Application Note
Varactor SPICE Models for
RF VCO Applications
APN1004
Varactor Equivalent Circuit Model
Definitions
A simplified equivalent circuit of varactor is shown in
Figure 1.
This varactor model is useful for RF VCO applications
although it neglects some parasitic components often
needed for higher frequency microwave applications, such
as the distributed line package model and some
capacitance due to ground proximity. For most RF VCO
applications, to about 2.5 GHz, these parasitic
components would not be important unless higher
harmonics generated by the varactor affects performance
of the VCO. In this case, a more detailed equivalent circuit
model is needed. The technique used should be based
on the varactor model extraction procedure from
S-parameter data.
A SPICE model, defined for the Libra IV environment, is
shown in Figure 2, with the description of the parameters
employed. It neglects the package capacitance, C
P
, its
typical 0.10 pF value is absorbed within the junction
capacitance C
V
.
C
V
Cathode
Junction Capacitance
R
S
Series
Resistance
L
S
Series
Inductance
Anode
D
Junction Diode
C
P
Parallel Capacitance
Figure 1. Simplified Equivalent Circuit of Varactor
Figure 2. Libra IV SPICE Model
Alpha Industries, Inc.
[781] 935-5150
•
Fax
[617] 824-4579
•
Email
sales@alphaind.com
•
www.alphaind.com
Specifications subject to change without notice. 6/99A
1
Varactor SPICE Models for RF VCO Applications
APN1004
Parameter
IS
R
S
N
TT
C
JO
V
J
M
E
G
XTI
KF
AF
FC
B
V
I
BV
ISR
NR
IKF
NBV
IBVL
NBVL
T
NOM
FFE
Series resistance
Description
Saturation current (with N, determine the DC characteristics of the diode)
Emission coefficient (with IS, determines the DC characteristics of the diode)
Transit time
Zero-bias junction capacitance (with V
J
and M define nonlinear junction capacitance of the diode)
Junction potential (with V
J
and M define nonlinear junction capacitance of the diode)
Grading coefficient (with V
J
and M define nonlinear junction capacitance of the diode)
Energy gap (with XTI, helps define the dependence of IS on temperature)
Saturation current temperature exponent (with E
G
, helps define the dependence of IS on temperature)
Flicker noise coefficient
Flicker noise exponent
Forward-bias depletion capacitance coefficient
Reverse breakdown voltage
Current at reverse breakdown voltage
Recombination current parameter
Emission coefficient for ISR
High-injection knee current
Reverse breakdown ideality factor
Low-level reverse breakdown knee current
Low-level reverse breakdown ideality factor
Nominal ambient temperature at which these model parameters were derived
Flicker noise frequency exponent
Unit
A
Ω
-
S
F
V
-
EV
-
-
-
-
V
A
A
-
A
-
A
-
°C
-
Default
1e-14
0
1
0
0
1
0.5
1.11
3
0
1
0.5
Infinity
1e-3
0
2
Infinity
1
0
1
27
1
Table 1. SPICE Model Parameters
Table 1 describes the model parameters. It shows default
values appropriate for silicon varactor diodes, which may
be used by the Libra IV simulator unless others are
specifically defined.
The effect of the diode junction is ignored in this model.
This simplification ignores the rectifying effect of diode
during a positive voltage swing. However, for most RF VCO
applications, the lowest practical DC control voltage value
is 0.5 V and the magnitude of RF voltage rarely exceeds
0.2 V peak. Therefore, the varactor is maintained in its
reverse bias state. However, in a large signal application
where it is necessary to consider the diode’s rectifying
properties, it may be done by entering the additional diode
parameters in the SPICE model defined for the LIBRA IV
environment.
According to the SPICE model in Table 1, the varactor
capacitance, C
V
, is a function of the applied reverse DC
voltage, V
R
, and may be expressed as follows:
C
V
=
C
JO
+ C
P
This equation is a mathematical simulation of the
capacitance characteristic. The model is accurate for
abrupt junction varactors (SMV1400 Series); for
hyperabrupt junction varactors the model is less accurate
but very reliable. The form is similar to the traditional
varactor equation but uses values for V
J
, M and C
P
, that
were extracted individually from measured C
V
(V
R
) data
for each varactor part number.
