sensors Article
A High Sensitivity Preamplifier for Quartz Tuning Forks in QEPAS (Quartz Enhanced PhotoAcoustic Spectroscopy) Applications Tomasz Starecki and Piotr Z. Wieczorek *
ID
Institute of Electronic Systems, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warsaw, Poland;
[email protected] * Correspondence:
[email protected] Received: 1 October 2017; Accepted: 2 November 2017; Published: 3 November 2017
Abstract: All the preamplifiers dedicated for Quartz Enhanced PhotoAcoustic Spectroscopy (QEPAS) applications that have so far been reported in the literature have been based on operational amplifiers working in transimpedance configurations. Taking into consideration that QEPAS sensors are based on quartz tuning forks, and that quartz has a relatively high voltage constant and relatively low charge constant, it seems that a transimpedance amplifier is not an optimal solution. This paper describes the design of a quartz QEPAS sensor preamplifier, implemented with voltage amplifier configuration. Discussion of an electrical model of the circuit and preliminary measurements are presented. Both theoretical analysis and experiments show that use of the voltage configuration allows for a substantial increase of the output signal in comparison to the transimpedance circuit with the same tuning fork working in identical conditions. Assuming that the sensitivity of the QEPAS technique depends directly on the properties of the preamplifier, use of the voltage amplifier configuration should result in an increase of QEPAS sensitivity by one to two orders of magnitude. Keywords: quartz tuning fork; quartz enhanced photoacoustic spectroscopy; QEPAS sensor preamplifier design; transimpedance amplifier
1. Introduction Trace gas sensors are used in numerous applications, such as environmental science (e.g., monitoring of atmospheric pollutants) [1], medical diagnostics (e.g., breath analysis) [2], industrial control [3] and the detection of dangerous substances (e.g., toxic gases or explosives) [4]. There are many methods that can be used to implement trace gas sensors. One of them, which is particularly well suited for such applications, is photoacoustic spectroscopy (PAS) [5–7]. In photoacoustic spectroscopy, the investigated gas is illuminated with light, and its wavelength is adjusted to the absorption line of interest. Absorption of light results in an increase of the local temperature and pressure. Modulation of the light intensity or wavelength with a given frequency f will thus lead to periodic temperature and pressure changes. Such pressure changes (i.e., photoacoustic signal) can be measured with a microphone or piezoelectric transducer. One of the most important facts about the induced photoacoustic signal is that its amplitude is proportional to the concentration of the absorbing gas. This allows the design of photoacoustic sensors that are capable of concentration measurements with the linearity of several orders of magnitude. For obvious reasons, solutions dedicated to trace gas detection applications are usually optimized towards the highest possible sensitivity, i.e., capability of detecting as low concentrations as possible. One of the methods of increasing sensitivity of the photoacoustic equipment is the use of an acoustic resonance for amplification of the photoacoustic signal. In such a case the signal gain is equal to the quality factor of the applied resonance [8]. A particular solution of that kind uses a quartz tuning fork (QTF) as the Sensors 2017, 17, 2528; doi:10.3390/s17112528
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photoacoustic signal detector/transducer. For this reason the described modification of photoacoustic Sensors 2017, 17, 2528 2 of 15 spectroscopy is called QEPAS (Quartz Enhanced PhotoAcoustic Spectroscopy) [8–12]. Due to the 4 5 [8,13–15], a very high signal gain can fact that QTFs may have quality factors of the orderFor of 10 as the photoacoustic signal detector/transducer. this–10 reason the described modification of photoacoustic spectroscopy is called QEPAS (Quartz Enhanced PhotoAcoustic Spectroscopy) [8–12]. be obtained. 5 [8,13–15], a very high signal Due to the fact block that QTFs may have factors of the order of 104in –10Figure A simplified diagram of aquality QEPAS setup is presented 1. In the most common gain can be obtained. QEPAS implementation, a light beam produced with a laser diode is collimated between the QTF A simplified block diagramby ofaa current QEPAS amplifier, setup is presented in turn Figure In the most prongs. The laser diode is driven which in is 1. controlled bycommon a waveform QEPAS implementation, a light beam produced with a laser diode is collimated between the QTF generator. The output signal from the waveform generator consists of two components, slow ramp of prongs. The laser diode is driven by a current amplifier, which in turn is controlled by a waveform relatively high amplitude and a small amplitude sine wave. Taking into consideration that wavelength generator. The output signal from the waveform generator consists of two components, slow ramp of theoflight emitted by amplitude a laser diode the current through theconsideration diode, the slow relatively high anddepends a small on amplitude sineflowing wave. Taking into thatramp implements wavelength scanning, the diode sine wave component resultsflowing in additional wavelength of the light emitted while by a laser depends on the current throughsmall-deviation the diode, wavelength Absorption of the scanning, modulated lightthe by sine the investigated gas produces the slowmodulation. ramp implements wavelength while wave component results in local additional small-deviation wavelength deflect modulation. of the light by the light gas pressure changes, which periodically prongsAbsorption of the tuning forkmodulated synchronously to the investigated gas produces local gas pressure changes, which periodically deflect prongs of the tuning modulation. Each deflection of the prongs results in change of the charge/voltage at the resonator fork synchronously the light Eachadeflection of theand prongs in changeisof the terminals (nodes). Suchto a signal is modulation. passed through preamplifier, thenresults its amplitude measured charge/voltage at the terminalsby (nodes). Such a(PC). signalIfisthe passed a preamplifier, and by a lock-in amplifier andresonator can be recorded a computer sinethrough wave modulation frequency is then its amplitude is measured by a lock-in amplifier and can be recorded by a computer (PC). If the appropriately selected, the QEPAS signal can be substantially amplified due to the resonance properties sine wave modulation frequency is appropriately selected, the QEPAS signal can be substantially of theamplified tuning fork. due to the resonance properties of the tuning fork.
Figure 1. An example of a QEPAS setup block diagram.
Figure 1. An example of a QEPAS setup block diagram.
