This set of Microelectronics Multiple Choice Questions & Answers (MCQs) focuses on “MOS Current Mirror”.

1. The drain current of M_{2} is 5mA. Neglecting channel length modulation, what should be the ratio of the aspect ratio of M_{2} upon M_{1}?

a) 5

b) 4

c) 36

d) 2/9

View Answer

Explanation: Neglecting C.L.M., we readily note that the ratio of drain current is simply equal to the ratio of aspect ratio of each transistor. Hence, the aspect ratio of M

_{2}will have to be no less than 5 times that of M

_{1}so that it can carry a drain current of 5mA.

2. If the overdrive voltage of M_{2} is 10 times of M_{1}, what should be the ratio of the aspect ratio if the drain current of both the transistors is constant?

a) .1

b) 23

c) .01

d) 3

View Answer

Explanation: It is said that the drain current of each MOSFET is same. If the ratio of overdrive voltage of the MOSFETs are in the ratio of 10:1, the aspect ratio of M

_{2}will have to be .01 times of M

_{1}. Hence, the ratio is 1/100.

3. If both the transistors suffer from channel length modulation, λ_{1}=1 & λ_{1}=1/2 (in reality, the value is pretty low) and the drain voltage of both the transistors is 2V (a big assumption) – what should be the ratio of the aspect ratio if M_{3} has a drain current of 5 mA?

a) 5

b) 2

c) 6

d) 10

View Answer

Explanation: Since both the transistors suffer from channel length modulation, the ratio of drain current is equal to the ratio of the product of aspect ratio and (1+λ*(V

_{DS})) of each transistor. We can put the given values and determine that the ratio is 10. Note that the ratio has increased in presence of a higher channel length modulation parameter in M

_{2}.

4. If both the transistors suffer from channel length modulation, λ_{1}=1 & λ_{1}=1/2 (in reality, the value is pretty low) and the drain voltage of both the transistors is 2V (a big assumption) – what should be the ratio of the aspect ratio if the overdrive voltage of M_{3} is 5 times of M_{1}?

a) 32

b) .015

c) .065

d) .013

View Answer

Explanation: We note that if the same drain current flows through both the transistors, then the product of aspect ratio, the overdrive voltage and (1+λ*(V

_{DS})) is equal for both the transistors. Hence, we can equate them for each transistor and we will find that the ratio of aspect ratio becomes .015.

5. If the channel length modulation parameter of only M_{2} is .1V^{-1}, what is the impedance looking into the drain of M_{2} if the aspect ratio of each transistor is constant for a constant overdrive voltage but the drain current of M_{2} is 4 times that of M_{1}?

a) 5KΩ

b) 5.1KΩ

c) 4.6KΩ

d) 4.8KΩ

View Answer

Explanation: The impedance looking into the drain of M

_{2}is r

_{0}=1/λI

_{D}& λ=.1V

^{-1}. This leads us to the impedance, connected from the drain to the source of M

_{2}as 5KΩ since the drain current are same for both the MOSFETs.

6. If the channel length modulation parameter of only M_{2} is .1V^{-1}, what is the factor by which the aspect ratio of M_{2} is to be multiplied to make it equal to the aspect ratio of M_{1}, when the drain current of M_{2} is 4 times that of M_{1}?

a) .30702

b) .32895

c) .31465

d) .30769

View Answer

Explanation: If the drain current of M

_{2}is 4 times of M

_{1}, then for a constant overdrive voltage, the aspect ratio of M

_{2}is 4/(1+λV

_{DS2}) since only M

_{2}suffers from channel length modulation. Thus, the aspect ratio is greater than a factor of (.30769) since V

_{DS2}is equal to 3V with the drain current being 2mA. Note that the magnitude of the drain current is given and we need not find the drain current separately. Moreover, the ratio of currents allows us to find the drain current separately and then we can check for convergence of the magnitude of drain current and voltages.

7. If the channel length modulation parameter of only M_{2} is .1V^{-1}, what is the ratio of the transconductances of M_{2}/M_{1}, when the drain current of M_{2} is 4 times that of M_{1}?

a) 1.7145

b) 1.7541

c) 1.7451

d) 1.7514

View Answer

Explanation: The transconductance of a MOSFET in presence of channel length modulation becomes divided by a factor of √(1+λ V

_{DS}). Therefore, the transconductance, for a constant drain current, becomes proportional to √(W/L)/(1+λ V

_{DS}). We readily note that W/L will be in a ratio of 4:1 and the ratio of transconductance becomes 1.7541.

8. If the channel length modulation parameter of only M_{2} is .1V^{-1}, what is the total impedance connected to the drain of M_{1}, when the drain current of M_{2} is 4 times that of M_{1}?

a) .836

b) .823

c) .833

d) .839

View Answer

Explanation: The drain current of M

_{2}is 2mA and the resistance due to channel length modulation in the MOSFET is 5KΩ. We note that the total resistance connected to the drain of the device is 1KΩ||5KΩ=.833KΩ.

9. By what factor should the aspect ratio of M_{2} be multiplied to get the aspect ratio of M_{1} such that the ratio of drain current in M_{2} and M_{1} is equal to 8/3 and proportional to I_{D0}? Neglect Channel Length Modulation.

a) 48/71

b) 8/11

c) 18/21

d) 78/41

View Answer

Explanation: If the drain current in M

_{1}& M

_{2}is proportional to that of M

_{0}, we can say that the drain current of M

_{2}is 8/11 times that of M

_{0}. Then the aspect ratio of M

_{2}is less than M

_{1}by a factor of 8/11. Note that the gate current is almost 0 since the gate is made of the Oxide layer. The gate voltage of M

_{0}is shorted to M

_{1}and M

_{2}and the drain currents become proportional to M

_{0}.

10. What is the ratio of transconductance of M_{1} and M_{0}, for a constant overdrive voltage, if the ratio of drain current in M_{2} and M_{1} is equal to 8/3 and proportional to I_{D0}? Neglect Channel Length Modulation.

a) .2772

b) .2745

c) .9295

d) .2727

View Answer

Explanation: The transconductance is proportional to the product of the aspect ratio and the overdrive voltage for a MOSFET. Hence, the ratio of transconductance of M

_{1}/M

_{0}is 3/11, i.e. 0.2727, since the drain current of M

_{1}is 3/11 times that of M

_{0}.

11. If the transconductance of M_{2} & M_{0} is 4:1 for a constant overdrive voltage, what is the ratio of the resistances generated between the drain and the source if the ratio of their intrinsic gains is 16:1?

a) 4:99

b) 5:6

c) 3.99:1.1914

d) 4:1

View Answer

Explanation: The intrinsic gain of the MOSFET is a product of its transconductance and the resistance between the source and the drain which arises due to channel length modulation. This leads us to the fact that the ratio of these resistances in M

_{2}& M

_{0}is 4:1

12. Why do we intend to use a Cascode Current Mirrors as follows?

a) To overcome the effect of channel length modulation

b) To increase the speed

c) To increase the aspect ratio

d) To increase the effective oxide thickness

View Answer

Explanation: When we use a Cascode current mirror, we find that the drain voltages of M

_{0}and M

_{2}can be made equal and fixed to eliminate the channel length modulation. Henceforth, M

_{3}does not reflect much change in its drain voltage when its source voltage is changing.

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