Vermont Technical College Electronics I – Laboratory ELT-2051 Lab 07: Transistor Biasing Circuits and Q-point Stability Objectives: • To set an operating point for a transistor using three different bias techniques • To explore amplification of an AC signal • To use MultiSim to verify your experimental data General: In this laboratory, you will be supplied with two NPN transistors with varying ß’s. Prelab: Calculate values of Rb in Figures 1 and 2 assuming ß = 200, VCE = 6V . For Figure 3, calculate R1 and R2 so that their parallel resistance is about 20KΩ or 10% of (ß+1)RE. Also, calculate the critical frequency of the 1uF capacitor in Figure 4. Materials: • 2N3904, 2N4123 NPN TXs (1 high ß, 1 low ß) • (2) 1 k Ohm, 100 k Ohm, assorted resistors • 1uF, 10uF capacitors • Curve Tracer • DC Power Supply • Multimeter • Signal Generator • Oscilloscope • Breadboard Procedure: 1. Use the curve tracer to plot the curves for each of your transistors. From these curves, again using the curve tracer, determine the ßDC for each transistor at the IC currents of 1mA, 3mA, 6mA, and 10mA with VCE = 6V. Of course, be sure to keep track of which transistor goes with which curve. Verify that the ßDC values that you obtain are within the manufacturer’s specifications. Remember– ßDC = hFE ! 2. For each of the three circuits shown in Figures 1-3, using the R values calculated in your prelab, determine the operating points IC and VCE for each of the transistors. Be sure to table your data. In addition, plot ß vs IC for both transistors on a single graph so that the data is meaningful! What conclusions can be reached for the 3 biasing circuits? 3. Lastly – Build Figure 4 and determine the ratio (Gain) of Vout/Vin at 1KHz. Now vary the frequency of Vin to determine at what frequencies this ratio decreases to 0.707 of the value at 1KHz. 4. Use the Bode Plotter feature in MultiSim to verify your data of Part 3. Is the cut-off frequency the same as you measured in the lab? Base Bias: Parameter Calculated Value Simulated Value Measured Value VCE1 (high β) VCE2 (low β) n/a n/a |VCE1 – VCE2| 0 0 IC1 (high β) IC2 (low β) n/a n/a |IC1 – IC2| 0 0 Emitter Bias: Parameter Calculated Value Simulated Value Measured Value VCE1 (high β) VCE2 (low β) n/a n/a |VCE1 – VCE2| 0 0 IC1 (high β) IC2 (low β) n/a n/a |IC1 – IC2| 0 0 Voltage Divider Bias: Parameter Calculated Value Simulated Value Measured Value VCE1 (high β) VCE2 (low β) n/a n/a |VCE1 – VCE2| 0 0 IC1 (high β) IC2 (low β) n/a n/a |IC1 – IC2| 0 0 Laboratory Report: This lab is a semi-formal lab. Be sure to collect all data necessary to make observations and answer questions before you leave the lab. Also, you and your lab partner should discuss the results and outcomes prior to leaving. Take notes, fill in tables and include diagrams as needed. Your report should include: • Data Table • Beta Plot • MultiSim Frequency Response • Comparison of biasing schemes • Comparison of measurements vs. simulations and expectations.

