Lect. 23: High-Frequency Response of MOSFET CS
Lect. 23: High-Frequency Response of MOSFET CS
Lect. 23: High-Frequency Response of MOSFET CS
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<strong>Lect</strong>. <strong>23</strong>: <strong>High</strong>-<strong>Frequency</strong> <strong>Response</strong> <strong>of</strong> <strong>MOSFET</strong> <strong>CS</strong><br />
How fast can this operate?<br />
R L<br />
, C L<br />
due to<br />
Q 2<br />
and external load<br />
Electronic Circuits 1 (06/2)<br />
Pr<strong>of</strong>. Woo-Young Choi
<strong>Lect</strong>. <strong>23</strong>: <strong>High</strong>-<strong>Frequency</strong> <strong>Response</strong> <strong>of</strong> <strong>MOSFET</strong> <strong>CS</strong><br />
It can be shown from an exact (but complicated ) analysis (6.6.3) that<br />
'<br />
−( gmR ) ⎡<br />
L ⎣<br />
1 −s( Cgd / gm)<br />
( ) ⎤ ( ) ⎡<br />
V<br />
⎤<br />
o<br />
=<br />
⎦<br />
Vsig<br />
1+ s{ ⎡C C 1 g R R C C R } s ( C C ) C C C ⎤<br />
⎣<br />
+ +<br />
⎦<br />
+ + +<br />
⎣<br />
+ +<br />
⎦<br />
R R<br />
' ' 2 '<br />
gs gd m L sig L gd L L gd gs L gd sig L<br />
Too complex. A simpler way <strong>of</strong> estimating f H<br />
, high-frequency 3-dB frequency?<br />
Electronic Circuits 1 (06/2)<br />
Pr<strong>of</strong>. Woo-Young Choi
<strong>Lect</strong>. <strong>23</strong>: <strong>High</strong>-<strong>Frequency</strong> <strong>Response</strong> <strong>of</strong> <strong>MOSFET</strong> <strong>CS</strong><br />
Open-Circuit Time Constant Method for approximating f H<br />
1. Select one capacitor, C i<br />
, and set others to open.<br />
2. Determine R i<br />
, the resistance seen by C i<br />
.<br />
3. Repeat above for all capacitors.<br />
Then,<br />
ω<br />
H<br />
<br />
∑<br />
i<br />
1<br />
CR<br />
i<br />
i<br />
Electronic Circuits 1 (06/2)<br />
Pr<strong>of</strong>. Woo-Young Choi
<strong>Lect</strong>. <strong>23</strong>: <strong>High</strong>-<strong>Frequency</strong> <strong>Response</strong> <strong>of</strong> <strong>MOSFET</strong> <strong>CS</strong><br />
For C gs<br />
,<br />
R gs<br />
= ?<br />
R gs<br />
=R sig<br />
Electronic Circuits 1 (06/2)<br />
Pr<strong>of</strong>. Woo-Young Choi
<strong>Lect</strong>. <strong>23</strong>: <strong>High</strong>-<strong>Frequency</strong> <strong>Response</strong> <strong>of</strong> <strong>MOSFET</strong> <strong>CS</strong><br />
For C gd<br />
,<br />
R gd<br />
= ?<br />
I<br />
V<br />
I<br />
I<br />
Vgs<br />
+ V<br />
= g V +<br />
R '<br />
x m gs<br />
= −I R<br />
gs x sig<br />
− I R + V<br />
=− g I R +<br />
RL<br />
'<br />
Rsig<br />
Vx<br />
(1 + g R + ) =<br />
R ' R '<br />
x m x sig<br />
x m sig<br />
L<br />
L<br />
x<br />
x sig x<br />
L<br />
V<br />
I<br />
x<br />
x<br />
Rsig<br />
= (1 + g R + ) R '= R ' + g R R ' + R<br />
R '<br />
m sig L L m sig L sig<br />
L<br />
∴ R = R (1 + g R ') + R '<br />
gd sig m L L<br />
Electronic Circuits 1 (06/2)<br />
Pr<strong>of</strong>. Woo-Young Vgs = V−I= xChoi<br />
R−<br />
sig<br />
I R<br />
gs x sig
