1. [Current Source and Cascode Current Source]
(a) λ≠0 and γ=0) Derive analytical expressions for the output impedance of current source (i) and (ii) below.
(b) (λ≠0 and γ=0) For VX = 2 V, Va = 1.2 V, Vb = 2.2 V, (W/L)1 = 20 µm / 2 µm, (W/L)2 = 100 µm / 2 µm, what are the output impedance values of current source (i) and (ii) below? Does the cascode structure significantly increase the output impedance?
(c) [10%] What are the minimum values of VX for M1 of circuit (i) and M2 of circuit (ii) to stay in the saturation region?
(d) [30%] For circuit (i) and (ii) below, plot the IX as a function of VX (from 0 V to 5 V) using Pspice in DC sweep mode. Confirm whether the hand-calculation results in (b) and (c) are consistent with the simulation results here.
Vacuum permittivity (𝛜𝐨) = 𝟖. 𝟖𝟓 × 𝟏𝟎−𝟏𝟐 (F / m)
Silicon oxide dielectric constant (𝛜𝐫) = 𝟑. 𝟗