## Vermont Technical College Electronics I – Laboratory ELT-2051 Lab 07: Transistor Biasing Circuits and Q-point Stability Objectives: • To set an operating point for a transistor using three different bias techniques • To explore amplification of an AC signal • To use MultiSim to verify your experimental data General: In this laboratory, you will be supplied with two NPN transistors with varying ß’s. Prelab: Calculate values of Rb in Figures 1 and 2 assuming ß = 200, VCE = 6V . For Figure 3, calculate R1 and R2 so that their parallel resistance is about 20KΩ or 10% of (ß+1)RE. Also, calculate the critical frequency of the 1uF capacitor in Figure 4. Materials: • 2N3904, 2N4123 NPN TXs (1 high ß, 1 low ß) • (2) 1 k Ohm, 100 k Ohm, assorted resistors • 1uF, 10uF capacitors • Curve Tracer • DC Power Supply • Multimeter • Signal Generator • Oscilloscope • Breadboard Procedure: 1. Use the curve tracer to plot the curves for each of your transistors. From these curves, again using the curve tracer, determine the ßDC for each transistor at the IC currents of 1mA, 3mA, 6mA, and 10mA with VCE = 6V. Of course, be sure to keep track of which transistor goes with which curve. Verify that the ßDC values that you obtain are within the manufacturer’s specifications. Remember– ßDC = hFE ! 2. For each of the three circuits shown in Figures 1-3, using the R values calculated in your prelab, determine the operating points IC and VCE for each of the transistors. Be sure to table your data. In addition, plot ß vs IC for both transistors on a single graph so that the data is meaningful! What conclusions can be reached for the 3 biasing circuits? 3. Lastly – Build Figure 4 and determine the ratio (Gain) of Vout/Vin at 1KHz. Now vary the frequency of Vin to determine at what frequencies this ratio decreases to 0.707 of the value at 1KHz. 4. Use the Bode Plotter feature in MultiSim to verify your data of Part 3. Is the cut-off frequency the same as you measured in the lab? Base Bias: Parameter Calculated Value Simulated Value Measured Value VCE1 (high β) VCE2 (low β) n/a n/a |VCE1 – VCE2| 0 0 IC1 (high β) IC2 (low β) n/a n/a |IC1 – IC2| 0 0 Emitter Bias: Parameter Calculated Value Simulated Value Measured Value VCE1 (high β) VCE2 (low β) n/a n/a |VCE1 – VCE2| 0 0 IC1 (high β) IC2 (low β) n/a n/a |IC1 – IC2| 0 0 Voltage Divider Bias: Parameter Calculated Value Simulated Value Measured Value VCE1 (high β) VCE2 (low β) n/a n/a |VCE1 – VCE2| 0 0 IC1 (high β) IC2 (low β) n/a n/a |IC1 – IC2| 0 0 Laboratory Report: This lab is a semi-formal lab. Be sure to collect all data necessary to make observations and answer questions before you leave the lab. Also, you and your lab partner should discuss the results and outcomes prior to leaving. Take notes, fill in tables and include diagrams as needed. Your report should include: • Data Table • Beta Plot • MultiSim Frequency Response • Comparison of biasing schemes • Comparison of measurements vs. simulations and expectations.

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Assignment 2 Conditional Probability, Bayes Theorem, and Random Variables Conditional Probability and Bayes’ Theorem Problems 1-14 from Problem Set on Conditional Probability and Bayes’ Theorem I am including all the question here so that there is no confusion. Q1. Pair of six sided dices are rolled and the outcome is noted: What is the sample space? What is the size of the sample space? Suppose all we are interested in is the sum of the two outcomes. What is the probability that the sum of the two is 6? 7? 8? (Note: This can be solved using both enumeration and conditional probability method). Here, it makes more sense to use the enumeration approach than conditional probability. It is, however, listed here to set the stage for Q5. What is the probability that the sum of the two is above 5 and the two numbers are equal? Express this question in terms of events A, B, and set operators. What is the probability that the sum of the two is above 5 or the two numbers are equal? Express this question in terms of events A, B, and set operators. Q2. If P(A)=0.4, P(B)=0.5 and P(A∩B)=0.3 What is the value of (a) P(A|B) and (b) P(B|A) Q3. At a fair, a vendor has 25 helium balloons on strings: 10 balloons are yellow, 8 are red, and 7 are green. A balloon is selected at random and sold. Given that the balloon sold is yellow, what is the probability that the next balloon selected at random is also yellow? Q4. A bowl contains seven blue chips and three red chips. Two chips are to be drawn at random and without replacement. What is the probability that the fist chip is a red chip and the second a blue? Express this question in terms of events A, B, and set operators and use conditional probability. Q5. Three six sided dices are rolled and the outcome is noted: What is the size of the sample space? What is the probability that the sum of the three numbers is 6? 13? 