1. 1 Problem to be solved: Impedance spectrum of dynamic systems is time dependent. Examples: (a) cardiovascular system; (b) microfluidic device. Excitation must be: 1) as short as possible to avoid significant changes during the spectrum analysis; 2) with maximum energy content in the frequency range of interest for maximum signal-to-noise ratio. * The unique property of chirp function – scalability – enables to meet the needs for spectrum bandwidth (BW) and excitation time (t exc =T ch ). However, changes in pulse duration (Tch) reflect in spectral density of the excitation. The question to be answered: A short chirp wave excitation (titlets) can contain one cycle (or even less), but what would be a good shape of the signal to achieve a maximum energy content in the frequency range of interest? Min M, Pliquett U, Nacke T, Barthel A, Annus P, Land R, 2007. Signals in bioimpedance measurement: different waveforms for different tasks. – Proc. of 13th International Conference on Electrical Bioimpedance and EIT (ICEBI’2007, Graz, Austria, Aug 29–Sept 2, 2007), 181-184. Electronics’ 2010 18-20 May, 2010, Kaunas, Lithuania Nonlinear Chirp Pulse Excitation Nonlinear Chirp Pulse Excitation for the Fast Impedance Spectroscopy Jaan Ojarand Jaan Ojarand, Paul Annus, Raul Land, Toomas Parve and Mart Min ELIKO Competence Centre and Department of Electronics, Tallinn University of Technology, both Tallinn, Estonia, E-mail : jaan.ojarand@eliko.ee

2. 2 Electronics’ 2010, May 18-20, 2010, Kaunas, Lithuania Nonlinear Chirp Pulse Excitation for the Fast Impedance Spectroscopy Jaan Ojarand Jaan Ojarand, Paul Annus, Raul Land, Toomas Parve and Mart Min Single-cycle linearly modulated titlet (short chirp pulse) - 40 dB/dec RMS spectral density (normalized) 10 1 10 -1 10 -2 10 -3 10 -4 1k 10k 100k 1M f, Hz 1 mV / Hz 1/2 Acceleration dω(t)/dt = 2π f fin / T ch = 2π(0. 5 ∙10 10 ), rad/s 2 B exc ≈ f fin = 100 kHz Current phase, rad, Instant frequency, rad/s θ fin |t = T ch = 2π

3. For the exponential titlet: 3 Electronics’ 2010, May 18-20, 2010, Kaunas, Lithuania Nonlinear Chirp Pulse Excitation for the Fast Impedance Spectroscopy Jaan Ojarand Jaan Ojarand, Paul Annus, Raul Land, Toomas Parve and Mart Min Single-cycle nonlinearly modulated titlet to improve the flatness of spectral density curve Instant frequency changes nonlinearly during the excitation interval. Modulating waveforms Titlet waveforms It is possible to shape the spectral density curve by controlling the speed of the frequency change of the chirp. PSD of the signal in the particular frequency range is inversely proportional to the chirp rate in that particular frequency. In the field of impedance spectroscopy an equal spectral density at all frequencies of interest is desirable though smooth PSD curve above level of 0.5 is often also satisfactory. The advantage of using an exponential relationship is in ease of realization Exp.2 and Exp.3 are a sums of upward- sloping and downward-sloping exponential signals

4. 4 Electronics’ 2010, May 18-20, 2010, Kaunas, Lithuania Nonlinear Chirp Pulse Excitation for the Fast Impedance Spectroscopy Jaan Ojarand Jaan Ojarand, Paul Annus, Raul Land, Toomas Parve and Mart Min Exponentially modulated titlets Exponentially modulated waveform source V p is a peak amplitude of the signal, and K f is the frequency sensitivity of the VCO in Hz/V. V p is kept constant at the 1V level. More flat in a usable bandwith! Normalized RMS spectral density - 40 dB/dec - 60 dB/dec V o express an initial voltage, k is growth constant and τ is the e-folding time. In the simplest case only one exponentially changing voltage V exp drives a VCO. However, it was found, that by combining two or more exponential signals with different growth factors it is possible to generate chirp waveforms with substantially steeper slope of spectral curve above the cut-off frequency.

5. 5 Electronics’ 2010, May 18-20, 2010, Kaunas, Lithuania Nonlinear Chirp Pulse Excitation for the Fast Impedance Spectroscopy Jaan Ojarand Jaan Ojarand, Paul Annus, Raul Land, Toomas Parve and Mart Min PSD curves of linear and exponential titlets Modulating waveforms Peak amplitudes of all waveforms are same, +/- 1V. Duration of signals is in the region of 40-50 μs, and was varied intentionally to get the same cut-off frequency (36 kHz ) where PSD falls to the level of 0.5 (-6 dB ) Normalized PSD, logarithmic scale Steeper slopes The slope of distribution curve above the cut-off frequency characterizes the ratio of the energies laying in the desired frequency range and above of it. However, most likely it is more adequate to compare distribution of the energy of different waveforms in the frequency range of interest. As we can see, in this case difference between signals Exp.1 and Exp.3 is not significant. Normalized PSD linear scale Small difference in shapes

6. 6 Electronics’ 2010, May 18-20, 2010, Kaunas, Lithuania Nonlinear Chirp Pulse Excitation for the Fast Impedance Spectroscopy Jaan Ojarand Jaan Ojarand, Paul Annus, Raul Land, Toomas Parve and Mart Min PSD curves and energy content PSD, normalized against the max. value of linear titlet, linear scale PSD curves, where the spectra are normalized separately for each signal are not suitable for the comparison of the energy content of different signals since the maximum values are not equal. To compare the spectral content of different signals, they must be normalized against one of them. According to Parseval’s theorem, the total energy in the frequency domain must be the same as in time time domain. Due to the higher frequency components, a certain part of the signal energy falls outside of the useful bandwidth. Summing up of the PSD values using a small predetermined frequency interval Δf over the full frequency range and dividing the sum of the useful frequency range with total sum, we can find the ratio of useful energy content to the total energy content of the excitation signal. Computer simulation using Δf = 10 Hz and bandwith 320 kHz was done. Results are presented in the column of EBW/ E of the table on the next slide.

