Atlas

of Electrochemical Nyquist Diagrams.

I. One semicircle and straight line
A guide to select equivalent circuits

-А4 -А4
0 0 0 0 0 0
0 0 0 0 0 0

0 0 0 0

0 0

0 0 0 0 0 0

0 0 0 0
0 0 0 0
0 0 0 0

0 0 0 0

0 0 0 0 0 0
0 0 0 0 0 0

0 0 0 0

0 0 0 0
0 0 0 0

0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

Bio-Logic @ www.bio-logic.info

September 28, 2011

2
Contents

1 Nyquist diagrams made of one straight line 5

1.1 Capacitive straight line . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.1 C1 element . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.2 R1+C1 circuit . . . . . . . . . . . . . . . . . . . . . . . . 6
1.1.3 Q1 element . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.1.4 R1+Q1 circuit . . . . . . . . . . . . . . . . . . . . . . . . 6
1.1.5 Q1 element, α1 = 1/2 . . . . . . . . . . . . . . . . . . . . 6
1.1.6 W1 element . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.1.7 R1+Q1 circuit, α1 = 1/2 . . . . . . . . . . . . . . . . . . 6
1.1.8 R1+W1 circuit . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Inductive straight line . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.1 L1 element . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.2 R1+L1 circuit . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.3 Q1 element, α1 < 0 . . . . . . . . . . . . . . . . . . . . . 8
1.2.4 R1+Q1 element, α1 < 0 . . . . . . . . . . . . . . . . . . . 8
1.2.5 L1+C1 circuit . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.6 R1+L1+C1 circuit . . . . . . . . . . . . . . . . . . . . . . 8

2 Nyquist diagrams made of one semicircle 9

2.1 One capacitive semicircle . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 R1/C1 circuit . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.2 R1+R2/C2 circuit . . . . . . . . . . . . . . . . . . . . . . 10
2.1.3 R1/(R2+C2) circuit . . . . . . . . . . . . . . . . . . . . . 12
2.2 One inductive semicircle . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.1 R1/L1 circuit . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 R1/L1 circuit, R1 < 0 . . . . . . . . . . . . . . . . . . . . 13
2.2.3 R1+R2/L2 circuit . . . . . . . . . . . . . . . . . . . . . . 14
2.2.4 R1+R2/L2 circuit, R2 < 0 . . . . . . . . . . . . . . . . . 14

3 Nyquist diagrams made of one semicircle and straight line 15

3.1 Capacitive semicircle and straight line . . . . . . . . . . . . . . . 15
3.1.1 C1/(C2+R2) circuit . . . . . . . . . . . . . . . . . . . . . 15
3.1.2 C1+R2/C2 circuit . . . . . . . . . . . . . . . . . . . . . . 15
3.1.3 R1+C1/(C2+R2) circuit . . . . . . . . . . . . . . . . . . . 16
3.1.4 R1+C1+R2/C2 circuit . . . . . . . . . . . . . . . . . . . . 17
3.1.5 C1/(Q2+R2) circuit . . . . . . . . . . . . . . . . . . . . . 17
3.1.6 Q1+R2/C2 circuit . . . . . . . . . . . . . . . . . . . . . . 17
3.1.7 R1+C1/(Q2+R2) circuit . . . . . . . . . . . . . . . . . . 17

