4.(30%) Figure 3 shows the common-source amplifer with an ideal current source I = 0.4 mA, = 200 kΩ, R_G = 2 MΩ, R_D =R_L = 20 kΩ, C₁ = C₂ = C₃ = 1 HF. The MOSFET has the device parameters: I = 0.2 μm, W = 2 μm, = 10 fP/μm², μn = 450 cm²/V-s, r₀ = 100 kΩ, = 3.2 fF, can be neglected, and the source terminal of MOSFET is connected to its body terminal. Please calculate (1) the transconductance gm of the MOSFET, (2) the A_M，  f₁，f₂，f₃ (let f₁ ＜f₂＜f₃) values of the overall low- frequency transfer function , (3) the upper 3-dB frequency fr by using open-circuit time constants method. (5%, 5%*4, 5%) 

1. (25%) Consider an ideal Si p-n diode with abrupt junction at T = 300 K (VT= 25.9 mV) for which the doping concentrations are NA =. The cross-sectional area A = 100 μm2. When this p-n diode is reverse biased with the reverse voltage VR = 1 V, please calculate the depletion width of n-side Wn and p-side Wp, the charge stored on each side of the depletion region QJ, the reverse saturation current Is and the junction capacitance Cj. Let Si intrinsic concentration ni = 1.5 cm , and Si permittivity εsi = 11.7 x 8.85 xF/cm. Diffusion length and diffusion coefficient of electron in p-side are Ln = 10 pum and Dn= 18 cm2/s, respectively. Diffusion length and diffusion coeticient of hole in n-side are Lp = 5 um and Dp = 10 cm2 /s, respectively. (Wn, Wp, QJ, Is, Cj: 5%*5)

2. (30%) Figure 1 shows a four-stage bipolar op-amp circuit. If all transistors are operating in the active n with the same B = 100, and VT= 25mV.(1) Please perform an approximate dc analysis PoEl =0.7 V, and neglecting the Early effect) to calculate the quiescent power dissipation in this cireuit, (2) What is the input common mode voltage range of this op-amp? (3) Calculate the voltage gain of the first stage and (4) the overall voltage gain. (5%, 5%, 5%, 15%)

3. (15%) Figure 2 shows a peak rectifier fed by a 100-Hz sinusoid having a peak value Vp = 120 V. The load resistance R = 20 kΩ. The output voltage shows a peal-to-peak ripple of 1.5V. Please calculate (1) the value of the capacitor C, (2) the fraction of the cycle during which the diode is conducting, (3) the average of the diode current. (5%, 5%, 5%)

4. (30%) Figure 4 shows a CC-CE amplifier with = RL = 5 kΩ, I1 = I2 = 1mA, and identical transistors with β = 100, fT = 500 MHz, Cμ = 5pF, and Cc = 2uF. The thermal voltage VT= 25mV. For simplicity, neglect ro and rx effect. Please find (a) the input resistance(b) the midband gain AM, (c) the Cπof the BJTs, and (d) 3-dB frequency of the upper end of the midband, fH (using open-circuit time- constants method). (5%, 5%, 5%, 15%)

3. (30%) Figure 3 is the two-stage CMOS op amp configuration. All NMOSFETs have the same W/L = 10um/0.5um, = 0.5V, = 200 uA/V2. All PMOSFETs have the same WIL = 40um/0.5pμm, = -0.5V, = 50 μA/V2. IVAI (for all devices) = 100μ.A. Neglect the effect of VA on bias current. Please find (a) the transconductance gm and ro of Q2, (b) the voltage gain of the furst stage A1 and the second stage A2, (c) the input common-mode range, and (d) the output voltage range.(10%, 10%, 5%, 5%)

2.(25%) Consider the voltage amplifier of Figure 2 with a BJT device having β =100 when it is biased in the active region, the AC signal voltage Vsig, signal resistance = 10kΩ and coupling capacitors and which can block DC component and pass AC component. The voltage supplies = 10V and the thermal voltage VT= 25mV. The constant voltage drop 0.7V approximation can be used for the turn- on of a p-n junction, and the constant voltage drop ~ 0.2V approximation can be used when the BJT is biased in the saturation region. In addition, other resistances are also included, such like R1 = 2MΩ, R2 = 2MΩ, RE = 5kΩ, Rc = 5kΩ, RL= 5kΩ. Please come out following parameters: (a) transconductance gm, (b) input resistance, (c) overall AC voltage gain (d) Please describe the advantages of the existing of emitter resistance Re compared with no RE. (5%, 5%, 5%, 10%)

1. (15%) Figure 1 shows the inverting configuration voltage amplifier with R = 1 kΩ. (a) Please find the close loop gain of Vo/VI if the operational amplifier (op amp) is ideal. (b) Please find the close loop gain of Vo/VI  if the open loop gain of op amp is 10 V/V. (c) If the op amp is a low-pass STC withT , please find the high frequency close loop gain of Vo/VI at f= 1 GHz. (5%, 5%, 5%)  

4.(30%) Consider the BiCMOS amplifier shown in Fig. 4 has= 100 kΩ, RG = 10 MΩ, Rs = 6.8 kΩ, Rc = 3kΩ, RL= 1 kΩ, CI= 0.1 μF, C2 = 1 μF. The BJT has 0.7 V, β = 200, Cμ = 0.8 pF, fT = 600 MHz, and thermal voltage VT= 25 mV. The MOSFET has = 1 V, = 2 mA/V2, and= 1 pF. Neglect the Early effect and channel length modulation effect. (a) Consider the DC bias circuit. Neglect the base current of Q2 in determining the current in Q1. Find the DC drain current in Q1 and collector current in Q2. (b) Consider the circuit at low frequencies. Deternine the frequency of the poles due to C1 and C2. (c) Consider the circuit at higher frequencies. Use open-circuit time constants to estimate fH. (5%,5%,5%,5%,10%)

3.(30%) The amplifier shown in Fig. 3 has =RL = 1 kΩ, Rc= 1 kΩ, RB = 47 kΩ. The BJT has 0.7 V, β= 100, Cμ = 0.8 pF, fT = 600 MHz, and thermal voltage VT = 25 mV. Assume the coupling capacitors to be very large. Neglect the Early effect. (a) Find the collector current of the transistor. (b) Find the overall gain vdvsig and the input resistance at midband frequency. (c) Find the high frequency response fH. (5%,5%,10%,10%)

2.(20%) Figure 2 shows a BJT circuit with the = 200 kΩ, RE = 5kΩ, Rc =2 kΩ, RL= 5 kΩ. The BJT has0.7 V, β = 100, thermal voltage VT = 25 mV. Neglect the Early effect. (a) Please find the DC collector current Ic. (b) For AC analysis, please find the input resistance Rin, output resistance Rout and overall gain . (5%*4)

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