Lecture 15. Writing Circuit Equations Lecture 15. Writing Circuit Equations
Jaeha Kim
Mixed-Signal IC and System Group (MICS) Seoul National University
jaeha@ieee.org
Outlines
Readings
Willy M C Sansen “Analog Design Essentials ” Ch 2
Willy M. C. Sansen, Analog Design Essentials, Ch. 2
Overview
Despite the advance in circuit simulators and optimizers,
Despite the advance in circuit simulators and optimizers, tools can never replace designers’ intuition and expertise.
The best way to cultivate such expertise is to exercise writing as many equations as possible, since analytical equations y q p y q can tell how the performance metrics will change with the design parameters while each simulation only tells the point- wise information.
However, most students find writing equations difficult and necessary. It is often because they try to model everything – let’s focus only on the design intent (that is everything is ideal in the way you want). Then you will find it much easier.
2
g
m/I
DMethodology
Characterizes the operating region of a saturated MOS device by the ratio Gm/Ids
MOS device by the ratio Gm/Ids
According to the square law model, Gm/Id is an
equivalent measure to the gate overdrive (Vgs-Vth):q g ( g )
If so, why bother using Gm/Id?
3
g
m/I
DMethodology
Often, we need to increase Gm/Id ratio:
For a fixed IB and R, the largest gm maximizes the gain
gain
Av = gm R
The largest gm also minimizes the input- referred noise:
4
Why use g
m/I
D?
35 40
0.18um NMOS
25 30
/A]
2/VOV
BJT (q/kT)
15 20 g m/I D [S/
Th l d l
5
10 The sqaure-law model overestimates gm, as Vov approaches to zero!
-0.20 -0.1 0 0.1 0.2 0.3 0.4 0.5
VOV [V]
Using g /I directly sustains the accuracy into the W I
5
Using gm/ID directly sustains the accuracy into the W.I.
Basic Figures of Merit
• Current efficiency
Square Law
• Current efficiency
– Want large gm, for as little
current as possible D
m
I g
VOV
2
• Transit frequency gm 3 VOV
– Want large gm, without large Cgg I t i i i
Cgg 2 L2
• Intrinsic gain
– Want large gm, but no gds
ds m
g g
VOV
2
6
Transit Frequency Plot
50
0.18um NMOS 40
0.18um NMOS Square Law Model
20 30
f T [GHz]
gm
f 1
10
f 20
gg
T C
f 2
-0.20 -0.1 0 0.1 0.2 0.3 0.4 0.5
V [V]
VOV [V]
Intrinsic Gain Plot
80
0.18um NMOS
60
70 Long Channel Model, =0.3
30 40 50
g m/g ds
Short Channel Device
10 20 30
-0.20 -0.1 0 0.1 0.2 0.3 0.4 0.5
10
V [V]
VOV [V]
V
DS,SAT So far, we assumed the MOS device operated in saturated region (hence considered its g )
saturated region (hence considered its gm)
We need to make sure that VDS > VDS,SAT
VDS SATDS,SAT = VGSGS-VTHTH = VOVOV according to the square-law modelg q
But, what if we use gBut, what if we use gmm/I/IDD, f, fTT, and intrinsic gain to , and intrinsic gain to describe the device characteristics instead of VOV?
Need a way to estimate VDS,SAT with these metrics
Often use VDS,SAT 2/(gm/ID)
This is a conservative estimate, esp. in the velocity saturation region
region
9
V
DSsatEstimate Based on g
m/I
D0 35 0.4
NMOS, L=0.18um VDSsat
0.25 0.3
0.35 2/(g
m/I
D)
VOV “VDSsat” defined
0.15 0.2 0.25
[V] (arbitrarily) as VDS
at which 1/gds is equal to ½ of the
0.05
~4kT/q 0.1
q
value at VDS = VDD/2
2/(g /I ) is a reasonable estimate of “V ”
0 0.05 0.1 0.15 0.2 0.25 0.3
0
VOV [V]
2/(gm/ID) is a reasonable estimate of VDSsat
Sizing with g
m/I
DNMOS, 0.18...0.5um (step=20nm), V
DS=0.9V
For the chosen
For the chosen gm/ID and L, one can
101
W [A/m] L=0.18um one can
determine W from this
I D/W
L=0.5um “sizing chart” –
current density /I
5 10 15 20
/I [S/A]
vs. gm/ID
gm/I
D [S/A]
Other Viewpoint: Max f
Tand f
MAX Dickson, et al., “The Invariance of Characteristic Current Densities in Nanoscale MOSFETs ” JSSC 08/2006
in Nanoscale MOSFETs…, JSSC 08/2006.
max fT @ 0.3mA/um max fmax @ 0.2mA/um min NF@ 0.15mA/um
12
Writing Design Equations for Analog
Analog building blocks:
CS/CD/CG stages differential pair current mirror
CS/CD/CG stages, differential pair, current mirror, …
Let’s review their characteristics focusing on their intents
13
Review: Single-Stage Configurations
voltage buffer current buffer voltage buffer
14
current buffer
Common-Source Amplifier
Gain =
BW =
GBW =
Exercise: size transistor for GBW = 100MHz when C =3pF I = 0 2mA
CL=3pF, IL = 0.2mA
The required gm : 2mS gm/ID = 10
Fi d I /W d th W f th ii h t
15
Find ID/W and thus W from the sizing chart
CS Amplifier with Large R
Sand C
GS Gain =
BW =
GBW =
16
CS Amplifier with Feedback Capacitance
Gain =
BW =
GBW
17
CS Amplifier with Source Degeneration
gm,eff =
Rout =
Cin =
18
CS Amplifier with Source Degeneration (2)
gm,eff =
Rout =
Zin =
19
CS Amplifier with Diode-Connected Load
Rout =
Gain =
Gain =
20
Push-Pull Amplifier
Rout =
Gain =
BW =
GBW =
21
Source Follower
G i
Gain =
R t
Rout =
22
Active Inductor
Gain =
Zout =
Lout =
Lout =
23
Active Inductor Loads
Compare their output bias voltagesg
24
Cascode
Gain =
Rout =Rout
BW =
BW
GBW =
GBW =
The GBW remains unchanged!
25
g
Folded Cascode
Gain =
Rout =Rout
BW =
BW
GBW =
GBW =
26
Regulated Cascode
Gain =
Rout =Rout
BW =
BW
GBW =
GBW =
27
Current Mirrors
Compare their output resistances and minimum Vout’s
28
Single-Stage OTA
Gain =
Rout =Rout
BW =
BW
GBW =
GBW =
29
Two-Stage OTA
Gain =
BW
BW
GBW
30