3
4 CONTENTS

3.1.8 R1+Q1+R2/C2 circuit . . . . . . . . . . . . . . . . . . . 17

3.1.9 C1/(R2+W2) circuit . . . . . . . . . . . . . . . . . . . . . 18
3.1.10 R1+C1/(R2+W2) circuit . . . . . . . . . . . . . . . . . . 18
3.1.11 W1+R2/C2 circuit . . . . . . . . . . . . . . . . . . . . . . 18
3.1.12 R1+W1+R2/C2 circuit . . . . . . . . . . . . . . . . . . . 19
3.2 Capacitive semicircle and inductive straight line . . . . . . . . . . 21
3.2.1 L1+R2/C2 circuit . . . . . . . . . . . . . . . . . . . . . . 21
3.2.2 R1+L1+R2/C2 circuit . . . . . . . . . . . . . . . . . . . . 21
3.2.3 Q1+R2/C2 circuit, α1 < 0 . . . . . . . . . . . . . . . . . 21
3.2.4 R1+Q1+R2/C2 circuit, α1 < 0 . . . . . . . . . . . . . . . 22
3.3 Inductive semicircle and straight line . . . . . . . . . . . . . . . . 24
3.3.1 R1/L1+L2 circuit . . . . . . . . . . . . . . . . . . . . . . 24
3.3.2 L1/(R1+L2) circuit . . . . . . . . . . . . . . . . . . . . . 24
3.3.3 R1+R2/L2+L3 circuit . . . . . . . . . . . . . . . . . . . . 24
3.3.4 R1+L2/(R2+L3) circuit . . . . . . . . . . . . . . . . . . . 25
3.3.5 R1/L1+Q1 circuit, α1 < 0 . . . . . . . . . . . . . . . . . . 25
3.3.6 R1+R2/L2+Q1 circuit, α1 < 0 . . . . . . . . . . . . . . . 25
3.4 Inductive semicircle and capacitive straight line . . . . . . . . . . 27
3.4.1 R1/L1+C1 circuit . . . . . . . . . . . . . . . . . . . . . . 27
3.4.2 R1+R2/L2+C1 circuit . . . . . . . . . . . . . . . . . . . . 27
3.4.3 R1/L1+Q1 circuit . . . . . . . . . . . . . . . . . . . . . . 27
3.4.4 R1+R2/L2+Q1 circuit . . . . . . . . . . . . . . . . . . . . 27
3.4.5 R1/L1+W1 circuit . . . . . . . . . . . . . . . . . . . . . . 28
3.4.6 R1+R2/L2+W1 circuit . . . . . . . . . . . . . . . . . . . 28
Chapter 1

Nyquist diagrams made of

one straight line

1.1 Capacitive straight line

Table 1.1: Six different Nyquist diagrams made of one capacitive straight line.

-А4 -А4
0 0 0 0 0 0
0 0 0 0 0 0

cf. 1.1.1, p. 5 cf. 1.1.2, p. 6 cf. 1.1.3, p. 6 cf. 1.1.4, p. 6 cf. 1.1.5, p. 6 cf. 1.1.7, p. 6
cf. 1.1.6, p. 6 cf. 1.1.8, p. 7

(1 )

1.1.1 C1 element
Fig. 1.1.

C1

Figure 1.1: C1 element. For an electrochemical system C1 denotes the electrochemical

double layer capacity Cdl .

1 Nyquist diagrams are always plotted using convention of electrochemists: orthonormal

parametric plot −Im Z vs. Re Z. The arrows always indicate the increasing frequency
direction.

5
6 CHAPTER 1. NYQUIST DIAGRAMS MADE OF ONE STRAIGHT LINE

1.1.2 R1+C1 circuit

Fig. 1.2.

C1

R1

Figure 1.2: R1+C1 circuit. For an ideally polarized electrode C1 denotes the elec-
trochemical double layer capacity Cdl and R1 the ohmic (RΩ ) or uncompensated re-
sistance (Ru ) [1].

1.1.3 Q1 element
Fig. 1.3.

Q1

Figure 1.3: Q1 element (CPE element, cf. Handbook of Electro-

chemical Impedance Spectroscopy. Electrical circuits containing CPEs:
http://www.bio-logic.info/potentiostat/notesheis.html)

1.1.4 R1+Q1 circuit

Fig. 1.4 [1, 2].

Q1

R1

Figure 1.4: R1+Q1 circuit [1, 2].

1.1.5 Q1 element, α1 = 1/2

Fig. 1.3 with α1 = 1/2.

1.1.6 W1 element
Fig. 1.5.

1.1.7 R1+Q1 circuit, α1 = 1/2

Fig. 1.4 with α1 = 1/2.
 1.2. INDUCTIVE STRAIGHT LINE 7

W1

Figure 1.5: W1 element (Warburg impedance, cf. Handbook

of Electrochemical Impedance Spectroscopy. Diffusion impedances:
http://www.bio-logic.info/potentiostat/notesheis.html).

1.1.8 R1+W1 circuit

Fig. 1.6.

W1
R1

Figure 1.6: R1+W1 circuit.

1.2 Inductive straight line

Table 1.2: Four different Nyquist diagrams made of one inductive straight line and
two diagrams made of one capacitive and one inductive straight line.

0 0 0 0

0 0

0 0 0 0 0 0

cf. 1.2.1, p. 7 cf. 1.2.2, p. 8 cf. 1.2.3, p. 8 cf. 1.2.4, p. 8 cf. 1.2.5, p. 8 cf. 1.2.6, p. 8

1.2.1 L1 element
Fig. 1.7.

L1

Figure 1.7: L1 element.

