Development of fpga based system for neutron flux monitoring in fast breeder reactors

Innovative Systems Design and Engineering www.iiste.org
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol.4, No.8, 2013
30
Development of FPGA Based System for Neutron Flux
Monitoring in Fast Breeder Reactors
M.Sivaramakrishna, Dr. P.Chellapandi, IGCAR, Dr.S.V.G.Ravindranath (BARC),
IGCAR, Kalpakkam, India
(sivarama@igcar.gov.in)
Abstract
The project aims to calculate the frequency of the neutron flux by monitoring the signal from neutron detector
from shutdown to full power over 10 decades. This neutron flux signal is input to the FPGA based MODULE. A
mathematical relationship has been established between the neutron flux (frequency of the neutrons) and the area
under the signal. Variable amplitude and occurrence have been accounted for. White noise has also been added
and tested for. VHDL has been used to simplify the otherwise complicated logic gate design. Mathematical
modeling has been used as it is the most accurate of the available methods.
Index Terms -- Neutron flux monitoring, area, pulses
1. Need of the system
Currently, neutron flux is monitored in all states of the reactor by Neutron flux monitoring systems. The system
consists of several sets of detectors and instrument channels. For smooth transition from one set of instrument
channel to other, interlocks with auto inhibition in safety logic are provided. In each channel, there is a trade-off
between response time and accuracy. Volume of electronics involved is very high.
In addition, the pulses from the neutron detector are not periodic. Hence counting techniques do not result in
accurate prediction of frequency. It can also be seen that as the frequency goes up the pulses over lap. Hence
estimating the power using pulse counting can’t predict the power correctly.
Currently, the detector is operated in pulse and Campbell modes. Even in Campbell mode, there is a trade-off
between the accuracy and response time and linearity is obtained only for 4 decades.
FPGAs are currently the most user friendly and economically viable option for logic circuit design. They can be
programmed to match user’s requirements.
The work aims to find a relation between the frequency of the neutron flux signal and a mathematical function.
The code designed will be able to calculate frequency for signals with constant amplitude, random amplitude,
random occurrence and signals with noise from the samples supplied by the analog to digital convertor (ADC)
connected to the FPGA.
2. Data and assumptions
• The pulse width varies. However, a width of 100 ns is a good estimate. The signal rise time varies from
5 ns to 20 ns. The fall time varies from 50 ns to 120 ns
• The amplitude of the signal is varying 0.7 uA to 1.3 uA
• The individual signals might overlap resulting in a single larger pulse.
• The signals will be affected by noise, which is also random in nature.
• The occurrence of signals follows a Poisson distribution.
• There is almost no overlap of signals for a frequency of less than 104
Hz. Beyond this, pulses will
overlap. Due to this, the standard deviation will be proportional to the neutron flux, as per campbell
theorm (which is applicable to statistical random occurring, discrete overlapping incidents).
• At very high frequencies, the pulse over lap fully to give average DC current.
To solve the problems such as range, accuracy with the existing techniques of neutron detector instrumentation,
new techniques are investigated such as calculation of the area under the signal pattern (Curve).
Presently software simulation is completed to find out the relation between the above frequency parameters and
the incident neutron flux. Hardware simulation is being carried out. Finally FPGA based simple embedded
systems will be made for need of real time high computation required.
3. APPROACH
3.1 INITIAL STAGES
At first, sample signals were generated to mimic the neutron flux signals in terms of rise time, fall time, overlap,
noise etc. From this signal mathematical functions such as average, variance and area were calculated.
While considering the overlap, a linear relationship was taken. For each decade starting from 10^4 Hz, a 20%
overlap was considered upto 10^9 Hz.

