# (e V BC/V T. α F I SE = α R I SC = I S (3)

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1 Experiment #8 BJT witching Characteristics Introduction pring 2015 Be sure to print a copy of Experiment #8 and bring it with you to lab. There will not be any experiment copies available in the lab. Also bring graph paper (cm cm is best). Purpose In this experiment, you will measure some of the important parameters of a bipolar transistor, and to study a general large-signal model, the Ebers-Moll model, that we can then simplify to obtain working models for switching circuits. Parts 1 - TN3019A NPN transistor 2-1N270 Germanium diode Theory 1. The Ebers-Moll (EM) Model of a Bipolar Transistor The basis for the models that we use in studying transistor circuits is referred to as the Ebers-Moll model and is shown in Figure 1. It contains two diodes (D E and D C ) and two controlled current sources whose contract is to deliver currents that are proportional to the currents flowing in the diagonally located diodes. These current sources represent the effects of transistor action. Without them the model would simply reduce to two back-to-back diodes. The diodes in the model are idealized p-n junction diodes, and therefore the diode currents are given by: ) I DE = I E (e V BE/V T ) I DC = I C (e V BC/V T (1) (2) ThevaluesI E andi C aresaturationcurrentvaluesthatareconstantatagiventemperature. The reference directions of voltages V BE and V BC are chosen so that when they are positive the diodes are forward-biased. A relationship exists between the four parameters of the EM model and the transistor scale current I α F I E = α R I C = I (3) The currents flowing at the emitter and collector terminals can be written directly from the model in Figure 1 as follows: I E = I DE α R I DC (4) I C = I DC +α F I DE (5) drafted by Dr. Vahe Caliskan 1 of 4

2 Experiment #8 BJT witching Characteristics pring 2015 where I DE and I DC are the diode currents defined in (1) and (2). By combining expressions in (1) (5), the terminal currents can also be expressed in terms of the applied voltages V BE and V BC as I E = I ( ( ) e V BE/V T ) I e V BC/V T α F ) I C = I (e V BE/V T I ( ) e V BC/V T α R (6) (7) The base current can be determined from Kirchhoff s current law and is found to be Hence, using (4) and (5), I B = I E I C (8) or using Eqs. (6) and (7), I B = I DE (1 α F )+I DC (1 α R ) (9) I B = I ( ) e V BE/V T + I ( ) e V BC/V T β F β R (10) where β F = α F 1 α F (11) β R = α R 1 α R (12) Equations (6) and (7) describe what is called the Ebers-Moll (EM) model of the transistor. This mathematical model provides very useful general relationship that applies to a transistor under any bias condition. However, as was true for diodes, we find that some key approximations can greatly simplify the model while keeping it accurate enough for many applications. Our modified models will permit us to do this. 2. Normal-mode Active-region Models We define the normal-mode active region for the following conditions: (a) Base-Emitter Voltage V BE is equal to or larger than the threshold voltage of diode D E. (b) Base-Collector Voltage V BC is less than the threshold voltage of diode D C. In this latter case I DC can be treated as zero. Hence in Figure 1 the diode D C and the current source α R I DC can be dropped out of the model to give us the model shown in Figure 2. Under these conditions the expression for I C becomes Hence, from (11) I C = α F I E = α F I B 1 α F (13) drafted by Dr. Vahe Caliskan 2 of 4

3 Experiment #8 BJT witching Characteristics pring 2015 I C = β F I B (14) The term β F is called the forward (as opposed to reverse) dc current gain of a transistor and is a parameter most commonly given on discrete-transistor data sheets. On transistor data sheets, this parameter is sometimes called h FE. Nevertheless, common practice is to refer to this as beta (β). In digital ICs, β F is centered around approximately 60, while for the linear ICs it is approximately 200. If necessary, the value of α F can be determined from by β F by transposing (11) to obtain α F = β F β F +1 (15) 3. Inverted-mode Active-region Model In certain applications of transistors we will find that the collector is forward-biased and the emitter is reverse-biased. This condition is referred to as inverted operation. The operating conditions are then (a) V BC is equal to or larger than V BC,on. (b) V BE is less than V BE,on. Hence, I DE is treated as zero, and we have the model given in Figure 2. In a completely analogous fashion as in the normal-mode active-region model, we express as I E as I E = I 1 = α R 1 α R I B = β R I B (16) For digital ICs, β R is usually less than 1 and can be as low as For discrete transistors β R can range from 1 to 10. We shall find in later experiments that a low value of β R is desirable for the input transistors in a popular family of digital ICs. 4. The aturation Mode Consider first the normal saturation mode. In the circuit of Figure 3(a) if a current I B is pushed into the base and if its value is sufficient to drive the transistor into saturation, the collector current I C will be smaller than β F I B. The parameter σ defined as follows σ = I C β F I B (17) serves as a measure of the extent to which the transistor has been driven into saturation. As long as σ = 1 (that is, I C = β F I B ), the transistor is in its active region. As σ decreases below unity, the transistor is driven progressively further into saturation. In saturation both junctions are forward-biased. Thus V BE and V BC are both positive, and their values are much greater than V T. Thus in (7) and (10), we can assume that e V BE/V T 1 and e V BE/V T 1. Making these approximations and substituting I C = σβ F I B results in two equations that can be solved to obtain V BE and V BC. The saturation voltage V CE,sat can be then obtained as the difference between these two voltage drops: V CE,sat = V t ln drafted by Dr. Vahe Caliskan 3 of 4 σβ F β R + 1+β R β R 1 σ (18)

4 Experiment #8 BJT witching Characteristics pring 2015 The transistor in the circuit of Figure 2(a) will saturate (that is, operate in the reverse saturation mode) when the emitter-base junction becomes forward-biased. In this case I 1 < β R I B. Procedure 1. Construct the circuit of Figure 4 and determine the parameters β F = I C /I B and V BE,on as a function of collector current I C. Use I C values of 0.5, 1, 2, 5, 10, and 20 ma. Adjust R and V BB to set the I C values. Fill in the table below with the values obtained in the experiment. R (Ω) V BB (V) I C (ma) I B (µa) β F V BE,on (V) 2. Reverse the emitter and collector leads of the transistor to determine β R = I 1 /I B for I 1 = 0.1, 1, and 10 ma. R (Ω) V BB (V) I 1 (ma) I B (ma) β R Measure V BE,sat and V CE,sat as a function of σ = I C /(β F I B ) in the circuit of Figure 5. Record these in the table below. Also, calculate V CE,sat using (18) by choosing typical values from the data from Part 1 and 2 for β F and β R. Make a graph of V CE,sat vs. σ. Compare the graph computed with (18) to the actual experimental curve. Do the measured and calculated values agree? If not, explain why? I C (ma) σ I B (ma) V CE,sat (V) V CE,sat (V) V BE,sat (V) (measured) (calculated) (measured) Report In your report state the results of Parts 1 and 2 above. Do the comparison requested in Part 3. Also, try to make estimates for the parameters in the Ebers-Moll model of Figure 1. drafted by Dr. Vahe Caliskan 4 of 4

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