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1. Find the Input impedance of the following Amplifier 2. Comment on the pole frequency at the input

1. Find the Input impedance of the following Amplifier 2. Comment on the pole frequency at the input

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1. Find the Input impedance of the following Amplifier 2. Comment on the pole frequency at the input

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Figure 1 shows a single stage common source MOSFET amplifier circuit. We wish to design the circuit to meet the following design specifications: Load Resistance: RL = 100 KΩ Input Resistance: Ri > 200 KΩ Mid-band Gain: Gv = Vo/Vi = −50 ± 20% Supply Voltage: +15 Volts Circuit Capacitors: CG = 10μF; CS = 47μF; CD = 10μF Figure 1. Common Source MOSFET Amplifier Pre-lab: (a) Design the amplifier to meet the specifications above by choosing values for resistors R1, R2, RD and RS. Begin your design by choosing an appropriate value for the bias current ID. If ID ≈ 0.3 mA, assume VT ≈ 1.7 V, Kn ≈ 0.02 A/V2 and VA = 100 V(λ = 0.01 V−1). Find the small signal approximation of the input resistance Rin where Rin = R1∥R2 Find the small signal approximation of the output resistance Ro, where Ro is given as Ro = RD∥RL∥ro. The small signal mid-band gain of the amplifier is given by Gv = −gmRo where gm = 2knID = kn(VGS−VT) Once you choose ID the DC biasing of the transistor can be found using simple rules of thumb. The voltage VG should be approximately equal to VDD/3 > VT. For maximum symmetry, VD should be biased at the midpoint between VD(Max) and VD(Min). Clearly, the maximum VD is VDD and the minimum VD > VG−Vt. For example, if Vt = 1.7 V and VG = 1/3VDD = 5 V, then VD ≈ 9 V for maximum symmetry.

