Homework Assignment 10

Transcription

1 Homework Assignment 10 Question The amplifier below has infinite input resistance, zero output resistance and an openloop gain. If, find the value of the feedback factor as well as so that the closed-loop gain is 100. For, provide you answer to 3 significant figures. (6 points) Also 1

2 Question 1 For the op-amp below,, and the output resistance is, but the openloop gain is finite. (a) Write the closed-loop gain in the form. (b) What is the expression for (c) If and what is the required and? Provide your answer to 4 significant figures. (d) If decreases by 10%, what is the percent change in Part (a) and (b) The resistors form a voltage divider that generates a voltage at the inverting input. This voltage is subtracted from the input so that the feedback factor is The closed-loop gain is Part (c) [ ] Further Part (d) 2

3 Question 2 For the non-inverting op-amp circuit below, the parameters are, and. Determine and respectively (6 points) Question 3 The open-loop gain and input resistance of the op-amp below is and 1 respectively. What is the closed-loop gain and input resistance? (5 points) This is series-shunt (voltage-voltage) feedback, with. Further,. Thus 3

4 Question 4 The table below summaries the characteristics of a desired amplifier, along with the characteristics of an amplifier in hand. Show that we can meet the desired characteristics and provide a corresponding (10 points) Gain Lower 3-dB frequency Upper 3-dB frequency Change in gain over a range of power supply fluctuations Desired Amplifier Amplifier in hand 20% 150% The specifications require that Gain Sensitivity Sorting through the inequalities shows that any that satisfies will work. In other words, 4

5 Question 5 Consider a general negative feedback system with parameters, and. If the magnitude of A decreases by 20%, show that the corresponding percentage change in is 0.002%. (6 points) and Question 6 A negative feedback amplifier has an open-loop gain of, an open-loop bandwidth of rad/s, and a closed-loop low-frequency gain of Assume the amplifier has one dominant pole, and determine the bandwidth of the closed-loop system. (4 points) The gain-bandwidth product is rad/s The bandwidth when the loop gain is 100 is then ( ) rad/s 5

6 Question 7 A negative feedback amplifier has a closed-loop gain, and an open-loop gain. (a) What is the feedback factor? (4 points) (b) If a manufacturing error results in a reduction of to 10 3, what closed-loop gain results? (4 points) (c) What is the percentage change in corresponding to this factor 100 reduction in? (2 points) Part (a) Part (b) Part (c) Alternative solution 6

7 Question 8 A capacitively-coupled amplifier has a midband gain of 100, a single highfrequency pole at 10 khz, and a single low-frequency pole at 100 Hz. Negative feedback is employed so that the midband gain is reduced to 10. What are the upper and lower 3-dB frequencies of the closed-loop gain? (6 points) The open-loop gain is shown in red in the figure, and the closed loop response is in black. Beyond the 10 khz pole, the amplitude drops at 20 db/decade, or equivalently, by a factor 10 for every decade. Thus, when the gain has dropped a factor 10, frequency is one decade above the 3-dB frequency (point b). One decade above 10 khz is 100 khz. A similar argument shows that the closed-loop, low frequency 3-dB frequency is 10 Hz (point a). Question 9 An op-amp has an open-loop low-frequency gain of A = 10 5 and an open loop, 3-dB frequency of 4 Hz. If an inverting amplifier with closed-loop low-frequency gain of uses this op-amp, determine the closed-loop bandwidth. Assume the amplifier has one dominant pole. (4 points) The gain-bandwidth product is is.. The bandwidth of the closed-loop amplifier is then 7

8 Question 10 A newly constructed negative feedback amplifier undergoes a performance test with the following results. With the feedback connection removed, a source signal of 2 mv is required to provide a 10 V output to the load; with the feedback connected, a 10 V output requires a 200 mv source input. For the amplifier, identify values of the open-loop gain the closed-loop gain, the feedback factor and the loop gain. (8 points) Question 11 A transconductance (voltage input, current output) amplifier has a gain of 800. After adding negative feedback, measurement shows that the gain is 25. Determine the value of the feedback factor β. Be sure to supply the units. (5 points) Solve for β and find 8

9 Question 12 An amplifier with 10% negative feedback has an open-loop gain of 3,000. If the open-loop gain increases by 10%, what is the percentage change in the gain with feedback? (4 points) Alternate solution Closed-loop gain before 10% change: Closed-loop gain after 10% change Percentage change in closed-loop gain: 9

10 Question 13 Consider an op-amp having a single-pole open-loop response with and an open-loop 3-dB bandwidth 10 Hz. The amplifier is ideal otherwise. The amplifier is connected as a unity gain buffer. Find the frequency at which. Also, find the phase margin. Because has the same reponse as the open-loop amplifier. From the plot, at f = 10 6 Hz. The phase at f = 10 6 Hz is, leaving another is before the phase shift becomes is and making the amplifier unstable. Thus, the phase margin is. 10