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ECE2280 Homework #1 Fall 2011

1. Use: ignore ro, |VBE|=0.7, ββββ=100

VI = 20+0.001sin(20t) For DC analysis, assume that the capacitors are open

(a) Solve for the DC currents:

a. IB

b. IE

c. IC

(b) Solve for the DC voltages:

a. VB

b. VE

c. Vo

(c) Prove or disprove the region of operation you assumed to

solve for your answers in (a) and (b)?

Vo

Rout

VI

IE

VB

VE

IB

IC

Vx 0≠

+

-

10k

2k C4

100mQ1

Q2N3904

I1

1m

8V

1k

900

10V

6V

C3

100m

100

6kΩ

4kΩ

6.7V

100Ω

2V

1mA 100Ω

4kΩ

16V

4kΩ

2

~ Vsig

gm2Vπ2

3kΩ

gm1Vπ1

+

Vπ1

- Rin

1kΩ

Rout

Vo 2kΩ

2kΩ

100Ω

rπ1

rπ2

+

Vπ2

-

2k

6kΩ

4kΩ 4kΩ 3kΩ

2. Use: ignore ro, |VBE|=0.7, ββββ=100

VI = 5+0.001sin(500t)

rππππ1=2, 000 gm2=50mA/V, and IB2=12.5µµµµA

For the following hybrid-π equivalent circuit below, find the following values:

(a) Rin (input resistance –ignore only the input source, Vsig and include all resistors at the base)

(b) Rout (output resistance-include all resistors at the collectorno load is connected)

(c) midband gain, Vsig

Vo

3. For the circuit shown below, draw

Make sure that everything is labeled in terms of the transistor number. (e.g. g

transistors. vsig=0.001sin(10t) AC. Assume all capacitors are shorted.

vsig

+15V

R4

R

3

draw the AC small-signal equivalent circuit(use hybrid

Make sure that everything is labeled in terms of the transistor number. (e.g. gm1, vπ2, etc.).

=0.001sin(10t) AC. Assume all capacitors are shorted.

+15V

-15V

R6

signal equivalent circuit(use hybrid-π or model T).

, etc.). Include ro for all

4

4. Use:

Vt=2V

kn’(W/L)=4mA/V2

λλλλ=0

VI = 10+0.002sin(20t) For DC analysis, assume that

the capacitors act as open

(d) Solve for the DC currents:

a. I1

b. ID

c. IS

(e) Solve for the DC voltages:

a. VG

b. VS

c. Vo

(f) Verify that the transistor is saturated.

(g) State the DC bias point.

(h) Assuming that the transistor amplification Vo/VI = -7V/V. What is the total (AC and DC)

instantaneous output for Vo (VI value stated above).

~

3C

VI +

+

2k 3k

4V

2k

1k

4C oV

GV

SV

NMOS 100m

1m

+9V

DI

SI

1I

inR

outR

500Ω

500Ω

1.7V

5

5. Use: Vt=2V

kn’(W/L)=3mA/V2

Vsig is an AC source

Transistor 1 has DC values: VGS=4V, ID=6mA

Transistor 2 has DC values: VGS=5.3V, ID=16.7mA

λ=0 (for all transistors)

For the following hybrid-π equivalent circuit, find the following values:

(a) Rin (input resistance –ignore the input source, Vsig)

(b) Rout (output resistance-ignore RLno load is connected)

(c) midband gain, Vsig

Vo

inR

~ gs1vgs2v sigv

outR

LR 1k= Ω

2kΩ

m1 gs1g v 1kΩ2MΩ

3MΩ

1kΩ

+ +

1kΩ

oV m2 gs2g v

6

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6. For the circuit shown below, draw the AC small-signal equivalent circuit(use hybrid-π or model T).

Make sure that everything is labeled in terms of the transistor number. (e.g. gm1, vgs2, etc.). λ=0 for all

transistors. vsig=0.005sin(20t) AC. Assume all capacitors are closed for the AC circuit.

~

3C

sigV

+15V

1mA

5V

2R

8R

1R 6R

NMOS

1V

100m

+10V 3R

10R

9R

5R

4R

+

+

NMOS

7R

-15V

1C

2M

1M

10m

8

7 (a) Design the cascode amplifier with 2 PMOS transistors for the current source(as shown in class or Fig.

7.11) at a current of 0.1mA with all devices operating at |Vov|=0.25V. All devices have |VA|=4V. Find gm1,

the output resistance of the amplifier, Ron, the output resistance of the current source, Rop, the overall output

resistance, Rout, and the voltage gain, Av.

(b) Use the same circuit with the following DC voltages: VIn=0.8V, VG2=1.2V, VG3=1.3V, VG4=1.7V, and

VDD=2.5V. If all devices are matched, that is kn1= kn2= kp3= kp4, and have equal |Vt|=0.5V, what is the

overdrive voltage at which the four transistors are operating(Note this is different from part (a))? What is the

allowable voltage range at the output?

(a)

(b)

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8. Design the cascode amplifier that utilizes 2 PMOS transistors for the current source to have the following

specifications: gm1=2mA/V, and Av=-200V/V. Assume that the available fabrication process has

V’A=5V/µm for both NMOS and PMOS devices and that µnCox= 4µpCox=400µA/V

2 . Use the same channel

length L for all devices and operate all four devices at |Vov|=0.2V. Determine the required channel length L,

the bias current I, and the W/L ratio for each of four transistors. Assume that suitable bias voltages have been

chosen, and neglect the Early effect in determining the W/L ratios.

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9. A cascode current source formed of two pnp transistors for which β=50 and VA=5V supplies a current of

0.5mA. What is the output resistance?

10. The figures below show four possible realizations of the folded cascode amplifier. Assume that the BJTs

have β=100 and that both the BJTs and the MOSFETs have |VA|=5V. Let I=100µA, and assume that the

MOSFETs are operating at |VOV|=0.2V. Assume the current sources are ideal. For each circuit determine,

Rin, Rout, and the gain Vo/VI. Comment on your results.

(a)

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(b)

(c)

(d)