Figure 1 shows a single stage common source MOSFET amplifier circuit. We wish to design the circuit to meet the following design specifications: Load Resistance: RL = 100 KΩ Input Resistance: Ri > 200 KΩ Mid-band Gain: Gv = Vo/Vi = −50 ± 20% Supply Voltage: +15 Volts Circuit Capacitors: CG = 10μF; CS = 47μF; CD = 10μF Figure 1. Common Source MOSFET Amplifier Pre-lab: (a) Design the amplifier to meet the specifications above by choosing values for resistors R1, R2, RD and RS. Begin your design by choosing an appropriate value for the bias current ID. If ID ≈ 0.3 mA, assume VT ≈ 1.7 V, Kn ≈ 0.02 A/V2 and VA = 100 V(λ = 0.01 V−1). Find the small signal approximation of the input resistance Rin where Rin = R1∥R2 Find the small signal approximation of the output resistance Ro, where Ro is given as Ro = RD∥RL∥ro. The small signal mid-band gain of the amplifier is given by Gv = −gmRo where gm = 2knID = kn(VGS−VT) Once you choose ID the DC biasing of the transistor can be found using simple rules of thumb. The voltage VG should be approximately equal to VDD/3 > VT. For maximum symmetry, VD should be biased at the midpoint between VD(Max) and VD(Min). Clearly, the maximum VD is VDD and the minimum VD > VG−Vt. For example, if Vt = 1.7 V and VG = 1/3VDD = 5 V, then VD ≈ 9 V for maximum symmetry.
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CS Amplifiers vs. CG Amplifiers [19 points] (a) (b) Fig. P2 All NMOS transistors are biased at saturation region, but only small-signal equivalent circuits are shown in the figures. Each individual NMOS transistor has C2d = 0.1•Cgs, Cdb = Csb = 0.2•Cgs and intrinsic gain gmr0 = 40(>>1). However, the transistor is used as a CS amplifier in Fig. P2(a), but a CG amplifier in Fig. P2(b). Note that the intrinsic output impedance, r8, of the NMOS transistor still exists even though the value of Rsig and RL. have been assigned as rd/2 and re, respectively. For the following questions, please include device capacitances Cb, C2 d, Cb, and Cb if necessary. (a) Find the low frequency gain |vo/vi| of the CS amplifier in Fig. P2(a). (b) Use OCTC method only to find the expression of the time-constant, τ1,cs in terms of Cpd and ro, across the gate and source of the NMOS in Fig. P2(a). (c) Use OCTC method only to find the expression of the time-constant, τ22Cs in terms of Cpd and ro, across the drain and source of the NMOS in Fig. P2(a). (d) Use OCTC method only to find the expression of the time-constant, τ3, cs in terms of C84 and ro, across the drain and gate of the NMOS in Fig. P2(a). (e) Based on (b), (c), and (d), find the expression of 3-dB frequency, fucs in terms of Cp4 and rC, of the CS amplifier. (f) Find the low-frequency gain |v9/vi | of the CG amplifier in Fig. P2(b). (g) Use OCTC method only to find the expression of the time-constant, τ1,CG in terms of Cpd and r6, across the source and gate of the NMOS in Fig. P2(b). (h) Use OCTC method only to find the expression of the time-constant, τ2CG in terms of C84 and ro, across the drain and gate of the NMOS in Fig. P2(b). (i) Based on (g) and (h), find the expression of 3-dB frequency, f fh,co in terms of CBd and r0, of the CG amplifier. (j) Based on (a) and (f), find the ratio of low-frequency gains, |Av,co/Av, cs|. (k) Based on (c) and (i), find the ratio of 3-dB frequencies, fH,co/fH,cs. Result Summary: (a) Av,Cs = (b) τ1,Cs = (c) τ2,Cs = (d) τ3,Cs = (e) fH,CS = (f) Av,CG = (g) τ1,CG = (h) τ2,CG = (i) fH,CG = (j) |Av,CG/Av,CS| = (k) fH,CG/fH,CS =CS Amplifiers vs. CG Amplifiers [19 points] (a) (b) Fig. P2 All NMOS transistors are biased at saturation region, but only small-signal equivalent circuits are shown in the figures. Each individual NMOS transistor has C2d = 0.1•Cgs, Cdb = Csb = 0.2•Cgs and intrinsic gain gmr0 = 40(>>1). However, the transistor is used as a CS amplifier in Fig. P2(a), but a CG amplifier in Fig. P2(b). Note that the intrinsic output impedance, r8, of the NMOS transistor still exists even though the value of Rsig and RL. have been assigned as rd/2 and re, respectively. For the following questions, please include device capacitances Cb, C2 d, Cb, and Cb if necessary. (a) Find the low frequency gain |vo/vi| of the CS amplifier in Fig. P2(a). (b) Use OCTC method only to find the expression of the time-constant, τ1,cs in terms of Cpd and ro, across the gate and source of the NMOS in Fig. P2(a). (c) Use OCTC method only to find the expression of the time-constant, τ22Cs in terms of Cpd and ro, across the drain and source of the NMOS in Fig. P2(a). (d) Use OCTC method only to find the expression of the time-constant, τ3, cs in terms of C84 and ro, across the drain and gate of the NMOS in Fig. P2(a). (e) Based on (b), (c), and (d), find the expression of 3-dB frequency, fucs in terms of Cp4 and rC, of the CS amplifier. (f) Find the low-frequency gain |v9/vi | of the CG amplifier in Fig. P2(b). (g) Use OCTC method only to find the expression of the time-constant, τ1,CG in terms of Cpd and r6, across the source and gate of the NMOS in Fig. P2(b). (h) Use OCTC method only to find the expression of the time-constant, τ2CG in terms of C84 and ro, across the drain and gate of the NMOS in Fig. P2(b). (i) Based on (g) and (h), find the expression of 3-dB frequency, f fh,co in terms of CBd and r0, of the CG amplifier. (j) Based on (a) and (f), find the ratio of low-frequency gains, |Av,co/Av, cs|. (k) Based on (c) and (i), find the ratio of 3-dB frequencies, fH,co/fH,cs. Result Summary: (a) Av,Cs = (b) τ1,Cs = (c) τ2,Cs = (d) τ3,Cs = (e) fH,CS = (f) Av,CG = (g) τ1,CG = (h) τ2,CG = (i) fH,CG = (j) |Av,CG/Av,CS| = (k) fH,CG/fH,CS =
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Question: (MOSFET Amplifier) Consider the given MOSFET amplifier circuit and solve the following questions by showing all the solution steps clearly. (Use appropriate component models according to the given parameters). (µn•Cox = 100µA/V2 , W/L = 9/0.18, Vt = 1 V ) a) (30p) Draw the small signal model of the amplifier circuit. Find the input impedance Rin. b) (40p) We want to get a voltage gain Av = -10 with a Q-Point (Id=10mA). Calculate the values of Rd, VGS, VDS and check the operating mode of the MOSFET. c) (30p) Calculate the maximum voltage gain |Av| that can be obtained from this amplifier with a Q-Point (Id=10mA) gm = 2µnCoxW/LIDS IDS = µnCox W/L(VGS - Vt – VDS/2)•VDS, IDS = 1/2 µnCox W/L (VGS - Vt)^2
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