CC BY
129Electronic Journal «Technical Acoustics» http://www .ejta.org
2007, 15
Frederic Coutard, Etienne Tisserand, Patrick Schweitzer*
Nancy Electronic Instrumentation Laboratory (LIEN), Henri Poincare University of Nancy, BP 239, 54506 Vandoeuvre les Nancy, France
Optimal low noise amplifier for ultrasonic receptor
Received 12.06.2007, published 01.08.2007
The paper describes a detailed investigation of the noise generated by an ultrasonic chain of reception carried out on a piezoelectric receiver of standard characteristics amplified by an LNA (Low Noise Amplifier) of optimum design. The objective is to provide the conditions which will allow the best signal-to-noise ratio of the entire chain. The noise chain factor is studied theoretically. It is shown that the noise factor is minimal if the noise characteristics of the LNA and the gain resistance of the first amplification stage are jointly matched to the transducer’s internal resistance. A two-stage 56 dB amplifier optimized for transducers with a resonant frequency between 1 and 10 MHz and with an internal resistance of approximately 390 Q is designed. Measurements show a low noise factor (1.46). This advantage reveals the direct correlation between noise PSD of the chain and the real part of the transducer impedance.
INTRODUCTION
The electronic conditioning of a piezoelectric receiver requires a thorough understanding of its electric impedance Z, which must also be perfectly adapted to the characteristics of the noise of the first amplification stage [1]. We describe how we were able to obtain the conditions of optimization of the signal to noise ratio of an amplified reception chain from a standard transducer vibrating in thickness mode.
In a first time we study the design of a 56 dB amplification stage adapted to the characteristics of the frequency and impedance of the transducer.
The piezoelectric transducer impedance is studied in the second part. We present in particular the measurements done around the frequency resonance of the transducer (in air and in water). The last part studies the optimization condition for a PZT transducer. We specify the values of the components and present the measurements of the noise at chain output.
1. AMPLIFIER DESIGN - OPTIMISATION OF NOISE FACTOR
1.1. Project specifications
For the design of the amplifier module, our project specifications impose a gain of about 60 dB and a bandwidth between 1 MHz and 10 MHz. This band is very used in echography and non-destructive testing. The amplifier noise must be minimized in particular when the transducer is in air; in this case its electric impedance is the highest.
*
corresponding author, e-mail: [email protected]
Moreover, the module must be equipped at the output with a 50 Q driver for impedance matching and RF measuring.
The chain of amplification is represented in Figure 1.
Figure 1. Structure of the amplification module
R R
We note that A1 = 1 + —, A2 = —- and A3 = 1 in the figure are the amplification factors of
R3 R6
the three stages 1, 2 and 3.
1.2. Theoretical noise factor
By definition the noise factor of a voltage amplifier is given by [2]:
F =
(N
iy OUT
V ANin j
(1)
where Norn and Nn are the noise voltage at the input and the output of the amplifier respectively without load and A is the amplification factor of the amplifier. For a chain which consists of three stages, the noise factor can be determined by the following Friss formula:
77 77 F2 — 1 F3 — 1
F = F + 2 . + 3
Aj2 A2A2
(2)
where Fj, F2 and F3 are the factors of noise of the first, second and third stage respectively.
Since A1 and A2 have high values, F is very close to the first stage noise factor.
Introducing a variety of source resistances of noise and the LNA produces the diagram of the first stage shown in Figure 2.
Figure 2.
Noise model of the first amplifier stage
The noise factor is given by the formula
F ,, el + 'I(Ri,+((.||R3)2) (3)
F - 1 + 4kBT( +(R)) • (3)
In practice we must choose R4 > R3 to obtain a high amplification factor A1 and R1 > RS
in order to avoid excessively attenuating the signal delivered by the transducer. Under these
conditions the noise factor can be reduced to
r , e2n + 'l ( + Rl)
F - 1 + 4k T((S + R ) • (4)
4kBT\RS + R3 )
1.3. Theoretical noise factor minimizing
A study of the function F( RS, R3) shows that it can be lowered to a minimal value when the following equation is satisfied:
R32 - 2R3RS - RS + Rl - 0 > where Rn - — • (5)
n
The solutions to this equation are R3 - RS ±^J2R2 - R2 when the following condition
R
RS >^j= is respected.
We have several solutions for minimizing the noise factor of the amplifier and for all of them we have to choose an LNA whose noise characteristics (en, in) are matched to the output resistance of the transducer. Knowing that R3 must have a low value, we can for example consider one of the following possibilities:
Solution 1 Solution 2 Solution 3
RS = Rn * R3 = 0 n Rs=ll * Ri=Rs RS = Rn * R3 = 2RS
+ II su + ll su + II s3
The second solution guarantees the weakest noise factor. According to our application, the transducer source resistance in air reaches 350 Q and resistance R3 must be low in order to
obtain a high amplification A1. We are close to the conditions required in solution 1.
2. IMPEDANCE OF PIEZOELECTRIC TRANSDUCER
2.1. Electrical model
The standard electric model of a piezoelectric transducer is shown in Figure 3 [3].
Figure 3.
Standard electrical model of a piezo transducer
The frequencies of resonance (fs) and antiresonance (fp) of this model are given by the expressions:
f = U2*4lC and fr = f,4(C„ + C,)/€„ . (6)
The impedance of the transducer is roughly real to these frequencies. In particular, at the optimal frequency of reception, very near to fp, we have [4, 5]:
1____________
^ Z, (7)
Z
1
- + -
R (Ri + R)2C„ + L,k2
where R1 and R1 respectively represent the internal losses of the transducer and the acoustic resistance’s external radiation, k is the total piezoelectric coupling coefficient.