7. 7 Electronics’ 2010, May 18-20, 2010, Kaunas, Lithuania Nonlinear Chirp Pulse Excitation for the Fast Impedance Spectroscopy Jaan Ojarand Jaan Ojarand, Paul Annus, Raul Land, Toomas Parve and Mart Min Titlet Tch E, V 2 ∙μs P, V 2 EBW/ EEBW/ EBWmax Modulation type μs nJ @ 1 kOhm mW @ 1 kOhm % Linear 40 18.00.45 7360 Exp.1 40 15.50.39 7383 Exp.2 40 16.10.40 7678 Exp.3 40 15.40.39 7283 2. Average power of the generated signal,, V 1. Energy of the generated signal, V 2 ∙ s Energy and power of titlets E- energy content in full bandwith observed (320 kHz). EBW- energy content in frequency range of interest (36 kHz), where the energy level is above 0.5 (-6dB) EBWmax – maximum possible energy content in frequency range of interest (rectangular PSD curve) Thermal noise: 4nV/Hz 1/2

8. 8 Electronics’ 2010, May 18-20, 2010, Kaunas, Lithuania Nonlinear Chirp Pulse Excitation for the Fast Impedance Spectroscopy Jaan Ojarand Jaan Ojarand, Paul Annus, Raul Land, Toomas Parve and Mart Min Practical measurements Normalized PSD for ½ of excitation, linear scale Titlet1 waveform Vch(t), V Practical measurements were carried out in the Institute for Bioprocessing and Analytical Measurement Techniques (Heilbad Heiligenstadt, Germany). Excitation signal was generated by Tektronix AGF3252 ARB signal generator, current and voltage were measured using Tektronix DPO70804 digital oscilloscope. Spectra of the module and phase of the impedance were calculated in the LabView environment.

9. 9 Electronics’ 2010, May 18-20, 2010, Kaunas, Lithuania Nonlinear Chirp Pulse Excitation for the Fast Impedance Spectroscopy Jaan Ojarand Jaan Ojarand, Paul Annus, Raul Land, Toomas Parve and Mart Min - Nonlinear modulation of the VCO allows to shape the PSD curve of the chirp excitation waveforms. - Usage of the exponential modulation signals improves the flatness of spectral density curve of one cycle chirp‘s and increases the energy content in the usable frequency range by more than 20 %, compared to its linear counterpart. - Short chirp excitation (titlet) is a perspective candidate for implementation in wideband spectroscopy of dynamic impedances. Conclusions

10. 10 Electronics’ 2010, May 18-20, 2010, Kaunas, Lithuania Nonlinear Chirp Pulse Excitation for the Fast Impedance Spectroscopy Jaan Ojarand Jaan Ojarand, Paul Annus, Raul Land, Toomas Parve and Mart Min References 1. Nahvi, M., Hoyle, B.S. Electrical Impedance Spectroscopy Sensing for Industrial Processes// IEEE Sensors Journal. – 2009. – No. 12 (9). – P. 1808-1816. 2. Min M., Giannitsis A. T., Land R., Cahill B. P., Pliquett U., Nacke T., Frense D., Gastrock G., Beckmann D. Comparison of rectangular wave excitations in broad band impedance spectroscopy for microfluidic applications //IFMBE Proceedings, Vol.25: VII World Congress on Medical Physics and Biomedical Engineering. – Munich (Germany), 2009. – P.85-88. 3. Min M., Pliquett U., Nacke T., Barthel A., Annus P., Land R.. Signals in bioimpedance measurement: different waveforms for different tasks // IFMBE Proceedings, Vol. 17: 13th Int. Conf. on Electrical Bioimpedance (ICEBI’2007). – Graz (Austria), 2007. – P. 181-184. 4. Min, M., Land, R., Annus, P., Ojarand, J. Chirp Pulse Excitation in the Impedance Spectroscopy of Dynamic Subjects: signal modelling in time and frequency domain // Transactions on Systems, Signals and Devices. – Aachen: SHAKER Verlag (Germany), 2010. – in print (2p.). 5. Min M., Land R., Paavle T., Parve T., Annus P. Broadband spectroscopy of a dynamic impedance// Journal of Physics: Proceedings ICEBI2010. – London: IOP, 2010. – in print (4p). 6. Annus, P., Min, M., Ojarand, J. Shortened square wave waveforms in synchronous signal processing// Proceedings I 2 MTC2008. – Victoria, British Columbia (Canada), 2008. – P. 1259 - 1262. 7.Skolnik M.I. Radar Handbook (3 rd edition). – McGraw-Hill, 2008. – 1352 p. 8. Darowicki K., Slepski P. Determination of electrode impedance by means of exponential chirp signal // Electrochemistry Communications. – 2004. – No. 6. – P.898–902. 9. Doerry A.W. Generating Nonlinear FM Chirp Waveforms for Radar (Research Report). – Sandia National Laboratories (New Mexico, USA), 2006. – 34 p. Acknowledgments The research was supported by the European Union (EU) through the European Regional Development Fund, Enterprise Estonia through the ELIKO Competence Center. Thank you for your attention !