EE05813B1 - Method and device for frequency response measurement - Google Patents

Abstract

The present invention relates to a method and device for frequency response measurement, including generation of an excitation signal (like sinewave) with time-depending frequency (e.g. linear chirp) for the measured object, and in a relatively short time-domain sliding analyzing window of the response signal, wherein the time instants of the sampling of the response signal are generated according to the pre-defined phase increments of the excitation signal and the mentioned sliding analysis window includes the pre-defined number of sequential response samples. This analysis in the mentioned short-time window can be implemented as the multiplication-and-accumulation of the response signal in parallel to first and second reference waveforms, one of which could be the sine-chirp waveform, similar to the excitation signal, and the other reference waveform could be the corresponding cosine-chirp, giving accordingly real and imaginary parts of the frequency response.

Description

Technical field

The invention belongs to the field of measurement technology, more specifically to the field of frequency response measurement. This field also includes electrical circuit analyzers and vector impedance meters, which also determine the frequency dependence of electrical transfer characteristics. Important areas of application of the invention are electrical bioimpedance meters (with applications in medical diagnostics), electrical and electronic circuit testers, electrochemical cell analyzers (e.g. for assessing the condition of batteries) and solutions for studying and identifying the properties of materials through their electrical properties.

State of the art

There are known solutions where the transmission of a circuit or circuit is measured by multiplying and accumulating the response signal generated as a result of excitation with an alternating signal (e.g. a sinusoidal signal) with the said excitation signal, i.e. by convolution of the excitation and response signals. Similarly, a second reference signal (shifted in phase by 90° with respect to the excitation signal) may be used to find the second convolution (so-called quadrature component), see US7428683B2. The disadvantage of such a solution is that the result is generated as a result of the convolution (multiplication and accumulation) of two signals (the measured response signal of the reference) into one integral result over the entire measurement cycle, which, firstly, does not show the transmission of the circuit or object to be measured at different frequencies separately ("frequency response") and, secondly, such an integral measurement cannot correctly reflect a time-varying (dynamic) circuit or object.

For measuring frequency characteristics and measuring time-dynamic circuits and objects, there are known technical solutions that use a broadband excitation signal, including one with a time-varying frequency (e.g. chirp), and for the analysis of (response) signals, frequency transforms in a relatively short time sliding window, for example the short-time Fourier transform (STFT). Such a solution is described in the article by K. Darowicki, P. Slepski, influence of the analyzing window on electrode impedance measurement by the continuous frequency scanning method Journal of Electroanalytical Chemistry, vol.533, issue 1-2, 20 Sept 2002, pp.25-31, Elsevier Science. The solution closest to the invention and most similar in terms of technical result is described in patent specification EE05616B1 (US8854030B2) “Method and device for measuring frequency characteristic”. In this solution, an excitation signal with a time-varying frequency (e.g. chirp) is used as the excitation signal, and the measurement result is calculated by convolution of the response signal received from the measured object (digitally realized by multiplication and

accumulation) in a relatively short time sliding time window with a first reference signal (which has the same waveform in the time domain as the excitation signal) in one ("in-phase") measurement channel and a second ("quadrature") reference signal (e.g. cosine chirp, if the first reference signal is a sine chirp) in the other measurement channel.

In the solutions with variable signal frequency (e.g. chirp excitation), simple (uniform) sampling is used in the sampling of continuous (analog) signals in time, in analog-to-digital conversion, in response signal acquisition, and also vice versa (digital-to-analog conversion) - in the generation of the excitation signal. Also, the first and second reference signals (e.g. Fourier coefficients in the case of STFT) are given by sampling the response signal at the same discrete instants with uniform time steps.

One of the significant drawbacks of all the described solutions with variable signal frequency (e.g. chirp excitation) is the measurement error, which is related to the continuous change of the signal frequency with respect to the sampling frequency, as a result of which a non-integer number of sampling intervals falls into the mentioned relatively short analysis (convolution) window, the constantly changing (and not included in the analysis) fractional part of which creates a hopping error component. An analogous effect in the case of fixed-frequency signals (when the sampling intervals are, for example, non-integer in the Fourier transform analysis window) is known as “spectral leakage”.

The essence of the invention

The aim of the invention is to increase the accuracy of the frequency response measurement solution. The aim is achieved, compared to the known solution, which also uses an excitation signal with a frequency that changes relatively quickly in time and an analysis of the response signal in a relatively short sliding time window, by generating the response signal sampling moments according to a given phase step of the excitation signal and taking a given number of response signal samples in said relatively short sliding time window.

It is reasonable to perform the analysis of the response signal in the said relatively short sliding time window by multiplying and accumulating in the said time window in parallel with two different taken reference waveforms, one of which has the same shape as the excitation signal in the time domain and the second reference waveform is a 90° phase shifted variant of the first reference waveform and the result of said multiplication and accumulation with the first and second reference waveforms is the real and imaginary parts of the frequency response, respectively, as a frequency response according to the sliding of the window. It may be reasonable that the excitation signal and the first reference waveform are sine chirps and the second reference waveform is the corresponding cosine chirp. It is expedient that the said chirp signals have a frequency that varies linearly in time (so-called “linear” chirps).

