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# Ve311 Homework #4

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Ve311 Homework #4

Note:
(1) Please use A4 size papers.
(2) Please use the SPICE model on page 3 for simulation and calculation.
1. [MOSFET DC Biasing, 60%] Use the drain current equations below.
Don’t consider channel-length modulation and body effect. Assuming
Wdrawn / Ldrawn = 20 µm / 2 µm, sketch IX of M1 as a function of VX
increasing from 0 V to VDD = 5 V. (Note: finish this part before the
midterm exam)
𝐈𝐃 = µ𝐧
𝐂𝐨𝐱
𝐖
𝐋𝐞𝐟𝐟
[(𝐕𝐆𝐒 − 𝐕𝐓𝐇)𝐕𝐃𝐒 −
𝟏
𝟐
𝐕𝐃𝐒
𝟐
] (NMOS in triode region)
𝐈𝐃 =
𝟏
𝟐
µ𝐧
𝐂𝐨𝐱
𝐖
𝐋𝐞𝐟𝐟
(𝐕𝐆𝐒 − 𝐕𝐓𝐇)
𝟐
(NMOS in saturation region)
𝐈𝐃 = µ𝐩
𝐂𝐨𝐱
𝐖
𝐋𝐞𝐟𝐟
[(𝐕𝐒𝐆 − |𝐕𝐓𝐇|)𝐕𝐒𝐃 −
𝟏
𝟐
𝐕𝐒𝐃
𝟐
] (PMOS in triode region)
𝐈𝐃 =
𝟏
𝟐
µ𝐩
𝐂𝐨𝐱
𝐖
𝐋𝐞𝐟𝐟
(𝐕𝐒𝐆 − |𝐕𝐓𝐇|)
𝟐
(PMOS in saturation region)
2
2. [MOSFET Small-Signal Model] Assume Wdrawn / Ldrawn = 20 µm / 2 µm.
(a) [20%] Use Pspice to plot the drain current of a NMOS as a function
of VDS increasing from 0 V to 5 V, at VGS = 1 V, 1.5 V and 2 V. Label
the off, triode and saturation regions for each curve. Derive ro from each
curve in the saturation region and compare it with hand-calculation result.
(b) [20%] Use Pspice to plot the drain current of a NMOS as a function
of VGS increasing from 0 V to 3 V, at VDS = 5 V. Derive gm from the
curve when VGS = 2 V and compare it with hand-calculation result.
3
Vacuum permittivity (𝛜𝐨) = 𝟖. 𝟖𝟓 × 𝟏𝟎−𝟏𝟐 (F / m)
Silicon oxide dielectric constant (𝛜𝐫
) = 𝟑. 𝟗 Ve311 Homework #4
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