Impedance Spectroscopy
523
2.1 Frequency Domain Techniques
2.1.1 Audio Frequency Bridges
In earlier times, reactively substituted Wheatstone bridges operating at radio frequencies were used to measure impedance. Hague [21] has explained the mathematics
and methodology of these bridges. Although, audio frequency bridges can still be
applied in applications involving high precision yet these bridges suffer from some
high frequency limitations such as stray capacitive shunts which can be considerably
reduced by using Wagner earthing for measurements of 10
5 Hz frequencies [22, 23].
However, the effectiveness of Wagner earthing changes with the value of measured
impedance. While low frequency limitations are due to the null detection system
consisting of filter, amplifier and ac voltmeter. Harmonic distortion arising in the
oscillator may lead to noise at the detector. Mains pickup can be another source
of noise which may cause the superimposing of hundreds of millivolts on the test
signal. Phase sensitive detectors can be used to lessen the above effects by separately
measuring the real and imaginary parts of the signal.
2.1.2 Transformer Ratio Arm Bridges
The transformer ratio arm bridge was developed to circumvent the high frequency
limitations of the reactively substituted Wheatstone bridge. This bridge was made
by replacing the conventional ratio arms by a transformer which could handle heavy
capacitive loads without affecting the voltage ratio [24]. The ratio of impedance is
proportional to the square of the number of turns in this bridge. It is highly insensitive
to stray capacitances and accurate ratio values that do not depend on frequency
are obtained. It suffers from some drawbacks such as uncompensated electrolyte
resistance but use of small electrodes can reduce it.
2.1.3 Berberian-Cole Bridge
This type of bridge was designed by Berberian and Cole [25] which can measure
null admittance. It includes the merits of transformer ratio arm method and obviates
some of the demerits of passive bridges. The major advantages of this type are: null
adjustment does not change the current through the unknown impedance because it
uses buffer amplifiers, impedance can be measured over wide range of frequencies
i.e. from <10
–3 to 10
9
and in all quadrants by using standard capacitance and
resistance, elimination of anomalies due to impurity of standards. Some negligible
errors can occur at high frequencies due to inaccuracies in gain functions as amplifier
open loop gain is decreased [26].
523
2.1 Frequency Domain Techniques
2.1.1 Audio Frequency Bridges
In earlier times, reactively substituted Wheatstone bridges operating at radio frequencies were used to measure impedance. Hague [21] has explained the mathematics
and methodology of these bridges. Although, audio frequency bridges can still be
applied in applications involving high precision yet these bridges suffer from some
high frequency limitations such as stray capacitive shunts which can be considerably
reduced by using Wagner earthing for measurements of 10
5 Hz frequencies [22, 23].
However, the effectiveness of Wagner earthing changes with the value of measured
impedance. While low frequency limitations are due to the null detection system
consisting of filter, amplifier and ac voltmeter. Harmonic distortion arising in the
oscillator may lead to noise at the detector. Mains pickup can be another source
of noise which may cause the superimposing of hundreds of millivolts on the test
signal. Phase sensitive detectors can be used to lessen the above effects by separately
measuring the real and imaginary parts of the signal.
2.1.2 Transformer Ratio Arm Bridges
The transformer ratio arm bridge was developed to circumvent the high frequency
limitations of the reactively substituted Wheatstone bridge. This bridge was made
by replacing the conventional ratio arms by a transformer which could handle heavy
capacitive loads without affecting the voltage ratio [24]. The ratio of impedance is
proportional to the square of the number of turns in this bridge. It is highly insensitive
to stray capacitances and accurate ratio values that do not depend on frequency
are obtained. It suffers from some drawbacks such as uncompensated electrolyte
resistance but use of small electrodes can reduce it.
2.1.3 Berberian-Cole Bridge
This type of bridge was designed by Berberian and Cole [25] which can measure
null admittance. It includes the merits of transformer ratio arm method and obviates
some of the demerits of passive bridges. The major advantages of this type are: null
adjustment does not change the current through the unknown impedance because it
uses buffer amplifiers, impedance can be measured over wide range of frequencies
i.e. from <10
–3 to 10
9
and in all quadrants by using standard capacitance and
resistance, elimination of anomalies due to impurity of standards. Some negligible
errors can occur at high frequencies due to inaccuracies in gain functions as amplifier
open loop gain is decreased [26].