Vol.4, No.8, 2013
31
Initially samples were run for constant overlap. After the appropriate mathematical function was obtained, it was
extended to random amplitude and to noise.
Functions considered:
1) Average
We can see that for average, a straight line relation is obtained with frequency in case of both no overlap and
overlap in signals.
There is no discrepancy from the straight line at any frequency. However, calculation with such precision will
require very high sampling rates at the order of GHz. Hence, we search for a better option
Fig 1: plot of average value of neutron flux vs. frequency
2) Variance
For variance, at lower frequencies and no overlap, we get a straight line relationship. However as the frequency
and overlap increase, there is an exponential variation.
We also see that the rise of variance with frequency is sudden and large making it harder to distinguish between
the higher frequencies. Hence, this is not the best method to follow as accuracy will be low.
Fig 2: plot of variance of neutron flux vs. frequency
3) Area under curve
For area under curve we see that like variance and average, there is a straight line relationship at lower frequency
and in the absence of overlap. However, with increase in frequency and overlap, the area under curve increases
polynomially.
We can see that at each level of overlap, the frequencies follow a linear pattern. Overall, when we look at the
curve, we see the increase is more gradual and a more distinguishable pattern is observed.

Innovative Systems Design and Engineering
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online
Vol.4, No.8, 2013
Fig 3: plot of area under curve of neutron flu
A clearer pattern is observed, when the curve is spilt into different portions and more values are taken in each
range.
Hence, we decide to go ahead with area under curve as it is best suited for the situation.
Now we tried the pattern for random amplitude.
Initially we taook only 3 amplitudes at 0.7, 1 and 1.3 times the constant amplitude considered (1V)
Fig 4. Area under curve vs. frequency (for amplitude of 0.7, 1, 1.3 V)
We see that due to the randomness in amplitude, the patter
waveform.
However, if we take this further and completely the randomize the amplitude to all values between 0.7 to 1.3 ( a
3 sigma Poisson variation), we notice that the amplitudes average out to give a
This linear pattern is observed at all frequencies. However the error is lower at higher frequencies because more
the pulses, higher are the chances of the averaging of the values to the mean level.
2871 (Online)
32
Fig 3: plot of area under curve of neutron flux vs. frequency
Hence, we decide to go ahead with area under curve as it is best suited for the situation.
for random amplitude.
only 3 amplitudes at 0.7, 1 and 1.3 times the constant amplitude considered (1V)
We see that due to the randomness in amplitude, the pattern immediately disappears and is replaced by a random
3 sigma Poisson variation), we notice that the amplitudes average out to give a linear pattern
the pulses, higher are the chances of the averaging of the values to the mean level.
www.iiste.org
only 3 amplitudes at 0.7, 1 and 1.3 times the constant amplitude considered (1V)
n immediately disappears and is replaced by a random
linear pattern

Innovative Systems Design and Engineering
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online
Vol.4, No.8, 2013
Fig 5. Area under curve vs. frequency
3.2 PATTERNS OBSERVED
Once area under curve was finalized as the function to be considered, more tests were run with multiple values in
all ranges. Pattern was identified for each range of frequency and ov
Fig 6. Area under curve vs. frequency (0 to 10^4 Hz)
Below are the plots obtained for each range. In the curve, the equation corresponding and the variation of points
from the plot are mentioned.
2871 (Online)
33
Fig 5. Area under curve vs. frequency (for completely randomized amplitude 0.7
all ranges. Pattern was identified for each range of frequency and overlap.
Fig 6. Area under curve vs. frequency (0 to 10^4 Hz)
www.iiste.org
(for completely randomized amplitude 0.7-1.3 V)

Vol.4, No.8, 2013
34

Vol.4, No.8, 2013
35
3.3 DEVELOPMENT OF CODE
After all patterns were identified, code was developed on VHDL for calculation of frequency from sampled
signal.
Value will be read from a text file containing 107
values per second. The output frequency will be stored in
another text file. A signal of ‘1’ is output if frequency is below threshold else ‘0’ is output.
The VHDL code for identifying mathematical, for sample signal generation, test values and for frequency
calculation is in Appendix.

