Devices and built-in models

This section gives an overview of the devices and their built-in models with their parameters. SLiCAP distinguishes two kinds of models:

1. Models that have an associated matrix stamp.

2. Models that will be expanded into models with an associated matrix stamp.

Model data will be listed in tables. The fields in these tables have the following meaning:

1. name: the name of the model. This name is associated with the implementation type:

2. type: the implementation type of the model:

   a stamp: a matrix stamp is associated with the model

   b expansion: the model is expanded into elements with models that have associated matrix stamps

3. Ii: TRUE if a dependent variable for an input current is added to the vector with dependent variables else: FALSE. This field applies only for models with type=stamp. The name of this current is the concatenation of two strings:

a "Ii_" and the device name for two-port elements with model type H and HZ

b "I_" and the device name for twoport elements with model type F

4. Io: TRUE if an output current is added to the vector with dependent variables, else: FALSE. This field applies only for models with type=stamp. The name of this current is the concatenation of two strings:

   a "Io_" and the device name for two-port elements that have model type E, EZ, G, H, HZ or N

   b "I_" and the device name for one port elements with model type L, r, V and Z

Valid model parameters and their default values are listed in the subsequent rows of the table:

1. param: the name of the parameter (case sensitive)

2. value | {expression}: the default value or expression for the model parameter

3. Laplace: a boolean TRUE | FALSE indicating if the Laplace variable s is allowed in the device expression

4. description: a description of the parameter

C: Capacitor

Below the syntax and the symbol for a capacitor and the matrix stamp for model C.

Model C

Figure C: Syntax, symbol and matrix stamp of a capacitor.

name	description	type	Ii	Io
C	Linear capacitor	stamp	FALSE	FALSE

Parameters model C

name	description	default	Laplace
value	capacitance	1	FALSE
vinit	initial voltage	0	FALSE

Examples

C1 nodeP nodeN 100n                      ; Capacitor of 100n between nodeP and nodeN

C1 nodeP nodeN C value = 100n            ; Same as above

C1 nodeP nodeN C value = 100n vinit = 0  ; Same as above with initial condition (not yet implemented)

C1 nodeP nodeN {1/tau/R}                 ; Capacitance as an expression

C1 nodeP nodeN C value = {1/tau/R}       ; Same as above

C1 nodeP nodeN myCap                     ; Same as above with a .model line
.model myCap C value={1/tau/R} vinit = 0

D: Diode

Below the syntax, the symbol and the small-signal model expansion for the a diode: model D.

Model D

Figure D: Syntax, symbol and small-signal model expansion for a diode.

name	description	type
D	Small-signal model diode	expansion

Parameters model D

name	description	default	Laplace
gd	conductance	1	FALSE
cd	capacitance	0	FALSE
rs	series resistance	0	FALSE

Examples

D1 nodeA nodeC D ; Diode anode connected to nodeA cathode to nodeC and default parameters.

D1 nodeA nodeC D1N4148
+ gd = {q_e*I_D/K_b/T_A}
+ cd = {q_e*I_D/K_b/T_A/2/PI/tau_F}
+ rs = 25
.model D1N4148 D
.param tau_F = 4n I_D = 1m

E: Voltage-controlled voltage source

SLiCAP has two models for voltage-controlled voltage sources: model E and model EZ. The later one includes a series output impedance but has a compact matrix stamp.

Models

name	description	type	Ii	Io
E	VCVS	stamp	FALSE	TRUE
EZ	VCVS with Z-series	stamp	FALSE	TRUE

Model E

Syntax, symbol and matrix stamp of a VCVS model E

Parameters model E

name	description	default	Laplace
value	voltage gain	1	TRUE

Model EZ

Syntax, symbol and matrix stamp of a VCVS with series impedance: model EZ

Parameters model EZ

name	description	default	Laplace
value	voltage gain	1	TRUE
zo	series impedance	1	TRUE

Examples

E1 outP outN inP inN 1M

E1 outP outN inP inN {1M/(1 + s/2/PI/f_-3dB)}

E1 outP outN inP inN EZ
+ value = {A_0/(1 + s*tau)}
+ zo = {R_out*(1 + s*L_out/R_out}

E2 outP outN inP inN simpleOpamp
.model simpleOpamp EZ
+ value = {A_0/(1 + s*tau)}
+ zo = {R_out*(1 + s*L_out/R_out}

F: Current-controlled current source

Below the syntax, the symbol and the matrix stamp for a CCCS: model F.