Resistances R and R and the C0 capacity emphasize the influence of the propagation
medium and the geometrical characteristics of the transducer on the real part of the electric impedance.
2.2. Impedance of used transducer
For testing our amplifier, we use a 20 mm square transducer vibrating in thickness mode (central frequency of 2.23 MHz). It has a maximum resistance of 350 Q when it is in air and 100 Q when it is immersed in water (figure 4).
Re(Z) (Q)
Figure 4.
Measurement of the real part of the transducer impedance
3. MEASUREMENT OF AMPLIFIER PERFORMANCES
3.1. Choice of components of amplifier
With en = 0.92 nV/Hz05 and in = 2.3 pA/Hz05 and so Rn = 400 Q, the circuit LMH6624 (Analog Devices) is adapted [6]. Its product GainxBandwidth of value 1.5 GHz allows high
ei
closed loop amplification. By using the equation Fmin = 1 +—the theoretical noise factor
2kBT
of the first stage reaches the lower value of 1.255.
The total gain, approximately 56 dB (A = 658), is distributed between the two amplification stages in order to satisfy the project specifications. Resistance R3 is set at the lowest value recommended by Analog Devices (22 Q). Table 1 gives the values of the components used for our structure.
Table 1. Amplifier component values
Stage 1 Stage 2 Stage 3
A, : 46 (33 dB) 4 : 14.3 (23 dB) A3 : 1 (0 dB)
LNAi : LMH6624 LNAi :LMH6624 IC3 : MAX4178
R, : 4700 Q q : 1 nF C2: 100 nF
K : 27 Q R5 : 41 Q R: 1 kQ
R, : 22 0. R6 : 41 Q R9:41Q
R4: 1 kQ Rj : 680 Q
* R2 is imposed in order to avoid an attack at null impedance mismatched with the stability of the circuit
3.2. Noise PSD of amplifier
The bandwidth reaches 11 MHz to -1 dB and 26 MHz to -3 dB. The amplifier has a constant gain within the measuring band of 56.3 dB ± 0.05 dB with RS equal to 50 Q.
The noise output PSD is measured on a 50 Q load for various values of RS with a
spectrum analyser (Figure 5) at a room temperature of 293 K. With a low source impedance, the output noise reaches the lower value of 420 nV/Hz05.
3 Noise PSD (^V/Hz05)
Rsource = OO
Rsource = 390 Q Rsource = 50 Q
Rsource = 0 T
2 Frequency (MHz) 3
2
0
Figure 5.
Output Noise PSD for different RS
3.3. Experimental noise factor
The DSP of the noise voltage applied to the amplifier input is
R R
Nin =44kBTRs,„ with Rteq = (8)
RS + R1
It is possible to evaluate the real noise factor of the amplifier using the relation
F =
OUT
ANin J
by knowing the output noise voltage without load. The results shown in
Table 2 confirm that the amplifier is optimized for a transducer having an output resistance of approximately 400 Q. For such a source, the total noise factor is set to the minimum value of 1.46, whereas the theoretical study predicted 1.25. This difference can be explained by the R3
resistance which is not equal to zero and by the noise of the other two stages which slightly deteriorate the noise factor of the chain.
Table 2. Experimental noise factor versus RS
Rs( Q) Nm (nV/Hz0-5) Norn (nV/Hz0-5)* F
50 0.9 1040 3.08
390 2.51 2000 1.46
4700 6.16 5700 1.97
ie DSP noise at the output without charge is twice the value measured by the analyzer
•!<
3.4. Output noise PSD of ultrasonic chain
The amplifier factor of noise is sufficiently weak to consider the output noise representative of the noise generated by the transducer. We represent in figure 6 the output chain spectral density output for the transducer in air and in water.
Noise Level (nV/Hz"0:)
900-i
600 ■ ' \
:oo-m.^
f (MHz)
300---------1--------1--------1--------1-------1--------
2.1 2.15 2.2 2.25 2.3 2.35 2.4
— air
- - water
ij. . .
f (MHz)
Figure 6.
Noise level measurement for different media
We see a high degree of concordance between these noise measurements and the impedance curves given in figure 4.
These measurements confirm that the noise of a piezoelectric transducer is comparable to a thermal noise generated by its resistance according to Johnson’s law [7, 8, 9]:
Noise PSD = 4kBTRe(Z), (9)
where kB is the Boltzmann's constant and Tis the temperature.
CONCLUSIONS
The optimal design of an ultrasonic amplified chain of reception requires a precise knowledge of the internal resistance of the piezoelectric transducer, particularly at the frequency of antiresonance where its sensitivity is at a maximum. We then sought the conditions which would allow the design of an amplification device adapted to the electrical characteristics of a transducer. We have shown that the noise factor is minimal if the noise characteristics of the LNA and the resistance (which determine the amplification of the first stage) are jointly assigned to the internal resistance of the transducer. Several optimization solutions are possible and by adopting the solution nearest to our application, we have been able to design a three-stage amplifier with the integrated circuit LMH6624. This module is optimized for a transducer having a resistance of approximately 390 Q and a gain of 56 dB on a bandwidth exceeding 26 MHz. Its noise factor is established at 1.46. Generalizing this step to the design of any type of amplifier would, in our opinion, represent a fruitful area of research.
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