4. (15%) While \( V{C} \) denotes the DC component of the output voltage, \( v{0} \) and \( v{1} \) denote the AC components of the output and input voltages. Determine the small-signal voltage gain \( A{\nu} = v{0} / v{1} \) of the BJT amplifier shown in Fig. 4. Assume the thermal voltage \( V{\mathrm{T}} = 25\mathrm{mV} \), \( V{\mathrm{BE}} = 0.7\mathrm{V} \), \( \beta = 100 \).

5. (10%) Determine the output voltage \( v{0} \) of the circuit shown in Fig. 5. Assume the threshold voltage of the NMOS transistor \( V{\mathrm{TH}} = 1\mathrm{V} \), its transconductance parameter \( k{n} = \mu{n}C_{\mathrm{ox}}(W / L) = 1\mathrm{mA} / \mathrm{V}^{2} \), and neglect the channel-length modulation effect \( \lambda = 0 \).

6. (20%) Determine the small-signal voltage gain \( A{s} \) of the MOS amplifier shown in Fig. 6. The transistor has \( V{\mathrm{TH}} = 3\mathrm{V} \), \( k{n} = \mu{n}C{\mathrm{ox}}(W / L) = 0.25\mathrm{mA} / \mathrm{V}^{2} \) and \( \lambda = 0.02\mathrm{V}^{-1} \), and assume that the coupling capacitors \( C1 \) and \( C2 \) are sufficiently large to shorten the AC signals at their frequencies of interest, and \( A{s} \equiv -g{m}R{L} \), where \( R_{L} \) is AC equivalent resistance.

7. (10%) For the Op-Amp differentiator shown in Fig. 7, show the relation between the input and output as:$$V{\mathrm{out}} = -RC \frac{dV{\mathrm{in}}}{dt}$$

8. (10%) Suppose the sinusoidal voltage and current across an circuit component are $v(t) = V{\mathrm{in}} \cos(\omega t + \theta{\mathrm{v}})$ and $i(t) = I{\mathrm{in}} \cos(\omega t + \theta{\mathrm{i}})$, respectively. Show the average power (over a complete period) delivered to the component is$$P = \frac{V{\mathrm{in}} I{\mathrm{in}}}{2} \cos(\theta{\mathrm{v}} - \theta{\mathrm{i}})$$

1. For a pn-junction in Fig. 1, explain (a) why are there free electrons (holes) on the n-side (p-side), (b) why are there positive (negative) ions on the n-side( p-side) of the depletion region. (10%)

2. Draw the small-signal model and prove the dc gain and -3dB frequency of the circuit in Fig. 2. (10%)

3. Q₁, QREF and QF in Fig. 3 have the same current gain β. Q₁ and QREF have emitter area n•AE and AE, respectively. Assume that the collector current of QF is equal to its emitter current. IREF is the input current, compute the output current Icopy? (10%)

4. Determine the transfer function \( V_{out}(s)/V_{in}(s) \) of the circuit shown in Fig. 4, find the zero and pole frequency? (10%)

5. For the circuit shown in Fig. 5, the input current is IREF that goes into N1. Applying the devices dimensions N1=(W/L), N2=2(W/L), N3=4(W/L), N4=8(W/L), N5=16(W/L), P1=(W/L), P2=2(W/L), where W and L are channel width and length, respectively. What are the currents for N3 and N5, respectively? (10%)

6. Explain (a) drift current, (b) velocity saturation of electrons. (10%)

115年 - 115 台灣電力公司_大學及研究所獎學金甄選_智慧配電物聯網：物聯網系統#147326

115年 - 115 台灣電力公司_大學及研究所獎學金甄選_核工：核工原理#147323

115年 - 115 台灣電力公司_大學及研究所獎學金甄選_地質模擬與風險分析：普通地質學#147320

115年 - 115 國立臺北大學_碩士班一般入學考試試題_資訊工程學系：線性代數與離散數學#147267

114年 - 114 國立臺北大學_碩士班一般入學考試試題_資訊工程學系：線性代數與離散數學#147271

114年 - 114 國立臺北大學_碩士班一般入學考試試題_民俗藝術與文化資產研究所：語文論述能力(民俗與文化)#147240

113年 - 113 國立臺北大學_碩士班一般入學考試試題_資訊工程學系：線性代數與離散數學#147270

113年 - 113 國立臺北大學_碩士班一般入學考試試題_民俗藝術與文化資產研究所：語文論述能力(民俗與文化)#147238

112年 - 112 國立臺北大學_碩士班一般入學考試試題_民俗藝術與文化資產研究所：語文論述能力(民俗與文化)#147239

111年 - 111 國立臺北大學_碩士班一般入學考試試題_資訊工程學系：線性代數與離散數學#147257