Model F

Syntax, symbol and matrix stamp of a CCCS model F

Please notice the independent variable \(I_{Fx}\) which is added to the vector of independent variables equals the product of the denominator of the current gain \(Df_s\) and the input current \(Ii_{Fx}\), rather than the input current.

name	description	type	Ii	Io
F	VCVS	stamp	TRUE	FALSE

Parameters model F

name	description	default	Laplace
value	current gain	1	TRUE

Examples

F1 outP outN inP inN 20

F1 outP outN inP inN {100/(1 + s/2/PI/f_-3dB)}

F1 outP outN inP inN F value={A_i/(1 + s*tau)}

F2 outP outN inP inN myCCCS
.model myCCCS F value = {A_i/(1 + s*tau)}

G: Voltage-controlled current source

SLiCAP has two models for voltage-controlled current sources, model ‘G’ for a complex transfer and model ‘g’ for a real transfer.

Model ‘G’ can be used for sources that need to be selected as loop gain reference variable according to the asymptotic-gain model. The transadmittance can be a function of the Laplace variable ‘s’. Model ‘g’ is intended to be used as conductance or transconductance and cannot be selected a loop gain reference variable.

Models

name	description	type	Ii	Io
G	VCGS	stamp	FALSE	TRUE
g	VCGS	stamp	FALSE	FALSE

Model G

Syntax, symbol and matrix stamp of a VCCS: model G

Parameters model G

name	description	default	Laplace
value	transadmittance	1	TRUE

Model g

Syntax, symbol and matrix stamp of a VCCS: model g

Parameters model g

name	description	default	Laplace
value	transconductance	1	FALSE

Examples

G1 outP outN inP inN 20m

G1 outP outN inP inN {1m/(1 + s/2/PI/f_-3dB)}

G1 outP outN inP inN G value = {A_y/(1 + s*tau)}

G2 outP outN inP inN myVCCS
.model myVCCS G valu e= {A_y/(1 + s*tau)}

G3 outP outN inP inN g value = 1m

G3 outP outN inP inN g value = {q*I_c/k/T}

H: Current-controlled voltage source

SLiCAP has two models for current-controlled voltage sources: model H and model HZ. The later one includes a series output impedance but has a compact matrix stamp.

Models

name	description	type	Ii	Io
H	CCVS	stamp	TRUE	TRUE
HZ	CCVS with Z-series	stamp	FALSE	TRUE

Model H

Syntax, symbol and matrix stamp of a CCVS model H

Parameters model H

name	description	default	Laplace
value	transimpedance	1	TRUE

Model HZ

Syntax, symbol and matrix stamp of a CCVS with series impedance: model HZ

Parameters model HZ

name	description	default	Laplace
value	transimpedance	1	TRUE
zo	series impedance	1	TRUE

Examples

H1 outP outN inP inN 1M

H1 outP outN inP inN {1M/(1 + s/2/PI/f_-3dB)}

H1 outP outN inP inN HZ
+ value = {R_T/(1 + s*tau)}
+ zo = {R_out*(1 + s*L_out/R_out}

H2 outP outN inP inN simpleTransimpedanceAmp
.model simpleTransimpedanceAmp HZ
+ value = {R_T/(1 + s*tau)}
+ zo = {R_out*(1 + s*L_out/R_out}

I: Independent current source

Below the syntax, the symbol and the matrix stamp for an independent current source: model I.

Model I

Syntax, symbol and matrix stamp of an independent current source: model I

name	description	type	Ii	Io
I	Independent current source	stamp	FALSE	FALSE

Parameters model I

name	description	default	Laplace
value	Current (Laplace transform)	0	TRUE
dc	DC value [A]	0	TRUE
dcvar	Variance of DC value [A^2]	0	TRUE
noise	Noise current density [A^2/Hz]	0	TRUE

Examples

* Both definitions are equivalent:
I1 n1 n2 1m
I1 n1 n2 I value = 1m

Iin 0 input I value = {I_s} noise = 1e-24 dc=10n dcvar = 4e-18
.param I_s = {1m/s}; Step of 1mA starting at t=0

J: Junction FET

Like the PN diode, the JFET model J is expanded into network elements that have a matrix stamp.

Model J

Syntax, symbol and network expansion of a junction FET: model J

name	description	type
J	Small-signal model JFET	expansion

Parameters model J

name	description	default	Laplace
cgs	contactance	0	FALSE
cdg	capacitance	0	FALSE
gm	forward transconductance	1E-3	FALSE
go	output conductance	0	FALSE

Examples

J1 nodeD nodeG nodeS myJFET
.model myJFET J cgs=20p cdg=1p gm=15m go=500u

K: Coupling factor

Below the syntax, the symbol and the matrix stamp for a coupling between two inductors: model K.