<strong>Lect</strong>. <strong>23</strong>: <strong>High</strong>-<strong>Frequency</strong> <strong>Response</strong> <strong>of</strong> <strong>MOSFET</strong> <strong>CS</strong><br />
For C L<br />
, R L<br />
= ?<br />
R CL<br />
=R L<br />
’<br />
Electronic Circuits 1 (06/2)<br />
Pr<strong>of</strong>. Woo-Young Choi
<strong>Lect</strong>. <strong>23</strong>: <strong>High</strong>-<strong>Frequency</strong> <strong>Response</strong> <strong>of</strong> <strong>MOSFET</strong> <strong>CS</strong><br />
ω<br />
Open-Circuit Time Constant Method for approximating f H<br />
1. Select one capacitor, C i<br />
, and set others to open.<br />
2. Determine R i<br />
, the resistance seen by C i<br />
.<br />
3. Repeat above for all capacitors.<br />
<br />
1 1<br />
= , where τ = C R + C [ R (1 + g R ') + R '] + C R '<br />
τ<br />
H<br />
CR<br />
H H gs sig gd sig m L L L L<br />
∑<br />
i<br />
i<br />
i<br />
Miller Effect!<br />
Electronic Circuits 1 (06/2)<br />
Pr<strong>of</strong>. Woo-Young Choi
<strong>Lect</strong>. <strong>23</strong>: <strong>High</strong>-<strong>Frequency</strong> <strong>Response</strong> <strong>of</strong> <strong>MOSFET</strong> <strong>CS</strong><br />
Example 6.9<br />
Determine f H<br />
for the <strong>CS</strong> shown left.<br />
I REF<br />
=100μA, W/L=7.2μm/0.36μm<br />
k n<br />
’=387μA/V 2 , k p<br />
’=86μA/V 2 ,<br />
V An<br />
’=5V/μm, |V Ap<br />
’|=6V/μm,<br />
C gs<br />
=20fF, C gd<br />
=5fF, C L<br />
=25fF, R sig<br />
=10kΩ.<br />
It can be shown<br />
τ<br />
τ<br />
τ<br />
gs gs gs<br />
L<br />
200ps<br />
= C R = 714ps<br />
gd gd gd<br />
C L C<br />
L<br />
246ps<br />
τ = τ + τ + τ = 1160ps<br />
f<br />
H gs gd C<br />
H<br />
= C R =<br />
= C R =<br />
L<br />
1 1<br />
= = = 137 MHz<br />
−12<br />
2πτ<br />
2π<br />
× 1160×<br />
10<br />
H<br />
Electronic Circuits 1 (06/2)<br />
Pr<strong>of</strong>. Woo-Young Choi
<strong>Lect</strong>. <strong>23</strong>: <strong>High</strong>-<strong>Frequency</strong> <strong>Response</strong> <strong>of</strong> <strong>MOSFET</strong> <strong>CS</strong><br />
How accurate is f H<br />
= 137MHz estimated<br />
by the open-circuit time constant method?<br />
From the exact analysis,<br />
'<br />
−( gmR ) ⎡<br />
L ⎣<br />
1 −s( Cgd / gm)<br />
( ) ⎤ ( ) ⎡<br />
V<br />
⎤<br />
o<br />
=<br />
⎦<br />
Vsig<br />
1+ s{ ⎡C C 1 g R R C C R } s ( C C ) C C C ⎤<br />
⎣<br />
+ +<br />
⎦<br />
+ + +<br />
⎣<br />
+ +<br />
⎦<br />
R R<br />
f<br />
H<br />
145.3MHz<br />
' ' 2 '<br />
gs gd m L sig L gd L L gd gs L gd sig L<br />
What is the most influential capacitor<br />
for f H<br />
?<br />
Electronic Circuits 1 (06/2)<br />
Pr<strong>of</strong>. Woo-Young Choi
<strong>Lect</strong>. <strong>23</strong>: <strong>High</strong>-<strong>Frequency</strong> <strong>Response</strong> <strong>of</strong> <strong>MOSFET</strong> <strong>CS</strong><br />
Homework: Do your design project: Part 1 and 2 (No need to hand it in)<br />
ITOTAL<br />
≤150μ<br />
A<br />
Electronic Circuits 1 (06/2)<br />
Pr<strong>of</strong>. Woo-Young Choi