All the preamplifiers dedicated to QEPAS applications that have been so far reported in the
All the preamplifiers dedicated to QEPAS applications that have been so far reported in the literature literature have been based on operational amplifiers working in transimpedance configurations have been based on operational amplifiers working in transimpedance configurations [8,12–16]. However, [8,12–16]. However, QEPAS sensors are based on quartz tuning forks, and that quartz is a QEPAS sensors are basedwith on aquartz tuning that and quartz is a piezoelectric material with a piezoelectric material relatively high forks, voltageand constant relatively low charge constant [17]. relatively high voltage constant and relatively low charge constant [17]. This lead us to the conclusion This lead us to the conclusion that a transimpedance amplifier is probably not an optimal solution, that aand transimpedance is probably optimal solution, thatpreamplifier properties isof the that properties amplifier of the preamplifier cannot be an substantially improvedand if the preamplifier can be implemented in substantially a different way.improved if the preamplifier is implemented in a different way. 2. Preliminary Considerations 2. Preliminary Considerations 2.1. Preamplifiers Dedicated PiezoelectricSensors Sensors 2.1. Preamplifiers Dedicated forfor Piezoelectric Operation of the quartz tuningforks forks isis based based on effect. A force applied to a to a Operation of the quartz tuning on aa piezoelectric piezoelectric effect. A force applied piezoelectric material results in its mechanical deformation and produces an electric charge on certain piezoelectric material results in its mechanical deformation and produces an electric charge on certain opposite faces of the material [18,19]. Piezoelectric materials can be characterized by means of several opposite faces of the material [18,19]. Piezoelectric materials can be characterized by means of several properties, in particular by a piezoelectric charge constant and piezoelectric voltage constant. The properties, in particular by a piezoelectric charge constant and piezoelectric voltage constant. The first first one reflects the electric polarization generated in a material per unit of mechanical stress applied one reflects the electric polarization generated in a material per unit mechanical stressunit applied to this material. The second, is defined as the electric field produced in aofmaterial per applied of to this material. The second, is defined as the electric field produced in a material per applied unit of mechanical stress. Values of the two constants and their ratio depend strongly on the material and mechanical stress. Values of the two constants and their ratio depend strongly on the material and
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may vary in a relatively wide range. To give an example: quartz has quite a high voltage constant (118 V ·m/N) a low charge while commonly (Lead Zirconate may vary and in a relatively wide constant range. To (4.6 give pC/N), an example: quartz has quiteused a highPZT voltage constant Titanate) has a lower constant (38 V ·m/N), its charge constant (580(Lead pC/N) is over two (118 V·m/N) and avoltage low charge constant (4.6 pC/N),but while commonly used PZT Zirconate orders of magnitude higher thanconstant the corresponding of quartz Titanate) has a lower voltage (38 V·m/N), sensitivity but its charge constant[17]. (580 pC/N) is over two ordersaofquartz magnitude higher corresponding sensitivity of quartz [17]. Since tuning forkthan is a the piezoelectric sensor, it should be considered as a high impedance Since a quartz tuning fork is a piezoelectric sensor, it should be considered as a high impedance signal source. Hence, the primary role of a preamplifier used in QEPAS equipment is conversion signal source. Hence, the primary role of a preamplifier used in QEPAS equipment is conversion of the signal available at high-impedance terminals of the QTF to a low-impedance voltageofsignal the signal available at high-impedance terminals of the QTF to a low-impedance voltage signal source. Preamplifiers dedicated to piezoelectric sensors are usually implemented with operational source. Preamplifiers dedicated to piezoelectric sensors are usually implemented with operational amplifiers (op-amps) working as voltage amplifiers, charge amplifiers or transimpedance amplifiers amplifiers (op-amps) working as voltage amplifiers, charge amplifiers or transimpedance amplifiers (Figure 2) [20]. (Figure 2) [20].
Figure 2. Basic configurations of preamplifiers dedicated for use with piezoelectric sensors:
Figure Basic amplifier; configurations of preamplifiers dedicated for use with piezoelectric sensors: (a) voltage (a)2. voltage (b) charge amplifier; (c) transimpedance amplifier. amplifier; (b) charge amplifier; (c) transimpedance amplifier. Resistor R3 used in the voltage amplifier circuit (Figure 2a) is required to supply bias current to Resistor R3 usedinput in the amplifier (Figure 2a)range is required to supply bias current to the non-inverting of voltage the op-amp, and its circuit value can be in the of gigaohms if the input stage of the op-ampinput is built Junction and Fieldits Effect Transistors or Metal Oxide Semiconductor the non-inverting ofwith the op-amp, value can be in(JFET) the range of gigaohms if the input stage EffectisTransistors In such a case, the electrical load the QTF is negligible and the Field of theField op-amp built with (MOSFET). Junction Field Effect Transistors (JFET) orof Metal Oxide Semiconductor sensor works in the voltage-emitting mode. Signal produced at the electrodes of the QTF is amplified Effect Transistors (MOSFET). In such a case, the electrical load of the QTF is negligible and the sensor with the kf gain of (1 + R2/R1). works in the voltage-emitting mode. Signal produced at the electrodes of the QTF is amplified with In the charge amplifier configuration (Figure 2b), a piezoelectric sensor is connected to the the kf gain of (1 + R2 /R1 ). inverting input of the operational amplifier. Due to the feedback loop of the op-amp formed by the In the charge amplifier configuration (Figure 2b), a piezoelectric sensor is connected to the Cext and R2 that are connected in parallel, voltage at the inverting input is very close to the ground inverting of the amplifier. Duethe tosensor the feedback loop of theto op-amp formed byand the Cext (zeroinput voltage). Thisoperational means that voltage across electrodes is forced be virtually zero, and Rthe areworks connected in parallel, voltage the inverting input changes is very close to by thethe ground 2 that sensor in the charge-emitting mode.atObviously, the charge induced sensor(zero voltage). This means that across the sensor is forced of to C be zero, and the can be considered as a voltage current flowing through theelectrodes parallel connection ext virtually and R2, producing voltage the output of themode. amplifier [19,21,22].the Resistor is used to ensure by thethe inverting sensor workssignal in theatcharge-emitting Obviously, chargeR2changes induced sensor can input polarity for DC voltage, limit the voltage gain and prevent from output voltage saturation be considered as a current flowing through the parallel connection of Cext and R2 , producing (as voltage offset voltage at the output amplified the voltage gain). The R2 resistor also signalinput at the output of theappears amplifier [19,21,22]. Resistor Rwith is used to ensure the inverting input polarity 2 influences the bandwidth of the amplifier, by setting the upper bandwidth frequency to the value of for DC voltage, limit the voltage gain and prevent from output voltage saturation (as input offset (1/2π·R2·Cext). The charge amplifiers are used mainly with the sensors of relatively high inherent voltage appears at the output amplified with the voltage gain). The R2 resistor also influences the capacitance Cs, because voltage gain kf of the charge amplifier is defined by the Cs/Cext ratio. Taking bandwidth of the amplifier, by setting the upper bandwidth frequency to the value of (1/2π·R2 ·Cext ). into consideration that the equivalent capacitance of a quartz tuning fork is of the order of a few The charge amplifiers used(parasitic) mainly with the sensors relatively high inherent capacitance picofarads, and that are the stray capacitance of the of circuit is of a similar level, obtaining high Cs , because voltage gainsignal kf of working the charge amplifier is definedconfiguration by the Cs /Cis ratio. Taking into consideration extnot gains of the QTF in the charge amplifier possible. The main reason that the equivalent capacitance of a quartz fork is ofisthe of a few and that for using a capacitor in the feedback loop of tuning charge amplifiers thatorder if the sensor is apicofarads, capacitive signal source, its impedance will change the frequency. thelevel, use of an ordinaryhigh inverting amplifier the stray (parasitic) capacitance of with the circuit is of a Thus, similar obtaining gains of the QTF with a resistor thecharge feedback loop willconfiguration result in a frequency of the gain.reason If both for source signal working in in the amplifier is notdependence possible. The main using a and feedback impedances are capacitors, the gain will not vary with the frequency. However, if the capacitor in the feedback loop of charge amplifiers is that if the sensor is a capacitive signal source, signal source produces a sine wave of a fixed frequency f, the capacitor in the feedback loop can be its impedance will change with the frequency. Thus, the use of an ordinary inverting amplifier with replaced by a resistor R2 of appropriately selected value (R2 = kf/2π·f·Cs), converting a charge amplifier a resistor in the feedback loop will result in a frequency dependence of the gain. If both source and into a transimpedance amplifier (Figure 2c). It can be easily noticed from the above description, that feedback impedances capacitors, the gain will not vary with the frequency. However, if the the structure of the are transimpedance amplifier is identical to the charge amplifier (Figure 2b). The onlysignal source produces a sine wave of a fixed frequency f, the capacitor in the feedback loop can be replaced difference is that the main feedback loop component that sets the gain of such a circuit is R2, while
by a resistor R2 of appropriately selected value (R2 = kf /2π·f ·Cs ), converting a charge amplifier into a transimpedance amplifier (Figure 2c). It can be easily noticed from the above description, that the
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structure of the transimpedance amplifier is identical to the charge amplifier (Figure 2b). The only C ext is a stray (or is loop a capacitor usedthat to sets limit bandwidth). a difference is thatcapacitance the main feedback component thethe gainsignal of such a circuit is R2Obviously, , while Cext is transimpedance amplifier applied as a QTF signal amplifier has similar drawbacks as the charge a stray capacitance (or is a capacitor used to limit the signal bandwidth). Obviously, a transimpedance amplifier. amplifier applied as a QTF signal amplifier has similar drawbacks as the charge amplifier. As As already already mentioned, mentioned, it it seems seems as as though though all all the the QTF QTF preamplifiers preamplifiers used used in in QEPAS QEPAS applications applications described in the literature have been so far implemented as transimpedance amplifiers described in the literature have been so far implemented as transimpedance amplifiers [8–12,16]. [8–12,16]. Moreover, the cited cited solutions solutions used used feedback feedback resistors resistors R R22 of Moreover, the of relatively relatively high high values; values; the the most most common common of which was 10 MΩ [8,10,16].This was probably done to obtain a high gain factor; however, of which was 10 MΩ [8,10,16].This was probably done to obtain a high gain factor; however, if if we we assume values of R 2 = 10 MΩ and stray capacitance C ext = 2.5 pF, we obtain a resulting upper assume values of R2 = 10 MΩ and stray capacitance Cext = 2.5 pF, we obtain a resulting upper limit limit frequency frequency of of approx. approx. 6.4 6.4 kHz. kHz. This This in in turn turn means means that that virtually virtually all allthe thecited citedQEPAS QEPAS preamplifiers preamplifiers that that were used with the 32.768 kHz QTFs were working outside the preamplifier bandwidth, and thus were used with the 32.768 kHz QTFs were working outside the preamplifier bandwidth, and thus the the QEPAS signal subjected to substantial attenuation. QEPAS signal waswas subjected to substantial attenuation.