Model K

Syntax, symbol and matrix stamp of a coupling between two inductors: model K

name	description	type	Ii	Io
K	Coupling factor	stamp	FALSE	FALSE

Parameters model K

name	description	default	Laplace
value	coupling factor	1	FALSE

Examples

L1 n1 n2 {L_a}
L2 n3 n4 {L_b}
k12 L1 L2 0.98

L: Inductor

Below the syntax, the symbol and the matrix stamp for an inductor: model L.

Model L:

Syntax, symbol and matrix stamp of an inductor: model L

name	description	type	Ii	Io
L	Linear inductor	stamp	FALSE	FALSE

Parameters model L

name	description	default	Laplace
value	inductance	1	FALSE
iinit	initial condition	0	FALSE

Examples

L1 n1 n2 {L_a}

L1 n1 n2 L value = {L_a}

L1 n1 n2 L myL
.model myL L value = {L_a}

L1 n1 n2 L myL
.model myL L value = {L_a} iinit = 0

M: 4-terminal MOS

SLiCAP has two models for 4-terminal MOS transistors. Model M for a single MOS transistor and model MD for a differential-pair MOS. The latter one facilitates the design and analysis of negative-feedback amplifiers in which one controlled source that models the gain of the differential-pair MOS can be selected as loop gain reference variable.

Models

name	description	type
M	Four-terminal MOS	expansion
MD	Four-terminal diff. pair MOS	expansion

Model M

Syntax, symbol and network expansion of a 4-terminal MOS: model M

Parameters model M

name	description	default	Laplace
cgs	gate-source capacitance	0	FALSE
cgb	gate-bulk capacitance	0	FALSE
cdg	drain-gate capacitance	0	FALSE
cdb	drain-bulk capacitance	0	FALSE
csb	source-bulk capacitance	0	FALSE
gm	forward transconductance	1E-3	FALSE
gb	bulk transconductance	0	FALSE
go	output conductance	0	FALSE

Model MD

Syntax, symbol and network expansion of a 4-terminal MOS: model MD

Parameters model MD

name	description	default	Laplace
cgg	gate-gate capacitance	0	FALSE
cdg	drain-gate capacitance	0	FALSE
cdd	drain-drain capacitance	0	FALSE
gm	forward transconductance	1E-3	FALSE
go	output conductance	0	FALSE

Examples

Below three ways of defining a MOS in a circuit. The first example calls the mos model M with its default parameters and then overrides these parameters by local definitions in the call. The model parameter gm is passed as global parameter gm.

M1 D G S B M gm={g_m} gb = 150u go = 100u cgs = 0.2p cdg = 10f

The second example calls the model from a library file and redefines g_m as a global parameter.

M1 D G S B myMOS gm = {g_m}
.include myMOS.lib

The third example calls a model and its parameters. For a given process, geometry and device operating point, these small-signal parameters can be obtained from a SPICE simulation.

M1 D G S B M1
.model M1 M gm = 2m gb = 150u go = 100u cgs = 0.2p cdg = 10f

The next example shows the application of a differential-pair MOS.

M1 D1 D2 G1 G2 myDiffPairMOS
*parameters of the single MOS
.param g_m = 1m g_o = 100u c_gs = 0.2p c_dg = 10f c_db = 5f
*parameters of the diff. pair MOS
.model myDiffPairMOS MD
+ gm  = {g_m/2}
+ go  = {g_o/2}
+ cgg = {c_gs/2}
+ cdg = {c_dg}
+ cdd = {c_db/2}

N: Nullor

Model N

Syntax, symbol and matrix stamp of a nullor: model N

name	description	type	Ii	Io
N	Nullor	stamp	FALSE	TRUE

Examples

N_amp out 0 in+ in-

O: Operational amplifier

SLiCAP has two built-in models for operational amplifiers:

1. A small-signal model for a voltage-feedback operational amplifier: model OV

2. A small-signal model for a current-feedback operational amplifier: model OC

Models

name	description	type
OV	Voltage-feedback OpAmp	expansion
OC	Current-feedback OpAmp	expansion

Model OV

Syntax, symbol and network expansion of a voltage-feedback operational amplifier: model OV

