Analyze the following common-gate amplifier. (Ignore the channel length modulation effect, λ = 0) a) Draw the Small signal model of the amplifier. b) If it is known that ID is 0.5 mA and Kn = 1 mA/V2, find the values of the input resistance Rin and the overall gain Gv.
Ex 4.10: Consider the circuit shown in Figure 4.35 with circuit parameters V+ = 5 V, V− = −5 V, RS = 4 kΩ, RD = 2 kΩ, RL = 4 kΩ and RG = 50 kΩ. The transistor parameters are: Kp = 1 mA/V2, VTP = −0.8 V, and λ = 0. Draw the small-signal equivalent circuit, determine the small-signal voltage gain Av = Vo/Vi, and find the input resistance Ri. (Ans. Av = 2.41, Ri = 0.485 kΩ)
Q6. For the amplifier circuit shown in Fig. Q6, the MOS Transistor Ml has the following parameters: Kn = 1 mAV−2, and VTHN = 1 V. MOS transistors M2 and M3 are identical and have the following parameters: Kp = 1 mAV−2, and VTHP = −1 V. Fig. Q6 (a) Perform the DC analysis of the amplifier circuit shown in Fig. Q6, and show that the DC gate voltage of Ml is 5 V. You need to explain briefly your answer. (b) Calculate the value of RS such that the drain current of MI is 4 mA. Verify that the Ml is operating in the saturation region. [ Ans: Rs = 0.5 kΩ] (c) Calculate the parameters, gm and ro, of the small-signal model of the transistor Ml. [Ans: gm, M1 = 4 mAV−1, and ro, M1 = ∞ ] (d) What is the configuration of this amplifier? (e) Calculate the values of Rin , and Rout . [Ans: Rin = 5 kΩ and Rout = 2 kΩ ] (f) Estimate the voltage gain, Av( = vout /vin ). [ Ans: AV = −1.78]
Q2. Consider the amplifier shown in Fig. Q2. The npn bipolar junction transistor has the following parameter values: β = 100, VA = 100 V. Fig. Q2 (a) For the maximum power transfer to load, RL, what should Rout be? [ Ans: Rout = 100 Ω] (b) To have the desired Rout of part (a), what should the specified gm, Q1 be? (You may need to make some assumption for resistors R1, R2 and RE ) [Ans: gm,Q1 = 10 mA/V] (c) What is the amplifier configuration? Sketch the equivalent 2-port network of the amplifier circuit in Fig. Q2. (d) Set R1 = 100 kΩ and RE = 5 kΩ, calculate R2 to complete the design. [Ans: R2 = 64 kΩ] (e) Calculate the input resistance of the amplifier, Rin. [ Ans: Rin≈13.2 kΩ] (f) Calculate the voltage gain vout /vs. [ Ans: vout/vs ≈ 0.49]
Q3. Figure Q3 shows a single-stage amplifier with current mirror biasing. For the two p channel MOSFETs, VTHP1 = VTHP2 = −1 V, λP1 = λP2 = 0, Kp,M1 = Kp,M2 = 2 mAV−2. For the pnp BJT, β = 100, VA = 100 V. Fig. Q3 (a) Design RREF such that ID,M1 = 1 mA. [ Ans: RREF = 8.29 kΩ] (b) Calculate the small signal parameters of Q1, i. e. , gm,Q1, rπ,Q1 and ro,Q1. (c) Identify the configuration of the single-stage amplifier. (d) Determine the parameters, Gm, Rin and Rout of the two-port network of the amplifier. (e) Determine the gain vo/vs of the amplifier using the 2-port network parameters derived in part (d). [Ans: vo/vs ≈ −180]
Q4. Consider the amplifier shown in Fig. Q4. The transistor M1 has Kp = 500 μA/V2, VTHP = −0.5 V and λp = 0.01 V−1. Fig. Q4 (a) What is the amplifier configuration? (b) Determine the DC drain current of M1, ID, M1 and verify the assumption used. [Ans: ID,M1 = 5.65 mA ] (c) What is the Rin for this amplifier? [Ans: Rin ≈ 120 Ω ] (d) What is the Rout for this amplifier? [ Ans: Rout ≈ 0.8 kΩ] (e) Use the concept of two-port network and the important results derived in the lecture notes, determine the voltage gain of this amplifier. [Ans: gain ≈ 0.27 ]
Q6. An amplifier circuit using an n-MOSFET is shown in Fig. Q6. The n-MOSFET has the following parameters: Kn = 1 mA/V2 and λ = 0.02 V−1. vin is a small signal AC voltage source. Fig. Q6 (a) Calculate the DC gate voltage, VG. (b) Assuming that the n-MOSFET is operating in the saturation region and neglecting channel length modulation, calculate the threshold voltage, VTHN, given that the voltage drop across the dc current source, IBUS, has been designed to be approximately 0 V. Verify that the n-MOSFET is operating in the saturation region. (c) Find the values of small signal parameters gm and ro of the n-MOSFET. (d) What is the configuration of the amplifier circuit? (e) Draw the small signal ac equivalent circuit of Fig. Q6. You may assume that in the small signal ac equivalent circuit, all the coupling capacitors behave like short circuits. (f) Calculate the input resistance, Rin, and output resistance, Rout . (g) Calculate the voltage gain, vout/vin.