2.2. Quartz Quartz Tuning Fork Model QEPAS sensors are based based on on quartz quartz tuning tuning forks forks working working in in resonance resonance conditions. conditions. Hence, Hence, theoretical analysis analysis of of a QEPAS preamplifier requires use of a QTF model that would reflect the resonance fork. ThisThis can be with awith Butterworth–Van Dyke model resonance properties propertiesofofthe the fork. canobtained be obtained a Butterworth–Van Dyke (Figure model 3) [13–15]. (Figure 3) [13–15].
Figure 3. 3. Butterworth–Van Butterworth–Van Dyke Dyke model model of of aa quartz quartz crystal crystal resonator. resonator. Figure
In the the above abovefigure, figure,the theresistor resistorRRmodels modelsthe theenergy energylosses, losses, the capacitor inductor, 1 and In the capacitor C1Cand thethe inductor, L1 L represent the potential and the kinetic energy storage, and the parallel capacitor C corresponds to 1 represent the potential and the kinetic energy storage, and the parallel capacitor C00 corresponds to the total stray capacitance of the electrodes, crystal enclosure, leads, etc. Obviously, in order to model the total stray capacitance of the electrodes, crystal enclosure, leads, etc. Obviously, in order to model behavior of of aa preamplifier L11 and and R) R) for for behavior preamplifier used used with with aa given given QTF, QTF, all all four four component component values values (C (C00,, C C11,, L this particular resonator must be estimated first. Probably the most straightforward way to extract the this particular resonator must be estimated first. Probably the most straightforward way to extract parameters is tois measure thethe admittance ofof the calculations, the parameters to measure admittance theQTF QTFvs. vs.frequency, frequency,and andperform perform some some calculations, taking into consideration that [13,14]: taking into consideration that [13,14]: 1.
2. 3. 4. 4.
seriesresonant resonant frequency frequencyfsfs can can be be easily easily ,, measurements measurements as as aa frequency frequency at at which the QTF has series thehighest highest admittance; admittance; the series anti-resonant anti-resonant frequency frequency fafa can can be be easily easily determined determined from from the the measurements, measurements, as as at this series frequency the the QTF QTF has has the the lowest lowest admittance; admittance; frequency CC00for forthe thequartz quartzcrystals crystalsisisusually usuallyof of aa few few pF pF and and its its typical typical value value for for the given resonator is specified manufacturerininthe thedatasheet. datasheet.For For32.768 32.768 kHz crystals assume 0 = 2.5 specified by the manufacturer kHz crystals wewe cancan assume C0 =C2.5 pF; pF; knowing that: knowing that: 1 √ fs = (1) 2π L1 · C1 and:
and:
fs =
1 2π L1 C1
(1)
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C C fa = 1 / 2π L1 0 1 C 0 + C1 s
we get C1 as:
f a = 1/2π
L1
C0 · C1 C0 + C1
fa 2 C1 = C0 1 ; fs fa2
we get C1 as:
(2)
(2)
(3) !
C1 = C0 · −1 ; (3) fs and then L can be calculated from (1); 5. quality of the crystal and thenfactor L can(Q) be calculated fromcan (1); be estimated from the measured crystal admittance vs. frequency values, taking into consideration that: quality factor (Q) of the crystal can be estimated from the measured crystal admittance vs. 5. frequency values, taking into considerationfsthat: Q= (4) Δ f − 3 dB fs Q= (4) ∆ f −3dB 6. Finally we can obtain R from: 6.
Finally we can obtain R from:
R=
2π fs L1 . 2π f s · L1 Q . R= Q
(5) (5)
2.3. 2.3. Quartz Tuning Tuning Fork Fork Measurements Measurements As As described described above, above, estimation of the component values used in the the QTF QTF model model requires requires determination QTF admittance vs. frequency characteristics. In orderInto order evaluate properties determinationofofthethe QTF admittance vs. frequency characteristics. to such evaluate such of the QTF used our experiments, designed a we dedicated system, whose block diagram is given properties of thein QTF used in our we experiments, designed a dedicated system, whose block in Figure is 4. given in Figure 4. diagram
Figure 4. 4. Block Block diagram diagram of of aa system system used used for for QTF QTF characterization. characterization. Figure
The USB interface). AsAs a result, substantial parts of The system systemwas wascontrolled controlledby byaaPC PCcomputer computer(via (via USB interface). a result, substantial parts the control software, numerical calculations and and useruser interface werewere implemented on the of the control software, numerical calculations interface implemented onPC, theand PC,thus and itthus wasitpossible to haveto thehave hardware and firmware the system significantly simplified. Admittance was possible the hardware and of firmware of the system significantly simplified. of the crystal of wasthe measured a given (programmable) of frequencies. As can Admittance crystal point-by-point was measuredfor point-by-point for a givenrange (programmable) range of be seen from As the can Figure signal from generator, implemented a DDS frequencies. be 4,seen from thea programmable Figure 4, signalsine from a programmable sinewith generator, (Direct Digital with Synthesis) circuit, was applied to a transimpedance in awhich the output implemented a DDS (Direct Digital Synthesis) circuit, was amplifier, applied to transimpedance amplitude is which proportional to the admittance of the crystal given frequency. The DDS amplifier, in the output amplitude is proportional to for the aadmittance of the crystal for acircuit given with a reference clock basedwith on aa crystal oscillator (OSC) a high quality wave with a frequency. The DDS circuit reference clock based onproduces a crystal oscillator (OSC)sine produces a high precisely known programmable) amplitude and frequency. Due to expected very high quality quality sine wave(and with a precisely known (and programmable) amplitude and frequency. Due to factors of the QTFs, resulting in very narrow resonance curves, we used a DDS circuit with a frequency
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expected expected very very high high quality quality factors factors of of the the QTFs, QTFs, resulting resulting in in very very narrow narrow resonance resonance curves, curves, we we used used aa DDS circuit with a frequency resolution of the output sine wave better than 0.1 Hz. In order DDS circuit with a frequency resolution of the output sine wave better than 0.1 Hz. In order to to resolution of the output sine wave better than 0.1 Hz. In order from to obtain high dynamic range of the obtain obtain high high dynamic dynamic range range of of the the measurements, measurements, the the signal signal from the the DDS DDS generator generator is is passed passed measurements, the signal from the DDS generator is passed through a low-noise, high-precision PGA through through aa low-noise, low-noise, high-precision high-precision PGA PGA (Programmable (Programmable Gain Gain Amplifier) Amplifier) whose whose gain gain is is digitally digitally (Programmable Gain Amplifier) whose gain iswith digitally programmable in the range of −output 95.5–+31.5the dB programmable