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Supplemental material for the paper
“A Center Frequency Adjustable Narrow Band Filter for the
Detection of Weak Single Frequency Signal”
contents
Figure 1. the amplitude frequency response of the filter ................................................................... 1
Figure 2. the curve of output signal tested by the oscilloscope ( DPO7054C, Tektronix, Inc. USA)
for the minimum valid input signal amplitude test.................................................................... 2
a.
fi=10Hz, Ai=0.1μV; fr=32.7738KHz, Ar=250mV. .............................................................. 2
b.
fi=10Hz, Ai=0.5μV; fr=32.7738kHz, Ar=250mV. ............................................................. 3
c. fi=1kHz, Ai=0.1μV; fr=33.7638KHz, Ar=250mV. .................................................................. 4
d .fi=10Hz, Ai=0.5μV; fr=33.7638kHz, Ar=250mV.................................................................... 4
e. fi=10kHz, Ai=0.1μV; fr=42.7638KHz, Ar=250mV. ................................................................ 5
f. fi=10kHz, Ai=0.5μV; fr=42.7638KHz, Ar=250mV.................................................................. 5
g. fi=100kHz, Ai=0.1μV; fr=132.7638KHz, Ar=250mV. ............................................................ 6
h. fi=100kHz, Ai=0.5μV; fr=132.7638KHz, Ar=250mV. ............................................................ 6
Figure 3. the print circuit board(PCB) .............................................................................................. 7
a.
global PCB figure.............................................................................................................. 7
b.
Local magnified and function labeled PCB figure ............................................................ 7
Responses to General Comments ...................................................................................................... 8
Responses to Specific Comments ..................................................................................................... 9
0
Figure 1. the amplitude frequency response of the filter
The y-axis is for the decibel of the ratio of the output signal amplitude at
different frequencies to the maximum output value when input amplitude
keeps constant; the x-axis is for the frequency difference between the
DB
frequency of input signal and that of the filter set.
20Hz
100Hz
1KHz
10KHz
100KHz
200KHz
0
-10
-20
-30
-40
-50
-4
-2
0
1
2
4
F
Figure 2. the curve of output signal tested by the oscilloscope
( DPO7054C, Tektronix, Inc. USA) for the minimum valid input
signal amplitude test.
a. fi=10Hz, Ai=0.1μV; fr=32.7738KHz, Ar=250mV.
2
b. fi=10Hz, Ai=0.5μV; fr=32.7738kHz, Ar=250mV.
3
c. fi=1kHz, Ai=0.1μV; fr=33.7638KHz, Ar=250mV.
d .fi=10Hz, Ai=0.5μV; fr=33.7638kHz, Ar=250mV.
4
e. fi=10kHz, Ai=0.1μV; fr=42.7638KHz, Ar=250mV.
f. fi=10kHz, Ai=0.5μV; fr=42.7638KHz, Ar=250mV.
5
g. fi=100kHz, Ai=0.1μV; fr=132.7638KHz, Ar=250mV.
h. fi=100kHz, Ai=0.5μV; fr=132.7638KHz, Ar=250mV.
6
Figure 3. the print circuit board(PCB)
a. global PCB figure
b. Local magnified and function labeled PCB figure
7
Responses to General Comments
Q1
Crystal filters have a long history starting from early 1920s. They are widely used to filter signals in
analog devices. The authors have circumvented the main disadvantage of the crystal filters, i.e. the
resonance frequency is fixed. Instead of trying to build a filter with tunable center frequency, they shift
the frequency of the incoming signal to the resonance frequency of the crystal using frequency mixing.
The technique bears resemblance to a lock-in amplifier, where a reference frequency is mixed with the
signal to shift the signal to a low frequency signal, to which a low pass filter is applied (Gaspar et al.,
Microprocessors and Microsystems, 28 (2004) 157– 162). The authors should explain why using a
band pass filter at 32 kHz is better than using a low pass filter.