It may be reasonable that the aforementioned relatively short sliding time domain analysis window always contains a constant number of consecutive samples (N) and the step of the excitation signal phase change, according to which the sample moments are generated, is constantly a quotient of 360° (or an integer multiple of this value) by (N+1).

A frequency response measuring device comprising a time-varying frequency reference waveform calculator (1) and first and second reference waveform buffers (2 and 3) initialized by said reference waveform calculator (1), a subtraction generator (4); a digital-to-analog converter (5), the signal input of which is connected to the output of the first reference waveform buffer (2), and the subtraction of which is controlled by the subtraction generator (4), and the output of which is connected to the excitation input of the measured object (6); an analog-to-digital converter (7), the signal input of which is connected to the response signal received from the measured object (6), and the subtraction of which is also controlled by the subtraction generator (4); a response signal buffer (8), the input of which is connected to the output of the analog-to-digital converter (7); a sliding two-channel analysis window (9) which analyses the values of the waveform samples of the response signal buffer (8) in a given window in parallel with the corresponding waveform values of the first and second reference waveform buffers (2, 3) in the same analysis window (9) and which outputs a complex frequency response of the impedance values of the object (6) to be measured. The object of the invention is achieved in that the device includes a sampling instant pattern calculator (10) which controls the sampled reference waveform calculator (1) and a sampling generator (4), wherein the sampling instant pattern calculator generates the sampling pattern in such a way that the phase step between two consecutive samples in the first and second reference waveform buffers (2, 3) is a given value and said sliding analysis window (9) always contains a given number of samples from both the first and second reference waveform buffers (2, 3) as well as from the response signal buffer (8).

It is reasonable that said sliding analysis window (9) includes means for multiplying and accumulating the received signal values in parallel with the values of both the first and second reference signals (shifted by 90° with respect to the first) in the reference waveform buffers (2, 3) in the corresponding analysis window (9); the outputs of said accumulation and multiplication means respectively indicate the real and imaginary parts of the frequency response to be measured

List of drawings

Figure 1 shows a block diagram of an example of implementing the proposed solution.

Figure 2 shows phase angles with uniform pitch.

Figure 3 shows examples of the first and second reference waveforms and the response signal in the time domain with sampling times.

Figure 4 shows an example of the impedance frequency response measured from one simulation compared to the expected one.

Example of carrying out the invention

The proposed solution (Fig 1) includes a sampling instant pattern calculator (10) and a sampled reference waveform calculator (1), which calculates the first and second reference waveforms (Fig 2, sinChirp(ti). cosChirp(ti)) at the time instants specified by the sampling instant pattern calculator (10). In the example shown in Fig 2-4, there are 11 sampling points (Fig 2, shown with a 30° phase step) in one convolution sliding time window (Fig 1 (9), Fig 3). With the samples of the first and second reference waveforms found by the reference waveform calculator (1) (Fig 3, sinChirp(ti) cosChirp(ti)), the buffers (2 and 3) of the first and second reference waveforms are initialized. From the output of the first waveform buffer, the signal (Fig 3, sinChirp(ti) is sent as an analog signal through the digital-to-analog converter (DAC) (5) to the object to be measured (6), as an excitation. The response signal from the object to be measured (6) is digitized in the analog-to-digital converter (ADC) (7) and stored in the response signal buffer (8) (Fig 3, BsinChirp(ti)). The sampling of the ADC (7) and DAC (5) is controlled by the sampling generator (4), according to the time instants given to the latter by the sampling instant pattern calculator (10) (in the example of Fig 3, 11 sampling instants BsinChirp(ti) in the sliding time window of the given convolution). The sampling instants of the DAC (5) are generated by the sampling instant pattern calculator (10) and the sampling generator (4). Said instants may be the same as those of the ADC (7) or generated (e.g. with interpolated intermediate values) overconfident.

In a sliding two-channel analysis window (9), the values of the waveform samples of the response signal buffer (8) are analyzed in parallel with the corresponding waveform values of the first and second reference waveform buffers (2, 3) in the same analysis window (9), resulting in a complex frequency response of the impedance values of the object being measured (6).

The said analysis (in the sliding analysis window (9)) is reasonably performed by multiplying and accumulating over the values of the samples in the said analysis window (9); the values from the response signal buffer (8) (11 samples in the given example, Fig. 3) are multiplied and accumulated with the values of the corresponding 11 samples of the first reference waveform to obtain the real part ("in phase") of the current result, and with the values of the corresponding 11 samples of the second reference waveform to obtain the imaginary part ("quadrature part") of the current result.

In this way, according to the sliding of the analysis window (9) in time and according to the changing frequency, the transfer function of the measured object (6) is obtained as a frequency response. Knowing the complex transfer function, the impedance of the measured complex circuits can be calculated, if they are part of the measurement scheme for a given object (6).

