17-07-2012, 12:15 PM
A real time FFT-based impedance meter with bias compensation
[attachment=27802]
Introduction
This paper relates to the development of a software running
on a standard PC Windows-based equipped with a
low cost two channels data acquisition board, with the
interesting characteristic of being able to measure impedances
with high accuracy, at lower cost compared with
analogous commercially available meters. It is based on
the Fast Fourier Transform (FFT) and a method to shrink
bias errors. Fig. 1 is a simple schematization of the acquisition
side of the meter: the DUT (Device Under Test), in series
with a known reference resistor, is supplied by a
sinusoidal generator digitally synthesized via software.
Least Mean Square (LMS) method
Literature reports several error-minimization criteria,
and the Widrow–Hoff least square approximation is the
most widely known and used. Basically it consists of a
function that minimizes the sum of the squared errors to
estimate two variables W1 e W2, being recursively computed
as the coefficient of the adaptive linear combiner,
so to obtain the wanted Zx as [4]:
Material and methods
The method we propose is capable to correctly measure
impedances with high accuracy but being based on a simple
low-cost commercially available acquisition board. For
simplicity we realized a home-made prototype using a
standard PCM2902 (USB A/D–D/A converter 16 bit up to
96 kHz of frequency sampling) plus a double operational
amplifier LM358 to get an high input impedance. Obviously,
it is necessary an appropriate choice of the system
parameters, such as frequency sampling of the A/D converter,
number of acquired samples for each data buffer,
and the frequency of the generated test signal.
Hardware phase error
The two voltages Vrm and Vzx are acquired from two different
channels of the acquisition board (Fig. 1). Many
acquisition boards use only one A/D converter for all the
supported channels, by means of a hardware multiplexer.
In many cases this means that the two channels have a
phase differences of at least one sample. This is the case,
for instance, of the acquisition board we used in our test
system. A relative delay of one sample means a delay equal
to Ts i.e. the period of the sampling frequency.
Results
We completely tested our impedance meter to verify
the correctness of the results, comparing them with the
ones provided by commercial meters with a known uncertainty,
supported by calibration documents (Tables 1
and 2). The instruments we selected as references were
the Agilent digital multimeter 34405A, 5.5 digit, capable to
measure resistance and capacitance, and the Digimess
RLC200 impedance meter, 3.5 digit for the inductance measurements.
Also the value of the reference resistor (Fig. 1)
was measured again with the Agilent digital multimeter
(the accuracy of this measurement is crucial for the global
accuracy of the impedance meter).
[attachment=27802]
Introduction
This paper relates to the development of a software running
on a standard PC Windows-based equipped with a
low cost two channels data acquisition board, with the
interesting characteristic of being able to measure impedances
with high accuracy, at lower cost compared with
analogous commercially available meters. It is based on
the Fast Fourier Transform (FFT) and a method to shrink
bias errors. Fig. 1 is a simple schematization of the acquisition
side of the meter: the DUT (Device Under Test), in series
with a known reference resistor, is supplied by a
sinusoidal generator digitally synthesized via software.
Least Mean Square (LMS) method
Literature reports several error-minimization criteria,
and the Widrow–Hoff least square approximation is the
most widely known and used. Basically it consists of a
function that minimizes the sum of the squared errors to
estimate two variables W1 e W2, being recursively computed
as the coefficient of the adaptive linear combiner,
so to obtain the wanted Zx as [4]:
Material and methods
The method we propose is capable to correctly measure
impedances with high accuracy but being based on a simple
low-cost commercially available acquisition board. For
simplicity we realized a home-made prototype using a
standard PCM2902 (USB A/D–D/A converter 16 bit up to
96 kHz of frequency sampling) plus a double operational
amplifier LM358 to get an high input impedance. Obviously,
it is necessary an appropriate choice of the system
parameters, such as frequency sampling of the A/D converter,
number of acquired samples for each data buffer,
and the frequency of the generated test signal.
Hardware phase error
The two voltages Vrm and Vzx are acquired from two different
channels of the acquisition board (Fig. 1). Many
acquisition boards use only one A/D converter for all the
supported channels, by means of a hardware multiplexer.
In many cases this means that the two channels have a
phase differences of at least one sample. This is the case,
for instance, of the acquisition board we used in our test
system. A relative delay of one sample means a delay equal
to Ts i.e. the period of the sampling frequency.
Results
We completely tested our impedance meter to verify
the correctness of the results, comparing them with the
ones provided by commercial meters with a known uncertainty,
supported by calibration documents (Tables 1
and 2). The instruments we selected as references were
the Agilent digital multimeter 34405A, 5.5 digit, capable to
measure resistance and capacitance, and the Digimess
RLC200 impedance meter, 3.5 digit for the inductance measurements.
Also the value of the reference resistor (Fig. 1)
was measured again with the Agilent digital multimeter
(the accuracy of this measurement is crucial for the global
accuracy of the impedance meter).