Field Effect Field Effect Transistors Transistors

Circuit Circuit AnalysisAnalysis

EE314

HP PA8000

Fujitsu 68903

Fairchild Clipper C100

Chapter 12: Field Effect Transistors

1.MOS Small Signal Equivalent

2.Transconductance3.Common-Source

Amplifiers4.Source Follower5.Logic gates

FET Circuit Analysis

Small-Signal Equivalent Circuit for FETsOutput signal from an amplifier using FET can be effectively modulated by small changes of input signal current. In this way it is possible to make small changes from the Q point. Symbols:The total quantities: iD(t), vGS(t)The dc point values: IDQ, VGSQ

The signal id(t), vgs(t) Characteristic

)()( tiIti dDQD

)()( tvVtv gsGSQGS

Small-Signal Equivalent Circuit -Transconductance

Schematic

20tGSD VvKi

20)()( tgsGSQdDQ VtvVKtiI

)(2)( 20

20 tKvtvVVKVVKtiI gsgstGSQtGSQdDQ

20tGSQDQ VVKI

0)( tGSQgs VVtv

Analysis… (a little bit of math)

We know that

Also we assume that

*

Small-Signal Equivalent Circuit -Transconductance

Schematic

)(2)( 20

20 tKvtvVVKVVKtiI gsgstGSQtGSQdDQ

20tGSQDQ VVKI

0)( tGSQgs VVtv

)(2)( 0 tvVVKti gstGSQd

We know that

Also we assume that

Drain current generated by signal

*

Small-Signal Equivalent Circuit -Transconductance

)(

)(

tv

tig

gs

dm

We define the transconductance as

or

so

)()( tvgti gsmd

02 tGSQm VVKg

Small-Signal Equivalent Circuit -Transconductance

20tGSD VvKi

Thus the transconductance

K

IVv DQtGS 0

so

DQtGSQm KIVVKg 22 0

Small-Signal Equivalent Circuit -Transconductance

The transistor has KP=50A/V2, Vto=2V, L=10m, and W=400m

Exercise

mSVVKg tGSQm 4)24(22 0

2/12

VmAKP

L

WK

Small-Signal Equivalent Circuit

0)( tigAlso we assume that

DQm KIg 2

Better performance is obtained with higher values of gm.Please notice that gm is proportional to the square root of the Q point drain current. Simply, we can increase gm by choosing a higher value of IDQ.

2

KP

L

WK

More Complex Equivalent Circuits

For more accurate analyses of FET transistor we have to add more components to an equivalent circuit.Small capacitance: for high response FET amplifiersDrain resistor: account for the effect of vDS on the drain current

ddsgsmd rvtvgti /)()(

Correction for id

Please read section: Transconductance and … pp.591Example 12.3

Drain Resistance Calculation

mSmS

V

mA

v

i

r DS

D

d

175.04

7.0

610

107.101

krd 7.5

so at vGS=4V

DS

D

d v

i

r

1

Common-Source Amplifier

Schematic

Equivalent circuit

GD

S

The dc supply voltage acts as a short circuit for the ac current.

Common-Source Amplifier

Schematic

Equivalent circuit

ac signal

Cs -bypass C

C1, C2 -coupling C

GD

S

The dc supply voltage acts as a short circuit for the ac current.

Common-Source Amplifier: Gain, Rin and Rout

Equivalent circuit (once more)

Voltage gain

LDdL RRrR

/1/1/1

1'

'0 Lgsm Rvgv gsin vv

'0Lm

inv Rgv

vA

21 RRRi

vR G

in

inin

Input resistance

From bias point analysis

Common-Source Amplifier: Gain, Rin and Rout

To find out the Rout we have to: disconnect the load, replace the signal source by short circuit – Thevenin equivalent resistance

No source connected to the input

if vgs=0 then gmvgs=0

dDout rRR

/1/1

1

Output resistance

Example 12.4

Source Follower

Small-Signal Equivalent Circuit –Source Follower

Notice that small signal IDS goes up. Why?

Voltage gain

LSdL RRrR

/1/1/1

1'

'0 Lgsm Rvgv '1 Lmgsogsin Rgvvvv

11 '

'0

Lm

Lm

inv Rg

Rg

v

vA

21 RRRi

vR G

in

inin

Input resistance

Small-Signal Equivalent Circuit –Source Follower

Since the output voltage is almost equal to the input – hence the name source follower

Logic gates – COMS Inverter

Vin V out

0 1

1 0

Logic truth table

Switch level equivalentcircuits

Logic gates – COMS NAND gate

A B V out

0 0 1

0 1 1

1 0 1

1 1 0

Logic truth table

Logic gates – COMS NOR gate

Exercise

Draw switch level circuits for different inputs and derive the truth table for this gate

A B V out

0 0 1

0 1 0

1 0 0

1 1 0

Logic truth table

Logic gates – COMS NOR gate