Fall 2005 6.012 Microelectronic Devices and Circuits Prof. J. A. del AlamoHomework #9 - November 18, 2005Due: November 30, 2005 at recitation 2 PM latest)(late homework will not be accepted)Please write your recitation session time on your problem set solution.1. [30 points] The figure below shows six possible ways of connecting an npn bipolartransistor that may yield a diode-like behavior. Using the ideal Non-Linear Hybrid-π Model,calculate the I-V characteristics of the two-terminal device in each configuration. Expressyour result as a function of IS, βF, and βR.ABCDEFVVVVVVIII IIIWhich of these configurations exhibit dio de-like I-V characteristics?2. [20 points] Problem P8.10 of Howe & Sodini. Don’t do (e). Do instead:e) Calculate the maximum amplitude of a sinusoidal signal signal applied to the input sothat the output waveform does not clip. What makes the output waveform clip ifthis maximum signal is exceeded?(3. [50 points] I-V characteristics of npn Bipolar Junction TransistorIn this problem, you will characterize the current-voltage characteristics of an npn bipolarjunction transistor through WebLab. This exercise involves three separate phases: (i)measurement and graphing, (ii) SPICE model parameter extraction, and (iii) comparisonof SPICE model with measurements. Take the measurements specified below. When youare happy with the results, download the data to your local machine for more graphing andfurther analysis.Important note: For all mesurements, hold VBE(or VBC) between 0 and 0.9 V , and VCEbetween 0 and ±4 V .Here is your assignment.1. (5 points) Measure and download the common-emitter output characteristics of theBJT. This is a plot of IC(linear scale) vs. VCE(linear scale) with IBas parameter,for positive VCE. Do this for 0 ≤ VCE≤ 4 V and 0 ≤ IB≤ 100 µA with ∆IB=20 µA. In your local machine and using your favorite software tool, graph the outputcharacteristics. Turn in a printout of this graph (graph 1).2. (5 points) Measure and download the common-emitter transfer characteristics of theBJT in the forward active regime (also known as Gummel plot). This is a semilog plotof ICand IB(logarithmic scale) vs. VBE(linear scale). Do this for VCE=2.5 V .Inyour local machine graph the Gummel plot. Turn in a printout of this graph (graph2).3. (5 points) Measure and download the reverse common-emitter output characteristicsof the BJT. This is a plot of IC(linear scale) vs. VCE(linear scale) with IBasparameter, for negative VCE. Do this for −4 ≤ VCE≤ 0 V and 0 ≤ IB≤ 100 µAwith ∆IB=20µA. In your local machine graph the reverse output characteristics.Turn in a printout of this graph (graph 3).4. (5 points) Measure and download the reverse common-emitter transfer characteris-tics of the BJT (also known as reverse Gummel plot). This is a plot of IEand IB(logarithmic scale) vs. VBC(linear scale). Do this for VEC=2.5 V . In your localmachine graph the reverse Gummel plot. Turn in a printout of this graph (graph4).5. (6 points) From the forward and reverse Gummel plots, extract VBEonand VBCon,respectively. Define these voltages as the values of VBEand VBCthat yield IB=10 µA. Derive VCEsat= VBEon− VBCon.6. (4 points) From the forward and reverse Gummel plots, extract the SPICE parametersIS, BF and BR.7. (20 points) Using the SPICE parameter set just derived, play back the characteristicsof the BJT and compare them with the measurement data. Construct the followinggraphs that include both measurements and SPICE model calculations. Use individ-ual dots for the data points and continuous lines for model calculations.graph 5: Common-emitter output characteristics in forward regime. Print this graph.graph 6: Gummel plot in forward regime. Print this graph.graph 7: Common-emitter output characteristics in reverse regime. Print this graph.graph 8: Gummel plot in reverse regime. Print this graph.8. (optional) The SPICE model can by refined by accounting for the finite output con-ductance of the device. From the forward output characteristics, extract the SPICEparameter VA .9. (optional) Replay the common-emitter output characteristics of the device in theforward regime using the SPICE model set that incorporates VA .Additional information and assorted advice• For the SPICE parameter extraction portion of the exercise, there is no need touse an optimizer or any other fancy software. The ideal mo del does not match theexperimental characteristics all that well. Simple extraction algorithms that you candevise should do an adequate job. Make sure the resulting values of the extractedparameters make physical sense.• You have to exercise care with these devices. Please do not apply a higher voltagethan suggested. The BJTs are real and they can be damaged. If the characteristicslook funny, try a different device and let us know.• For research purposes, the system keeps a record of all logins and all scripts that eachuser
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