18? Solve using conditional probability How does the concept of conditional probability help? Q6. A grade school boy has 5 blue and four white marbles in his left pocket and four blue and five white marbles in his right pocket. If he transfers one marble at random from his left pocket to his right pocket, what is the probability of his then drawing a blue marble from his right pocket? Q7. In a certain factory, machine I, II, and III are all producing springs of the same length. Of their production, machines I, II, and III produce 2%, 1%, and 3% defective springs respectively. Of the total production of springs in the factory, machine I produces 35%, machine II produces 25%, and machine III produces 40%. If one spring is selected at random from the total springs produced in a day, what is the probability that it is defective? Given that the selected spring is defective, what is the probability that it was produced on machine III? Q8. Bowl B1 contains 2 white chips, bowl B2 contains 2 red chips, bowl B3 contains 2 white and 2 red chips, and Bowl B4 contains 3 white chips and 1 red chip. The probabilities of selecting bowl B1, B2, B3, and B4 are 1/2, 1/4, 1/8, and 1/8 respectively. A bowl is selected using these probabilities, and a chip is then drawn at random. Find P(W), the probability of drawing a white chip P(B1|W): the probability that bowl B1 was selected, given that a white chip was drawn. Q9. A pap smear is a screening procedure used to detect cervical cancer. For women with this cancer, there are about 16% false negative. For women without cervical cancer, there are about 19% false positive. In the US, there are about 8 women in 100,000 who have this cancer. What is the probability that a woman who has been tested positive actually has cervical cancer? Q10. There is a new diagnostic test for a disease that occurs in about 0.05% of the population. The test is not perfect but will detect a person with the disease 99% of the time. It will, however, say that a person without the disease has the disease about 3% of the time. A person is selected at random from the population and the test indicates that this person has the disease. What are the conditional probabilities that The person has the disease The person does not have the disease Q11. Consider two urns: the first contains two white and seven black balls, and the second contains five white and six black balls. We flip a fair coin and then draw a ball from the first urn or the second urn depending on whether the outcome was a head or a tails. What is the conditional probability that the outcome of the toss was heads given that a white ball was selected? Q12. In answering a question on a multiple-choice test a student either knows the answer or guesses. Let p be the probability that she knows the answer. Assume that a student who guesses at the answer will be correct with probability 1/m where m is the number of multiple choice alternatives. What is the conditional probability that a student knew the answer given that she answered it correctly? Q13. A laboratory blood test is 95% effective in detecting a certain disease when it is, in fact, present. However, the test also yields a “false positive” result for 1% of the healthy persons tested (i.e., if a healthy person is tested, then, with probability 0.01, the test result will imply that he has the disease.). If 0.5% of the population actually have the disease, what is the probability a person has the disease given that his test results are positive? Q14. An urn contains b black balls and r red balls. One of the balls is drawn at random, but when it is put back in the urn, c additional balls of the same color are put in it with it. Now suppose that we draw another ball. What is the probability that the first ball drawn was black given that the second ball drawn was red? Random Variables Q15. Suppose an experiment consists of tossing two six sided fair dice and observing the outcomes. What is the sample space? Let Y denote the sum of the two numbers that appear on the dice. Define Y to be a random variable. What are the values that the random variable Y can take? What does it mean if we say Y=7? What does it mean if I say that Y<7? Q16. Suppose an experiment consists of picking a sample of size n from a population of size N. Assume that n≪N. Also, assume that the population contains D defective parts and N-D non defective parts, where n<D≪N. What is the sample space? If we are interested in knowing the number (count) of defective parts in the sample space, describe how, the concept of a random variable could help. Define a random variable Y and describe what values the random variable Y can take? What does it mean if we say Y=5? Q17. Suppose an experiment consists of tossing two fair coins. Let Y denote the number of heads appearing. Define Y to be a random variable. What are the values that the random variable Y can take? What does it mean if we say Y=1? What are the probabilities associated with each outcome? What is the sum of the probabilities associated with all possible values that Y can take? Q18. A lot, consisting of 100 fuses, is inspected by the following procedure. Five fuses are chosen at random and tested: if all 5 fuses pass the