Series resistance, R
S
, is a function of applied voltage and
operating frequency and may be considered constant. The
value used should be taken from the specified maximum
value or derived from its Q specification.
Series inductance, L
S
, is also considered constant at a
value of 1.7 nH. This incorporates the 1.5 nH package
inductance with some insertion inductance typical for PC
boards in RF wireless applications.
(
1 + V
R
)
V
J
M
2
Alpha Industries, Inc.
[781] 935-5150
•
Fax
[617] 824-4579
•
Email
sales@alphaind.com
•
www.alphaind.com
Specifications subject to change without notice. 6/99A
Varactor SPICE Models for RF VCO Applications
APN1004
Table 2 gives values for Alpha’s plastic packaged
varactors that may be used for SPICE model simulation
equation. It may be employed for each varactor junction
in the SOD-323 and SOT-23 package. It also gives
calculated values for the capacitance ratio between
0.5–2.5 V for each diode that is a typical voltage range
for battery operated wireless VCO circuits.
Note: The values listed for V
J
, M and C
P
in the table were
empirically determined and do not represent the precise
physical or electronic properties of the semiconductor or
the package.
Part Number
SMV1127
SMV1129
SMV1139
SMV1140
SMV1141
SMV1142
SMV1143
SMV1144
SMV1145
SMV1146
SMV1147
SMV1148
SMV1175
SMV1206
SMV1207
SMV1212
SMV1213
SMV1214
SMV1215
SMV1223
SMV1224
SMV1225
SMV1227
SMV1228
SMV1229
SMV1232
SMV1233
SMV1234
SMV1235
SMV1236
SMV1237
SMV1245
SMV1247
SMV1248
SMV1249
SMV1250
SMV1251
C
JO
(pF)
23.9
27.5
8
70.44
7.32
13.38
18.99
24.01
41.8
61.13
89.52
104.7
13.43
26.11
59.4
72.47
28.9
22.74
14.36
25.19
25.19
17.46
52.46
130.1
271.72
4.2
4.12
8.75
16.13
21.63
66.16
6.9
9.22
21.54
39
47
60
V
J
(V)
2.2
2.8
1.2
3.5
2.2
2.2
2.2
2.2
2.5
2.5
2.5
2.25
3
4
6.5
110
190
190
190
100
100
110
5
5
5
1.7
1.7
2.3
8
8
10
3.5
100
13
17
17
17
M
1
1.1
0.65
1.4
1
1
1
1
1.1
1.1
1.1
1.1
1.15
1.45
2.3
67
105
106
115
45
45
47
1.8
1.8
1.8
0.9
0.9
1.1
4
4.2
5.3
1.7
100
10.5
14
14
14
C
P
(pF)
0
0
0
0
0
0
0
0
0
0
0
0
0
0.3
2
4.5
2.2
1.5
1.1
2.5
2.5
1.6
0
0
0
0
0.7
1.2
2
3.2
9
0.47
0.55
0
0
0
0
R
S
(Ω)
0.5
0.4
0.6
0.3
0.7
0.7
0.65
0.65
0.6
0.6
0.55
0.5
1.0
0.7
0.4
0.45
0.8
0.7
1.0
1.5
1.5
1.8
0.55
0.32
0.25
1.5
1.2
0.8
0.6
0.5
0.13
2
2
1.8
1.5
1.5
1.3
L
S
(nH)
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.7
C0.5/C2.5
1.68
1.73
1.68
1.68
1.66
1.67
1.67
1.67
1.68
1.68
1.68
1.7
1.68
1.69
1.73
2.82
2.53
2.60
2.73
2.10
2.10
2.05
1.75
1.75
1.75
1.87
1.71
1.82
1.84
1.86
2.05
1.82
2.15
6.2
6.75
5.41
5.86
Table 2. Plastic Packaged Varactor Values for SPICE Model Simulation Equation
Alpha Industries, Inc.
[781] 935-5150
•
Fax
[617] 824-4579
•
Email
sales@alphaind.com
•
www.alphaind.com
Specifications subject to change without notice. 6/99A
3
Analog electronics
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