology DC Analysis The function of the DC Analysis is to allow DC biasing of the design to be verified. The DC biasing does not involve capacitors as DC is not transmitted by capacitors. The DC design is mainly used to establish the Q-points in the circuit. Q-points are the operating points in the circuit for which the transistor will perform at optimum performance. The circuit used for the DC Analysis is shown in the following diagram; Figure 2: Circuit used for DC Analysis Choosing and Before DC Analysis could be done, the various components which will be used in the circuit need to be calculated. These components are; , , , . From the specifications given, the voltage supply has a value of 15V and this is used to power the circuit. Before the values of these components could be calculated, the quiescent currents must be known, as well as the current flowing through the potential divider resistor . The data sheet used is based on the 2N3904 transistor. A range for the collector current is given, within which the transistor will operate with optimum performance. Using the Base Emitter ON Voltage vs Collector Current graph found on the data sheet, a value of was read off. The graph used is shown in the following diagram; Figure 3: Graph used to find a collector current The transistor will be built in an environment where the temperature is approximately 25. Hence the 25 line on the graph was used a reference line. From the data sheet, the Base Emitter ON Voltage was given as 0.65V. Hence, using the 25 line and reading off a voltage of 0.65V, the collector current was found to be 1. The base voltage , of the transistor depends on the current flowing through the potential divider. i.e. the current sets the base of the transistor and hence the value of . Any change in the resistance or gain of the transistor would result in an unwanted change in the base current . Also, the potential divider resistors contribute to the input impedance of the amplifier. This input impedance needs to be much more than the output impedance of the function generator. Hence, this is another reason to keep small. was chosen as Calculating The emitter resistor voltage , must be chosen accordingly as this voltage will affect the stability, maximum symmetrical swing and the gain of the amplifier. This voltage should be chosen such that it is greater than the base emitter voltage of the transistor. As mentioned before, the base emitter voltage as taken from the data sheet is 0.65V. This is to ensure that the emitter resistor voltage will not be significantly affected by small changes in . This condition would increase the stability of the transistor. For maximum symmetrical voltage swing, the emitter resistor voltage should be as small as possible. The base current and the collector current will both flow out of the common emitter terminal. Hence, for to remain constant, the base current must be as small as possible to allow negligible current to flow through the base terminal. Assuming the variation possible across the emitter and collector resistors caused variations in is , is calculated using the following equation; (1) The emitter resistor was calculated using the following equation; (2) Calculating From previous statements, For maximum symmetrical swing, half of the remaining voltage should be dropped across the collector resistor . The maximum symmetrical output voltage is calculated using the following equation; (3) Therefore, the voltage across the collector emitter terminal and the collector resistor is 6.75V. From the data sheet, the maximum device dissipation for the NPN 2N3904 transistor is at 25. Since all the power dissipation occurs at the collector junction for the active region, the following equation must be satisfied; (4) This is the range for which the transistor will operate with optimum performance. The power dissipated in the transistor from equation (4) is; , which is well within the specified range. A value for the component was found using the following equation; (5) Calculating and The current flows through the resistor . The value of is calculated using the following equation; (6) Since the current approaches a junction, it splits into and . flows through the potential divider resistor and flows to the base terminal. As previously stated, the base current, must not affect the base voltage by much. Hence the base current is considered negligible and all the current from is assumed to flow through . Hence, is calculated using the following equation; (7) Since some of the component values calculated was not available in stores, the closest value had to be chosen. The standard value that was chosen for each component is shown in the following table; Resistor Calculated Value/ Standard Value/ 6.75 6.8 1.5 1.5 128.5 130 21.5 24 Table 1: Standard values chosen for resistors Calculation of Input Impedance of transistor From the design specifications listed above, the lower