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Electric Circuits, Fall 2017 HW3 Due: Nov. 1, 2017 Wednesday (In Class)

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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.

1. [6%] Use the following three different methods to find i in Figure 1. (a) Node Method (b) Superposition (c) Alternate Thevenin/Norton Transformations

Figure 1

Solution:


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2.[8%] For the circuit shown in Figure 2, use superposition to find v in terms of the R’s and source amplitudes.

. Figure 2

Solution:

3.

V


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3. [6%] Find the Norton equivalent for the circuit in Figure 3-1 and Figure 3-2

Figure 3-1 Figure 3-2

Solution: (1) Sincetherearenoindependentsources, I 0

Since V 1 , V V,

i 0.5 ∗ ∗ 20 i 0.3A,

Thus, R.

Ω

(2)


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4.[6%] For the bridge circuit shown in Figure 4 find the load RL for maximum power transfer and the maximum power absorbed by the load.

Figure 4

Solution:


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5.[8%] A resistance array is connected to a load resistor R and a 9-V battery as shown in Fig.5 (a) Find the value of R such that = 1.8 (b) Calculate the value of R that will draw the maximum current. What is the maximum current?

Figure 5

Solution:


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6. [7%] Calculate v in this circuit.

Solution：

0 0 0 0

(


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7.[7%] For the circuit, find the Thevenin equivalent at terminals a-b. (Hint: To find R , apply a current source i and calculate V .)

Solution：


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8.[7%] In the circuit, find k in the voltage transfer function v = k .

Solution：


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9.[7%] Determine the gain v /v of the circuit.

Solution:


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10.[7%] Determine v in the op amp circuit.

Solution:


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11. [10%] The circuit in Figure 11 is called a differential amplifier. a) Using the ideal Op Amp model, derive an expression for the output voltage vo in terms of v1, v2, R1, R2, R3, and R4. b) Does connecting a load resistor RL between the output and ground change the previous expression for vo? Why? c) Let v1 = v2 and R1 = 1 kΩ, R2 = 30 kΩ, and R3 = 1.5 kΩ. Find R4 so that vO = 0. d) Let v2 = 0 and v1 = 1 V. Using the preceding resistor values (including that computed for R4), find vO.

Fig. 11

Solution:

a) V

15V,v 15V

, 15 ＜ 15

15V,v 15V

b) No. The derivation for v is not affected by the addition of R .

c) R 45

d) v 15 , since the op amp. Saturates here, v cannot be more negative.


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12.[7%] Consider the circuit in Fig. 12. vA=0.1V. vB=0.2V. Find vO assuming that all Op Amps are ideal and operating in the linear region.

Fig. 12

Solution:


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13.[7%] The circuit shown in Fig.13 is very similar to the standard non-inverting Op Amp except that RL is some external resistor, and we are interested in showing that the current through RL is nearly constant, regardless of the value of RL, that is, the circuit acts like a current source for driving RL.

Fig.13 a). Using the ideal Op Amp assumption of large gain, zero output resistance, infinite input resistance, show that the expression for as a function of VL is independent (or weakly dependent) on RL. b). To verify the “current source” action more directly, find the Th’evenin equivalent resistance looking to the left of terminals AA’, with RL an open circuit. Solution:


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14.[7%] For the circuit in Fig. 14 find vo in terms of v1 and v2. You can use in your analysis the ideal Op Amp model.

Fig. 14

Solution:

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