being developed. Most up and coming drugs are extremely expensive and limited in

Transcription

1 Introduction In the pharmaceutical industry, it is important to know fluid properties of the drug being developed. Most up and coming drugs are extremely expensive and limited in quantity. A device that can measure fluid properties with minimal sample sizes could potentially save the developer a significant amount of money. There are many devices on the market that can be used to obtain fluid viscosity, but none of them operate on a volume of less than 150 µl. The small volume requirement is the greatest design obstacle that eliminates many of the methods that we considered. The design approach that will be considered here uses piezoelectric crystals as the main component. Peizoelectric crystals have been used in previous research, but the design allowed only one measuring frequency. Design Our design consists of three main parts: 1) a piezoelectric crystal setup that can create a range of frequencies 2) impedance analysis of the crystal setup 3) preparing the signal for output to a personal computer and obtaining fluid properties from impedance. Design Setup: 1

2 Crystal Setup The focal measurement of this design is taken by a piezoelectric ceramic device, likely an ultrasonic transducer. The heart of a piezoelectric ultrasonic transducers is compiled of a single, or double thick disc of some sort of piezoelectric ceramic, either quartz crystal or man-made material. This disc is slotted between two metal blocks, made of either aluminum or steel, which are compressed to a known value by high strength bolts. The piezoelectric ceramic is equipped with electrodes on either side, which provide a contact point for electrical contact. Voltage is applied to the crystal through these electrodes, thus causing the piezoelectric ceramic to expand and contract. This physical displacement on the x, y, and z axis produces sound waves, which propagate as transverse waves in liquid media. Piezoelectric ultrasonic transducers are now manufactured with an option of a sweeping frequency mechanism. This allows the ceramic inside the transducer to resonate at a series of frequencies between two set frequencies. Due to the customer request for a viscometer that functions at a range of frequencies, this sweeping style will be ideal for the design. The frequency range is obtained by first finding the resonant frequency of the specific piezoelectric ceramic, or the frequency at which the ceramic most readily vibrates in response to applied voltage and most efficiently converts electrical energy to mechanical energy. This frequency is represented as a dip in the log impedance versus frequency curve, and occurs at the minimum impedance, or maximum admittance, for the system, as seen below: 2

3 Where f s is the series resonance frequency and is roughly equal to f m, the resonance frequency; f p is the parallel resistance in the crystal and is roughly equal to f n, the maximum impedance frequency. Once this resonant frequency is established, the manufacturer is able to create a range by utilizing harmonic multiples, or overtones, of the initial primary frequency. That is, if the resonant frequency is represented as F, the overtones will be 2F, 3F, 4F, and so on, and appear as similar wave functions with increasing or decreasing amplitudes. A physical representation of harmonic overtones is demonstrated here by vibration direction: Figure 1: Proposed Displacement of Piezoelectric Crystals 3

4 The typical range of frequencies for these ultrasonic devices is between 20 and 200 MHz, this will adequately fulfill the requirements of the design. For this design, the ultrasonic transducer will be affixed to incoming voltage, and the initial wave will be established. The transducer will then be loaded with the sample liquid, and the outgoing waveform will again be monitored. The phase shift between these waves will be found and analyzed by the impedance analyzer chip, and the viscosity would be found using values established during experimentation. This device can be tested in a pharmacy laboratory, with a fluid of known viscosity and a previously designed piezoelectric viscometer, to determine if the impedance is accurate. A benefit to this design is that the transducer is able to function at a wide range of frequencies, and can measure the viscosity under varied conditions. However, these sweeping capabilities may ultimately be a flaw in the design, due to the use of overtones. Although the harmonic overtones grant the user more experimental variety, the use of overtones greater than the fifth multiple may leave the user with amplitudes and phase shifts that are too small to record, thus the integrity of the experimental values is questionable. Also, because the ceramic is compressed between the metal masses, it is questionable that a fluid load of less than 20 micro-liters will alter the frequency enough to provide the user with a viable phase shift. An alternative to using a piezoelectric ultrasonic transducer is to utilize between 3 and 4 single crystals in a series setting. These individual crystals are not capable of the sweeping range of frequencies that the transducer is equipped with; however individual overtones of each crystal can be employed. The primary frequency and the third overtone, the first harmonic multiple, are the most accurate, thus if each crystal is 4