8 CHAPTER 1. NYQUIST DIAGRAMS MADE OF ONE STRAIGHT LINE

1.2.2 R1+L1 circuit

Fig. 1.8.

L1
R1

Figure 1.8: R1+L1 circuit.

1.2.3 Q1 element, α1 < 0

Fig. 1.3 with α1 < 0.

1.2.4 R1+Q1 element, α1 < 0

Fig. 1.4 with α1 < 0.

1.2.5 L1+C1 circuit

Fig. 1.9.

C1
L1

L1+C1

Figure 1.9: L1+C1 circuit.

1.2.6 R1+L1+C1 circuit

Fig. 1.10.

C1
L1
R1

R1+L1+C1

Figure 1.10: R1+L1+C1 circuit.

Chapter 2

Nyquist diagrams made of

one semicircle

2.1 One capacitive semicircle

Table 2.1: Four different Nyquist diagrams made of one capacitive semicircle.

0 0 0 0
0 0 0 0
cf. 2.1.1, p. 9 cf. 2.1.1, p. 9 cf. 2.1.2, p. 11 cf. 2.1.2, p. 11
cf. 2.1.1, p. 10

2.1.1 R1/C1 circuit

Figs. 2.1, 2.2 (1 ).

R1, C1 > 0

Fig. 2.2.

R1 < 0, C1 > 0

Fig. 2.2.

1 Replacing C by Q (CPE element) in a parallel RC circuit changes a semicircle in a ”de-

pressed” semicircle arc, cf. Handbook of Electrochemical Impedance Spectroscopy. Electrical

circuits containing CPEs: http://www.bio-logic.info/potentiostat/notesheis.html

9
10 CHAPTER 2. NYQUIST DIAGRAMS MADE OF ONE SEMICIRCLE

C1

R1

Figure 2.1: R1/C1 circuit. For an electrochemical system C1 denotes the electro-
chemical double layer capacity and R1 the charge transfer resistance Rct .

Ωc = 1HR1C1L Ωc = - 1HR1C1L

0 0
0 R1 R1 0

Figure 2.2: Nyquist diagrams of the impedance for the R1/C1 circuit. Left: R1, C1 >
0, right R1 < 0, C1 > 0.

Voigt circuit with one time constant

Figs. 2.3, 2.4.

∑
n ∑n
Ri Ri
Z(ω) = = i=1 , τ = Ri Ci
i=1
1 + iωτ 1 + iωτ

C1 C2 C3 Cn

R1 R2 R3 Rn

Figure 2.3: Voigt circuit.

2.1.2 R1+R2/C2 circuit

Figs. 2.5 (2 ).
2 The R1+R2/C2 and R1/(R2+C2) circuits are non-distinguishable, i.e. these circuits can

be interchanged (cf. Handbook of Electrochemical Impedance Spectroscopy. Circuits made

of resistors and capacitors: http://www.bio-logic.info/potentiostat/notesheis.html).
2.1. ONE CAPACITIVE SEMICIRCLE 11

Ωc = 1HRiCiL

0
0 Ú Ri

Figure 2.4: Nyquist diagram of the impedance for Voigt circuit with one time con-
stant.

C2

R1

R2

R1+R2C2

Figure 2.5: R1+R2/C2 circuit. For an electrochemical system C2 denotes the electro-
chemical double layer capacity Cdl , R1 the ohmic (RΩ ) or uncompensated resistance
(Ru ) and R2 the charge transfer resistance Rct .

R1, R2, C2 > 0

Fig. 2.6.

Ωc = - 1HR2C2L
Ωc = 1HR2C2L

0 0
0 R1 R1+R2 R1+R2 0 R1

Figure 2.6: Nyquist impedance diagrams for the R1+R2/C2 circuit. Left:
R1, R2, C1 > 0, right: R1 < 0, R2 > 0, C1 > 0.

R1 > 0, R2 < 0, C2 > 0

Fig. 2.6.
12 CHAPTER 2. NYQUIST DIAGRAMS MADE OF ONE SEMICIRCLE

2.1.3 R1/(R2+C2) circuit

Figs. 2.7.