Q7. Assume that the AC small signal parameters of the BJT are gm,Q1, rπ,Q1, ro,Q1, βQ1, and the AC small signal parameters of the MOSFETs are gm,Mi, gmb,Mi, ro,Mi, where i = 1, 2. Write down the expressions for the small signal AC equivalent resistance (Rx) of each of the following circuit configurations: (a) Fig. Q7 a (b) Fig. Q7 b
For the single-stage npn BJT amplifier circuit shown in Fig. Q8, the BJT Q1 has the following parameters: IS = 10−15 A, β = 100 and VA = 100 V. (a) What is the amplifier configuration? (2 marks) (b) Calculate the biasing DC collector current of BJT Q1, IC,Q1. (6 marks) (c) Calculate the AC small signal model parameters of BJT Q1. (3 marks) (d) Calculate the two port parameters, Gm, Rin and Rout . ( 5 marks) (e) Estimate the voltage gain (vout/vin ) of the amplifier. (4 marks)
Q5. Figure Q5 shows a single-stage amplifier circuit. The device parameters are as follows -n-channel MOSFETs: Kn = 1 mA/V2, VTHN = 1 V and λn = 0.01 V−1. p-channel MOSFETs: Kp = 2.5 mA/V2, VTHP = −1 V, and λp = 0.01 V−1. Fig. Q5 MOSFET M1 is operating in saturation region and its DC drain current is 1 mA. Ignore Channel Length Modulation effect in DC analysis. (a) Determine the DC drain current of M3 and RREF. (b) Determine R2. (c) Identify the amplifier configuration. (d) Determine the small-signal parameters of MOSFET M M1:gm,M1, ro,M1 and gmb,M1. (e) Calculate the two-port network parameters of the amplifier: Rin, Rout and Gm (or Av ). (f) Estimate the voltage gain vout /vs of the amplifier.
Problem 3: MOSFET Subthreshold Leakage Current For a MOSFET operating in the subthreshold regime (VGS < VT), the reduction in gate voltage needed to reduce the drain current by one decade is defined as the "subthreshold swing": S = (kT/q)(ln10)[1 + (Cdep,min/Cox)] The units of S are mV/ decade. Note that the smallest value of S attainable at room temperature (300 K) is 60 mV/ decade. Consider a short n-channel MOSFET with Toxe = 2 nm and WT = 35 nm. Suppose the threshold voltage (VT) for this device is simply defined to be the value of VGS at which the normalized drain current IDS/(W/L) reaches 100 nA for VDS = 100 mV. (a) Find the subthreshold swing S (b) If the normalized leakage current must be less than or equal to 10 pA when VGS = 0 V and VDS = 100 mV, what is the minimum threshold voltage this device can have?
What is the subthreshold leakage current in nanoamps for a PMOS FET at 300∘K when it has Vgs = −158 mV ? Assume that this MOSFET has a steep retrograde body doping profile with a maximum depletion region thickness of Wdmax = 57 nm, and an effective oxide thickness, Toxe, of 26 angstroms. Use: W = 1.2 μm, L = 1.0 μm, Vt = −384 mV and kT/q = 26 mV at 300∘K. Note that since the answer for this question may be very small, be sure to give your answer to at least 3 significant figures! Answer: The correct answer is: -0.057