(a) Fiud an orthonormal basis for W.

(b) Find the projection matrix onto W.

(c) Compute the projection of v = (1, 1,0, 1)T on W.

1.(20pt) Figure 1 is a summing op-amplifier to produce the output v0 = -10v1 -4v2+5v3 + 2v4・ The resistors R1 = 20 kΩ and R3 = 80 kΩ. The op-amplifier is ideal. Please determine the values of resistors R2, R4, R5 and R6. (5pt*4)

2.(30pt) For the circuit shown in Figure 2, the transistor parameters of Q1 and Q2 are: = 1.2 V, = 1.6 mA/V2, and neglect channel length modulation effect. Let R1 + R2 + R3 = 300 kΩ and Rs = 10 kΩ. = 5 V, -Vs =-5 V. (a) Please determine the R1, R2, R3 and RD such that DC current ID = 0.4 mA and DC voltage Coupling capacitor Cc is large enough that can be treated as short circuit for AC analysis. Please also find the voltage gain of small signal. (5pt*6)

3.(25pt) The circuit configuration to be designed is shown in Figure 3 and the = -40. Assumingβ = 100, 0.7 V, and neglect Early effect. Thermal voltage VT = 26 mV. Please find the value of = 4 V and IE = 0.2 mA. And calculate the corresponding values of the AC voltage gain input resistance . Coupling capacitor Cc is large enough that can be treated as short circuit for AC analysis. (5pt*5)

4.(25pt) For the circuit shown in Figure 4, the parameters are: = 0.1 kΩ, R1 = 40 kΩ, R2 = 5.72 kΩ, RE = 0.5 kΩ, Rc = 5 kΩ, and RL = 10 kΩ. The transistor parameters are: β = 150,  0.7 V, neglect Early effect, Cπ = 35 pF, Cμ = 4 pF, Cc= 1 μF. Thermal voltage VT = 26 mV. Please determine the lower and upper corner frequency (fL and fH), midband gain. (10pt, 10pt, 5pt)

1. Consider an n-channel MOSFET with 15um gate width and 2um gate length. The oxide capacitance is . If the MOSFET is operated in a non-saturation region with a drain-to-source voltage = 0.1V. The drain current ID = 35 μA at gate-to-source voltage = 2.5V,  ID = 75 μA. Determine the (a) electron mobility (b) threshold voltage (20%)

2. Consider a contact between tungsten and n-type GaAs. The metal work function of tungsten is 4.55 V. Assume the GaAs is doped to a concentration of and the metal-semiconductor diode is operated under zero bias. Determine the (a) theoretical barrier height (b) built-in potential barrier (c) maximum electric field (20%)

3. An npn silicon (Er = 11.9) bipolar transistor (shown in Fig. 1) at T = 300K has uniform dopings of . The transistor is operating in the inverse- active mode with = 0.565 V. (a) Determine the minority carrier concentrations at x = xB and x" = 0(b) If the metallurgical base width is 1.1 um, determine the neutral base width (20%)

4. Consider an n-type semiconductor at T = 300K in thermal equilibrium. Assume that the donor concentration varies as over the range and L = 10 μm. (a) Determine the electric field as a function of x for 0 ≤x  ≤ L(b) Calculate the potential difference x = 0 and x = L (with the potential at x = 0 being positive with respect to that at x = L) (20%)

114年 - [無官方正解]114 臺灣綜合大學系統_學士班轉學生考試試題:線性代數#137898

112年 - 112 國立台灣大學_碩士班考試入學試題:線性代數(A)#130266

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110年 - 110 國立清華大學碩士班考試入學試題_數學系碩士班:線性代數#105741

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110年 - 110 國立中央大學_碩士班招生考試_數學系/數學、應用數學組(一般生、在職生):線性代數#105306

110年 - 110 國立清華大學碩士班考試入學試題_數學系:線性代數#104957

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110年 - 110 國立中山大學碩士暨碩士專班招生考試_應數系碩士班/丙組:線性代數丙#104308