inspection, the lot is accepted. Suppose that the lot contains 20 defective fuses. What is the probability of accepting the lot? Define the random variable, its purpose, and the formula/concept that you would use. Q19. In a small pond there are 50 fish, 10 of which have been tagged. If a fisherman’s catch consists of 7 fish, selected at random and without replacement. Give an example of a random variable that can be defined if we are interested in knowing the number of tagged fish that are caught? What is the probability that exactly 2 tagged fish are caught? Define the random variable, its purpose, and the formula/concept that you would use. Applied to Quality Control Q20. My manufacturing firm makes 100 cars every day out of which 10 are defective; the quality control inspector tests drives 5 different cars. Based on the sample, the quality control inspector will make a generalization about the whole batch of 100 cars that I have on that day. Let d denote the number of defective cars in the sample What are the values that d can take (given the information provided above)? What is the probability that the quality control inspector will conclude that: (a) 0% of the cars are defective- call this P(d=0); (b) 20% of the cars are defective- call this P(d=1); (c) 40% of the cars are defective- call this P(d=2); (d) 60% of the cars are defective- call this P(d=3),(e) 80% of the cars are defective- call this P(d=4), and (f) 100% of the cars are defective- call this P(d=5) What is P(d=0)+ P(d=1)+ P(d=2)+ P(d=3)+ P(d=4)+ P(d=5) Let’s assume that the quality control inspector has been doing the testing for a while (say for the past 1000 days). What is the average # of defective cars that he found? Q21. Assume that the quality control inspector is selecting 1 car at a time and the car that he tested is put back in the pool of possible cars that he can test (sample with replacement). Let d denote the number of defective cars in the sample (n) What are the values that d can take (given the information provided above)? What is the probability that the quality control inspector will conclude that: (a) 0% of the cars are defective, (b) 20% of the cars are defective, (c) 40% of the cars are defective, (d) 60% of the cars are defective, (e) 80% of the cars are defective, and (f) 100% of the cars are defective. Let’s call these P(d=0)….P(d=5) What is P(d=0)+ P(d=1)+ P(d=2)+ P(d=3)+ P(d=4)+ P(d=5) Let’s assume that the quality control inspector has been doing the testing for a while (say for the past 1000 days). What is the average # of defective cars that he found? Interesting Problems Q22. A closet contains n pairs of shoes. If 2r shoes are chosen at random (2r<n), what is the probability that there will be no matching pair in the sample? Q23. In a draft lottery containing the 366 days of the leap year, what is the probability that the first 180 days drawn (without replacement) are evenly distributed among the 12 months? What is the probability that the first 30 days drawn contain none from September? Q25. You and I play a coin-tossing game. If the coin falls heads I score one, if tails, you score one. In the beginning, the score is zero. What is the probability that after 2n throws our scores are equal? What is the probability that after 2n+1 throws my score is three more than yours?

## Assignment 2 Conditional Probability, Bayes Theorem, and Random Variables Conditional Probability and Bayes’ Theorem Problems 1-14 from Problem Set on Conditional Probability and Bayes’ Theorem I am including all the question here so that there is no confusion. Q1. Pair of six sided dices are rolled and the outcome is noted: What is the sample space? What is the size of the sample space? Suppose all we are interested in is the sum of the two outcomes. What is the probability that the sum of the two is 6? 7? 8? (Note: This can be solved using both enumeration and conditional probability method). Here, it makes more sense to use the enumeration approach than conditional probability. It is, however, listed here to set the stage for Q5. What is the probability that the sum of the two is above 5 and the two numbers are equal? Express this question in terms of events A, B, and set operators. What is the probability that the sum of the two is above 5 or the two numbers are equal? Express this question in terms of events A, B, and set operators. Q2. If P(A)=0.4, P(B)=0.5 and P(A∩B)=0.3 What is the value of (a) P(A|B) and (b) P(B|A) Q3. At a fair, a vendor has 25 helium balloons on strings: 10 balloons are yellow, 8 are red, and 7 are green. A balloon is selected at random and sold. Given that the balloon sold is yellow, what is the probability that the next balloon selected at random is also yellow? Q4. A bowl contains seven blue chips and three red chips. Two chips are to be drawn at random and without replacement. What is the probability that the fist chip is a red chip and the second a blue? Express this question in terms of events A, B, and set operators and use conditional probability. Q5. Three six sided dices are rolled and the outcome is noted: What is the size of the sample space? What is the probability that the sum of the three numbers is 6? 