Parameters model OV

name | description		default	Laplace
cd	differential-mode input capacitance	0	FALSE
cc	common-mode input capacitance	0	FALSE
gd	differential-mode input conductance	0	FALSE
gc	common-mode input conductance	0	FALSE
av	voltage gain	1E6	TRUE
zo	output impedance	0	TRUE

Model OC

Syntax, symbol and network expansion of a current-feedback operational amplifier: model OC

Parameters model OC

name	description	default	Laplace
cp	input capacitance non-inverting input	0	FALSE
gp	input conductance non-inverting input	0	FALSE
cpn	input capacitance	0	FALSE
gpn	input conductance	0	FALSE
gm	input stage transconductance	20E-3	FALSE
zt	output stage transimpedance	1E6	TRUE
zo	output impedance	0	TRUE

Examples

O1 inP inN out 0 AD8610
.model AD8610 OV
+ cd = 15p
+ cc = 8p
+ av = {300k*(1-s*1.3n)/(1+s*2.4m)/(1+s*1.3n)}
+ zo = 20

O1 inP inN out 0 LT1223
.model LT1223 OC
+ cp = 1.5p
+ gp = 100n
+ gm = 65m
+ zt = {5M/(1+s*680u)/(1+s*1.6n)}
+ zo = 30

Q: 4-terminal BJT

SLiCAP incorporates three models for 4-terminal Bipolar Junction Transistors (BJTs):

1. Model QV for a single vertical BJT

2. Model QL for a single lateral BJT

3. Model QD for a differential pair.

   The latter one facilitates the design and analysis of negative-feedback amplifiers in which one controlled source that models the gain of the differential-pair BJT can be selected as loop gain reference variable.

Models

name	description	type
QV	Four-terminal vertical BJT	expansion
QL	Four-terminal lateral BJT	expansion
QD	Four-terminal diff. pair BJT	expansion

Model QV

SLiCAP built-in model for a 4-terminal vertical BJT: model QV

Parameters model QV

name	description	default	Laplace
cpi	internal base-emitter capacitance	0	FALSE
cbc	internal base-collector capacitance	0	FALSE
cbx	external base-collector capacitance	0	FALSE
cs	collector-substrate capacitance	0	FALSE
gpi	internal base-emitter conductance	1E-3	FALSE
gm	transconductance	0	FALSE
go	output conductance	0	FALSE
gbc	internal base-collector conductance	0	FALSE
rb	base resistance	0	FALSE

Model QL

SLiCAP built-in model for a 4-terminal lateral BJT: model QL

Parameters model QL

name	description	default	Laplace
cpi	internal base-emitter capacitance	0	FALSE
cbc	internal base-collector capacitance	0	FALSE
cbx	external base-collector capacitance	0	FALSE
cs	base-substrate capacitance	0	FALSE
gpi	internal base-emitter conductance	1E-3	FALSE
gm	transconductance	0	FALSE
go	output conductance	0	FALSE
gbc	internal base-collector conductance	0	FALSE
rb	base resistance	0	FALSE

Model QD

SLiCAP built-in model for a differential-pair BJT: model QD

Parameters model QD

name	description	default	Laplace
cbb	internal base-base capacitance	0	FALSE
cbc	internal base-collector capacitance	0	FALSE
cbx	external base-collector capacitance	0	FALSE
gbb	internal base-base conductance	0	FALSE
gm	forward transconductance	1E-3	FALSE
gcc	colector-collector conductance	0	FALSE
gbc	internal base-colector conductance	0	FALSE
rb	base resistance	0	FALSE

Examples

Below a specification of a BJT of which the model parameters are expressed in SPICE model parameters, the operating point current I_C and the operating voltage V_CE. The expressions are simplifications of the nonlinear device equations for a bipolar transistor.

Q1 C B E S QV
+ gm  = {g_m}
+ gpi = {g_m/beta_F}
+ go  = {(I_c+V_ce)/VAF}
+ cbc = {c_bc}
+ cbx = {c_bx}
+ cpi = {(CJE + TAUF*g_m)}
+ rb  = {r_b}
+ gbc = {g_bc}
.param gm = I_c/U_T

Below a specification of a BJT that uses small-signal parameters in an operating point as they can be determined with the aid of a SPICE operating point simulation.

Q1 C B E S Q1
.model Q1 QV
+ gm  = 20m
+ rb  = 50
+ go  = 10u
+ gbc = 0
+ cpi = 2p
+ cbc = 0.05p
+ cbx = 0.05p
+ cs  = 0.2p

Below a specification of a lateral BJT that uses small-signal parameters in an operating point as they can be determined with the aid of a SPICE operating point simulation.