cut off frequency must be below 100Hz. Also, as a value for was found using a graph of Current Gain vs Collector Current from the data sheet, a value for was found. The graph used is shown in the following diagram; For a collector current of 1, a gain of 130 was read off from the graph. But since this gain is above the required voltage gain of 50, certain calculations had to be done to reduce this gain and these calculations will be shown in due course. The following equation is used to calculate the input impedance of the transistor; (8) Calculation of Voltage Gain in the Circuit The following equation was used to calculate the voltage gain of the circuit; (9) Calculation of The required voltage gain of the transistor is 50. Hence, in order to reduce this gain, resistors are usually bypassed with the aid of capacitors. In this particular case, the only resistor that needs to be bypassed is the emitter resistor. Using the AC equivalent circuit, the following equation will be used to calculate the value of the unbypassed resistor; (10) where is the unbypassed emitter resistor is From the specification sheet given, is Calculation of new emitter resistor But Hence, if is split into two resistors and , then is found from the following; (11) As there are no standard 1.4kà °Ã‚ Ã…“ ´ resistor is the stores, was used as 1.5kà °Ã‚ Ã…“ ´. The following table illustrates the standard emitter resistors; Resistor Calculated Value/ Standard Value/ 100 100 1400 1500 Table 2: Standard values chosen for emitter resistors CIRCUIT CALCULATIONS Figure 4: Diagram showing circuit analyzed The following circuit calculations involve the standard component values and is based on the circuit in the above diagram.. These circuit calculations show the theoretical value of the quiescent currents and voltages. Theoretical values occur due to the circuit being under ideal conditions. The voltage gain of this circuit will be calculated as well as the maximum symmetrical output voltage across the transistor. The calculations are as follows; which flows through the collector resistor Using the potential divider rule; The voltage drop across is the same as, as both resistors are in parallel. was found on the data sheet as specified previously as . Under ideal conditions, it is assumed that is negligible when compared with as stated previously. for small changes in where is 130 since negligible current flows into the base terminal AC ANALYSIS The AC Analysis is used to calculate the components which would not have worked under DC biasing. These components are , and . If placed in the DC circuit, the capacitors would act as an open circuit, not allowing any current to flow. Also, the input and output impedance of the circuit was calculated. Circuits Used The following circuit was used in the AC Analysis; Figure 5: Circuit used for AC Analysis The following figure illustrates the AC equivalent of the above circuit; Zout Zin Figure 6: Ac equivalent of circuit shown in figure 5 Calculation of Capacitors The capacitor values can now be calculated using the following equation; (12) where is the reactance of the circuit f is the frequency C is the capacitance The capacitors behavior is defined in terms of reactance. The reactance of a capacitor is the ratio of the voltage to the current. The equation relating the reactance to the capacitance is given in equation (12). is the total input impedance of the capacitor (13) where is the input impedance , as the input is taken from the ground to the output terminals of the function generator. (14) Using equation 12; But from the specification sheet, f must be less than 100Hz. f 100 (15) Calculation of For the input coupling capacitor ; Calculation of For the output coupling capacitor ; Where is and Calculation of For the bypass capacitor ; where (16) But As stores does not have these calculated capacitor values, the following standard capacitors were used; Capacitor Calculated Value/ Standard Value/ 0.175 10 0.234 10 14.985 100 Table 3: Standard values chosen for capacitors CIRCUIT CALCULATIONS The following circuit calculations involve the standard component values and are based on the circuit shown in figure 3. These circuit calculations show the theoretical value of the quiescent currents and voltages. Theoretical values occur due to the circuit being under ideal conditions. The voltage gain of this circuit will be calculated as well as the maximum symmetrical output voltage across the transistor. The calculations are as follows; which flows through the collector resistor Using the potential divider rule; (17) The voltage drop across is the same as, as both resistors are in parallel. was found on the data sheet as specified previously as . (18) (19) Under ideal conditions, it is assumed that is negligible when compared with as stated previously. (20) for small changes in (21) where is 130 (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) since negligible