3.3 Ultrasonic techniques
3.3.4 Pulse-modulated traveling wave methods
At frequencies above 3 MHz the distortion of resonator curves by higher order modes may be so strong that the separation of the satellite peaks from the main resonance curve becomes impossible. However, the simple proportionality, given by the expression:
pR(x)∼e−αx, (3.60)
allows to measure quasi-directly the sound attenuation coefficient α. The principle of
pulse-modulated method is shown in Fig.(3.10). Pulse-modulated measurement are per-formed at the transducer fundamental frequency and its odd overtones which follow the (2n+1)·fT-law. The shiftable receiver, as shown in Fig.(3.10), at the position X1detects the acoustical signal and transfers this into an alternating voltage UR(X1). At the position X2the alternating voltage UR(X2)is received. Hence, the attenuation coefficientαfollows as:
α = −ln|UR(X1)| −ln|UR(X2)|
X1−X2 . (3.61)
Pulse modulation of the sound wave avoids overlaps between the original signal and
Figure 3.10: Principle of pulse-modulated method: (1) transducer ; (2a) receiver (start position) ; (2b) receiver (end position) ; (3) exponentially decreasing sound wave ; (4) cell walls.
multiply reflected signals as well as the electrical crosstalk. At small transducer spacing, so-called acoustic delay lines (fused quartz) are used for pulse separation. The pres-sure amplitude pR of the sound wave (taking into account multiple reflections) can be expressed as:
pT : amplitude of the sound pressure at the transducer;
pR : amplitude of the sound pressure at the receiver;
X : transducer spacing;
r : reflection coefficient;
β=2π/λ : wave number;
γ=α+iβ : complex propagation constance.
The cosine function of the transfer function Eq.(3.62) describes the so-calledλ/2-ripple, caused by the multiple reflections of the signal at the transducers. Forαλ>3 the denomi-nator of Eq.(3.62) equals approximately 1, so that an exponential decay of the sound wave pR∼e−αX follows. In Fig.(3.11) a plot of Eq.(3.62) is given as an example. It illustrates that at decreasing sample length X the standing wave contributions of the ultrasonic field within the cell become more and more important.
Figure 3.11: Effects of the cosine term in Eq.(3.62) on the transfer function.
Fitting at a given frequency f Eq.(3.62) to experimental data yields the absorption coef-ficientα and the sound velocity cs =λf of the sample liquid. To raise the accuracy of α measurements it is usual to reduce the influence of the cosine function. This can be realized with the help of the pulse modulation as mentioned before. The transducer signal is pulsed with the aid of square-wave pulse, with the pulse length following the relation:
τ< 2Xstart cs
, (3.63)
τ=2−10 µs. From this relation it is evident that the knowledge of the sound velocity cs
of the liquid sample is essential for correct pulse adjustments.
• Sound velocity measurements:
The transducer and the receiver have to be brought to a distance fulfilling X <τc/2 or X < 3/α. At the range of 20·λ, the transfer function is measured and the experimental data at constant frequency are fitted to Eq.(3.62). Finally, with the help of cs=λ· f , the sound velocity cscan be calculated.
• Characteristic curve of electronic setup:
The accuracy of pulse methods depends on the accuracy of determining the char-acteristic curve of the electronic equipment. In the measurement mode the signal passes some electronic devices. At first, the voltage UR has to be demodulated and amplified. Unfortunately, non-linear effects in the electronic circuit, especially in the amplifier exist. Hence, the voltage UR is subject to the characteristic curve of the receiver
C
(UR)and the sound pressure amplitude at the receiver quartz:C
(UR(X)) = const.·|pR||pT|, (3.64)
Finally, it is possible, with the aid of linear regression to calculate the attenuation coefficient as given:
α = [ln(
C
(UR(X+∆X)))−ln(C
(UR(X)))]/∆X. (3.65)Here ∆X is the measurement distance. A central role in the determination of the characteristic curve of the electronic equipment plays the cut-off piston attenua-tor. Details about that device can be found in [63]. Calibration of the apparatus is performed after each run by switching from the measuring branch to the reference branch and utilizing the cut-off piston attenuator to vary the receiver voltage. The voltage characteristic obtained by this calibration procedure allows the correction of the originally measured UR values.
• Electronic equipment and measuring procedure:
A block diagram of the electronic apparatus is shown in Fig.(3.12). The full lines
Figure 3.12: Block diagram of the electronic apparatus: (1) frequency synthesizer; (2) mixer; (3) pulse generator; (4) amplifier; (5) HF-change over switch; (6) matching stub transformer; (7) fixed coaxial attenuator; (8) sample cell; (9) transmitter; (10) receiver; (11) stepping-motor; (12) step-motor control; (13) control unit of distance meter (Heidenhain);
(14) PT-100 thermometer; (15) cut-off piston attenuator; (16) mixer, (17) oscillator , (18) filter, (19) demodulator (20) amplifier; (21) boxcar integrator and A/D-converter; (22) pulse generator; (23) oscilloscope; (24) personal computer; (25) relays driver card. (the full line indicate the signal path and the dashed lines show the electronic control circuit).
indicate the signal path and the dashed lines show the electronic control circuit.
The frequency synthesizer (1) along with the pulse generator (3) and the mixer (2) generates a pulse-modulated HF signal with frequency of measurement f . The signal, via two coaxial HF-switches, is passed either through the measuring branch or the reference branch of the comparator circuit. After passing the sample cell or the below-cut-off piston attenuator, both signals are fed via HF change over switch (5) to a superheterodyne receiver (16-20). A boxcar integrator (21) adds up the signal over a sequence of 400 pulses. Finally, the result is transferred to a
personal computer and evaluated using the data of length l, measured by the digital distance meter (11) with control unit (13). The temperature is measured with a Pt-100 thermometer (14).
• Pulse cell parameters: In the present thesis, two kinds of pulse cells have been used to investigate the broadband spectrum of liquids, the 1-MHz- pulse-cell and the 10-MHz-pulse-cell. Some relevant data of the cells are tabulated in Table (3.2).
In Fig.(3.14) a cell construction of a 1-MHz-pulse-cell is shown on the last page
cell 1–MHz– 10–MHz–
position of dist. meter axial axial
xmin[nm] 125 125
xmax[mm] 40 25
V [ml] ≈130 ≈10
Table 3.2: Pulse transmission cells rq: radius and fq: fundamental frequency of transduc-ers; fn: possible measurement frequencies; fmax: maximum frequency;τ: pulse length; xmin: minimum and xmax: maximum distance between transmitter and receiver; V : sample volume.
of this Chapter. A description can be found in the figure caption. In Table (3.3) experimental errors for measurements with the pulse cells are given.