Vol.4, No.8, 2013
36
On changing the values in the places commented in the code, sample signal is generated for any frequency and
corresponding value calculated by VHDL simulation is obtained.
4. RESULTS
Below are the results obtained from the simulation of the VHDL simulation.
Table 1 shows the value of frequency used for sample signal generation on matlab and the corresponding value
obtained from VHDL for constant amplitude, random amplitude and occurrence and signals with noise. We see
error increases slightly with very high overlap and frequency and is more in case of overlap with noise.
For constant amplitude, 80 more samples were taken, distributed equally in every decade, and tested to check
deviation.The average error comes to 2.50699%.
Below is the plot of obtained value vs. average value. We see the pattern is almost linear and there is very slight
deviation in pattern
Fig 16. Obtained frequency vs. actual frequency
5. CONCLUSIONS
We see that the frequency calculation for constant amplitude is almost accurate with very small error. The error
falls and then increases again at very high frequency.
For random amplitude, the error is larger at lower frequencies but reduces significantly at larger frequencies as
the amplitudes average out.
For signals with noise, the error is lower at lower frequencies but is high at higher frequencies. However, here
we have considered the noise to be mixed with the signal. In practicality, however, the noise will be separated
out first. Hence error will be significantly lower. In this project, noise signals were analysed using the same
pattern as constant amplitude case. If patterns for this are analysed like for the other cases, the error can be
decreased. Due to lack of time this was not attempted.
BIBLIOGRAPHY
1. Perry, Douglas 1998, VHDL by Examples, 3rd
edition, Singapore: Mc GrawHill
2. Bhasker, Jayaram, 1998, VHDL Primer, New Jersey: P T R Prentice Hall
3. Ashden, Peter J, 1990, The VHDL Cookbook, Ashenden Designs
4. Chu, Pong P, 2008, FPGA prototyping by VHDL examples, New Jersey: John Wiley & Sons Inc.
5. http://www.cs.umbc.edu/portal/help/VHDL/math_real.vhdl
6. http://www.velocityreviews.com/forums/t22430-random-number-generator.html
7. http://verificationguild.com/dload/utils/vhdl/random1.vhd
8. http://www.freemodelfoundry.com/converters_vhdl.php
9. http://www.jjmk.dk/MMMI/Exercises/05_Counters_Shreg/No7_PWM_vs_SigmaDelta/index.htm
10. Singh, Om Pal, 2007, Interfacing Analog to Digital Converters to FPGAs

Vol.4, No.8, 2013
37
Table I: Values obtained for random test samples
Test
Frequency
With Constant
amplitude
% error With Random
amplitude
% error With noise % error
3 2.774 7.66 2.48 17.3 2.77 7.5
70 66.59 4.8 65.39 6.5 66.6 4.87
800 761.9 4.76 759.2 5.09 763 4.68
3300 3142. 4.78 3144 4.69 3140 4.75
22000 21703 1.34 20992 4.58 19300 12
864000 856085 0.915 823105 4.73 757000 12.4
6123400 5428491 11.3 5832320 4.75 4560000 25
49200000 45283660 7.96 36200000 26
729000000 706756500 3.05 644000000 11.6
Annexure:
VHDL CODE
1) Constant amplitude
--for constant amplitude
library ieee;
use ieee.std_logic_1164.all;
use std.textio.all;
use ieee.math_real.all;
entity area is
end area;
architecture freq_calc of area is
signal clk: std_logic;
begin
clockgen:process
begin
clk<='1';
wait for 1ns;
clk<='0';
wait for 1ns;
end process;
process
variable area:real:=0.0;
variable freq:real:=0.0;
FILE infile: TEXT is in "C:testsamples_const_9.txt"; --enter file name with samples here
FILE outfile: TEXT is out "C:/test/freq9.txt"; --enter file name to store result here
variable in_val,out_val:line;
variable val:real;
variable a:real:=0.0;
variable b:real;
variable c:real;
variable d:real;
variable flag:integer:=0;
variable check: std_logic:='0';