programmable in in the the range range of of −95.5–+31.5 −95.5–+31.5 dB dB with aa 0.5 0.5 dB dB resolution. resolution. Signal Signal from from the the output of of the with a 0.5 dB resolution. Signal from the output of the transimpedance amplifier is passed through an transimpedance transimpedance amplifier amplifier is is passed passed through through an an identical identical PGA. PGA. Amplitude Amplitude of of the the stimulating stimulating and and identical PGA. Amplitude of the stimulating and output signals is measured with a true RMS (root output output signals signals is is measured measured with with aa true true RMS RMS (root (root mean mean square) square) converter. converter. Switching Switching between between the the mean square) converter. Switching between the two signals is implemented with a multiplexer. A DC two two signals signals is is implemented implemented with with aa multiplexer. multiplexer. A A DC DC voltage voltage at at the the output output of of the the true true RMS RMS converter converter voltage at the output of thevalue true RMS converter is proportional to the RMS value of the input signal, is is proportional proportional to to the the RMS RMS value of of the the input input signal, signal, and and is is measured measured with with aa high-resolution high-resolution ADC ADC and is measured converter). with a high-resolution ADC (analog-to-digital converter). All themultiplexer settings of both (analog-to-digital All the settings of both PGA channels, DDS generator, (analog-to-digital converter). All the settings of both PGA channels, DDS generator, multiplexer and and PGA channels, DDS generator, multiplexer and acts ADC are controlled by a microcontroller, which acts ADC ADC are are controlled controlled by by aa microcontroller, microcontroller, which which acts according according to to the the commands commands sent sent via via USB USB from from according to the commands sent via USB from the PC computer. A photo of the system performing the the PC PC computer. computer. A A photo photo of of the the system system performing performing measurements measurements is is given given in in Figure Figure 5. 5. Admittance Admittance measurements is given in Figure 5. Admittance vs. frequency dependence of the QTF used in further vs. frequency dependence of the QTF used in further experiments, and measured with the vs. frequency dependence of the QTF used in further experiments, and measured with the presented presented experiments, and measured with the presented system is given in Figure 6. The measurements clearly system system is is given given in in Figure Figure 6. 6. The The measurements measurements clearly clearly show show that that removal removal of of the the crystal crystal package package cup cup show that removal of the crystal package cup (necessary for QEPAS experiments) results in a slight (necessary for QEPAS experiments) results in a slight decrease in the resonance frequency and (necessary for QEPAS experiments) results in a slight decrease in the resonance frequency and decrease in the resonance frequency of and substantial drop of the quality factor of the resonator. substantial substantial drop drop of of the the quality quality factor factor of the the resonator. resonator.
Figure A photo Figure5. photoof ofthe thedesigned designedsystem systemduring duringQTF QTFmeasurements. measurements. Figure 5.5.AAphoto of the designed system during QTF measurements.
Figure 6. QTF admittance vs. frequency measured with a frequency step of 0.1 Hz before (upper plot) Figure 6. QTF admittance vs. frequency measured with a frequency step of 0.1 Hz before (upper plot) Figure QTF admittance measured with a frequency step resonator, of 0.1 Hz model before and after6. (bottom plot) of thevs.QTFfrequency package cup removal (32.768 kHz crystal and after (bottom plot) of the QTF package cup removal (32.768 kHz crystal resonator, model (upper plot) and after (bottom plot) the Frequency QTF package cup removal (32.768 kHz crystal resonator, LFXTAL002996Bulk, manufactured byofIQD Products). LFXTAL002996Bulk, manufactured by IQD Frequency Products). model LFXTAL002996Bulk, manufactured by IQD Frequency Products).
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3. Theoretical Analysis of the Preamplifier Noise Properties Sensors 2017, 17, 2528 3. Theoretical Analysis
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The system described in the previous section was used to determine the fs and fa frequencies The system described in the previous section was used to determine thetemperature. fs and fa frequencies of turn of the3.QTF, operating under pressure conditions in ambient This, in Theoretical Analysis of atmospheric the Preamplifier Noise Properties the QTF, operating under atmospheric pressure conditions in ambient temperature. This, in turn allowed us to determine the L1 and C1 parameters for known C0 , giving C1 = 5.95 fF and L1 = 4768 H, The system describedthe in Lthe previous section was used toCdetermine fs and frequencies allowed us to determine 1 and C1 parameters for known 0, giving Cthe 1 = 5.95 fFfaand = 4768 of H, which seem to be within theatmospheric typical range according to [13,14]. Moreover, due This, toL1 the sufficient the QTF, operating under pressure conditions in ambient temperature. in turn which seem to be within the typical range according to [13,14]. Moreover, due to the sufficient frequency resolution of the system, we also estimated factorCaccording (4), andand as aL1result were allowed us resolution to determine the L 1 and Cwe 1 parameters forQknown giving C1to=to 5.95 4768we H, frequency of the system, also estimated Q factor0, according (4),fFand as a =result we able to estimate the value of Rthe = 190 kΩ.range which seem be within typical were able to to estimate the value of R = 190 k.according to [13,14]. Moreover, due to the sufficient Since in QEPAS applications the QTF operates inin close fsfsproximity, acts aa device in which which frequency resolution of the system, we also estimated Q factor accordingititto (4),as as a result we the Since in QEPAS applications the QTF operates close proximity, acts asand device in were able to estimate the value of R = 190 k. reactances of L , C and C do not contribute to the input parameters of preamplifier circuits shown in 1 1of L1, C1 0and C0 do not contribute to the input parameters of preamplifier circuits shown the reactances Since in QEPAS applications the QTF operates in close fs proximity, it acts as a device in which Figurein7.Figure Such7.parameters as gain, noise or sensitivity depend R, RR1,1 R ,R noise sources. Such parameters as gain, noise or sensitivity dependsolely solely on R, 2 and noise sources. 2 and the reactances of L1, C1 and C0 do not contribute to the input parameters of preamplifier circuits shown in Figure 7. Such parameters as gain, noise or sensitivity depend solely on R, R1, R2 and noise sources.
7. Noise sources analyzedconfigurations configurations of transimpedance FigureFigure 7. Noise sources of of thethe analyzed of the the preamplifier: preamplifier:(a)(a) transimpedance configuration; (b) voltage configuration. configuration; (b) voltage configuration.