Ωc = 1HHR1+R2LC2L

R1

C2

R2 0
0 R1 R2 R1
R1 + R2
R1HR2+C2L

Figure 2.7: R1/(R2+C2) circuit and Nyquist impedance diagram. R1, R2, C1 > 0
2.2. ONE INDUCTIVE SEMICIRCLE 13

2.2 One inductive semicircle

Table 2.2: Four different Nyquist diagrams made of one inductive semicircle.

0 0 0 0

0 0 0 0

cf. 2.2.1, p. 13 cf. 2.2.2, p. 13 cf. 2.2.3, p. 14 cf. 2.2.4, p. 14

2.2.1 R1/L1 circuit

Figs. 2.8, 2.9.

L1

R1

Figure 2.8: R1/L1 circuit.

R1 R1
0 0

Ωc = R1L1
Ωc = - R1L1
0 0

Figure 2.9: Nyquist impedance diagram for the R1/L1 circuit. Left: R1 > 0, right:
R1 < 0.

2.2.2 R1/L1 circuit, R1 < 0

Fig. 2.8, R1 < 0.
14 CHAPTER 2. NYQUIST DIAGRAMS MADE OF ONE SEMICIRCLE

2.2.3 R1+R2/L2 circuit

Figs. 2.10, 2.11.

L2

R1

R2

R1+R2L2

Figure 2.10: R1+ R2/L2 circuit.

R1 R1+R2 R1+R2 R1
0 0

Ωc = R2L2 Ωc = - R2L2

0 0

Figure 2.11: Nyquist impedance diagrams for the R1+R2/L2 circuit. Left: R2 > 0,
right: R2 < 0.

2.2.4 R1+R2/L2 circuit, R2 < 0

Figs. 2.10, 2.11.
 Chapter 3

Nyquist diagrams made of

one semicircle and one
straight line

3.1 Capacitive semicircle and straight line

Table 3.1: Six different Nyquist diagrams made of one capacitive semicircle and one
straight line (limiting cases).

0 0 0 0 0 0
0 0 0 0 0 0
cf. 3.1.1, p. 15 cf. 3.1.3, p. 16 cf. 3.1.5, p. 17 cf. 3.1.7, p. 17 cf. 3.1.9, p. 18 cf. 3.1.12, p. 19
cf. 3.1.2, p. 15 cf. 3.1.4, p. 17 cf. 3.1.6, p. 17 cf. 3.1.8, p. 17 cf. 3.1.11, p. 18 cf. 3.1.12, p. 19

3.1.1 C1/(C2+R2) circuit

Fig. 3.1 (1 ).

3.1.2 C1+R2/C2 circuit

Fig. 3.2.
1 C1/(C2+R2) and C1+R2/C2 circuits are non-distinguishable, i.e. these circuits can be

interchanged (cf. Handbook of Electrochemical Impedance Spectroscopy. Circuits made of

resistors and capacitors: http://www.bio-logic.info/potentiostat/notesheis.html).

15
16CHAPTER 3. NYQUIST DIAGRAMS MADE OF ONE SEMICIRCLE AND STRAIGHT LINE

C1

C2

R2
0
C1HC2+R2L 0

Figure 3.1: C1/(C2+R2) circuit and Nyquist impedance diagrams.

C2

C1

R2

C1+R2C2

Figure 3.2: C1+R2/C2 circuit.

3.1.3 R1+C1/(C2+R2) circuit

Fig. 3.3.

C1

C2

R1 R2
0
R1+C1HC2+R2L 0

Figure 3.3: R1+C1/(C2+R2) circuit and Nyquist impedance diagrams.

3.1. CAPACITIVE SEMICIRCLE AND STRAIGHT LINE 17

3.1.4 R1+C1+R2/C2 circuit

Fig. 3.4.

C2

C1

R1

R2

R1+C1+R2C2

Figure 3.4: R1+C1+R2/C2 circuit.

3.1.5 C1/(Q2+R2) circuit

Fig. 3.5.

C1

Q2

R2
0
C1HQ2+R2L 0

Figure 3.5: C1/(Q2+R2) circuit.

3.1.6 Q1+R2/C2 circuit

Fig. 3.6.

3.1.7 R1+C1/(Q2+R2) circuit

Fig. 3.7.

3.1.8 R1+Q1+R2/C2 circuit

Fig. 3.8.
18CHAPTER 3. NYQUIST DIAGRAMS MADE OF ONE SEMICIRCLE AND STRAIGHT LINE

C2

Q1

R2

Q1+R2C2

Figure 3.6: Q1+R2/C2 circuit and Nyquist impedance diagrams.