In this example, a linear chirpy (10kHz-1MHz, 1ms duration) was used as the excitation signal and the first reference waveform, and the corresponding cosine chirpy was used as the second reference waveform.

In order to achieve the objective of the invention, that in each sliding analysis time window (9) there would be strictly the same number of intervals despite the relatively rapidly changing frequency of the excitation signals (in this example NN = 12, which corresponds to NN -1 = 11 samples), the sampling moments and the corresponding intervals in time are chosen in such a way that the corresponding phase steps of the first and second reference waveforms are given in advance, in this example constantly 360° / 12 = 30° (Fig 2). A reasonable choice and sufficient size of NN depend on the required measurement accuracy and the degree of real non-idealities (noise, jitter of sampling moments, etc.).

The sliding analysis window (9) can be continuously moved forward one sample at a time, thus obtaining result values in time and, accordingly, frequency more closely or in larger increments, e.g. by a quarter, half or a full window width without overlap.

An example of the proposed solution has been simulated with a 1 ms linear chirp signal (in the frequency range 10kHz-1MHz) in a sliding time window (Fig 2, 3) with 11 samples and a 30° phase step, multiplying and accumulating the response signal with the reference waveforms to obtain the real and imaginary parts of the mentioned sine and corresponding cosine chirp, Fig 3. The excitation of the measured impedance Zx is through a 1kΩ resistor and the frequency response of Zx has been found from the obtained transfer function (Fig 4), compared with the expected one (calculated as the frequency response of Zx of a known complex circuit). The result shows a good agreement of the result of the proposed solution with the expected one.

Claims (7)

1. A method for measuring the frequency response, which includes generating an excitation signal applied to a measured object with a time-varying frequency and analyzing the response signal of the measured object in a response signal analyzer in a relatively short sliding time window, characterized in that the response signal sampling moments are generated according to a given phase step of the excitation signal and a given number of response signal samples are taken in a relatively short sliding time window. 2. The method according to claim 1, characterized in that the analysis of the response signal is performed in a relatively short sliding time window in the convolution calculation device by multiplying and accumulating in said time window in parallel with two different taken reference waveforms, one of which has the same shape as the excitation signal in the time domain and the second reference waveform is a variant shifted in phase by 90° from the first reference waveform, and the result of multiplying and accumulating the response signal with the first and second reference waveforms is the real and imaginary parts of the frequency response, respectively, in the form of a frequency response according to the sliding of the window. 3. The method according to claim 2, characterized in that the excitation signal and the first reference waveform are sine chirps and the second reference waveform is a corresponding cosine chirp. 4. The method according to claim 3, characterized in that the sine chirp of the excitation signal and the first reference waveform has a frequency that varies linearly in time, and the second reference waveform is a cosine chirp corresponding to said sine chirp. 5. The method according to claim 1, characterized in that said relatively short sliding time domain analysis window always contains a constant number (N) of consecutive samples, and the step of the phase change of the excitation signal, according to which the sample moments are generated, is constantly a quotient of 360° (or an integer multiple thereof) by (N+1). 6. A device for measuring frequency response, comprising a time-varying frequency reference waveform calculator (1) and first and second reference waveform buffers (2 and 3) initialized by the reference waveform calculator (1), respectively; a subtraction generator (4); a digital-to-analog converter (5), the signal input of which is connected to the output of the first reference waveform buffer (2), and the subtraction of which is controlled by the subtraction generator (4), and the output of which is connected to the excitation input of the measured object (6); an analog-to-digital converter (7), the signal input of which is connected to the response signal received from the measured object (6), and the subtraction of which is also controlled by the subtraction generator (4); a response signal buffer (8), the input of which is connected to the output of the analog-to-digital converter (7); a sliding two-channel analysis window (9) that analyzes the values of the waveform samples of the response signal buffer (8) in a given window in parallel with the corresponding waveform values of the first and second reference waveform buffers (2, 3) in the same analysis window (9), and the output of which is a complex frequency response of the impedance values of the measured object (6), characterized in that the device includes a sampling instant pattern calculator (10), which is controlled by the sampled reference waveform calculator (1), and a sampling generator (4), wherein the sampling instant pattern is generated by the sampling instant pattern calculator (10) in such a way that the phase step in the first and second reference waveform buffers (2, 3) between two consecutive samples is a given value, and said sliding analysis window (9) always contains a given number of samples from both the first and second reference waveforms (2, 3) and the response signal buffers (8). 7. The device according to claim 6, characterized in that said sliding analysis window (9) comprises means for multiplying and accumulating (MAC) the received signal values in parallel with the values of both the first and second reference signals (shifted by 90° with respect to the first) in the reference waveform buffers (2, 3) in the respective analysis window (9); the outputs of said accumulation and multiplication means respectively indicate the real and imaginary parts of the frequency response to be measured.