Figure 7. Noise sources of the analyzed configurations of the preamplifier: (a) transimpedance configuration; voltage configuration. The electrical(b) macromodels shown in Figure 7 consist of voltage and current noise sources, i.e.,
The electrical macromodels shown in Figure 7 consist of voltage and current noise sources, i.e., un , in+, in− (representing amplifier noise sources), an ideal operational amplifier, thermal noise sources in+ , inu−n,(representing amplifier noise sources), an ideal operational amplifier, thermal noisei.e., sources The electrical shown Figure 7 consist voltage and current noise sources, of the resistors R1macromodels and R2 (unR1 and unR2in , respectively) andofthe QTF model (see Figure 3). The QTF of theunresistors R and R (u and u , respectively) and the QTF model (see Figure 3). The QTF 1 2 nR1 nR2 , in+, in−was (representing amplifier noise sources), an ideal operational thermal noise sources model enhanced with a noise source unR, which represents bothamplifier, the thermal and flicker noise of model was enhanced with a noise source u , which represents both the thermal and flicker noise of nR of resistors and the QTF model (see Figure 3). The QTF thethe QTF [23]. R1 and R2 (unR1 and unR2, respectively) the QTF [23]. model enhanced withand a noise sourcethe unRoverall , whichcontribution represents both the thermal flicker noise of Inwas order to estimate compare of noise sourcesand in macromodels of the QTF [23]. In order to estimate and compare the overall contribution of noise sources in macromodels transimpedance and voltage topologies from Figure 7, we have transformed all sources to either of In order to estimate and compare the(Figure overall8b) contribution of the noise sources in macromodels of transimpedance and voltage topologies from Figure 7, we have transformed all sources to current current (Figure 8a) or voltage sources referred to amplifier inputs. It either is worth transimpedance and voltage topologies from Figure 7, we have transformed all sources to either mentioning that the noise model of 8b) the charge amplifier is identicalinputs. to the transimpedance one with that (Figure 8a) or voltage sources (Figure referred to the amplifier It is worth mentioning current (Figure 8a) orgain voltage sources (Figure tofrom the the amplifier inputs. in It parallel is worth respect to circuit 20’s and bandwidth, which8b) mainly Cext one connected to the noise model of the charge amplifier is identical to referred the result transimpedance with respect to circuit mentioning that thewhere noise kf model the amplifier is identical to the transimpedance one with R 2 (see Figure 2b), = (C 0 of + C 1)/Ccharge ext. 20’s gain and bandwidth, which mainly result from the Cext connected in parallel to R2 (see Figure 2b), respect to circuit 20’s gain and bandwidth, which mainly result from the Cext connected in parallel to where kf = (C0 + C2b), ext . kf = (C0 + C1)/Cext. 1 )/C R2 (see Figure where
Figure 8. Circuits presented in Figure 7 with the noise sources transformed to the amplifier inputs: (a) transimpedance configuration; (b) voltage configuration. Figure 8. Circuits presented in Figure 7 with the noise sources transformed to the amplifier inputs: Figure Circuits presented in Figure with the noise sources transformed to the amplifier inputs: (a)8. transimpedance configuration; (b) 7 voltage configuration.
(a) transimpedance configuration; (b) voltage configuration.
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In order to transform the sources, additional arithmetic operations were performed. The unR2 source was transformed from the amplifier’s output to its inverting input (see Figure 8a). For this reason its amplitude was divided by the close loop transimpedance gain (ki) of the amplifier. The voltage noise un source is placed between the feedback node and the inverting input. However, from a mathematical point of view, it can be treated as a voltage source connected to a non-inverting input. Therefore, its contribution to the feedback node results from voltage gain of the close loop amplifier, divided by transimpedance gain, i.e., (R2 + R)/R2 ·R. This way, the un source is transformed to the feedback node and converts into a noise current source connected in parallel to the amplifier’s noise in− source. Therefore, assuming the independence of noise processes, the total current variance itot referred to the input node (QTF) can be derived as: itot 2 = in− 2 +
1 1 2 2 2 2 · u + u + · u + u n n nR nR2 R2 R2 2
(6)
The overall variance of voltage noise sources referring to the non-inverting input of the circuit in Figure 8b can be derived when all of the noise sources are converted to the voltage sources referred to the input. Therefore, we have converted the in- and unR1 sources to current sources connected in parallel to R1 , and furthermore, we transferred these sources to the non-inverting input as voltage source ux , i.e.,: R ·R unR1 + in− · 1 2 (7) ux = R1 R2 + R1 The remaining unr2 source can be easily transferred to the non-inverting input by dividing its amplitude by the voltage close loop gain kf of the circuit in Figure 7b, i.e., kf = (1 + R2 /R1 ). This way we obtained a compact form of variance of the input voltage source of the circuit in Figure 8b, as derived in (8): u 2 · R1 2 + unR1 2 · R2 2 + in− 2 ( R2 · R1 )2 utot 2 = unR 2 + (in+ R)2 + un 2 + nR2 (8) ( R1 + R2 )2 The qualitative comparison of total noise described in (6) and (8) requires some simplifications. First of all, the output noise of both architectures shown in Figure 8 results from amplification of (6) and (8) by the transimpedance (ki = R2 ) and voltage (kf ) gain, respectively. Moreover, some of the factors in (6) and (8) can be neglected due to the major influence of other factors. Therefore, (6) multiplied by ki can be estimated by (9), whereas (8) leads to (10) when multiplied by kf : unouttrans 2 ≈ unoutvolt 2 ≈
R2 2 · unR 2 + un 2 + in− 2 · R2 2 2 R
2 R ( R1 + R2 ) 2 R2 ( R2 + R1 )2 2 2 2 2 2 2 · + u · u + u + i · + i · R n n+ n− 2 nR1 nR R1 R1 R1 2
(9)
(10)
One can see that the output noise derived in (10) contains two additional components, i.e.,: in+ 2 ·
R ( R1 + R2 ) R1
2
+ unR1 2 ·
R2 R1
2 ,
(11)
which result from the presence of an additional resistor R1 and the obvious fact that the non-inverting input is not connected to the ground. However, the total noise in both cases (i.e., transimpedance and voltage topology) is strictly determined by either the values of R2 and R2 /R (so obviously ki and the ki to series resonance resistance ratio values) or the R2 /R1 values (where R2 /R1 ∼ = kf ). Therefore, for (R2 /R) ≈ (R2 /R1 ) and R2 much greater than R1 , the overall noise is slightly higher in the case of the voltage op-amp topology, due to the presence of additional in − and unR1 sources. However, it is a rather small difference.
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amp topology, due to the presence of additional in− and unR1 sources. However, it is a rather 9small of 15 difference.
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4. Measurements Measurements 4. In order order to to experimentally experimentally evaluate evaluate properties properties of of the the preamplifier preamplifier configurations configurations discussed discussed in in In this paper, it and compare output signals from preamplifiers working with this it was wasnecessary necessarytotomeasure measure and compare output signals from preamplifiers working identical mechanical stimulation of theoftuning fork. The were performed in a circuit with identical mechanical stimulation the tuning fork.measurements The measurements were performed in a whose whose block diagram is presented in Figure The tuning wasfork stimulated by meansbyofmeans pressure circuit block diagram is presented in 9. Figure 9. Thefork tuning was stimulated of changes changes produced by a high-frequency speaker.speaker. The preamplifier was implemented in suchinasuch way pressure produced by a high-frequency The preamplifier was implemented between the voltage, charge or or transimpedance by athat waychanges that changes between the voltage, charge transimpedanceconfigurations configurationswere were possible possible by swapping three three connections connections made made with with short, short, flexible flexible cables cables (marked (marked with with dashed dashed lines). lines). As a result, swapping all preamplifier preamplifier configurations configurations were were based based on on the the same same operational operational amplifier amplifier and and the the same same tuning tuning all fork. Moreover, positions of the speaker speaker and the tuning tuning fork fork were were fixed, fixed, which which resulted resulted in in exactly exactly fork. identical conditions conditions during during measurements measurements of of preamplifiers. preamplifiers. Signals Signals from from the the preamplifiers’ preamplifiers’ outputs outputs identical wereobserved observedand andmeasured measuredwith withaaTektronix TektronixMDO3024 MDO3024oscilloscope. oscilloscope. were
Figure Block diagram diagram of of aa system used for experimental verification of Figure 9.9. Block of the the preamplifier preamplifier configurations configurations(voltage, (voltage,charge chargeand andtransimpedance). transimpedance).
