Homework Assignment 06

Transcription

1 Homework Assignment 06 Question 1 (Short Takes) One point each unless otherwise indicated. 1. Consider the current mirror below, and neglect base currents. What is? Answer: 2. In the current mirrors below, neglect base currents and take, What is? (a) (b) (c) (d) Answer: (a) 3. In the current mirrors below, neglect base currents and, What is? Answer: In the current mirrors below, neglect the base currents. What is? Answer: 1

2 5. What is the voltage gain of the amplifier below if and? (3 points) (a) (b) (c) Need additional information (i.e., ) (d) (e) Answer: ( ) ( ) so (e) is the correct answer. 6. True of false: For both the amplifiers below, the voltage gain increases when the drain/collector bias current is increased. 7. The small-signal output resistance of a BJT biased at = 1 ma is100k. What is when the transistor is biased at? Answer: is inversely-proportional to ( ) so that will be smaller at 5 ma, or. 8. Typically, the C-E saturation voltage for a BJT, namely ( ), is in the range of (circle one) (a) V (b) 0.7 V (c) 2 3 V (d) 100 V (e) 250 V Answer: Option (a) 2

3 9. True or false: the Early voltage for a small-signal BJT is in the order of (circle one). (a) 0.7 V (b) 0.2 V (c) 10 V (d) 100 V (e) 250 V Answer: Option (d) 10. Give one phrase/sentence that describes the primary advantage of an active load. Answer: Large effective resistance large voltage gain 11. True or false: assuming that for the amplifiers below, then is larger than. However, also more sensitive to FET parameter variation than. Answer: True 3

4 Question 2 Consider the amplifier shown. The transistor has an Early voltage A dc analysis reveals that, and. Assume that the coupling capacitors are large enough so that they are shorts at the operating frequency. (a) Draw the corresponding small-signal circuit. Incorporate the MOSFETs output resistance. (5 points). (b) Determine the amplifier s voltage gain. (10 points). (c) Determine the amplifier s input and output resistances. (5 points each) Part (a) The small-signal model for the amplifier is shown right. The numerical values for all components are known, except for. However, we can calculate that from. We can lump and together as. Part (b) write a KCL equation at the output node From the small-signal model it is clear that so that the equation above becomes Some algebraic manipulation yields ( ) ( ) Substituting, and yields 4

5 Part (c) Determine the input resistance using the standard procedure: turn off independent sources, drive the circuit with a test source and determine the current that flows. Then,. Referring to the small signal model given above, we can simply replace with and then However, we already determined that so we can write so that Determine the output resistance using the standard procedure: turn off independent sources, drive the circuit at the output with a test source and determine the current that flows. Then,. If we turn off the independent source, namely and add a test source, the model below results. Clearly the control voltage and the current source is off, so KCL at the drain gives Substituting the numerical values give. 5

6 Question 3 You can assume that for all the transistors in the circuit below, is large. Show that. Let and then determine V A, V B, V C, V D,, and Assume ( ) for all the transistors. Further, note that is small: for the purposes on this hand-analysis, ignore its effect. That is, assume. (14 Points) Throughout we will assume ( ) for all the transistors. Further, since is large, we will ignore base currents and take for all the transistors. ( ) ( ), which is mirrored as ( ) is very small, so Thus, Thus, ( ), which is practically the same current that flows through, and We are ignoring the effects of, so that ( ) is the mirror of. That is ( ) ( ). ( ), so ( )( ) Finally, 6

7 Question 4 The open-loop low-frequency gain of an op-amp is 100 db. At a frequency of the magnitude of the open-loop gain is 38 db. The op-amp has a dominant-pole open-loop response. Determine the frequency of the dominant pole and the unity-gain bandwidth. (5 points) Open-loop dominant pole response implies constant GBP, which is The dominant-pole frequency is The unity-gain bandwidth is the same as GBP. Question 5 The datasheet for a 5 V, three-terminal regulator indicate that the output voltage typically changes by 3 mv when the input voltage is varied from 7 V to 25 V, and by 5 mv when the load current is varied from 0.25 A to 0.75 A. Further, the ripple rejection ratio is 78 db at 120 Hz. (a) What is the output resistance of the regulator? (3 points) (b) Estimate the output ripple amplitude for every volt of input ripple at 120 Hz. (4 points) Part (a) ( ) Part (b) ( ) ( ) ( ) Thus, a 1-V, 120-Hz ripple at the input will result in an output ripple of mv 7

8 Question 6 Draw a small-signal model for the following circuit. is a bypass capacitor and for the FET. Be sure to supply all necessary details, polarities of, labeling the gate, source, and drain, an expression for and so on. (5 points) 8

9 Question 7 (Midterm, 2007) shown Consider the amplifier (a) Draw a small-signal model for the amplifier above. (6 points) (b) Derive an expression for the voltage gain (8 points) Account for the output resistance of the transistors, the supply voltage, and as appropriate. is large and may be considered a short Part (a) R 1 and Q 1 is a current source that sets up a current that is mirror through Q 2. We can replace R 1, Q 1, and Q 2 with a current source with output resistance r o2. Further C C is a coupling capacitor and a short at ac. Thus a small-signal model is then: Note: points are subtracted if you leave out a ground terminal, V O, the signs for V π, r o, etc. Part (b) ( ) ( ) ( ) 9

10 Question 8 (Midterm, 2009) shown. Consider the amplifier (c) Draw a small-signal model for the amplifier. (6 points) (d) Derive an expression for the voltage gain (8 points) Account for the output resistance of the transistors, the supply voltage,,, and as appropriate. Hint: Part (a) is large and may be considered a short Note: points are subtracted if you leave out a ground terminal, V O, the signs for V π, r o, etc. In the model is the output resistance of transistor. Part (b) ( ) ( ) ( ) ( ) 10

11 Question 9 The figure below is a plot of the open-loop gain function for the LF357 voltage amplifier. An engineer will use the amplifier in a negative feedback configuration to set the midfrequency voltage gain at 100. Use the plot and estimate the bandwidth of the feedback amplifier.. A gain of 100 is equivalent to a gain of ( ). A horizontal line at 40 db intercepts the LF357 gain curve at 100 khz (see above). Thus, the bandwidth ~ 100 khz. 11

12 Question 10 Determine the output resistance of the source follower. (12 points) To find, follow the standard procedure: turn off all independent sources ( in this case), add a test source and determine. Then,. The small-signal model for the amplifier is shown in (a) below. The gate current is zero, so that is zero, and the small-signal model becomes as is shown in (b). Note that and that is in parallel with. (a) (b) A KCL at the source gives ( ) Rearranging gives 12