current flows into the base terminal Figure 6 was used as a reference point to calculate the voltage gain and input impedance of the circuit. Equation (10) was used to calculate the voltage gain of the circuit; The maximum output voltage swing without clipping is calculated as using the following equation; (33) The following equation is used to calculate the input impedance of the circuit; (34) For simplification in calculation, (35) (36) COMPUTER SIMULATION DC Analysis This design was tested theoretically in the previous section and must now be tested on a computer simulation program. The simulation program used to simulate this circuit is Multisim 7. This software creates the circuit design and simulates the circuit practically and not theoretically. All quiescent voltages and currents were determined as well as the cut-off frequency, voltage gain and maximum symmetrical output voltage. The graph analyzer tool on the Multisim program was used to display these graphs. The following figure illustrates the simulation done for the DC Analysis; Voltage Gain The following circuit was used to observe the voltage gain of the BJT Amplifier; Figure 7: Showing circuit used for DC AnalysisThe voltage gain of the simulated circuit is the ratio of the maximum output voltage to the maximum input voltage. The voltage gain of the circuit is given by the equation; The following figure shows the settings used on the oscilloscope to obtain an input and output waveform; The maximum output and input signals was read off from the graph above using the Interpolator Line. Using the above equation, the voltage gain of the circuit was determined as follows; The following figure illustrates the bode plot obtained from the simulation; This graph was used to find the gain of the circuit using the following equation; From the above equation, the gain, in decibels is related to the above equation. Using the Interpolator Line, the gain, was determined to be 34.34. Hence the voltage gain was calculated as follows; The above calculation indicates that the design circuit would produce a satisfactory gain of approximately 50. Therefore the graph in figure 10 confirms that the design would produce a voltage gain of approximately 50. Cut-off Frequency The following bode plot was used to determine the lower cut-off frequency; The figure above was used to determine the lower-cut off frequency of the circuit. The lower-cut off frequency is the frequency at which the gain of the circuit decreases by 3 decibels. The Interpolator Line was placed at a gain of 30.861decibels, as this is the gain which corresponds to the lower-cut off frequency. The lower-cut off frequency was determined to be approximately . This lower cut-off frequency is much less than 100Hz and thus it meets the required specification. The following bode plot was used to determine the upper cut-off frequency; The figure above was used to determine the upper -cut off frequency of the circuit. The Interpolator Line was placed at a gain of 30.816 decibels, as this is the gain which corresponds to the upper-cut off frequency. The upper-cut off frequency was determined to be approximately . Lab Results The final test done on the designed circuit was done in the year 1 laboratory. The actual resistances and capacitances of the standard components used were measured using the LCR meter. The following table illustrates the measured resistances; Resistor Standard Resistance/ Measured Resistance/ Tolerance/% Lower Tolerance/ Upper Tolerance/ 6.8 6.7638 5 6.46 7.14 1.5 1.503 5 1.425 1.575 100 99.81 5 95 105 130 129.95 5 123.5 136.5 24 23.529 5 22.8 25.2 100 kÃŽÂ © 99.233 5 95 105 TABLE 6: Measured resistances AND THEIR TOLERANCE RANGE The following table illustrates the measured capacitances; Capacitor Standard Value/ Measured Value/ TABLE 8: Showing Measured capacitances used in the laboratory The BJT Amplifier was then built on the solder less breadboard. The DC LQD-421 dual power supply and the function generator were used to supply the input voltages. The following diagram shows the circuit built; As seen above, the capacitors were connected across their respective resistors and the Feedback FG 601 function generator was connected to the input capacitor. Before measuring the quiescent points of the circuit, tests had to be done to ensure that the required gain of 50 was achieved. This was done by connecting a Tektronix 2205 dual trace oscilloscope to the AC bias circuit. The channel 1 lead was connected to the input signal via the input capacitor and the channel 2 lead was connected across the output signal via the load. The settings on the Feedback FG 601 function generator were set to produce a 1kHz sine wave with an amplitude of . The channels on the Tektronix 2205 dual trace oscilloscope were grounded and the signals centered. The DC LQD-421 dual power supply was turned on and set to 15V and the Feedback FG 601 function generator and the