A1
It is real that the presented technique bears resemblance to a lock-in amplifier. The difference lies in
that we used a band pass filter at 32 kHz instead of using a low pass filter.
The aim of the presented technique is to measure the amplitude of a sinusoidal signal with a known
frequency. When using a lock-in amplifier to fulfill this task, the Fig. R1 shows its block diagram. It
can be seen that it needs two channels of the multiplier and the low pass filter, which must have the
exactly same properties. If the properties of the two channels were mismatch, the performance of the
system would become worse. In addition, to obtain a high performance, the low-pass filters must have
a high Q-factor (sharp edge), which also increases the difficulty to implement the system.
S
VI
UI
LPF
I
U I 2  UQ2
M
Q
VQ
UQ
LPF
Fig. R1. The lock-in amplifier block diagram
The advantages of using a band pass filter instead of using a low pass filter are as follows:
1) The presented system has only one signal process channel, which not only reduces the quantity
of requirement components, but also avoids the demand of channel match.
2) The characteristic of the crystal filter is its high Q-factor, so, it is much easier to implement a
high Q-factor band pass filter by crystal filter than to implement a high Q-factor low pass filter
by other components.
3) The crystal filter adopts the alternating-current coupling, which can effectively overcome the
direct-current drift of the circuits which is an important factor to influence the system
performance when the amplifier gain is very high.
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Q2
The highest frequency the authors have tested is 100 kHz.
Digital techniques are common at these
frequencies and they perform better. Crystal based filters outperform digital techniques at frequencies
higher than giga hertz. The authors should include tests at microwave frequencies to make the
technique appealing.
A2
The background of the paper is to develop a device for the fault points locating of the buried cables and
pipes, that device needs detect the weak signals with the frequencies ranged from 10 Hz to 100 kHz.
Digital techniques perform better at these frequencies for the signals with ordinary noise level. As for
the weak signals, there are some problems in using the digital techniques. Firstly, to pick up the weak
signal from the heavy noise background, it needs a very high Q-factor band digital filter that has more
than 100 steps. It will be a complex filter and increase the time delay of the output signal. Due to its
very high orders, the phenomenon of self-excitation sometimes appears in this type of filter. Secondly,
the proposed system is used to extract the signals with multiple frequencies. When it is realized with
digital techniques, it requires many groups of the filter parameters. The number of groups is the same
as that of the signal frequencies that will be detected, which will increase the complexity of the system.
In addition, the filter performance at different frequency point is difficult to achieve consistently.
Thirdly, the digitalization of the weak signal needs a very high resolution ADC (analog-to-digital
converter), for example, a 24-bit and 1MSPS ADC, the power consumption of this type of ADC is very
large, generally above several hundred mW, which will greatly reduce the working time of the battery
powered portable devices. Finally, the digital filtering technique is usually implemented by the special
chip, such as DSP (digital signal processor), it is difficult to achieve by an ordinary MCU (Micro
Control Unit). Relatively, our proposed circuit system has a simple structure, low power consumption,
as well as an excellent performance, and it is easy to implement.
This paper is mainly aimed at the filtering of low frequency weak signal. However, the high frequency
signal filtering, especially frequencies higher than giga hertz, is another technique, which can not be
realized by simple selecting the high frequency multiplier and high frequency crystal filter, it will be a
complex technique that involves many other problems.
Responses to Specific Comments
Q3
3. How were the amplitudes of the signal (0.1 μV or 0.5 μV) determined? The circuit itself does not
have any amplifier. Why does the oscilloscope show highly amplified values?
rather noisy signal.
The figures show
What is the source of the noise? The center frequency itself is about 32 kHz. One
can simply use 24 bit digitizer to digitize the signal, which might help to understand the source of the
noise.
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A3
The amplitudes of the signal (0.1 μV or 0.5 μV) are determined indirectly, it is implemented by the
voltage divider of two series resistors, the circuit is shown in Fig. R2. The value of R1 is 10 6 Ω and the
value of R2 is 10 Ω, the ratio of the amplitude of input and output signal approximately equals to 105:1.
