Transcript Field Effect Transistors Circuit Analysis EE314

Field Effect
Transistors
Circuit Analysis
HP PA8000
Fairchild Clipper
C100
Fujitsu 68903
EE314
FET Circuit Analysis
1.MOS Small Signal Equivalent
2.Transconductance
3.Common-Source Amplifiers
4.Source Follower
5.Logic gates
Chapter 12: Field
Effect Transistors
Small-Signal Equivalent Circuit for FETs
Output 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)
vGS (t )  VGSQ  v gs (t )
i D (t )  I DQ  id (t )
Characteristic
Small-Signal Equivalent Circuit -Transconductance
Schematic
Analysis… (a little bit of math)
iD  K vGS  Vt 0 
2

I DQ  id (t )  K VGSQ v gs (t )  Vt 0

2
2
I DQ  id (t )  K VGSQ  Vt 0   2K VGSQ  Vt 0 v gs t   Kv gs
(t )
2
We know that
Also we assume that
I DQ  K VGSQ  Vt 0 
2
v gs (t )  VGSQ  Vt 0 
*
Small-Signal Equivalent Circuit -Transconductance
Schematic
2
I DQ  id (t )  K VGSQ  Vt 0   2K VGSQ  Vt 0 v gs t   Kv gs
(t )
2
We know that
Also we assume that
Drain current generated
by signal
I DQ  K VGSQ  Vt 0 
2
v gs (t )  VGSQ  Vt 0 
*
id (t )  2 K VGSQ  Vt 0 v gs (t )
Small-Signal Equivalent Circuit -Transconductance
We define the
transconductance as
gm 
id (t )
vgs (t )
or
id (t )  g m v gs (t )
so
g m  2 K VGSQ  Vt 0 
Small-Signal Equivalent Circuit -Transconductance
iD  K vGS  Vt 0 
2
so
vGS  Vt 0  
I DQ
K
Thus the
transconductance
g m  2 K VGSQ  Vt 0   2 KI DQ
Small-Signal Equivalent Circuit -Transconductance
Exercise
The transistor has KP=50mA/V2, Vto=2V, L=10mm, and W=400mm
 W  KP
K  
 1mA / V 2
L 2
g m  2 K VGSQ  Vt 0   2(4  2)  4mS
Small-Signal Equivalent Circuit
Also we assume that
ig (t )  0
g m  2 KI DQ
 W  KP
K  
L 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.
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 amplifiers
Drain resistor: account for the effect of vDS on the drain current
Correction for id
id (t )  g m v gs (t )  vds / rd
Please read section: Transconductance and … pp.591
Example 12.3
Drain Resistance Calculation
1
i D

rd v DS
so at vGS=4V

1
iD
10.7  10mA 0.7



mS  0.175mS
10  6V
rd vDS
4
rd  5.7k
Common-Source Amplifier
Schematic
G
D
S
Equivalent circuit
The dc supply voltage acts as a short circuit for the ac current.
Common-Source Amplifier
C1, C2 -coupling C
Schematic
Cs -bypass C
ac signal
G
D
S
Equivalent circuit
The dc supply voltage acts as a short circuit for the ac current.
Common-Source Amplifier: Gain, Rin and Rout
Equivalent circuit (once more)
1
R 
1 / rd  1 / RD  1 / RL
'
L
Voltage gain
v0  g m v gs RL'
vin  v gs
v0
Av 
  g m RL'
vin
Input resistance
Rin 
vin
 RG  R1 R2
iin
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
Example 12.4
if vgs=0 then gmvgs=0
Output resistance
Rout
1

1 / RD  1 / rd
Source Follower
Small-Signal Equivalent Circuit –Source Follower
Notice that small
signal IDS goes up.
Why?
Small-Signal Equivalent Circuit –Source Follower
RL' 
1
1 / rd  1 / RS  1 / RL
Input resistance
Voltage gain
v0  g mvgs RL'

vin  vgs  vo  vgs 1  g m RL'
v0
g m RL'
Av 

1
'
vin 1  g m RL

vin
Rin 
 RG  R1 R2
iin
Since the output voltage is almost equal to
the input – hence the name source follower
Logic gates – COMS Inverter
Logic truth table
Vin
V out
0
1
1
0
Switch level
equivalent
circuits
Logic gates – COMS NAND gate
Logic truth table
A
B
V
out
0
0
1
0
1
1
1
0
1
1
1
0
Logic gates – COMS NOR gate
Exercise
Draw switch level circuits
for different inputs and
derive the truth table for
this gate
Logic gates – COMS NOR gate
Logic truth table
A
B
V
out
0
0
1
0
1
0
1
0
0
1
1
0