Tektronix 2205 dual trace oscilloscope also turned on. The channels were switched to AC and the input and output sine waves appeared on the screen. To obtain a clear waveform on the screen, the following settings were used on the Tektronix 2205 dual trace oscilloscope; The Volts/Div setting was set at The channel 1 setting was set at The channel 2 setting was set at The two waveforms were then used to determine the voltage gain of the BJT Amplifier. Using the following equation; The upper and lower cut-off frequencies were found for the BJT Amplifier. This was done by varying the frequency on the Feedback FG 601 function generator and plotting a graph of Gain vs Frequency. The range used for the Feedback FG 601 function generator was; 10Hz 100Hz for lower cut-off frequency The following table illustrates the frequency and gain for lower cut-off frequency; Frequency/Hz Input/mV Output/V Gain 10 0.01 5 50 20 0.01 5 50 30 0.01 5 50 40 0.01 5 50 50 0.01 5 50 60 0.01 5 50 70 0.01 4.8 48 80 0.01 4.6 46 90 0.01 4.2 42 100 0.01 2.6 26 Table4: showing frequencies used to get varying gain The lower cut-off gain was calculated from the equation; The original setting on the Feedback FG 601 function generator was set so that the maximum symmetrical swing of the BJT Amplifier could be determined using the Tektronix 2205 dual trace oscilloscope. This was done by increasing the frequency of the Feedback FG 601 function generator until clipping of the output waveform was seen. It was noted that the BJT Amplifier did not have maximum symmetrical swing as the negative peak of the waveform started clipping after the positive peak waveform. Hence, the positive swing and negative swing was calculated as shown in the following; Positive swing; Negative swing; The maximum voltage swing was found to be; The original setting on the Feedback FG 601 function generator was set as the effect of removing the bypass capacitor was explored. The equipment was first turned off for safety purposes and the bypass capacitor removed. The equipments was then turned on and the settings on the Tektronix 2205 dual trace oscilloscope configured to obtain a measurable waveform. The gain was then calculated using equation (>>>>). Hence, it can be stated that the gain of the BJT Amplifier decreased considerably when the bypass capacitor was removed. The maximum symmetrical swing for the amplifier was then tested. This was done as follows; The frequency of the Feedback FG 601 function generator was increased until clipping occurred. It was seen that maximum symmetrical swing was not observed as the negative peak of the waveform started clipping before the positive waveform. Hence the swing was calculated for both the positive waveform and the negative waveform. The calculations are as follows; Positive swing; Negative swing; The maximum voltage swing was found to be; The Tektronix 2205 dual trace oscilloscope was disconnected from the circuit and the Fluke 177 Multi-meter was used to measure the quiescent points of the circuit. The probes were placed across the different points and their readings were recorded. The Fluke 177 Multi-meter was set at when measuring currents and at DC voltage when measuring voltages. The DC voltage setting was used as the AC would not yield measurable readings. To measure the quiescent currents, wires were stripped and attached to the leads of the probes. The circuit had to be broken at the quiescent current point being measured. Then the wire attached to the probe was inserted into the solder less breadboard so that the wire was in series with the component removed. The removed component was placed where it was originally to ensure continuity in the circuit. This was repeated at all quiescent points. The following table illustrates the measured currents; The following table illustrates the measured currents; Current Value/ TABLE 5: AC ANALYSIS OF CIRCUIT The following table illustrates the measured voltages; Voltage Value/ 0.676 TABLE 4: AC ANALYSIS Quiescent Values Currents I / mA Voltages V / V Calculated Simulated Measured Current I / mA Voltage V/V Current I / mA Voltage V/V Current I / mA Voltage V/V 0.65 0.663 0.676 DISCUSSION The BJT Amplifier was built using the common emitter configuration. It was H-type biased to increase the stability in the transistor. Also, as is affected with temperature a change, the H-type biasing configuration ensures that changes in is minimal. Also, the resistors used were made from carbon. This means that the resistors are not required to have high temperature stability. Without a biasing arrangement, the BJT amplifier will not turn on because it will not be in the operating region according to the specifications (Boylestad, Nashelsky, 1987). The differences in values for quiescent points obtained can be explained because the calculated and simulated values were found under ideal conditions. The component values used varied from the standard values