1. Michael Thomas Flanagan's Java Scientific Library
ImpedanceSpectroscopy, ImpSpecSimulation and
ImpSpecRegression Classes
http://www.ee.ucl.ac.uk/~mflanaga/java
http://www.ee.ucl.ac.uk/~mflanaga
EQUIVALENT CIRCUIT MODELS
The 44 equivalent circuits, already coded within the ImpedanceSpectroscopy,
ImpSpecSimulation and ImpSpecRegression classes, and the associated model numbers are
listed below.
The list following the model number is the order in which the parameter values must be
enetered in the parameter array arguments in the relevant methods in the above classes.
Model 1 (R1)
R1
Resistor
Model 2 (C1)
C1
Capacitor
Model 3 (L1)
L1
Inductor
Model 4 (W1)
Warburg Impedance (infinite diffusion layer thickness)
[Z = W/√ω − jW/√ω]
W1
W
Model 5 (Fsigma1, Fdelta1)
Warburg Impedance (finite diffusion layer thickness)
[Z = (σ/√ω)(1 − j)tanh{δ(jω)1/2}]
F1
F
Model 6 (Qsigma1, Qalpha1)
Constant Phase Element [Z = σ (jω)−α]
Q1
>>
Model Circuits for Michael Thomas Flanagan's Java Library Impedance Spectroscopy classes: page 1 of 9

2. Model 7 (R1, C1)
C1 R1
Model 8 (R1, L1)
L1 R1
Model 9 (L1, C1)
L1 C1
Model 10 (R1, C1)
C1
R1
Model 11 (R1, L1)
R1
L1
Model 12 (L1, C1)
C1
L1
Model Circuits for Michael Thomas Flanagan's Java Library Impedance Spectroscopy classes: page 2 of 9

3. Model 13 (R1, C1, R2)
C1
R2
R1
Model 14 (R1, C1, R2, L1)
C1
L1
R2
R1
Model 15 (R1, C1, R2, L1)
L1
C1
R2
R1
Model 16 (R1, C1, C2)
C1
C2
R1
Model 17 (R1, C1, C2)
C1
C2 R1
Model Circuits for Michael Thomas Flanagan's Java Library Impedance Spectroscopy classes: page 3 of 9

4. Model 18 (R1, C1, R2, C2)
C1
R2 C2
R1
Model 19 (R1, C1, R2, C2)
C1 C2
R1 R2
Model 20 (R1, C1, R2, C2, R3)
C1 C2
R3
R1 R2
Model 21 (R1, C1, R2, C2, R3)
C2
C1
R3
R2
R1
Model 22 (R1, C1, R2,C2, R3, C3)
C1 C2 C3
R1 R2 R3
Model Circuits for Michael Thomas Flanagan's Java Library Impedance Spectroscopy classes: page 4 of 9

5. Model 23 (R1, C1, R2,C2, R3, C3, R4)
C1 C2 C3
R4
R1 R2 R3
Model 24 (R1, C1, W1, R2)
C1
R2
R1
W
W 1
Model 25 (R1, C1, Fsigma1, Fdelta1, R2)
C1
R2
R1
F
F 1
Model 26 (R1, C1, Qsigma1, Qalpha1, R2)
C1
R2
>>
R1 Q1
Model 27 (R1, C1, R2, C2, W1)
C1 C2
W1
W
R1 R2
Model Circuits for Michael Thomas Flanagan's Java Library Impedance Spectroscopy classes: page 5 of 9

6. Model 28 (R1, C1, R2, C2, W3, C3, R4)
C1 C2 C3
R2
W
W 3
R4
R1
Model 29 (R1, C1, R2, Qsigma1, Qalpha1)
C1 Q1
>>
R1 R2
Model 30 (R1, C1, R2, Qsigma1, Qalpha1, R3)
C1 Q1
R3
>>
R1 R2
Model 31 (R1, Qsigma1, Qalpha1, R2, Qsigma2, Qalpha2, R3, Qsigma3, Qalpha3)
Q1 Q2 Q3
>> >> >>
R1 R2 R3
Model 32
(R1, Qsigma1, Qalpha1, R2, Qsigma2, Qalpha2, R3, Qsigma3, Qalpha3, R4)
Q1 Q2 Q3
>> >> >>
R4
R1 R2 R3
Model Circuits for Michael Thomas Flanagan's Java Library Impedance Spectroscopy classes: page 6 of 9

7. Model 33
(R1, Qsigma1, Qalpha1, R2, Qsigma2, Qalpha2, R3, Qsigma3, Qalpha3, R4, C1)
C1
Q1 Q2 Q3
>> >> >>
R4
R1 R2 R3
Model 34 (C1, Qsigma1, Qalpha1, C2, Qsigma2, Qalpha2, C3, Qsigma3, Qalpha3)
Q1 Q2 Q3
>> >> >>
C1 C2 C3
Model 35
(C1, Qsigma1, Qalpha1, C2, Qsigma2, Qalpha2, C3, Qsigma3, Qalpha3, R1)
Q1 Q2 Q3
>> >> >>
R1
C1 C2 C3
Model 36
(R1, Qsigma1, Qalpha1, C1, R2, Qsigma2, Qalpha2, C2, R3, Qsigma3, Qalpha3, C3)
Q1 R1 Q2 R2 Q3 R3
>> >> >>
C1 C2 C3
Model 37
(R1, Qsigma1, Qalpha1, C1, R2, Qsigma2, Qalpha2, C2, R3, Qsigma3, Qalpha3, C3,
R4)
Q1 R1 Q2 R2 Q3 R3
>> >> >>
R4
C1 C2 C3
Model Circuits for Michael Thomas Flanagan's Java Library Impedance Spectroscopy classes: page 7 of 9

8. Model 38 (R1, Qsigma1, Qalpha1, C1, R2, Qsigma2, Qalpha2, C2)
Q1 R1 Q2 R2
>> >>
C1 C2
Model 39 (R1, Qsigma1, Qalpha1, C1, R2, Qsigma2, Qalpha2, C2, R3)
Q1 R1 Q2 R2
>> >> R3
C1 C2
Model 40 (R1, Qsigma1, Qalpha1, C1, R2, Qsigma2, Qalpha2, C2, R3)
C1
Q1 Q2 Q3
>> >> >>
R4
R1 R2 R3
Model 41
(R1, Qsigma1, Qalpha1, R2, Qsigma2, Qalpha2, R3, Qsigma3, Qalpha3, R4, C1)
C1
Q1 C2 Q3
>> >>
R4
R1 R2 R3
Model Circuits for Michael Thomas Flanagan's Java Library Impedance Spectroscopy classes: page 8 of 9

9. Model 42 (R1, Qsigma1, Qalpha1, R2, C2, R3, Qsigma3, Qalpha3, R4)
Q1 C2 Q3
>> >>
R4
R1 R2 R3
Model 43
(R1, Qsigma1, Qalpha1, R2, Qsigma2, Qalpha2, R3, Qsigma3, Qalpha3, R4, C1)
C1
Q1 Q2 Q3
>> >> >>
R4
R1 R2 R3
Model 44 (R1, Qsigma1, Qalpha1, R2, Qsigma2, Qalpha2, R3, C1)
C1
Q1 Q2
>> >>
R3
R1 R2
Model Circuits for Michael Thomas Flanagan's Java Library Impedance Spectroscopy classes: page 9 of 9