Impedance Spectroscopy
527
as Hewlett Packard interface bus (HPIB) or IEEE-488. This interface has proficiency in connecting computers with transient recorders, digital multi meters, Fourier
analyzers. Most precisely, it is capable of connecting any gadget that is required to
implement ac impedance technique in the time domain. IEEE-488 interface is a highly
flexible with moderate speed system which is suitable for laboratory purposes. It has
16 signal lines; out of which 8 lines are used for data, 5 for management of bus and
3 lines are used for establishing temporary connection link. Several devices with a
unique address can be connected to the interface simultaneously. The unique address
is used in making a connection.
3 Analysis of Measured Data
Numerous methods have been illustrated for the representation of impedance data.
The most common method is one in which imaginary parts or logarithms of the quantities such as Z, Y, M or ε showing variations is potted with respect to frequency. It is
deemed necessary to examine the plots of all immittance data before analysis. Data
in Z and M representations is mostly helpful when dielectric effects are minimum
i.e. in basically conducting case. In non-conducting situation, Y and ε are considered
to be appropriate.
IS data can be plotted in umpteen ways. In IS, when the capacitive effects dominate
the inductive effects, then complex plane impedance plot is drawn between –Im(Z)
= Z
on the y axis and Re(Z) = Z
on the x axis. Such graphical representation is
called Nyquist plot. These plots are very useful in the identification of any conduction
process occurring inside the system. But these plots do not indicate the frequency
response directly. Another alternative representation of impedance data is the Bode
plot. Bode graphs are of two types: (1) plot of log |Z | vs. log (f ) and (2) phase
angle versus log(f ). A bode graph is drawn logarithmically for the required range
of frequencies so that similar number of points is collected at each decade [34]. The
initial resistor can be quickly found since the graphs start at higher frequency side
and finish at the lower frequency [34].
The Debye response is the most important building block of IS. Debye was the
first to propose a theory of dielectric dispersion [35, 36]. This model represents a
simple dielectric or fully capacitive system in which transition occurs from high
frequency permittivity to low frequency permittivity [37]. This theory is based on
the assumption that the collision between neighbouring molecules resists the rotation
of the molecules. The resistance couple is proportional to the angular velocity of the
molecule. Debye derived a relationship between the complex quantity (ε
* ) and the
relaxation time (τ ) as follows:
ε
∗
= ε(∞) +
δε
1 + j f τ
(12)
527
as Hewlett Packard interface bus (HPIB) or IEEE-488. This interface has proficiency in connecting computers with transient recorders, digital multi meters, Fourier
analyzers. Most precisely, it is capable of connecting any gadget that is required to
implement ac impedance technique in the time domain. IEEE-488 interface is a highly
flexible with moderate speed system which is suitable for laboratory purposes. It has
16 signal lines; out of which 8 lines are used for data, 5 for management of bus and
3 lines are used for establishing temporary connection link. Several devices with a
unique address can be connected to the interface simultaneously. The unique address
is used in making a connection.
3 Analysis of Measured Data
Numerous methods have been illustrated for the representation of impedance data.
The most common method is one in which imaginary parts or logarithms of the quantities such as Z, Y, M or ε showing variations is potted with respect to frequency. It is
deemed necessary to examine the plots of all immittance data before analysis. Data
in Z and M representations is mostly helpful when dielectric effects are minimum
i.e. in basically conducting case. In non-conducting situation, Y and ε are considered
to be appropriate.
IS data can be plotted in umpteen ways. In IS, when the capacitive effects dominate
the inductive effects, then complex plane impedance plot is drawn between –Im(Z)
= Z
on the y axis and Re(Z) = Z
on the x axis. Such graphical representation is
called Nyquist plot. These plots are very useful in the identification of any conduction
process occurring inside the system. But these plots do not indicate the frequency
response directly. Another alternative representation of impedance data is the Bode
plot. Bode graphs are of two types: (1) plot of log |Z | vs. log (f ) and (2) phase
angle versus log(f ). A bode graph is drawn logarithmically for the required range
of frequencies so that similar number of points is collected at each decade [34]. The
initial resistor can be quickly found since the graphs start at higher frequency side
and finish at the lower frequency [34].
The Debye response is the most important building block of IS. Debye was the
first to propose a theory of dielectric dispersion [35, 36]. This model represents a
simple dielectric or fully capacitive system in which transition occurs from high
frequency permittivity to low frequency permittivity [37]. This theory is based on
the assumption that the collision between neighbouring molecules resists the rotation
of the molecules. The resistance couple is proportional to the angular velocity of the
molecule. Debye derived a relationship between the complex quantity (ε
* ) and the
relaxation time (τ ) as follows:
ε
∗
= ε(∞) +
δε
1 + j f τ
(12)