Twо lоng pаrаllel wires cаrry currents оf 10 A in opposite directions. They are separated by 40 cm. What is the magnitude of the magnetic field in the plane of the wires at a point that is 20 cm from one wire and 60 cm from the other? ( μ 0 = 4 π × 10 -7 T ∙ m/A)
Prоblem 1. (8 pts) - Multiple Chоice Refer tо the figure below, it is аn NMOS inverter circuit, the trаnsistor (M_1), hаs (V_{Th} = 2 V). Determine the required value of (k_n) for (V_{out} = 2) when (V_{in} = 5V). (a) (k_n = 0.025 frac{mA}{V^2}) (b) (k_n = 0.1 frac{mA}{V^2}) (c) (k_n = 0.075 frac{mA}{V^2}) (d) (k_n = 0.55 frac{mA}{V^2}) (e) (k_n = 0.75 frac{mA}{V^2}) (f) (k_n = 0.055 frac{mA}{V^2}) (g) (k_n = 0.128 frac{mA}{V^2}) Problem 2. (8 pts) - Multiple Choice In the four-resistor bias network shown, it is known that (V_{GS} = 3 V). Find the value of (R_D) (in (Omega)) which places the DC bias point, Q ((I_D),( V_{DS})), at (V_{DS} = V_{DS(sat)}). Given data: (V_T = 1 V), (lambda = 0 V^{-1}); (k_n = 2 mA/V^2), (R_S = 1,250 Omega); (a) 250 (b) 400 (c) 500 (d) 600 (e) 750 (f) 1,000 (g) 1,250 (h) 1,500 Problem 3. (8 pts) Multiple Choice Refer to the figure below, assume that the PMOS (enhancement model) has (k_p = 1.5 frac{mA}{V^2}), (R_2 = 1kOmega), (V_{Th} = |2V|) (V_{GS}=|4V|), find the value of (R_1). (a) ( R_1 = 500Omega ) (b) ( R_1 = 750Omega) (c) ( R_1 = 1kOmega) (d) ( R_1 = 1.25kOmega) (e) ( R_1 = 2kOmega) (f) ( R_1 = 3kOmega) (g) ( R_1 = 5kOmega) Problem 4. (8 pts) Multiple Choice Determine the voltage gain (A_v=frac{v_o}{v_i}) of the amplifier shown in the figure. Please, note that in this problem (k=0.8 mA/V^2) (lambda = 0.005 V^{-1}), (V_t=2.0V), and the capacitor values are large. (a) 1.79 (b) -1.31 (c) 1.32 (d) -0.76 (e) 0.56 (f) 2.13 (g) -2.13 Problem 5. (8 pts) Multiple Choice Refer to the figure below, assume that the Op Amp is ideal, (V_{s+}= V_{s-} = 5 V), if (V_p = 3V, V_n = -4V) what is the output voltage (V_o)? (a) (V_o = -1V) (b) (V_o = 1V) (c) (V_o = 0V) (d) (V_o = 7V) (e) (V_o = -7V) (f) (V_o = 5V) (g) (V_o = -5) Problem 6. (8 pts) - Multiple Choice The circuit below with large differential gain is implemented using multiple OP amplifiers and resistors. Find the differential gain (v_o/(v_2 -v_1)): (a) (-frac{R_2}{R_1}left(1+frac{R_3}{R_G} right)) (b) (-2frac{R_2}{R_1}left(1+frac{R_3}{R_G} right)) (c) (frac{R_2}{R_1}left(1+frac{R_3}{R_G} right)) (d) (2frac{R_2}{R_1}left(1+frac{R_3}{R_G} right)) (e) (2frac{R_2}{R_1}left(1+2frac{R_3}{R_G} right)) (f) (-2frac{R_2}{R_1}left(1+2frac{R_3}{R_G} right)) (g) (frac{R_2}{R_1}left(1+2frac{R_3}{R_G} right)) (h) (-frac{R_2}{R_1}left(1+2frac{R_3}{R_G} right)) Problem 7. (8 pts) - Multiple Choice Suppose that (R_1 C=R_4 C=1 mathrm{~s}, R_2 C=frac{1}{3} mathrm{~s}, R_3 C=frac{1}{2} mathrm{~s}), please derive the differential equations of output voltages (x, y) given input voltages (v_{s1}, v_{s2}). (a) (frac{mathrm{d} y}{mathrm{d} t}+x=v_{s1},quad frac{mathrm{d} x}{mathrm{d} t} + 2x + 3y = v_{s2}) (b) (frac{mathrm{d} y}{mathrm{d} t}+x=v_{s1},quad frac{mathrm{d} x}{mathrm{d} t} + 3 x + 2 y = v_{s2}) (c) (frac{mathrm{d} y}{mathrm{d} t}+2x=v_{s1},quad frac{mathrm{d} x}{mathrm{d} t} + 2x + 3y = v_{s2}) (d) (frac{mathrm{d} y}{mathrm{d} t}+2x=-v_{s1},quad frac{mathrm{d} x}{mathrm{d} t} + 2x + 3y = v_{s2}) (e) (frac{mathrm{d} y}{mathrm{d} t}+x=-v_{s1},quad frac{mathrm{d} x}{mathrm{d} t} + 3 x + 2 y = v_{s2}) (f) (frac{mathrm{d} y}{mathrm{d} t}+x=v_{s1},quad frac{mathrm{d} x}{mathrm{d} t} + 3 x + 2 y = -v_{s2}) (g) (frac{mathrm{d} y}{mathrm{d} t}+x=-v_{s1},quad frac{mathrm{d} x}{mathrm{d} t} + 2x + 3y = v_{s2}) (h) (frac{mathrm{d} y}{mathrm{d} t}+x=v_{s1},quad frac{mathrm{d} x}{mathrm{d} t} + x + 3y = -2v_{s2}) Problem 8. (8 pts) - Multiple Choice Find the current-to-voltage conversion gain of (v_2/i_1) (which is independent of the load (R_l)). (a) (- Rleft(1+frac{R_1}{R}+frac{R_2}{R}right)) (b) (Rleft(1+frac{R_1}{R}+frac{R_2}{R}right)) (c) (- Rleft(1+frac{R_2}{R_1}+frac{R_2}{R}right)) (d) (Rleft(1+frac{R_2}{R_1}+frac{R_2}{R}right)) (e) (- Rleft(1+frac{R_1}{R_2}+frac{R_1}{R}right)) (f) (Rleft(1+frac{R_1}{R_2}+frac{R_1}{R}right)) (g) (- Rleft(1+frac{R}{R_1}+frac{R_2}{R_1}right)) (h) (Rleft(1+frac{R}{R_1}+frac{R_2}{R_1}right)) Problem 9. (18 pts) - Free Response Draw the small-signal model for the amplifier circuit shown. Include the external capacitors in the small-signal model, but do not include internal capacitors. Problem 10. (18 pts) - Free Response Based on your small-signal model, derive (tau_{C1}, tau_{C2}) and (tau_{C_3}). Congratulations, you are almost done with Midterm Exam 1. DO NOT end the Honorlock session until you have submitted your work to Gradescope. When you have answered all questions: Use your smartphone to scan your answer sheet and save the scan as a PDF. Make sure your scan is clear and legible. Submit your PDF to Gradescope as follows: Email your PDF to yourself or save it to the cloud (Google Drive, etc.). Click this link to go to Gradescope to submit your work: Midterm Exam 1 Make Up Return to this window and click the button below to agree to the honor statement. Click Submit Quiz to end the exam. End the Honorlock session.