C1

Q2
R1 R2
0
R1+C1HQ2+R2L 0

Figure 3.7: R1+C1/(Q2+R2) circuit and Nyquist impedance diagrams.

C2
Q1
R1
R2
R1+Q1+R2C2

Figure 3.8: R1+Q1+R2/C2 circuit.

3.1.9 C1/(R2+W2) circuit

Fig. 3.9.

3.1.10 R1+C1/(R2+W2) circuit

Fig. 3.10.

3.1.11 W1+R2/C2 circuit

Fig. 3.11.
3.1. CAPACITIVE SEMICIRCLE AND STRAIGHT LINE 19

C1

W2

R2
0
C1HW2+R2L 0

Figure 3.9: C1/(R2+W2) circuit (Randles circuit) and Nyquist impedance diagrams.
(cf. Handbook of Electrochemical Impedance Spectroscopy. Diffusion impedances:
http://www.bio-logic.info/potentiostat/notesheis.html)

C1

W2

R1 R2
0
R1+C1HW2+R2L 0

Figure 3.10: R1+C1/(R2+W2) circuit and Nyquist impedance diagrams.

3.1.12 R1+W1+R2/C2 circuit

Fig. 3.12.
20CHAPTER 3. NYQUIST DIAGRAMS MADE OF ONE SEMICIRCLE AND STRAIGHT LINE

C2

W1

R2 0
0
W1+R2C2

Figure 3.11: W1+C2/R2 and Nyquist impedance diagrams.

C2
W1
R1
R2 0
0
R1+W1+R2C2

Figure 3.12: R1+W1+R2/C2 circuit and Nyquist impedance diagrams.

3.2. CAPACITIVE SEMICIRCLE AND INDUCTIVE STRAIGHT LINE 21

3.2 Capacitive semicircle and inductive straight

line

Table 3.2: Four different Nyquist diagrams made of one capacitive semicircle and one
inductive straight line (limiting cases).

0 0 0
0

0 0 0 0
cf. 3.2.1, p. 21 cf. 3.2.2, p. 21 cf. 3.2.3, p. 21 cf. 3.2.4, p. 22

3.2.1 L1+R2/C2 circuit

Fig. 3.13.

C2

L1

R2
0
L1+R2C2

Figure 3.13: L1+R2/C2 circuit and Nyquist impedance diagrams.

3.2.2 R1+L1+R2/C2 circuit

Fig. 3.14.

3.2.3 Q1+R2/C2 circuit, α1 < 0

Fig. 3.15.
22CHAPTER 3. NYQUIST DIAGRAMS MADE OF ONE SEMICIRCLE AND STRAIGHT LINE

C2

L1

R1

R2
0
R1+L1+R2C2

Figure 3.14: R1+L1+R2/C2 circuit and Nyquist impedance diagrams.

C2

Q1, Α1 < 0

R2
0
Q1+R2C2

Figure 3.15: Q1+R2/C2 circuit. α1 < 0.

3.2.4 R1+Q1+R2/C2 circuit, α1 < 0

Fig. 3.16.
3.2. CAPACITIVE SEMICIRCLE AND INDUCTIVE STRAIGHT LINE 23

C2
Q1, Α1 < 0
R1
R2
0
R1+Q1+R2C2

Figure 3.16: R1+Q1+R2/C2 circuit and Nyquist impedance diagrams. α1 < 0.

24CHAPTER 3. NYQUIST DIAGRAMS MADE OF ONE SEMICIRCLE AND STRAIGHT LINE

3.3 Inductive semicircle and straight line

Table 3.3: Four different Nyquist diagrams made of one inductive semicircle and one
inductive straight line (limiting cases).

0 0 0 0

0 0 0 0
cf. 3.3.1, p. 24 cf. 3.3.3, p. 24 cf. 3.3.5, p. 25 cf. 3.3.6, p. 25
cf. 3.3.2, p. 24 cf. 3.3.4, p. 25

3.3.1 R1/L1+L2 circuit

Fig. 3.17.

L1

L2

R1
0
R1L1+L2

Figure 3.17: R1/L1+L2 circuit and Nyquist impedance diagrams.

3.3.2 L1/(R1+L2) circuit

Fig. 3.18 (2 ).

