This document describes a simplified SPICE behavioral model for lithium-ion capacitors. The model allows circuit designers to predict performance by simulating charge and discharge times. It represents key capacitor specifications like capacity, ESR, and cutoff voltage. The model is parameterized so designers can adjust it to match real capacitor specifications. Simulations demonstrate how the model reproduces manufacturer charge and discharge time data at different currents.

1. Lithium Ion Capacitor
Simplified SPICE Behavioral Model
Copyright (C) Siam Bee Technologies 2015 1
PSpice Version
Bee Technologies

2. Contents
1. Benefit of the Model
2. Model Feature
3. Concept of the Model
4. Parameter Settings
5. Li-Ion Capacitor Specification (Example)
5.1 Charge Time Characteristic
5.2 Discharge Time Characteristic
Simulation Index
Copyright (C) Siam Bee Technologies 2015 2

3. 1. Benefit of the Model
• The model enables circuit designer to predict and optimize Li-Ion
Capacitor runtime and circuit performance.
• The model can be easily adjusted to your own Li-Ion Capacitor
specifications by editing a few parameters that are provided in the
datasheet.
• The model is optimized to reduce the convergence error and the
simulation time
Copyright (C) Siam Bee Technologies 2015 3

4. • This Li-Ion Capacitor Simplified SPICE Behavioral Model is for users who
require the model of a Li-Ion Capacitor as a part of their system.
• Capacitor Voltage(Vcap) vs. Capacitor Capacity Level (SOC) Characteristic,
that can perform battery charge and discharge time at various current rate
conditions, are accounted by the model.
2. Model Feature
Copyright (C) Siam Bee Technologies 2015 4
Equivalent circuit of Li-Ion Capacitor model
Capacity
Rself-Discharge
S O C
+
-
G 1
G V A L U E
-
+
+
-
E 2
E
0
R D C
E S RC A C
P L U S
M I N U S
d s c h
I N +
I N -
O U T +
O U T -
E 9
E V A L U E
1 0 5
+
-
G 3
G V A L U E

5. 3. Concept of the Model
Copyright (C) Siam Bee Technologies 2015 5
Li-Ion capacitor
Simplified SPICE Behavioral Model
[Spec: CAP,ESR,RDC, NS]
Adjustable SOC [ 0-100 (%) ]
+
-
• The model is characterized by parameters: C, which represent the capacitor
capacity and SOC, which represent the capacitor initial capacity level.
• Open-circuit voltage (VOC) vs. SOC is included in the model as an analog
behavioral model (ABM).
• NS (Number of Cells in series) is used when the Li-ion cells are in series to
increase battery voltage level.
Output
Characteristics

6. 4. Parameter Settings
CAP is the amp-hour capacity [F]
– e.g. C = 10, 100, or 1000 [F]
ESR is the equivalent series resistance of capacitors
– e.g. C = 0.1mΩ, 1mΩ, or 10mΩ [Ω]
RDC is the DC resistance of capacitors
– e.g. C = 0.1mΩ, 1mΩ, or 10mΩ [Ω]
NS is the number of cells in series
– e.g. NS=1 for 1 cell capacitor, NS=2 for 2 cells capacitor
(capacitor voltage is double from 1 cell)
SOC is the initial state of charge in percent
– e.g. SOC=0 for a empty capacitor (0%), SOC=1 for a full
charged capacitor (100%)
TSCALE turns TSCALE seconds into a second
– e.g. TSCALE=60 turns 60s or 1min into a second,
TSCALE=3600 turns 3600s or 1h into a second,
• From the Li-Ion Capacitor specification, the model is characterized by setting
parameters CAP, ESR, RDC, NS, SOC and TSCALE.
Copyright (C) Siam Bee Technologies 2015 6
Model Parameters:
(Default values)
U 1
L I - I O N _ C A P A C I T O R
C A P = 1 0 0 0
E S R = 0 . 8 m
R D C = 1 . 2 m
N S = 1
T S C A L = 1
S O C = 1 0 0

