ESE 572: Analog Integrated Circuits
Homework 1
1. (2 pts) A MOS transistor in the active region is measured to have a drain current of 20 μA when VDS = VGS-VT. When VDS is increased by 0.5 V, ID increases to 23 μA. Estimate the output impedance, r0, and the output impedance constant, λ .
2. (3 pts) Using the device parameters for the 0.18 μm technology PMOS device at the end of this HW and L = 0.2 μm, select the device width and required VGS to bias a transistor with an intrinsic gain of Ai = 10 and transconductance gm = 0.5 mA/V. What dc current consumption is required?
3. (3 pts) For the circuit below plot IX and gm as a function of VX as VX varies from 0 to 1.2 V. Assume M1 has a (W/L) = (3.5μm/0.35μm) and the model parameters for the 0.35 μmtechnology given at the end of the HW. Assume VDD = 2V and the source is tied to the body.
4. (3 pts) For the circuit below plot IX as a function of VX as VX varies from 0 to 2 V. Assume M1 has a (W/L) = (3.5μm/0.35μm) and the model parameters for the 0.35 μm technology. You may ignore the body effect.
5. (3 pts) For the circuit below plot IX and gm as a function of VX as VX varies from 0 to 1.2 V. Assume M1 has a (W/L) = (5μm/0.5μm) and the model parameters for the 0.5 μm technology given at the end of this HW.
6. (3 pts) For the circuit below plot Vout as a function of Vinas Vin varies from 0 to 1.2 V. Assume
M1 has a (W/L) = (5μm/0.5μm) and the model parameters for the 0.5 μm technology. Assume R1 = 20 kΩ and VDD = 3V.
7. (2 pt) Draw the transistor level schematic for the structure below
8. (3 pts) For the circuit in problem 7, assume that (W/L)M1 = 35 μm/0.35 μm, (W/L)M2 = 35 μm/1.4 μm, and ID1 = ID2 = 0.5 mA when both devices are in saturation. Assume VDD = 3V and the 0.35 μm model parameters. Recall that λ ∝ 1/L.
(a) Calculate the small-signal voltage gain.
(b) Calculate the maximum output voltage swing while both devices are saturated.
9. (4 pts) For the circuit below, assume that (W/L)1 = 50/0.5, RD = 2 kΩ, and λ= 0. Assume VDD = 3V and the 0.5 µm model parameters.
(a) What is the small-signal gain if M1 is in saturation andID = 1 mA?
(b) What input voltage places M1 at the edge of the triode region? What is the small-signal gain under this condition?
(c) What input voltage drives M1 into the triode region by 50 mV? What is the small-signal gain under this condition?
10. (4 pts) Suppose the common source amplifier from problem 9 is to provide an output swing from 1 V to 2.5 V.
(a) Calculate the input voltages that yield Vout = 1 V and Vout = 2.5 V.
(b) Calculate the drain current and the transconductance of M1 for both cases.
(c) How much does the small-signal gain, gmRD, vary as the output goes from 1 V to 2.5 V? (Variation of small-signal gain can be viewed as nonlinearity.)