Vol.4, No.8, 2013
38
begin
wait until clk'EVENT and clk='1';
while not(endfile(infile)) loop
check:='1';
readline(infile,in_val); -- each line from file being read
read(in_val,val); -- value from each line being read
area:=area+val*1.0E-7; -- area being calculated.
wait until clk'EVENT and clk='1'; --sampling time=10^-7 seconds
end loop;
if (area<0.00756) then --frequency calculation
freq:=(area-5.0E-9)/(6.0E-8);
elsif(area<0.625) then
a:=5.0E-15;
b:=1.0E-7;
c:=-0.0034-area;
d:=b**2-4.0*a*c;
freq:=(-b+sqrt(d))/(2.0*a);
a:=2.0E-15;
b:=2.0E-7;
c:=-0.3114-area;
d:=b**2-4.0*a*c;
elsif (area<306.0) then
a:=1.0E-15;
b:=1.0E-7;
c:=7.4409-area;
d:=b**2-4.0*a*c;
freq:=(area+1.0962)/(8.0E-7);
freq:=(area+1.1679)/(9.0E-7);
freq:=(area+0.9811)/(1.0E-6);
freq:=(area+0.9252)/(1.0E-6);
freq:=(area+0.6058)/(2.0E-6);
else
freq:=(area+0.3535)/(4.0E-6);
end if;
write(out_val,freq); --writing value into file
writeline(outfile,out_val);
wait ;

Vol.4, No.8, 2013
39
end process;
end freq_calc;
2) For randomized amplitude
--for randomly varying amplitude
--solving linear equation
library ieee;
use std.textio.all;
entity area is
end area;
begin
clockgen:process
begin
clk<='1';
wait for 1ns;
clk<='0';
wait for 1ns;
end process;
process
FILE infile: TEXT is in "C:testsamples_rand_8.txt";--enter file with ADC samples here
FILE outfile: TEXT is out "C:/test/freq_r_8.txt"; --enter file to store results here
variable val:real;
begin
check:='1';
readline(infile,in_val);
read(in_val,val);
area:=area+val*(1.0E-7); --area calculation
end loop;
freq:=(area-2.0E-8)/(6.0E-8); --frequency calculation
write(out_val,freq);
wait;
end process;
end freq_calc;
3) For signals with noise
--for constant amplitude
--with noise
library ieee;

Vol.4, No.8, 2013
40
use std.textio.all;
use ieee.math_real.all;
entity area is
end area;
begin
clockgen:process
begin
clk<='1';
wait for 1ns;
clk<='0';
wait for 1ns;
end process;
process
FILE infile: TEXT is in "H:testresult81.txt"; --enter file name with samples here
FILE outfile: TEXT is out "H:/test/a81.txt"; -- enter file to store results here
variable val:real;
variable a:real:=0.0;
variable b:real;
variable c:real;
variable d:real;
variable flag:integer:=0;
begin
check:='1';
readline(infile,in_val);
read(in_val,val);
area:=area+val*1.0E-7; --sampling interval of 10^-7 seconds
end loop;
area:=area*2.0/3.0
if (area<0.00756) then --frequency calculation
freq:=(area-5.0E-9)/(6.0E-8);
a:=5.0E-15;
b:=1.0E-7;
c:=-0.0034-area;
d:=b**2-4.0*a*c;
a:=2.0E-15;
b:=2.0E-7;
c:=-0.3114-area;

Vol.4, No.8, 2013
41
d:=b**2-4.0*a*c;
a:=1.0E-15;
b:=1.0E-7;
c:=7.4409-area;
d:=b**2-4.0*a*c;
freq:=(area+1.0962)/(8.0E-7);
freq:=(area+1.1679)/(9.0E-7);
freq:=(area+0.9811)/(1.0E-6);
freq:=(area+0.9252)/(1.0E-6);
freq:=(area+0.6058)/(2.0E-6);
else
freq:=(area+0.3535)/(4.0E-6);
end if;
write(out_val,freq); --writing value into file
wait ;
end process;
end freq_calc;

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