Download IEEE BCTM 2006 Presentation - MOS-AK

Verilog-A is for Equation
Specification, not for
Modeling
Colin McAndrew
Laurent Lemaitre
Zoltan Huszka
Geoffrey Coram
Freescale Semiconductor
Freescale Semiconductor
Austriamicrosystems
Analog Devices
MOS-AK Meeting
Saturday December 13, 2008
Overview
• A Brief History of Verilog-A for Compact Modeling
• A Brief Review of How Circuit Simulators Work
• How to Leverage Understanding of How Simulators Work to
Implement Desired Equations
 thinking outside the “equivalent network” modeling box
 example 1: BJT excess phase
 example 2: single formulation resistor that can handle R=0
• Summary
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 2
What is Verilog-A?
• Initially (mid to late 1990’s), a language for analog behavioral
modeling to enable
 top down AMS design at the block level
 efficient top-level AMS verification
• VHDL-AMS is a “competing” language developed around the
same time for the same purposes
• So how does Verilog-A relate to compact modeling?
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 3
Automation in Compact Modeling
• In the late 1980’s automation began to creep into the
development of simulators
 especially for the time-consuming and error-prone task of
implementing compact models (symbolic derivative generation)
 added impetus to the on-going migration from “diffused” model
code to “modular” model code
• Simulator-model interfaces of the 1980’s and 1990’s:






WATAND
Saber/MAST – major commercial success
Tektronix (very early pioneer)
ADMIT plus various compilers (AT&T)
iSMILE
CMC Type-II interface (DOA circa 1995; engineering ≠ CS)
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 4
VBIC
SP
R3_CMC
HiCUM
BSIM
Mextram
PSP
MM11
EKV
MOSVAR
Common Language/Interface
Problem
The Solution
Eldo
ADS
Spectre
Nexxim
aSPICE
APLAC Nanosim
HSPICE
Golden
Gate
Ultrasim
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 5
Automated Model Implementation
• Mostly flopped in mid 1990’s
 VBIC was the first public model defined in high level code
 generated FORTRAN and C also provided
> these were used
> high-level pseudo-code was not! (except by Tektronix)
> chasm between engineers and advanced software techniques
• Many misconceptions
 code is slow compared to hand-coded C
> within 10% of hand coded and getting better
> will be faster one day (proven already), then works for all models!
 cannot use for parameter extraction
> if it’s in a simulator it’s in your simulator-based extractor!
 different code for different simulators will give different results
> different compile flags on the same platform give different results!
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 6
Enter Verilog-A
• Significant issue with the concept (high-level language +
compilers) was the lack of a standard high-level language!
• Verilog-A was obviously the solution for this
 VHDL-AMS touted as well initially
• Minor deficiencies overcome by compact model additions
•
defined in LRM2.2
CMC accepted models defined in Verilog-A circa 2004
• Verilog-A has become the de facto standard language for
defining compact models
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 7
Moving Beyond “Models”
• You can use Verilog-A to define “physical” compact models
• But this can be very restrictive
 constrained to think in terms of equivalent networks
 constrained to think in terms of I(V), Q(V) relations
• A circuit simulator is an equation solver
• Think of what equations you want to force the simulator to
solve, then develop Verilog-A constructs to force this
 not thinking in terms of physical representation
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 8
How SPICE Works: Simple BJT Model and Circuit
Ibc
x
RB
Qbc
c
Icc
b
Ibe
Vc
Qbe
+
–
Ib
e
RE
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 9
System Equations (DC): MNA
• Unknowns are V(x), V(b), V(c), V(e), and Ic=I(Vc)
g B V (b)  V ( x)    I b
x
g B V ( x)  V (b)   I be (Vbe )  I bc (Vbc )  0
b
I be (Vbe )  I cc (Vbe ,Vbc )  g EV (e)  0
e
I bc (Vbc )  I cc (Vbe , Vbc )  I c  0
c
V (c)  Vc
• Vbe=V(b)–V(e) and Vbc=V(b) –V(c)
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 10
Branch Jacobian Entry (Element Matrix Stamp)
• Solve KCL SI (V)=f(V)=0 at each node, plus the “voltage
equation” for voltage sources (and inductors)
 nonlinear, so need iterative Newton solution
 Vk+1=Vk+dVk, JkdVk=-f(Vk), Jk= ∂I/∂V |V=Vk
• Easy to set up Jacobian Jk in an algorithmic fashion
 rows are defined by nodes that the current flows between
> +ve for flow into node, –ve for flow out-of node
 columns are defined by the branch control voltages
> +ve for first node, –ve for second, for Vab=V (a)-V (b)
 voltage sources and inductors add a row for the voltage equation
and a column (unknown system variable) for the current
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 11
Jacobian Assembly (“Stamping”)
V(x)
SI(x)
SI(b)
SI(c)
SI(e)
Vc
V(b)
V(c)
V(e)
Ic
 gB
0
0
0
 g B
 g


g

g

g

g

g
0
B
be
bc
bc
be
 B

 0
 g bc  g ce  g cc  g bc  g cc
 g ce
0


0

g

g

g

g

g

g

g

1
be
ce
cc
cc
be
ce
E


 0
0
1
0
0 
• gbece=∂Ibe
cc/Vbe, gcc=∂Icc/Vbc, gm= gce + gcc , go=  gcc
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 12
SPICE
• Circuit simulators are not really “circuit simulators”
 for DC they are multidimensional nonlinear equation solvers
 for transient they are nonlinear ordinary differential equation
(ODE) solvers
> multidimensional nonlinear equation solvers at each time point
• Instead of thinking of Verilog-A as a means to define
equivalent network models, think of it as a means of
specifying equations for numerical solution
 formulate the equations you want
 understand how MNA equations are set up
 work out how to use Verilog-A to set up the desired equations
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 13
Weil-McNamee Excess Phase for BJTs
• Goal: implement a phase shift for gm with the least possible
change in the magnitude of gm
 network approach leads to 2nd order Bessel (linear phase) filter
 straight forward to implement as RLC circuit (L. Wagner, IBM)
Itxf =V(xf2)
I tzf
I txf 
1
s
0