5 examined at these frequencies (F and 2F), a total of 6 to 8 varied frequencies are possible, thus fulfilling the customer requirements. A piezoelectric crystal consists of a quartz plate, natural or cultured, with gold metal plating, which functions as an electrode, on both sides of the device. The gold plate is then connected to insulated leads. The mechanics of the piezoelectric crystals can be equated to a relatively simple electrical circuit, as follows: Figure 2: Crystal Circuit Where C o is the capacitance due to the electrodes on the crystal plate plus the stray capacitances due to the crystal enclosure, and is applicable regardless of the crystal oscillations. R, C 1 and L 1 are the equivalent motional arm resistance, the motional capacitance of the quartz, and the motional inductance, which is a function of mass, respectively. The ratio of C o to C 1 is equal to the constant k, the piezoelectric coupling factor, and increases with the square of the overtone number. Although the crystal equivalent electrical circuit appears simplistic, the method of calculating frequencies is somewhat complicated, and can be found using the following equations: F s (Series resonance frequency) = 1 / [2π(L 1 C 1 ) 1/2 ] (Eq. 1) F p (Parallel Resonance frequency) = f s [1 + 1/(2γ)] (Eq. 2) γ (Capacitance ratio) = 2πf s C 0 / C 1 (Eq. 3) Q (Quality factor) = 2πf s L 1 / R 1 (Eq. 4) M (Figure of merit) = Q / γ (Eq. 5) 5

6 Piezoelectric crystals are manufactured in two different cuts, AT and SC. Their main manufacturing difference is that AT crystals are singly rotated cut, while SC crystals are doubly rotated cut, as demonstrated below. Figure 3: AT vs. SC Cut Crystals The AT and SC cut are each capable of a resonance frequency range from 1 MHz to 250 MHz, however the AT crystals are super-sensitive to stresses in the body of the resonator that are caused by temperature gradients or other outside forces. While the SC crystal is slightly more expensive, it has higher performance reliability, and thus will be used in this design. For the design setup, each crystal will be equipped with a switch, enabling only one crystal to be electrically stimulated at a time. The crystals will be sandwiched between two electrodes, which feed in and out the electrical signal, much the same as the transducer setup. For the single crystals, however, the fluid load will be applied directly to the gold plate on the crystal, and the impedance measured based on the change in oscillation of the SC. This impedance will by analyzed and evaluated by the impedance analyzer and RS232. These crystals will be tested in a similar fashion as the transducer; 6

7 with a fluid of know viscosity and viscoelasticity and a previously built piezoelectric viscometer by the customer, to determine if the impedance of the crystal by the fluid is accurate. The use of single crystals as opposed to an ultrasonic transducer is beneficial to the device due to the increased reliability and precision. The single crystals are more reliable because only one overtone per crystal is utilized to create a range of frequencies. However, since several crystals must be tested to find the range, a larger amount of sample fluid is wasted during testing, and the user loses a degree of ease when experimenting. It is the belief of the customer and the designers that precision is more essential than ease when using this device, thus the single crystal setup is likely the optimal design. Impedance Analysis An Impedance Analyzer is used to convert information from analog to digital (ADC).The Impedance Converter will be used to measure the impedance generated from the piezoelectric device into digital data. The AD5933 chip is a high precision impedance converter system solution which combines an on board frequency generator with a 12-bit 1 MSPS (Mega Samples per Second) ADC. The frequency generator allows an external complex impedance to be excited with a known frequency. The block requires a reference clock to provide digitally created sine waves up to 50 khz. This is a very useful factor for this device since the quartz crystal can be oscillated by the chip with a known frequency. The response signal from the crystal is then sampled by the on board ADC and FFT (Fast Fourier Transform) processed by an onboard DSP (Digital Signal Processor) engine. The 7

8 FFT algorithm returns a real (R) and imaginary (I) data word, allowing impedance to be conveniently calculated. The AD5933 builds its output based on 3 major sub circuits: Numerically Controlled Oscillator + Phase Modulator, SIN ROM, and Digital to Analog Converter. The Impedance magnitude and phase is easily calculated using the following equation: To determine the actual real impedance value Z(_), generally a frequency sweep is performed. The impedance can be calculated at each point and frequency Vs magnitude plot can be created. The system allows the user to program a 2V PK-PK sinusoidal signal as excitation to the piezoelectric device. Output ranges of 1V, 500mV, 200mV can also be programmed. The signal is provided on chip using DDS (Direct Digital Signal) techniques. Frequency resolution of 27 bits (less than 0.1 HZ) can be achieved. The clock for the DDS can be generated from an external reference clock, an internal RC oscillator or an internal PLL (Phase Lock Loop). The PLL has a gain stage of 512 and typically needs a reference clock of 32 khz on the MCLK pin. To perform the frequency sweep, the user must first program the conditions required for the sweep; start frequency, delta frequency, step frequency, etc. A Start Command is then required to begin the sweep. At each point on the sweep the ADC will take 1024 samples and calculate a Discrete Fourier Transform to provide the real and imaginary data for the waveform. The real and imaginary data is available to the user through the 1 2 C interface. 8

9 To determine the impedance of the load at any one frequency point, Z(w), a measurement system comprised of a trans- impedance amplifier, gain stage and ADC are used to record data. The gain stage for the response stage is 1 or 5. The ADC is a low noise, high speed 1 MSPS sampling ADC that operates from a 3 V supply. Clocking for both the DDS and ADC signals is provided externally via the MCLK reference clock, which is provided externally from a crystal oscillator. The AD5933 is available in a 16 ld SSOP. FEATURES 100 khz max excitation output Impedance range 0.1 k_ to 10 M_, 12-bit resolution Selectable system clock from the following: RC oscillator, external clock DSP real and imaginary calculation (DFT) 3 V/5 V power supply Programmable sine wave output Frequency resolution 27 bits (<0.1 Hz) Frequency sweep capability with serial I2C loading 12-Bit sampling ADC ADC sampling 1 MSPS, INL ± 1 LSB max On-chip temp sensor allows ±2 C accuracy Temperature range _40 C to +125 C 16 lead SSOP package 9