When the amplitude of input signal is 10 mV, the amplitude of output signal is 0.1 μV, and when the
amplitude of input signal is 50 mV, the amplitude of output signal is 0.5 μV.
+
R1=1MΩ
Vinput
+
R2=10Ω
Voutput
-
-
Fig. R2. The circuit of the voltage divider
The circuit itself is really a frequency-selectivity amplifier. The total gain of the circuit is (See Fig. 1,
Eq. (11) and Eq. (12) in the manuscript),
f out (t ) =
R
R
R
R1
R
Ч 21 Ч(1 + 23 ) Ч 31 Ч(1 + 33 ) Ч[ x1+ (t ) - x1- (t )]
Z x Z x + R21
R22 Z x + R31
R32
The gain of the circuit is not precisely set. As shown in the Fig. 4 of manuscript, it is slightly changed
with the variation of the input signal frequency, which is about 9.16*104 when the input signal
frequency is 10 kHz.
In our opinions, there are three main types of sources of the noise as the follows:
1)
The thermal noise of the resistor of voltage divider.
2)
The noise of the power supply.
3)
The crosstalk signal between the connecting wires and between the traces of the PCB board.
Due to the input signal is much small, the impact of noise on the output signal is significant and the
figures show rather noisy signal.
It is a good idea that using 24 bit digitizer to digitize the signal and understand the source of the noise,
this can be done in the next research.
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Q4
4. Page 3, column 1, line 12. The authors state “The output amplitude is becomes large with the
increase of the input frequency, that is caused by the input coupling capacitor.” Where is the input
coupling capacitor in the scheme? Is it before the mixer?
Why the authors don’t use direct coupling
when measuring low frequency signals?
A4
The input coupling capacitor is not presented in the scheme. As you asked, it is before the mixer. The
main reason for not using direct coupling is that the background of our application is to detect the
signals which frequency is higher than 10 Hz, and the other reason is that the direct coupling will affect
the quiescent operating point of multiplier, which is a sensitive factor for the performance of multiplier.
Q6
6.
Page 3, column 2, line 11.
“The maximum frequency of the valid input signal is determined by
that of the multiplier and DDS, not the subsequent crystal filter.” It would be nice to give indicative
number for the maximum frequency that multipliers and DDS used in the design can handle. Also an
idea about the maximum values that commercially available components can handle in general would
be good.
A6
Theoretically, the maximum frequency of the valid input signal is determined by that of the multiplier
and DDS. In our applied circuit, the DDS is AD9833 (Analog Devices Inc., USA), and the multiplier is
SA612A (NXP Semiconductors, Ltd). The maximum output frequency of AD9833 is 12.5 MHz, and
the maximum operation frequency of SA612A is 500 MHz. So, theoretically, the maximum frequency
of the valid input signal in our design is 12.5 MHz.
Actually, with the increase of signal frequency, the influence of the RF characteristics of the signal is
becoming increasingly significant. In this case, besides the multiplier and DDS, the performance of the
circuit depends largely on the techniques of High-Speed PCB design. Although the maximum
operation frequency of the commercially available multiplier or DDS is higher than giga hertz, the
valid maximum frequency of our designed circuit is 10 MHz. If the operation frequency is higher than
10 MHz, its performance would become worse.
11
Because of these reasons, the statements about the maximum frequency of the valid input signal are
modified too.
Q7
8. Page 3, column 2, line 14. “The background noise can be suppressed by further optimization of
PCB.” It is not clear which components of the PCB affect the noise characteristic the most.
A7
The MCU (C8051F020) and the DDS (AD9833) are the components which affect the noise
characteristic most. These two components add digital noise to the power supply. In addition, the
imperfect signals routing about them is easy to cause signal’s cross-talk between traces.
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