Q1 C B E S Q1
.model Q1 QL
+ gm=20m
+ rb=50
+ go=10u
+ gbc=0
+ cpi=2p
+ cbc=0.05p
+ cbx=0.05p
+ cs=0.2p

Below an example of a differential pair BJT of which the parameters are related to those of the single transistor stage, biased in the same operating point as the transistors of the differential pair.

Q1 C1 C2 B1 B2 myDiffPairBJT
.model myDiffPairBJT QD
+ gm  = {I_c/2/U_T}
+ gpi = {I_c/2/U_T/beta_AC}
+ go  = {2*(I_c+V_ce)/V_AF}
+ cbc = {c_bc}
+ cbx = {c_bx}
+ cpi = {(CJE + TAUF*I_c/U_T)/2}
+ rb  = {r_b}
* below the device parameters of the single transistor
.param r_b = 50 V_AF=50 g_bc = 0 CJE = 2p c_bc = 0.05p c_bx = 0.05p beta_AC=100
* below the operating point the single transistor
.param I_c = 1m V_ce=5

R: Resistor

The default model type for a resistor is R. Zero value for its resistance causes a divide by zero error while building the matrix. If zero value is required, e.g. because of parameter stepping, model type r should be used.

Models

name	description	type	Ii	Io
R	Resistor resistance > 0	stamp	FALSE	FALSE
r	Resistor resistance >= 0	stamp	FALSE	TRUE

Model R

Syntax, symbol and matrix stamp of a resistor: model R

Parameters model R

name	description	default	Laplace
value	resistance	1	FALSE
dcvar	variance	0	FALSE
dcvarlot	variance of lot	0	FALSE
noisetemp	noise temperature	0	FALSE
noiseflow	corner frequency 1/f noise	0	FALSE
dcvar	variance	0	FALSE

Model r

Syntax, symbol and matrix stamp of a resistor: model r

Parameters model r

name	description	default	Laplace
value	resistance	1	FALSE
dcvar	variance	0	FALSE
dcvarlot	variance of lot	0	FALSE
noisetemp	noise temperature	0	FALSE
noiseflow	corner frequency 1/f noise	0	FALSE
dcvar	variance	0	FALSE

Examples

The examples below illustrates four different ways for specifying a resistor that is connected between the nodes nP and nN and has a numerical value of 10kOhm.

R1 nP nN R value = {R} noiseTemp = {T} noiseflow ={f_ell} dcvar = {R * sigma_R^2}

R1 nP nN {20 * alpha}

R1 nP nN r value = {R_a} dcvar = {(sigma * R_a)^2}

R1 nP nN myR
.model myR R value = {20 * alpha}
.param alpha = 500

T: Ideal transformer

SLiCAP has a built-in model for an ideal transformer.

Model T

Syntax, symbol and matrix stamp of an ideal transformer: model T

name	description	type	Ii	Io
T	Ideal transformer	stamp	FALSE	TRUE

Parameters model T

name	description	default	Laplace
value	turns ratio	1	FALSE

Examples

T1 secP secN priP priN {Vpri/Vsec}

T1 secP secN priP priN T value={Vpri/Vsec}

T1 secP secN priP priN myTrafo

.model myTrafo T value={Vpri/Vsec}

V: Independent voltage source

Model V

Symbol, syntax and matrix stamp of an ideal independent voltage source: model V

name	description	type	Ii	Io
V	Independent voltage source	stamp	FALSE	TRUE

Parameters model V

name	description	default	Laplace
value	Voltage (Laplace transform)	0	TRUE
dc	DC value [V]	0	TRUE
dcvar	Variance of DC value [V^2]	0	TRUE
noise	Noise voltage density [V^2/Hz]	0	TRUE

Examples

* Both definitions are equivalent:
V1 n1 n2 20m
V1 n1 n2 V value = 20m

Vin 0 input V value = {V_s} noise = 1e-16 dc = 0 dcvar = 10e-8
.param V_s = {1/s}; Step of 1V starting at t = 0

W: Gyrator

SLiCAP is often used for conceptual design and for this reason the gyrator has been included.

Model W

name	description	type	Ii	Io
W	Gyrator	stamp	FALSE	FALSE

Parameters model W

name	description	default	Laplace
value	transconductance	1	FALSE

Examples

Below two definitions of a gyrator with a conversion gain of 10mA/V.

W1 outP outN inP inN 10m

W1 outP outN inP inN W value = 10m

X: Sub circuit call

See examples in section: .subckt … .ends lines.