Electric Circuits, Fall 2015 Homework #4 Due: Nov. 3, 2015 (Tue., in class)

Transcription

1 RULES: Please try to work on your own. Discussion is permissible, but identical submissions are unacceptable! Please show all intermediate steps: a correct solution without an explanation will get zero credit. Please submit on time. NO late submission will be accepted. Please prepare your submission in English only. No Chinese submission will be accepted. 4.1 [8%] The op amp in Fig. 1 has R i = 100kΩ, R o = 100Ω, A = 100,000. Find the differential voltage v d and the output voltage v o. Fig [6%] Determine the output voltage v o in the circuit of Fig. 2. Fig [9%] In the circuit shown in Fig. 3, find k in the voltage transfer function v o = kv s. Fig. 3 1

2 4.4 [11%] It is common in electronics to convert a current signal into a voltage signal. One case where this is necessary, is when converting the photocurrent generated by a photodiode into a voltage signal for downstream processing electronics. A photodiode acts similar to a normal diode except it converts input optical power into a photocurrent. A photodiode must also be reverse biased for optimal operation. As shown below (Fig. 4.1), we can model a photodiode as an ideal current source with photocurrent given by I ph = R i P opt where P opt is the aborbed optical power [W] and R i is the current responsivity assumed to be 0.9 [Amps/Watt]. Note that I ph flows from the cathode to the anode since the diode is reverse biased. For this problem, we can ignore the diode leakage current. Fig. 4.1 (a) One way to both reverse bias the photodiode and convert the current into a voltage is with the circuit below (Fig. 4.2) in which the photocurrent is sent into a resistor. For this configuration calculate: i) The voltage responsivity, R v = V out P opt ii) A drawback of this configuration is that the diode bias is not constant. Find the input optical power at which the diode is no longer reverse biased. Fig. 4.2 (b) A good way to convert the diode photocurrent into a voltage is with the following transimpedance amplifier (TIA), as shown in Fig For this problem calculate: i) The voltage across the diode. Does it depend on P opt? ii) The transimpedance gain, G = V out I ph iii) The voltage responsivity, R v = V out P opt 2

3 Fig [10%] For the circuit shown in Fig. 5, find the Thevenin equivalent at terminals a-b. (Hint: To find R Th, apply a current source i o and calculate v o.) Fig [10%] Design an op amp circuit such that v o = 4v 1 + 6v 2 3v 3 5v 4 Let all the resistors be in the range of 100Ω to 1kΩ. 3

4 4.7 [11%] Determine v o in the op amp circuit of Fig. 7. Fig [12%] (a) For the following schematic, determine a constraint on R 1, R 2, R 3 and R 4 such that the circuit behaves as a difference amplifier, i.e. v o = K(v 2 v 1 ). (b) Suppose that the resistors values chosen for part (a) are real resistors with 1% precision. What is the common-mode gain? In other words, if the inputs contain a common-mode signal v 1 = V c + v d 2 How much of V c appears at the output? v 2 = V c v d 2 Fig. 8 4

5 4.9 [11%] In the schematic below, the voltage source v s is separated from the load resistor R L by three amplifier stages. We have three different amplifier configurations as shown below. Fig. 9 (a) Suppose we go with the sequence BAC. If R 1 = 2kΩ, R 2 = 6kΩ, R 3 = 4kΩ, and R 4 = 8kΩ, calculate the overall voltage gain for the above circuit. What is the load resistance as seen by the voltage source? (b) Repeat the above calculations for the sequence ABC. Which of the two is better? (c) What is the voltage gain in both cases if we omit the third stage (C)? What is its purpose of having it in the circuit? 4.10 [12%] a) For the circuit shown in Fig. 10, show that if ΔR R, the output voltage of the op amp is approximately v o R f R 2 (R + R f ) (R + 2R f ) ( R)v in b) Find v o if R f = 470kΩ, R = 10kΩ, ΔR = 95Ω, and v in = 15 V. c) Find the actual value of v o in (b). d) If percent error is defined as approximate value % error = [ 1] 100 true value, show that the percent error in the approximation of v o above is e) Calculate the percent error in v o. % error = [ R R (R + R f ) (R + 2R f ) ] 100 5

6 Fig. 10 6