3.3.3 R1+R2/L2+L3 circuit

Fig. 3.19.
2 The R1/L1+L2 and L1/(R2+L2) circuits are non-distinguishable, cf. Handbook
of Electrochemical Impedance Spectroscopy. Circuits made of resistors and inductors:
http://www.bio-logic.info/potentiostat/notesheis.html
3.3. INDUCTIVE SEMICIRCLE AND STRAIGHT LINE 25

L1

L2
R1
0
L1HR1+L2L

Figure 3.18: L1/(R1+L2) circuit and Nyquist impedance diagrams.

L2

L3
R1

R2

R1+R2L2+L3

Figure 3.19: R1+R2/L2+L3 circuit and Nyquist impedance diagrams.

3.3.4 R1+L2/(R2+L3) circuit

Fig. 3.20.

3.3.5 R1/L1+Q1 circuit, α1 < 0

Fig. 3.21.

3.3.6 R1+R2/L2+Q1 circuit, α1 < 0

Fig. 3.22.
26CHAPTER 3. NYQUIST DIAGRAMS MADE OF ONE SEMICIRCLE AND STRAIGHT LINE

L2

L3
R1 R2
0
R1+L2HR2+L3L

Figure 3.20: R1+L2/(R2+L3) circuit and Nyquist impedance diagrams.

L1
Q1, Α1 < 0

R1
0
R1L1+Q1

Figure 3.21: R1/L1+Q1 circuit (α1 < 0) and Nyquist impedance diagrams.

L2
Q1, Α1 < 0

R1

R2

R1+R2L2+Q1

Figure 3.22: R1+R2/L2+Q1 circuit (α1 < 0) and Nyquist impedance diagrams.
 3.4. INDUCTIVE SEMICIRCLE AND CAPACITIVE STRAIGHT LINE 27

3.4 Inductive semicircle and capacitive straight

line

Table 3.4: Six different Nyquist diagrams made of one inductive semicircle and one
capacitive straight line.

0 0 0 0 0 0

0 0 0 0 0 0

cf. 3.4.1, p. 27 cf. 3.4.2, p. 27 cf. 3.4.3, p. 27 cf. 3.4.4, p. 27 cf. 3.4.5, p. 28 cf. 3.4.6, p. 28

3.4.1 R1/L1+C1 circuit

Fig. 3.23.

L1

C1

R1
0
R1L1+C1

Figure 3.23: R1/L1+C1 and Nyquist impedance diagrams.

3.4.2 R1+R2/L2+C1 circuit

Fig. 3.24.

3.4.3 R1/L1+Q1 circuit

Fig. 3.25.

3.4.4 R1+R2/L2+Q1 circuit

Fig. 3.26.
28CHAPTER 3. NYQUIST DIAGRAMS MADE OF ONE SEMICIRCLE AND STRAIGHT LINE

L2
C1
0
R1
R2
0
R1+R2L2+C1

Figure 3.24: R1+R2/L2+C1 and Nyquist impedance diagrams.

L1

Q1

R1
0
R1L1+Q1

Figure 3.25: R1/L1+Q1 circuit and Nyquist impedance diagrams.

L2
Q1
0
R1
R2
0
R1+R2L2+Q1

Figure 3.26: R1+R2/L2+Q1.

3.4.5 R1/L1+W1 circuit

Fig. 3.27.

3.4.6 R1+R2/L2+W1 circuit

Fig. 3.28.
3.4. INDUCTIVE SEMICIRCLE AND CAPACITIVE STRAIGHT LINE 29

L1

W1

R1
0
R1L1+W1

Figure 3.27: R1/L1+W1 circuit and Nyquist impedance diagrams.

L2
W1
0
R1
R2
0
R1+R2L2+W1

Figure 3.28: R1+R2/L2+W1 and Nyquist impedance diagrams.

30CHAPTER 3. NYQUIST DIAGRAMS MADE OF ONE SEMICIRCLE AND STRAIGHT LINE
Bibliography

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Sluyters, J. H. The analysis of electrode impedance complicated by the
presence of a constant phase element. J. Electroanal. Chem. 176 (1984),
275–295.
[2] Lonné, Q., Glandut, N., Labbe, J.-C., and Lefort, P. Fabrication
and characterization of ZrB2 -SiC ceramic electrodes coated with a proton
conducting, SiO2 -rich glass layer. Electrochimica Acta In Press, Corrected
Proof (2011), –.

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