13? 18? Solve using conditional probability How does the concept of conditional probability help? Q6. A grade school boy has 5 blue and four white marbles in his left pocket and four blue and five white marbles in his right pocket. If he transfers one marble at random from his left pocket to his right pocket, what is the probability of his then drawing a blue marble from his right pocket? Q7. In a certain factory, machine I, II, and III are all producing springs of the same length. Of their production, machines I, II, and III produce 2%, 1%, and 3% defective springs respectively. Of the total production of springs in the factory, machine I produces 35%, machine II produces 25%, and machine III produces 40%. If one spring is selected at random from the total springs produced in a day, what is the probability that it is defective? Given that the selected spring is defective, what is the probability that it was produced on machine III? Q8. Bowl B1 contains 2 white chips, bowl B2 contains 2 red chips, bowl B3 contains 2 white and 2 red chips, and Bowl B4 contains 3 white chips and 1 red chip. The probabilities of selecting bowl B1, B2, B3, and B4 are 1/2, 1/4, 1/8, and 1/8 respectively. A bowl is selected using these probabilities, and a chip is then drawn at random. Find P(W), the probability of drawing a white chip P(B1|W): the probability that bowl B1 was selected, given that a white chip was drawn. Q9. A pap smear is a screening procedure used to detect cervical cancer. For women with this cancer, there are about 16% false negative. For women without cervical cancer, there are about 19% false positive. In the US, there are about 8 women in 100,000 who have this cancer. What is the probability that a woman who has been tested positive actually has cervical cancer? Q10. There is a new diagnostic test for a disease that occurs in about 0.05% of the population. The test is not perfect but will detect a person with the disease 99% of the time. It will, however, say that a person without the disease has the disease about 3% of the time. A person is selected at random from the population and the test indicates that this person has the disease. What are the conditional probabilities that The person has the disease The person does not have the disease Q11. Consider two urns: the first contains two white and seven black balls, and the second contains five white and six black balls. We flip a fair coin and then draw a ball from the first urn or the second urn depending on whether the outcome was a head or a tails. What is the conditional probability that the outcome of the toss was heads given that a white ball was selected? Q12. In answering a question on a multiple-choice test a student either knows the answer or guesses. Let p be the probability that she knows the answer. Assume that a student who guesses at the answer will be correct with probability 1/m where m is the number of multiple choice alternatives. What is the conditional probability that a student knew the answer given that she answered it correctly? Q13. A laboratory blood test is 95% effective in detecting a certain disease when it is, in fact, present. However, the test also yields a “false positive” result for 1% of the healthy persons tested (i.e., if a healthy person is tested, then, with probability 0.01, the test result will imply that he has the disease.). If 0.5% of the population actually have the disease, what is the probability a person has the disease given that his test results are positive? Q14. An urn contains b black balls and r red balls. One of the balls is drawn at random, but when it is put back in the urn, c additional balls of the same color are put in it with it. Now suppose that we draw another ball. What is the probability that the first ball drawn was black given that the second ball drawn was red? Random Variables Q15. Suppose an experiment consists of tossing two six sided fair dice and observing the outcomes. What is the sample space? Let Y denote the sum of the two numbers that appear on the dice. Define Y to be a random variable. What are the values that the random variable Y can take? What does it mean if we say Y=7? What does it mean if I say that Y<7? Q16. Suppose an experiment consists of picking a sample of size n from a population of size N. Assume that n≪N. Also, assume that the population contains D defective parts and N-D non defective parts, where n

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After reading the supplement article on Business Analytics linked to the week 1 schedule, write an essay on how business analytics impacts you today, or its potential role in your chosen career path. Do research for your paper, or interview someone who works in your area. The goals of this paper are two-fold: (1) focus on high quality writing, using the COBE Writing Styles Guide for writing help and citations. (2) consider the importance of BI from a personal/work/career perspective.