10 APPLICATIONS Complex Impedance Measurement Impedance Spectrometry Biomedical and Automotive Sensors Proximity Sensors FFT Processing The piezoelectric quartz crystal shows a deformation or separation of charges which leads to a build up of potential difference across the 2 ends of the crystal with the magnitude of the developed potential difference being proportional to the applied stress. As the potential is reversed the crystal deflects in the opposite direction causing mechanical vibrations. The mechanical shifts are detected using electrodes which are placed on both sides of the crystal that send sinusoidal waveforms into the AD5933 Impedance Converter. Safety Features The AD5933 has a power down feature which will which will shut down all amplifiers and Oscillators. The device is also temperature sensitive and so in the case of over heating the chip will power down and stop the crystal from oscillating any further. The AD5933 Block Diagram 10

11 Figure 4 Pin Configuration Figure 5 Sending the Signal to the Computer Our client wants the final fluid properties as well as the raw data to be displayed on a personal computer. This will allow our client the ability to have more thorough documentation of the measurements and more freedom in evaluating the sample s properties. After the impedance is analyzed the data will be converted from analog to digital with a PIC16F874 (a 14-Bit 333 ksps Serial A/D Converter from Analog Devices) microprocessor. The data will then be prepared for serial port communication with the computer with a MAX232ACPE (MAXIM Dallas Semiconductor) microprocessor. The device will be connected to the personal computer through an RS- 11

12 232 serial cable. Overall circuit performance will be tested my selecting test points with predictable outputs throughout the circuit that can be measured with an oscilloscope. The client also prefers a wall outlet power source. A commercially available power supply will be used to power the device. Functionality of the power supply will be tested using a digital multi-meter. Determining Fluid Properties from Impedance Measurement After the impedance values are sent to the computer, a program such as one created with Labview will be used to create the user interface and display the raw and analyzed data. Another Labview program that simulates data can be created to test the overall performance of the user interface program. Figures 1 and 2 are circuit representations of the crystal when it is unloaded and loaded with the sample fluid. Where C 0 is the static plus stray capacitance, R 1 is the losses in the crystal due to friction or heat loss, C 1 is the energy stored in the crystal during each oscillation, L 1 is the inertial mass of the crystal, R 2 is the real component of the motional impedance due to the load, and X 2 =ωl 2 is the imaginary component of the motional impedance due to the load. 12

13 *Figure 6: A circuit representation of the unloaded crystal.* *Figure 7: A circuit representation of the loaded crystal* Our client is interested in measuring two fluid properties, loss modulus G (viscosity) and storage modulus G (viscoelasticity). R 2 is the change of the real part (resistance) of the impedance when the crystal is loaded. X 2 is the change in the imaginary part of the impedance when the crystal is loaded (X 2 =ωl 2 ). A is a constant associated with each crystal. ρ Liq is the density of the sample. Using piezoelectric crystals will allow measurement of both G and G. 13

14 (Eq. 6*) (Eq. 7*) Determining both G and G are important in studying Non Newtonian fluids, which are fluids that store some of the energy that is applied to them. Energy storage occurs in fluids with large molecules at high concentrations where molecular movement is inhibited by neighboring molecules. The intermolecular interaction that causes energy storage is an important fluid property that must not be confused with viscosity. However, in many viscometers, the storage modulus is ignored and causes the measured viscosity to deviate from actual viscosity. This is not a problem with Newtonian fluids because with Newtonian fluids X 2 = R 2 which causes G to go to zero. The following equation is normally used when calculating Newtonian viscosity. (Eq. 8*) Each crystal must be measured in order to determine the constant A before any fluid properties can be obtained. A fluid with known density and viscosity will be used to determine the constant A, which is equal to: Where N is the overtone number, K is the piezoelectric coupling constant, ω s is the series resonant frequency, C 0 is the static plus stray constant, and Z q is the quartz mechanical impedance. A is necessary because it allows us to calculate the mechanical impedance from the measured electrical impedance (where Z Elec = A*Z Mech ). Therefore, the electrical 14

15 values (X 2 and R 2 ) can be used in determining G and G when A is included in the equations. Once the device is assembled and all components are tested, fluids with known G and G values will be used to calibrate the device (determine the constant A) and test for overall accuracy and functionality. *Figures and equations were taken from Saluja A, Kalonia DS. Measurement of Fluid Viscosity at Microliter Volumes Using Quartz Impedance Analysis. AAPS PharmSciTech. 2004; 5(3): article 47, and 15