5. 5. Measurements Measurements of of QTF QTF Source Source Parameters Parameters The The investigated investigated circuits circuits shown shown in in Figures Figures 22 and and 99 were were implemented implemented in in the the Texas Texas Instruments Instruments Analog System Lab Kit PRO. We stimulated the QTF connected to the input of voltage Analog System Lab Kit PRO. We stimulated the QTF connected to the input of voltage amplifier, amplifier, charge and transimpedance transimpedanceamplifier amplifierwith withidentical identicalamplitude amplitude acoustic signal charge amplifier amplifier and of of thethe acoustic signal (as (as described in previous subsection) at the fs frequency. This way, we were able to estimate described in previous subsection) at the fs frequency. This way, we were able to estimate the the amplitude of the voltage currentsignals signals(in(inthe the case case of of the the voltage voltage amplifier amplitude of the voltage andand current amplifier and and charge/transimpedance topology, respectively) for a particular acoustic signal level. Since charge/transimpedance topology, respectively) for a particular acoustic signal level. Since the the voltage voltage and topology represent opposite conditions, i.e., theoretically infinite andcharge/transimpedance charge/transimpedanceamplifier amplifier topology represent opposite conditions, i.e., theoretically input impedance (for voltage amplifier) and zero impedance (for charge and transimpedance amplifier) infinite input impedance (for voltage amplifier) and zero impedance (for charge and transimpedance of the QTF load, were ablewe to estimate thetoThevenin parameter of the QTF at theoffsthe frequency. amplifier) of thewe QTF load, were able estimate model’s the Thevenin model’s parameter QTF at Any capacitance C connected in parallel with R reduces the bandwidth of the amplifier in both ext 2 the fs frequency. topologies. Therefore, it is not recommended to use R of the order of several megaohms, because in Any capacitance Cext connected in parallel with R22 reduces the bandwidth of the amplifier in both such a case the upper limit frequency: topologies. Therefore, it is not recommended to use R2 of the order of several megaohms, because in
such a case the upper limit frequency: fu =
1 21· πR2 Cext
(12)
fu = (12) 2 ofπRthe is solely defined not only by the bandwidth itself, but by the parasitic capacitances 2 Cop-amp ext present in the circuit. The use of moderate voltage and transimpedance gain (e.g., kf = 21 V/V and ki = 100 kΩ respectively) eliminates the influence of the op-amp parameters on the waveforms at the
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is solely defined not only by the bandwidth of the op-amp itself, but by the parasitic capacitances present the circuit. Theby usethe of bandwidth moderate voltage and transimpedance (e.g., kf =capacitances 21 V/V and is solely in defined not only of the op-amp itself, but by gain the parasitic ki = 100 kΩ respectively) eliminates the influence of the op-amp parameters on the waveforms the fs frequency. theuse experiment = 4.7 kMΩ and R2 = 100 gain kMΩ were In the present inTherefore, the circuit.in The of moderateR1voltage and transimpedance (e.g., kf =assumed. 21 V/Vatand fs frequency. Therefore, in the experiment R 1 = 4.7 kMΩ and R2 = 100 kMΩ were assumed. In the case ki =the 100charge kΩ respectively) eliminates of the parameters on the waveforms at the case of amplifier, the gainthe is influence defined by theop-amp (C0 + C )/C ratio. One can see that it is ext 1 offrequency. the chargeTherefore, amplifier, in thethe gain is definedRby the (C0 + C 1)/Cext ratio. One can see that it is difficult to fs experiment 1 = 4.7 kMΩ and R 2 = 100 kMΩ were assumed. In the case difficult to obtain high gain ratios in the case of the charge amplifier due to extremely low Cext values. obtain high gain ratios in the caseisof the charge amplifier to extremely low Cext values. In the case the charge the gain defined by the (C0 to + C61due )/C ext ratio. One can see that it is difficult to In theofcase of ouramplifier, QTF, in order to obtain gain close V/V, it was necessary to use Cext = 400 fF, of our QTF, in order to obtain gain close to 6 V/V, it was necessary to low use C Cext ext = 400 fF, whereas obtain high gain ratios in the case of the charge amplifier due to extremely values. In the case whereas parasitic capacitances of this order are present on the board. Therefore, extreme care must be parasitic capacitances of this order are present on the board. Therefore, extreme must be taken of our QTF, in order to obtain gain close to 6 V/V, it was necessary to use Cext care = 400 fF, whereas taken during during thedesign design the charge amplifier The resistor R2 ,iswhich is only necessary of of the amplifier PCB.PCB. The resistor R2Therefore, , which only necessary for bias in for the bias parasiticthe capacitances of charge this order are present on the board. extreme care must be taken in theduring chargethe configuration, was 100 MΩ. charge configuration, was 100 MΩ. design of the charge amplifier PCB. The resistor R2, which is only necessary for bias in the Figure 10a–c show waveformsof of the the op-amp op-amp working thethe voltage, charge and and Figure 10a–c show the output workinginin voltage, charge charge configuration, wasthe 100output MΩ.waveforms transimpedance amplifier respectively. acoustic signal obtained from a high transimpedance amplifier respectively. acoustic signal was obtained from a high Figure 10a–c showconfigurations theconfigurations output waveforms of the The op-amp working inwas the voltage, charge and frequency speaker connected a powerrespectively. amplifier. The was 0.70.7 W, W, the operating transimpedance amplifier configurations acoustic signal was obtained from aoperating high frequency speaker connected to to a power amplifier. The output outputpower power was the frequency was tothefs speaker and was placed inpower close proximity of operating the obtained QTF frequency speaker connected to a the power amplifier. The output was 0.7 W, the frequency was set to fsset and wasspeaker placed in close proximity of the QTF (4 cm). The (4 cm). Thewas obtained ACfs amplitudes were uv =was 208 placed mV andinui close = 6.5 proximity mV for theofvoltage and frequency set to and the speaker the QTF AC amplitudes were uv = 208 mV and ui = 6.5 mV for the voltage and transimpedance amplifier transimpedance amplifier respectively. In theucase of the charge amplifier configuration the output (4 cm). The obtained AC amplitudes were v = 208 mV and ui = 6.5 mV for the voltage and respectively. In the case of the charge amplifier configuration the output amplitude was 90 mV. amplitude was 90 mV. transimpedance amplifier respectively. In the case of the charge amplifier configuration the output amplitude was 90 mV.
FigureFigure 10. Output signals observed at at the preamplifier working in different 10. Output signals observed theoutput outputthe the investigated investigated preamplifier working in different configurations: (a) voltage amplifier; (b) charge amplifier; transimpedance amplifier. configurations: (a) voltage amplifier; (b) charge amplifier; (c) transimpedance amplifier. Figure 10. Output signals observed at the output the investigated preamplifier working in different configurations: (a) voltage amplifier; (b) charge amplifier; (c) transimpedance amplifier.