7. U 1
L I - I O N _ C A P A C I T O R
C A P = 1 0 0 0
E S R = 0 . 8 m
R D C = 1 . 2 m
N S = 1
T S C A L = 1
S O C = 1 0 0
5. Li-Ion Capacitor Specification (Example)
Copyright (C) Siam Bee Technologies 2015 7
Capacitance capacity, ESR
and DCR are input as a
model parameter
Capacitance capacity, ESR
and DCR are input as a
model parameter
Rated Voltage 3.8V
Minimal Operating Voltage
(Cutoff Voltage)
2.2V
Capacitance/Capacity 1000F
ESR 0.8mΩ
DCR 1.2mΩ

8. Ti me
0s 50s 100s 150s 200s 250s 300s 35 0s 400s
V( C)
1. 5V
2. 0V
2. 5V
3. 0V
3. 5V
4. 0V
5.1 Charge Time Characteristic
Copyright (C) Siam Bee Technologies 2015 8
• Rated Voltage: 3.8V
• Cutoff Voltage: 2.2V
• Charging Current: 5A
Capacity=100%
(second)
Measurement Simulation
SOC=0 means capacitor start
from 0% of capacity (empty)
SOC=0 means capacitor start
from 0% of capacity (empty)
U 1
L I - I O N _ C A P A C I T O R
C A P = 1 0 0 0
E S R = 0 . 8 m
R D C = 1 . 2 m
N S = 1
T S C A L = 1
S O C = 0

9. 5.1 Charge Time Characteristic
− Simulation Circuit and Setting
*Analysis directives:
.TRAN 0 350.85s 0 100m
.PROBE V(alias(*)) I(alias(*)) W(alias(*)) D(alias(*)) NOISE(alias(*))
Copyright (C) Siam Bee Technologies 2015 9
TSCALE turn 1 is equaled
1 second into a second
TSCALE turn 1 is equaled
1 second into a second
Charging CurrentCharging Current
I 1
5 A d c
C
0
U 1
L I - I O N _ C A P A C I T O R
C A P = 1 0 0 0
E S R = 0 . 8 m
R D C = 1 . 2 m
N S = 1
T S C A L = 1
S O C = 0

10. Ti me
0s 50s 100s 150s 200s 250s 3 00s 350s 400s
V( C)
1. 5V
2. 0V
2. 5V
3. 0V
3. 5V
4. 0V
Copyright (C) Siam Bee Technologies 2015 10
Measurement Simulation
(second)
• Rated Voltage: 3.8V
• Cutoff Voltage: 2.2V
• Discharge Current: 5A
SOC=0 means capacitor start
from 100% of capacity (Full)
SOC=0 means capacitor start
from 100% of capacity (Full)
5.2 Discharge Time Characteristic
U 1
L I - I O N _ C A P A C I T O R
C A P = 1 0 0 0
E S R = 0 . 8 m
R D C = 1 . 2 m
N S = 1
T S C A L = 1
S O C = 1 0 0

11. 5.2 Discharge Time Characteristic
− Simulation Circuit and Setting
Copyright (C) Siam Bee Technologies 2015 11
*Analysis directives:
.TRAN 0 315s 0 100m
.PROBE V(alias(*)) I(alias(*)) W(alias(*)) D(alias(*)) NOISE(alias(*))
Discharging CurrentDischarging Current
I 1
5 A d c
C
0
U 1
L I - I O N _ C A P A C I T O R
C A P = 1 0 0 0
E S R = 0 . 8 m
R D C = 1 . 2 m
N S = 1
T S C A L = 1
S O C = 1 0 0

12. Copyright (C) Siam Bee Technologies 2015 12
Topic Active Profile
5A Charge Voltage vs. Time Characteristic V-t_5A-Chrg-trans
5A Discharge Voltage vs. Time Characteristic V-t_5A-Dsch-trans
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