University of Pittsburgh

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1 University of Pittsburgh Experiment #8 Lab Report The Bipolar Junction Transistor: Characteristics and Models Submission Date: 11/6/2017 Instructors: Dr. Minhee Yun John Erickson Yanhao Du Submitted By: Nick Haver & Alex Williams Station #16 ECE 1201: Electronic Measurements and Circuits Laboratory

2 Introduction This lab is the introduction to working with a bipolar junction transistor, in this case the 2N2222 transistor. In the lab, the bipolar junction transistor (BJT) was analyzed with the curve tracer and then by hand to capture an idea of its functionality. Then the transistor was analyzed using small signal models to get an understanding of its functionality under various conditions. Purpose The purpose of this lab was to establish the value of the constant β, defined as the ratio of collector current to base current, and compare the curve tracer to manual measurements for the BJT circuit show in Fig. 1. Then, using this information allows for analysis of the transistor for various base currents to see how this would affect base-emitter voltage, which is often treated as a constant in analysis, and other BJT circuit parameters. Procedure First, the values for the various parts of the transistor were analyzed under ideal circumstances to get an idea of how the circuit will act. This was done assuming V CC = 10 V and V BB = 1.7 V, with V E attached to ground. The transistor was then measured by picking a value V BB, and then varying V CC and measuring the resulting I C, I E, I B, and V BE values. The curve tracer was used at the beginning of the experiment to analyze the base-emitter input characteristics, shown in Fig. 2, and then to analyze the transistor as a whole for different values of I B, as shown in Fig. 3. Then β was determined using Eq. 1. β = I C = 6 ma = (1) I B 35 µa Next, the rest of the values in the circuit were calculated using the new β. V E remains grounded so that is still 0V and V B is treated as a constant which does not change either. I B = k = 0.01 ma (2) I c = β I B = ma (3) I E = I C + I B = ma (4) The circuit in Fig. 1 was then constructed on the protoboard and connected to the DC power supply, with grounds for V BB and V CC connected. V CC was set to 10 V and then V BB was modified to attain a base current of 10 µa. V BE was then measured. V CC was then varied to move V CE over the range of 0 12 V. Measurements of both V CE and I C were taken over this range to simplify later analysis, as outlined in Table 1. These two steps were then repeated with different base currents of 4, 6, and 8 µa, shown in Tables 2, 3, and 4, with measurements of V CE and I C being taken at multiple points for all three sets of measurements. I C vs V CE for each of the four base currents were plotted, as shown in Fig. 4. Using the measurements from the previous three steps, the value of β was measured again to see how it matches up with the curve tracer. The values from the set of measurements with a base current of 6 µa were then used to determine g m, r, r o and the Early voltage V A from the following equations. g m = β I B V BE = 1.62 ms (5)

3 r π = β g m = kω (6) V A = V CE I C βi B 1 = 5 V (7) r o = V A I C = 4.95 kω (8) This step was then repeated for base current values of 4 and 8 µa. The values were then predicted for a doubled I C current using the same equations as before. Summary of Results Figure 1: BJT Circuit Analyzed in Experiment 8 Figure 2: Collector-Emitter Current Analysis of BJT Figure 3: Analysis of BJT for Different Values of Base-Emitter Current For a V CC of 10 V and a base current of 10 µa, V BB = V and V BE is measured at volts.

4 Table 1: Values of VCE and IC for Various Voltages of VCC When IB = 10 µa IB = 10 µa I B β = V BB V V V BE Table 2: Values of VCE and IC for Various Voltages of VCC When IB = 8 µa IB = 8 µa I B β = V BB V BE Table 3: Values of VCE and IC for various voltages of VCC when IB = 6 µa IB = 6 µa I B β = V BB V BE Table 4: Values of VCE and IC for various voltages of VCC when IB = 4 µa IB = 6 µa I B β = V BB V BE

5 Figure 4: Graph of IC vs VCE for the Four Different Base Currents Measured Figure 5: Hybrid-π Representing the Physical Meaning of the Values from Table 5 Table 5: Values of the Small Signal Model IB (µa) VCE (V) β VBE (V) Gm (ms) Rπ (Ω) Ro (kω) VA (V) Conclusion Analyzing the value of β from the curve tracer compared to the hand measured values yields a close match, with all of the values of β varying by less than 2%. The small variation may be due to small differences when measuring by hand, or also the fact that although in an ideal bipolar junction transistor, it is expected that beta is static, in the practice it will vary slightly as the material deal with varying voltages. When measuring V CE and I C for different levels of base current, the resultant graph came out as expected, matching the original curve tracer as higher base currents resulted in a greater I C gain. Since I C is proportional to I B based off the constant β, this result follows accordingly. Also, as I B was modified, the voltage V BE varied slightly throughout the experiments. In ideal analysis for a silicon bipolar junction transistor, V BE is considered to be 0.7 V. However, in the experiments it is seen that it is slightly below this value. In application, the

6 transistor is non-ideal, and so even when in the operating region it will vary slightly as the transistor gets closer and further from its saturation point. They hybrid pi model is a method of analyzing bipolar junction transistors as a collection of resistors and a single simplified gain. This model is useful because once the values are ascertained for the model. The model can then also be used to analyze values for ac current at lower frequencies, however this is not performed in this lab so we do not yet know how accurately they are represented yet. When analyzing the simplified pi model, if one decides to take the dc collector current and assume it to be doubled with the base current remaining the same, then β would become about twice the value of the actual measurements across the transistor. This is again because I C and I B are proportionally related by β. References ECE 1201 Website: