Exam #3 Review

(Last Modified: 04 November 2010 06:11:47 PM )

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Note: While we were unable to cover the cascade and the differential amplifier configurations in class and, therefore, you are not expected to have a detailed understanding of their specific behavior (so you may ignore Question #14 below), the fact remains that they are nothing more than transistor circuits and you should be able to perform the basic analysis steps learned in this chapter on ANY transistor circuit - at least in so far as setting up the small-signal equivalent circuits and the resulting equations necessary to determine the midband gain and the upper and lower cutoff frequencies.

Date of exam: 08 May 03

Topics Covered

This exam will cover Chapter 7 sections 7.1 through 7.8. However, this material builds on prior material and there is no way to divorce it from that prior material. The following topic areas will be the source for questions on the exam. Note that some of them represent basic concepts from prior chapters.

As with Chapter 6, we have covered a lot of material in this chapter. Not as much as in Chapter 6 but what we have covered is more complex and more abstract. It would probably be very productive, both in preparing you for this exam as well as giving you a concise review sheet for future reference, to spend some time writing a couple of short sentences (or equations or procedural steps as appropriate) for each of the above topic items. Most of the above topic descriptions can be turned into exam questions very easily. Hint. Hint.

Exam Format and Guidelines

The exam will be closed-book and closed note. At least 1/4 of the points on the exam will be from the following problems verbatim. Not all of these problems are trivial and might take quite a bit of time to solve the first time. But if the exam is the first time you are attempting to solve the problem, that will be the result of a choice you made with full knowledge of the potential consequences. In other words, ignore this review sheet at your own risk.

The exam will consist of a number of multiple choice or short answer questions followed by problem solving questions. The focus is on the fundamental concepts and your grasp of them. I am not looking for you to be able to solve complex problems involving lots of algebra within the framework of an hour exam. If you are getting bogged down in a lot of algebra, then take a step back and look for an easier way - because it almost certainly exists. I am looking for you to be able to apply the fundamental concepts to simple problems in a manner that demonstrates that you would know how to proceed if faced with a more formidable circuit. To that end, I give substantial partial credit if you can describe how to go about solving a particular problem - keep this in mind if you are running out of time. Also keep in mind that if you spend all of your time on Question #3 and don't get to Question #4, 5 or 6, that I cannot give partial credit for problems you didn't even attempt. Read through the entire exam and answer those questions you know how to tackle first. Then at least start all of the other problems by drawing the appropriate circuit diagrams and setting up the problem solution.

Unless specifically stated otherwise, assume that all answers are to be supported. This may be in the form of equations and mathematical manipulation or, if appropriate, through a logical line of reasoning. Just writing down a memorized result will not get full or even most of the credit - though certainly it will get considerably more credit than if no answer at all is given.

The chart on page 601 of the text will be reproduced on the exam for your reference. If there are any other equations or items that you would like to see on the reference sheet bring them to class on Tuesday 06 May 03 and we will decide at that time whether they will be on the reference sheet. The basic equations for the transistor parameters (such as gm, re, rpi and so forth) will NOT be placed on the reference sheet. Neither will the relationship between f_t and the device capacitances. To remember this one just remember that in order to determine a frequency you need an RC time constant and w = 2PI*f = 1/(RC). The C is the sum of the two capacitances that characterize a transistor, namely Cpi and Cmu, and the R is the basic resistive transistor parameter - the transconductance (which is 1/resistance). Therefore f_t = gm/(2PI(Cpi+Cmu)). Make the effort to know this relationship on exam day. After that, look it up if necessary.

Basic Analysis Flow

Note on your circuit diagrams. Most errors in the analysis of these circuits come from incorrect manipulation of the circuit schematic. If helpful, redraw the circuit in a form that might be easier for you to work with - such as the ground node being at the bottom, signal sources being on the left, output nodes being on the right, or whatever. Also, take advantage of any places where you can combine series and parallel components and where you can replace portions of the circuit with a Thevenin (or Norton) equivalent circuit. Don't try to do to much manipulation in a single step - it is far better to draw the circuit two or three times making minor changes at each step than to make careless mistakes because you tried to do too much in your head at one time. Also, be careful not to lose information such as combining two series components when you need the node voltage at their juncture.

  1. Determine the DC bias point conditions
    1. Turn off all signal sources.
    2. Turn on all DC sources (power supplies and bias supplies)
    3. Analyze the circuit to determine the collector current for every transistor in the circuit.
    4. Recognize that, with this collector current, you can determine any other small-signal parameter that might be needed (assuming that you have other device constants such as beta and the Early voltage).
  2. Draw the complete small signal equivalent for the circuit.
    1. Turn off all DC sources used in the Bias Point analysis.
    2. Turn on all signal sources.
    3. Replace all the transistors with any suitable small-signal equivalent.
    4. Make any circuit simplifications that will not be affected by which type of analysis you are doing later.
  3. Determine the Midband Gain
    1. Redraw the circuit with low frequency caps shorted and high frequency caps open.
    2. Redraw the circuit with any additional simplifications that result from the prior step.
    3. Analyze the circuit to determine the gain.
    4. This is the circuit that would also be used to determine the input and output resistances (at signal frequencies).
  4. Determine the Lower Cutoff Frequency
    1. Starting with the complete small signal equivalent circuit (Step 2.4), redraw the circuit with the signal sources turned off, the low frequency caps shown as real, and the high frequency caps open.
    2. Redraw the circuit with any additional simplifications that result from the prior step.
    3. Determine the short-circuit resistance seen by each low frequency cap in turn.
      1. Redraw the circuit from Step 4.2 with all but the target capacitor replaced by a short.
      2. Determine the resistance that is seen by the target capacitor - remember that if any controlled-sources are in play, that you will probably need to replace the target capacitor with a test voltage source and analyze the circuit to determine how much current would flow in that source in order to determine the effective resistance.
      3. That capacitor's time constant is then this resistance multiplied by the capacitance and the frequency is simply the reciprocal of the time constant (in radians per second, not hertz).
    4. The estimate of the lower cutoff frequency is the sum of the frequencies found Step 4.3.3.
  5. Determine the Upper Cutoff Frequency
    1. Starting with the complete small signal equivalent circuit (Step 2.4), redraw the circuit with the signal sources turned off, the high frequency caps shown as real, and the low frequency caps shorted.
    2. Redraw the circuit with any additional simplifications that result from the prior step.
    3. Determine the open-circuit resistance seen by each high frequency cap in turn.
      1. Redraw the circuit from Step 5.2 with all but the target capacitor replaced by an open.
      2. Determine the resistance that is seen by the target capacitor - remember that if any controlled-sources are in play, that you will probably need to replace the target capacitor with a test voltage source and analyze the circuit to determine how much current would flow in that source in order to determine the effective resistance.
      3. That capacitor's time constant is then this resistance multiplied by the capacitance and the frequency is simply the reciprocal of the time constant (in radians per second, not hertz).
    4. The estimate of the time constant associated with the upper cutoff frequency is the sum of the time constants found Step 5.3.3.
  • You need to KNOW the above analysis flow. Don't memorize it, understand it. You should be able to explain some reasonable rationale for the following:
    1. WHY is it reasonable to replace ALL the caps with either opens or shorts when performing the Midband Gain analysis?
    2. WHY is it reasonable to replace the high frequency caps with opens when finding the lower cutoff frequency but the low frequency caps are replaced with shorts when finding the upper cutoff frequency?
    3. WHY do we use short-circuit resistances in Step 4.3 but open-circuit resistances in Step 5.3?
    4. WHY do you sum the frequencies in Step 4.4 but sum the time-constants in Step 5.4?
    5. WHY is it reasonable to perform each analysis in Steps 4.3 and 5.3 with all but one capacitor replaced by an open circuit or a short circuit.

    Review Problems

    1) All homework problems. Be sure that you understand the principles behind the solutions for each. Many are of reasonable difficulty for exam questions and you can count on some of the exam problems either being homework problems or being closely related to homework problems. Certainly long homework problems will not be on the exam in their entirety - but portions of them might be.

    2) The Review for Exam #1 and Exam #1 itself. If you had difficulty on that exam and have failed to correct the deficiencies identified, do not expect to be able to ignore those deficiencies and somehow do well on Exam #2. Remember, much of the analytical steps performed in Chapter 7 are grounded in Chapter 6 (and earlier chapters). Continuing to neglect those issues is done at your own peril.

    Questions 3-9 reference the gain transfer function A(s) = Am * F_L(s) * F_H(s) as it pertains to "appropriate" circuits (i.e., the type we have been working with).

    3) For frequencies above the lower cutoff frequency, what is the magnitude of F_L(s)?

    4) For frequencies below the upper cutoff frequency, what is the magnitude of F_H(s)?

    5) In order for a pole in F_L(s) to be "sufficiently dominant" ("sufficiently" meaning that we can assume that the frequency of the dominant pole is a good estimate of the lower cutoff frequency) what conditions must be met?

    6) In order for a pole in F_H(s) to be "sufficiently dominant" ("sufficiently" meaning that we can assume that the frequency of the dominant pole is a good estimate of the upper cutoff frequency) what conditions must be met?

    7) What simplifications to the full circuit can (usually) be made in order to investigate the midband gain?

    8) What simplifications to the full circuit can (usually) be made in order to investigate the low frequency response?

    9) What simplifications to the full circuit can (usually) be made in order to investigate the high frequency response?

    10) Draw a basic CE single transistor amplifier driven by a capacitively coupled Thevenin source and driving a capacitively resistive load. Be sure to include any necessary biasing circuitry - do NOT use any current sources for this. 

    11) Draw a basic CB single transistor amplifier driven by a capacitively coupled Thevenin source and driving a capacitively resistive load. Be sure to include any necessary biasing circuitry - do NOT use any current sources for this. 

    12) Draw a basic CC single transistor amplifier driven by a capacitively coupled Thevenin source and driving a capacitively resistive load. Be sure to include any necessary biasing circuitry - do NOT use any current sources for this. 

    13) Draw a basic Cascode two-transistor amplifier driven by a capacitively coupled Thevenin source and driving a capacitively resistive load. Be sure to include any necessary biasing circuitry - do NOT use any current sources for this. 

    14) Draw a basic Cascade two-transistor amplifier driven by a capacitively coupled Thevenin source and driving a capacitively resistive load. Be sure to include any necessary biasing circuitry - do NOT use any current sources for this. 

    15) Draw the small signal circuit appropriate for determining the midband gain for each circuit in questions 10-14 above.

    16) Draw the small signal circuit appropriate for determining the lower cutoff frequency for each circuit in questions 10-14 above.

    17) Draw the small signal circuit appropriate for determining the upper cutoff frequency for each circuit in questions 10-14 above.

    18) Given two nodes with a bridging element between them, and given the relationship between the voltages on the two nodes such that V1 = K * V2, SHOW that the bridging element can be replaced with two components where each node has one of these components between it and ground. SHOW what the values of these components must be in terms of the original bridging component's value and the gain K.

    19) Describe the Miller Effect and how it can be detrimental to the frequency response of certain amplifier configurations.

    20) What are two ways of overcoming the Miller Multiplier effect that dominates the basic CE configuration? In other words, why don't the CB and CC configurations suffer from this phenomenon. Not just "what", but "why/how" do these methods work?