At resonance influenceofofreactances reactances on impedance is negligible. For thisFor reason, At resonance the the influence onthe theQTF QTF impedance is negligible. this the reason, QTF can be represented as an ordinary non-ideal voltage or current source, depending on the the the QTF can be represented as anofordinary or current source, depending on the At resonance the influence reactancesnon-ideal on the QTFvoltage impedance is negligible. For this reason, topology of the amplifier (in this case the voltage or transimpedance respectively). Knowing the QTF can be represented as an ordinary non-ideal voltage or current source, depending on the topology of the amplifier (in this case the voltage or transimpedance respectively). Knowing the amplitudes of waveforms (Figure 10), we were able to estimate the short circuitKnowing current ui/ki topology theoutput amplifier (in this(Figure case the voltage or transimpedance respectively). amplitudes ofofoutput waveforms 10), we were able to estimate the short circuit the current = 65 nA (Figure 11a),waveforms and the open circuit uv/kf 9.9 mVthe (Figure 11b). way,ui/ki we of output 10), amplitude weamplitude were able tou=estimate short circuitThis current ui/ki amplitudes = 65 nA (Figure 11a), and the (Figure open circuit /kf = 9.9 mV (Figure 11b). This way, v the internal resistance R ofcircuit the Thevenin source QTF (Figure 11c),way, i.e., R =estimated 65 nA (Figure 11a), and the open amplitude uv/kfrepresenting = 9.9 mV (Figure 11b). This we= we estimated the=internal resistance R of the the measured TheveninR source QTF (Figure 11c), i.e., (uv·ki)/(ku·ui) 152 kΩ.resistance One can see value isrepresenting close toQTF the estimate based on estimated the internal R ofthat the Thevenin source representing (Figure 11c), i.e., R(4) = R = (uand · ui) = 152 kΩ. One can see that the measured R value is close to the estimate based v ·ki)/(ku (5), i.e., 190 kΩ.kΩ. One can see that the measured R value is close to the estimate based on (4) on (uv·ki)/(ku·ui) = 152 (4) and (5), i.e., 190 kΩ. and (5), i.e., 190 kΩ.
Figure 11. Black box method of signal source model evaluation: (a) current measurement at short circuit signal source; (b) voltage measurement at open circuit signal source; (c) resulting signal source model with the amplitude of 9.9 mV and internal resistance of 152 kΩ.
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The measurements clearly showed that voltage and transimpedance topologies enforce different behavior of the QTF source. The open circuit voltage uv /kf = 9.9 mV is easy to detect and amplify with an ordinary op-amp, such as TL08x or TL07x used in the experiment. However, in the short circuit mode of the QTF operation (transimpedance topology), one needs at least ki = R2 = 152 kΩ of the transimpedance gain in order to obtain the same signal level (9.9 mV) as the one present at the open circuit QTF nodes (without any amplifier at all). The measurements performed with QTF stimulated by the acoustic signal are valuable, since in the QEPAS technique, QTF is used exactly in the same way, as an acoustic to electrical signal transducer. Let us compare the empirical behavior of QTF in both considered preamplifier topologies, i.e., voltage and transimpedance. In the voltage topology, we obtained uv = 208 mV for kf = 21 V/V (R1 = 4.7 kΩ and R2 = 100 kΩ). In order to obtain the same output signal in the case of the transimpedance topology, we should apply R2 = 208 mV/65 nA = 3.2 MΩ. From now on, the (9) and (10) seem to be more obvious options. The input current noise in− has to be amplified over an order of magnitude in the case of the transimpedance topology (i.e., R2 = 3.2 MΩ for transimpedance and R2 = 100 kΩ for the voltage mode topology for the identical output uv ). Therefore, even though the in+ in (10) is present, its contribution is negligible due to significantly lower R2 in the case of the voltage topology. Moreover, the ((unR 2 + un 2 )·R2 2 /R2 ) term is much higher in the case of transimpedance configuration. First of all, unR 2 results from the thermal noise, which is proportional to the value of R, however R2 is 32 times higher in comparison to the voltage topology. Moreover, in order to obtain the same level of signal at the outputs of both topologies, (ki/R) ∼ = (((R2 + R1 )/R1 )), which obviously enhances influence of the thermal R2 noise. One can see that if the presented case study is applied to both topologies, the noise level is approximately an order of magnitude higher for the same output signal level in the case of the transimpedance topology. For this reason the rough signal-to-noise ratio (SNR) is an order of magnitude higher for the voltage preamplifier topology. In order to confirm the theoretical considerations we performed two types of measurements for all three topologies. In the first one, with the MDO3024 oscilloscope, we recorded m = 107 samples for each topology with and without the acoustic signal applied. The bandwidth of the measurements was limited to 500 kHz, and AC coupling was used. In the second case, we utilized the MDO3024 with additional spectrum analyzer. In this case, the bandwidth was only 10 kHz–100 kHz, whereas the resolution bandwidth (RBW) was 50 Hz. To calculate the signal-to-noise ratio (SNR) in the first case, we used Equation (13), where ui stands for subsequent signal samples from the output of the preamplifier, and uni stands for the samples recorded without the acoustic stimulation: s 1 m
SNR = 20 log10 s 1 m
m
∑ ui 2
i =1 m
∑ uni
, m = 107
(13)
2
i =1
Our second proposed technique for an SNR assessment was to estimate the signal to noise ratio in the narrow bandwidth neighborhood of the fs frequency. For this purpose, we registered output power spectra of the voltage, transimpedance and charge amplifiers. The results are shown in Figure 12 and Table 1.
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Figure12. 12.Average Averagespectra spectraobtained obtainedfor forthe thevoltage, voltage,charge chargeand andtransimpedance transimpedancetopologies. topologies.The TheSNR SNR Figure values in the neighborhood of the fs frequency are marked. values in the neighborhood of the fs frequency are marked.
Resultsof ofboth bothmentioned mentionedmethods methodsused usedto toestimate estimatewideband widebandand andnarrowband narrowbandSNR SNRof ofall allthree three Results analyzed preamplifier topologies are given in Table 1. analyzed preamplifier topologies are given in Table 1. Table 1. Signal-to-noise ratio (SNR) for all considered topologies measured with 500 kHz and Table 1. Signal-to-noise ratio (SNR) for all considered topologies measured with 500 kHz and narrow narrow bandwidth. bandwidth. Wideband SNR(dB) (dB) Narrowband NarrowbandSNR SNR (dB) Wideband SNR (dB) Voltage amplifier Voltage amplifier Charge amplifier Charge amplifier Transimpedance amplifier Transimpedance amplifier
29.74 29.74 23.29 23.29 11.21 11.21
68.2 68.2 59.9 59.9 52.7 52.7
The signal-to-noise values in Table 1 prove previous considerations regarding voltage and The signal-to-noise values Table 1 prove previous voltage transimpedance topologies. Oneincan see that the SNR in theconsiderations case of voltageregarding preamplifier is 18.5and dB transimpedance topologies. can see that configuration. the SNR in the case of voltage preamplifier is 18.5 dB higher in comparison to the One transimpedance higherNarrow in comparison to the transimpedance bandwidth SNR estimates show configuration. better results for all considered topologies. In such a case, Narrow bandwidth SNR show part betterofresults for all considered topologies. a EMI influence is minimized toestimates a very narrow the spectrum, which is similar to theIn 1/fsuch noise. case, EMI influence is that minimized to aofvery narrowpreamplifier, part of the spectrum, which15.5 is similar to the 1/f However, it turns out in the case the voltage the SNR yields dB improvement noise. However, it turns out that in the case of the voltage preamplifier, the SNR yields 15.5 and dB over the transimpedance topology (SNR = 68.2 dB, 59.9 dB and 52.7 dB for the voltage, charge improvement over the transimpedance topology (SNR = 68.2 dB, 59.9 dB and 52.7 dB for the voltage, transimpedance topologies, respectively). charge and transimpedance topologies, respectively). 6. The Proposal of the High Sensitivity Preamp–Discussion 6. The Proposal of the High Sensitivity Preamp–Discussion The theoretical consideration and measurement results led us to the concept of a multistage high The theoretical consideration and measurement results led us toamplifier the concept of a multistage high sensitivity preamp dedicated for the QEPAS. First of all, the voltage topology seems to be the sensitivity preamp dedicated thesignal QEPAS. First of all, voltage amplifier topology seemshigh to beR obvious choice when the noisefor and amplitudes arethe considered. Moreover, due to rather the obvious choice when theamplifier noise and signalbeamplitudes are considered. due to rather values, the input stage of the should fully differential, so that anyMoreover, external electromagnetic high values, the would input stage of the amplifier should be fully differential, so that anyThe external (EM)Rdisturbances not interfere with the weak signal available at the QTF nodes. input electromagnetic disturbances would notaninterfere the weak signal the the QTFR resistance of the (EM) op-amp should be of at least order of with magnitude higher thanavailable QTF’s R.atSince nodes. input of the op-amp which shouldminimizes be of at least an order magnitude than value isThe high, we resistance suggest guard shielding, leakage of theof input voltage higher stage. In the QTF’s R. Since the R value is high, we suggest guard shielding, which minimizes leakage of the input tested solution, we used AD 623 instrumentation amplifier at the first stage. voltage stage. In the solution, we usedused AD 623 instrumentation atoptimistic, the first stage. The scenario of tested the acoustic stimulation in our measurementsamplifier was rather since we scenario of the acoustic stimulation in our measurements was the rather optimistic, since usedThe a powerful source of acoustic signal. used In real QEPAS applications, required kf gain of we a powerful sourcedue of acoustic signal.concentration In real QEPAS thegas required kf gain of the theused op-amp is unknown, to unknown ofapplications, the measured solution. Therefore, op-amp is unknown, due to unknown concentration of the measured gas solution. Therefore, the
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preamplifier should have a variable gain stage. Figure 13 shows a block diagram of the proposed the preamplifier should have a variable gain stage. Figure1313shows showsaablock blockdiagram diagram of of the the proposed preamplifier should have a variable gain stage. Figure proposed QEPAS multistage preamplifier. QEPAS multistage preamplifier. QEPAS multistage preamplifier.
