Instrumentation & Measurement Magazine 23-5 - 45

Fig. 5. Test platform. (a) Digital board; (b) Analog board; (c) PM prototype including PM sensors; (d) The structure of the test platform including signal generator,
the PM sensor and the PM prototype.

For the MPM method presented in [16], ten parallel MFM
method channels are designed in FPGA. The execution time interval of each channel is about 10 ms. An MCU is employed to
read the counting number of ten channels from FPGA. Then, the
average calculation of ten channels is performed in the MCU to
obtain the measured frequency. Hence, the frequency measurement result of the MPM method can be calculated by (28):
	

f MPM 

2N  9 9
1
	(28)
fs 
10
i 0 a[2 N  (9  i )]  a[i ]

From (27) and (28) we can know that:
◗◗ The time length of capturing raw data (counting time)
is the same for both methods, which is about (N + 0.5)TX.
◗◗ To perform the MPM method, the addition operation is
performed 12 times, and the multiplication is performed
13 times according to (28). Correspondingly, the addition
operation is performed N + 3 times, and the multiplication
is performed 2N/3 + 3 times for the proposed method.
Obviously, the time-consumption of the proposed
method is larger than the MPM method. Nevertheless, the
floating-point multiplication operation time of STM32F2
series embedded MCU is smaller than 1 μs. If N equals
1200, the execution time of the proposed method will be
less than 1 ms, which can be ignored compared with the
counting time.
August 2020	

◗◗ The relative error of the MPM method is 10 times
smaller than that of the MFM method because average calculation of ten channels is adopted by the MPM
method. According to (24), if N equals 1200, the precision
of the proposed method is about six times higher than the
MPM method. In a word, the proposed method is suitable
for portable instruments because of the higher precision
and shorter time-consumption.

Experiment and Analysis
PM Prototype and Experiment Equipment
A PM prototype, displayed in Fig. 5a, Fig. 5b, and Fig. 5c, and
consisting of a PM sensor, a digital board, an analog board, a
shell and a battery fixed in shell, was developed to verify the
effectiveness of the proposed method for improving the precision and sensitivity of PM. Combined with a signal generator
(33500B, Keysight) and a PC, the developed test platform
structure is displayed in Fig. 5d. The signal generator was
used to produce the measured frequency for the frequency
measurement comparison experiment, and the sine signal
output from the generator was divided into micro-levels (less
than 10 μV) by a resistor attenuator. The amplifier in the analog board was used to amplify the weakness of FID signal
which output from the PM sensor, and the gain of the amplifier is about 200,000 V/V. In the front of the amplifier, a series

IEEE Instrumentation & Measurement Magazine	45



Instrumentation & Measurement Magazine 23-5

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