TD /3
s2
2
30
xf1
Itzf
1
0 
, s  j  ddt()
TD
TD
xf2
1W
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 14
How Can We Get Rid of the Pesky Inductor?
I tzf


V (xf2)  I txf
 I txf 1  sTD  s 2 TD2 3


 I txf  sTD I txf  s TD I txf 3
 I txf  sTDV (xf1)
V (xf1)  I txf  s TD I txf 3
xf2
xf1
Itzf
TD
V(xf2)
V(xf1)
TD /3
1W
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 15
Can We Better Approximate an Ideal Phase Shift?
I txf
 I tzf e  jTD
Itxf =2V(xf) Itzf
 I tzf 1  sTD 
1  sTD 2
 I tzf
1  sTD 2
I tzf
2
 I tzf
1  sTD 2
 2V (xf)  I tzf
xf
Itzf
TD /2
1W
• Only 1 added system variable!
I tzf  V (xf)  ddt TDV (xf) 2
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 16
Phase Response
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 17
Magnitude Response
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 18
What about Resistors?
p
m
V  RI or I  GV ?
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 19
The “Solution” ... sort of
• For “reasonable” R:
 natural for NA (SPICE)
 efficient for NA
 nasty for R=0 or small R
• For “small” R:
 extra MNA system variable
 no worries for R=0 or small R
I  GV
V  RI
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 20
The “... sort of” Solution
`include "disciplines.h"
`define rm 0.001
module
r_va(p,m);
inout
p,m;
electrical
p,m;
parameter real R = 1.0 from[0.0:inf);
analog begin : analogBlock
if (R<`rm)
V(p,m) <+ I(p,m)*R;
EASY TO DEFINE 
else
I(p,m) <+ V(p,m)/R; HARD TO IMPLEMENT 
end // analogBlock
endmodule
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 21
Why “... sort of” is not Enough
• Does work in Verilog-A
 excellent feature of the language
• Does not (easily) work for
 built-in model implementation via ADMS
 some model interfaces for some simulators
 dynamic switching for the case when R varies with bias
• Do not want to switch formulations during iterative solution
 dynamically adds extra system variable I(p,m)
• Observation: must have this current for V=RI formulation
• Conclusion: explicitly include in model formulation
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 22
How do We Force Verilog-A to do What We Want?
• For simplicity of implementation in model interfaces, need to
get rid of voltage contribution
 only want strict nodal analysis formulation
• How can we do this for R=0?
• Want V(p,m)=0
• Set up current
contribution for
this as the only flow
into a node
• Forces set up of
equation we want!
V(p)
I_r
V(m)
. . . . . . .


0  1 0 0 0  1 0 


 . . . . . . . 
V(p,m)
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 23
The R=0 Solution
`include "disciplines.h"
module
r_va(p,m);
inout
p,m;
electrical
p,m,I_r;
parameter real R = 1.0 from[0.0:inf);
analog begin : analogBlock
I(I_r) <+ V(p,m);
I(p,m) <+ 1.0e-6*V(I_r);
end // analogBlock
endmodule
second equation forces V(I_r) to be current flowing between p and m
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 24
Extension for Small Nonzero R
`include "disciplines.h"
module
r_va(p,m);
inout
p,m;
electrical
p,m,I_r;
parameter real R = 1.0 from[0.0:inf);
analog begin : analogBlock
I(I_r) <+ V(p,m)-1.0e-6*R*V(I_r);
I(p,m) <+ 1.0e-6*V(I_r);
end // analogBlock
endmodule
first equation forces V(p,m)=I*R (voltage on node I_r is current p→m)
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 25
Final Result
`include "disciplines.h"
`define rm 0.001
module
r_va(p,m);
inout
p,m;
electrical
p,m,I_r;
parameter real R = 1.0 from[0.0:inf);
analog begin : analogBlock
I(I_r) <+ V(p,m)-1.0e-6*R*V(I_r);
if (R<`rm)
I(p,m) <+ 1.0e-6*V(I_r);
else
I(p,m) <+ V(p,m)/R; // I=G*V formulation
end // analogBlock
endmodule
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 26
Final Model
• Manipulated Verilog-A equations we want to solve
• Resistor model that does not switch formulations from current
contribution to voltage contribution




strictly nodal formulation
easy to implement in all simulator model interfaces
numerically well behaved for all R≥0
can be adapted to use same “switch” for voltage variable R
> direct bias dependence
> indirect bias dependence (e.g. self-heating)
• Cost is added system variable V(I_r) is added for all values
of R, not just R<`rm
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 27
Summary
• Circuit simulators are equation, not circuit, solvers
• Historical modeling approach of equivalent networks and a
physical approach may not always give desired result
• By thinking about what equations you want to implement or
solve, and understanding how MNA is set up, you can use
Verilog-A to implement “non-obvious” but useful models
• Note: if “currents” are mapped to node voltages (i.e. system
variables), they need to be scaled by the voltage/current
tolerance ratio (default is 1.0e6)
McAndrew/Lemaitre/Huszka/Coram MOS-AK December 2008
Slide 28