Figure 13. Block diagram of the proposed preamplifier. Figure 13. 13. Block diagram diagram of of the the proposed proposed preamplifier. preamplifier. Figure
In order to minimize the noise contribution to the system presented in Figure 13, we used a PGA In order to minimize thefrequency noise contribution to thewith system presented in Figure 13, we as used a PGA (AD 603 dedicated for radio applications) externally limited bandwidth a middle (AD 603 dedicated radio frequency applications) with of externally a middle frequency stage. This way thefor noise amplitude added to the signal the firstlimited stage isbandwidth minimized.asThe third stage. This way the noise amplitude added to the signal of the first stage is minimized. The third stage stage.ofThis way the noise amplitude addedtwo to amplifiers, the signal of first stage minimized. The third stage the designed preamplifier contains i.e.,the inverting andisnon-inverting, in order of the designed preamplifier contains two amplifiers, i.e., inverting and non-inverting, in order to stage of the designed preamplifier contains two amplifiers, i.e., inverting and non-inverting, in order to produce differential output signal. This way, the output signal is insensitive to additive produce differential output signal. This way, the output signal is insensitive to additive electromagnetic to produce differential output signal. This way, the output signal is insensitive to additive electromagnetic interferences (EMI). The printed circuit board (PCB) of the proposed solution is interferences (EMI). The printed circuitThe board (PCB)circuit of the board proposed solution shown in Figure 14.is electromagnetic interferences (EMI). printed (PCB) of theis proposed solution shown in Figure 14. shown in Figure 14.
Figure 14. Photos of the assembled preamplifier with QTF used for measurements. Figure Figure 14. 14. Photos Photos of of the the assembled assembled preamplifier preamplifier with with QTF QTF used used for for measurements. measurements.
The proposed amplifier circuit was assembled on a 50 mm × 38 mm × 1.55 mm two-layer PCB The proposed amplifier circuit was assembled on aa50 mm ×× 38 × 1.55 mm PCB proposed wasthe assembled 38 mm mm × 1.55 mm two-layer two-layer PCB madeThe from an FR-4amplifier material.circuit Whereas bottom on layer50ofmm the PCB consists mainly of a ground made from an FR-4 material. Whereas the bottom layer of the PCB consists mainly of a ground made from an FR-4 material. Whereas the bottom layer of the PCB consists mainly of a ground shielding and some supply nodes, the top layer is used for signal paths. The AD623 and AD603 shielding and some supply nodes, thethe toptop layer is used for signal paths.paths. The AD623 and AD603 circuits shielding somein supply nodes, is used signal The AD623 and AD603 circuits areand located the top-middle part oflayer the PCB (see for Figure 14), in close proximity to the QTF are located in the top-middle part of the PCB (see Figure 14), in close proximity to the QTF connections. circuits are located in the top-middle part of the PCB (see Figure 14), in close proximity to the QTF connections. The differential amplifier output stage is located at the left edge of the board. This way, The differential amplifier output stage isoutput locatedstage at the left edgeatofthe theleft board. This way, we minimized connections. The differential amplifier is located edge of the board. This way, we minimized the asymmetric signal path, and therefore, reduced EMI influence. The circuit was the signal path, and therefore, reduced EMI influence. The EMI circuit was subjected to the SNR we asymmetric minimized asymmetric signal and therefore, influence. The(13) circuit was subjected to thethe SNR measurements as path, described previously.reduced The first method utilizing yielded measurements as described previously. The first method utilizing (13) yielded SNR = 37.13 dB, and the subjected to the SNR measurements as described previously. The first method utilizing (13) yielded SNR = 37.13 dB, and the second one (i.e., with the narrow band spectrum analysis) gave SNR = 64 dB. second one (i.e., withthe the narrow band spectrum analysis) gave SNR = 64 dB. Narrowband is SNR = 37.13 dB, and second one (i.e., the narrow band spectrum analysis) gave SNR =SNR 64 dB. Narrowband SNR is slightly worse in with comparison to the presented measurements of the basic slightly worse in comparison to the presented measurements of the basic preamplifier structures due Narrowbandstructures SNR is slightly comparison to the presented measurements of the basic preamplifier due to worse the factinthat the preamplifier was designed as a high-dynamic and to the fact thatstructures the preamplifier was designed as apreamplifier high-dynamic anddesigned programmable circuit that could preamplifier due to the fact that the was as a high-dynamic and programmable circuit that could be used in practical QEPAS applications. Such an approach resulted be used in practical QEPAS applications. Such an approach resulted in a much more complex solution, programmable thatsolution, could be used practical components QEPAS applications. Suchincreased an approach resulted in a much morecircuit complex with in additional that slightly noise level. in a much more complex solution, with additional components that slightly increased noise level.
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with additional components that slightly increased noise level. Better wideband SNR results were obtained from the use of differential signal path, which reduces influence of EMI. 7. Conclusions In this paper, we presented both theoretical and experimental comparisons of the transimpedance preamplifier (so far the only solution used in QEPAS circuits), charge preamplifier and voltage preamplifier. The theoretical analysis, as well as the preliminary measurements, proved that the proposed voltage preamplifier solution results in a much higher output signal and better signal-to-noise ratio. The improvement over transimpedance circuits is at the level of one order of magnitude. Hence, the use of the voltage amplifier configuration should substantially increase sensitivity of the QEPAS technique. Acknowledgments: The work was supported from the statutory founds granted by the Polish Ministry of Science and Higher Education. Author Contributions: Both authors performed the presented measurements, did the data analysis and prepared the manuscript. Tomasz Starecki did most of the investigations on the QEPAS topic prior to this work and designed a dedicated system for extraction of the QTF properties. Piotr Wieczorek designed the preamplifier circuits, performed simulations and prepared the measurement set-up. Conflicts of Interest: The authors declare no conflict of interest.
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