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All the transistors in the circuits shown in Fig. P5.43 have the same values of |Vt|, k

All the transistors in the circuits shown in Fig. P5.43 have the same values of |Vt|, kAll the transistors in the circuits shown in Fig. P5.43 have the same values of |Vt|, k

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All the transistors in the circuits shown in Fig. P5.43 have the same values of |Vt|, k

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Consider MOSFET-based current source circuits shown below. Assume that the n-type MOSFET transistors follow the long-channel model with μnCox = 100 μA/V2 and Vth,n = 0.5 V. All the transistors have a fixed channel length L = 0.25 μm. The bias voltage VB1 is at 0.8 V. Assume that all transistors have no back-bias effect. (1) (2) (a) For a basic current source in Fig. (1), size the NMOS transistor M1's width ( = W1) so that it conducts a current of 1 mA when it operates in saturation region. You may assume λn = 0. (b) What is the minimum value of Vout for this circuit that keeps M1 in saturation region? (c) For a cascode current source in Fig. (2), assume that the transistor M2 has the same width with M1 you determined from part (a). Determine the value of VB2 that yields the lowest minimum VOUT keeping both M1 and M2 in saturation regions. (d) Now, let's assume that the transistors M1 and M2 have a finite output resistance with λn = 0.1 V−1. Compute the value of the output resistance (Rout) of this cascode current source when M1 and M2 are in the saturation region. (Hint: Calculate the output impedance in a small signal equivalent circuit.)
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For each of the circuits shown in Fig. P5.57, find the labeled node voltages. The NMOS transistors have Vt = 0.9 V and k’n(W/L) = 1.5 mA/V2 .
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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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