Capacitance Measurements System Using RC Circuit
1. Introduction
Microcontroller systems can be implemented to measure capacitance by using 3 ways: (1) using an RC or LC relaxation oscillator (
R
and
L
values are known), measuring the output frequency, and calculating capacitance using resonance frequency equations
[13];
(2) using RC MonostableMV
(R
value known), measure
TON
pulse width, and calculating capacitance using pulse width equation
[45];
and (3) using a capacitor charging system in RCseries circuit with a stable DC voltage source, measuring the charging time until the capacitor voltage reaches a certain value, and calculating capacitance using the charging equation of the capacitor [69]. The accuracy of the capacitance measurement by measuring the charging time can be increased using Arduino M0 which has a 12bit ADC [10].
Figure 1
RC circuit with DC voltage source.
2. Methods and Equipment
Methods
RC
charging circuit
The RC charging circuit is realized using a DC voltage source, resistor, and capacitor connected in series as shown in Figure 1 [11]. When the switch is closed, current
i(t)
flows from the voltage source through resistors and capacitors so that equations (1) to (3).
(1)
(2)
(3)
The capacitor voltage can be calculated using equation (4). If the values of
R
, VS, and
Δt
(the charging time of VC(t)
=0.5VS
to
VS
) is known, then capacitance can be calculated using equations (5) to (7) [11].
(4)
(5)
(6)
(7)
Figure 2
Capacitance measurement system circuit.
Description of the capacitance measurement system
The capacitance measuring system (Figure 2) was built using the concept of charging a capacitor
CX
in an RCseries circuit that is controlled by Arduino M0 using pinMode
()
and digitalWrite Before the charging cycle, the
CX
voltage is emptied through
RDISCHARGE
which is connected to the ground through a digital pin 6.
CX
charging cycle is done through
R CHARGE
which is connected to a voltage of 3.3 Volts via digital pin 7.
CX
charging time from
0VS
to
0.5VS(Δt)
is calculated using the micros
()
function and then the capacitance can be calculated (equation 7) and displayed to the ERM20004FB2 LCD with
I2C
serial module. The pseudocode of the Arduino M0based capacitance measuring system uses the concept of charging capacitors in the RCseries circuit as described below:
• discharging
CX
until
VCX=0
Volts,
• charging
CX
and save time (t1),
• stop charging when the ADC
=2048(VCX=0.5VS)
,
• save time (t2),
• calculate
Δt
and
CX
using equation 7,
• show
CX
and
Δt
values to LCD, and
• repeat step 1.
Figure 3
Capacitance measuring system when measuring
CX(323K
or 32nF
±
5%.
3. Results
R DISCHARG Γ NG
is set at 100Ohm1% to get a fast discharge time
(t6RC=120μSec)
when connected with
CX
maximum
(100nF)
and
R CHARGING
determined at 89. 7MOhm (9 resistors in series) to get
Δt
minimum
>50000μS
when connected to
CX
minimum
(1nF)
. Level data converter module
(3.3
Volt to 5Volt) is used to connect SDA and SCL signals from Arduino M0 to
4×20
char LCD boards (with
I2C
serial module). Capacitor measurement system has been successfully created (Figure 3, not calibrated, and has been tested to measure the capacitance of 14 ceramisdisks capacitors alternately using GWinstek LCR821 (5 times each) and the results are shown in Table 1. Sketch ofthe system is created using Arduino IDE ver. 1.9.0Beta and written in the following paragraph:
Table 1
Data from measurement of 14 capacitors.


capasitor (ceramics disk) value

measurement results

No.

LCR821

capacitance measuring system

% measurement error


C
X
(nF) 
SD

C
X
(nF) 
SD

Δt(μS)


1 
2 
3 
4 
5 
6 
7 
8 
1 
102K (10nF 10%) 
0,9208 
0,0091 
0,9271 
0,0110 
68,732 
0,68 
2 
302M (3nF 20%) 
3,1005 
0,0143 
3,0948 
0,0509 
219,994 
0,18 
3 
472K (4n7F 10%) 
4.4351 
0,0016 
4.4334 
0,0859 
229,528 
0.04 
4 
103G (10nF 2%) 
9,4243 
0,0018 
9,4108 
0,0058 
567,639 
0,14 
5 
103K (10nF 10%) 
9,7432 
0,0068 
9,7289 
0,0109 
586,508 
0,15 
6 
153J (15nF 5%) 
15,4270 
0,0083 
15,4217 
0,0377 
899,649 
0,03 
7 
223K (22nF 10%) 
20.7686 
0,0103 
20.6276 
0,0392 
1,266,618 
0.68 
8 
273K (27nF 10%) 
25.9722 
0,0181 
25.7965 
0,0241 
1,590,332 
0.68 
9 
333K (33nF 10%) 
31.9410 
0,0113 
31.9659 
0,0796 
1,984,776 
0.08 
10 
473J (47nF 5%) 
41.9192 
0,0274 
41.8124 
0,1494 
2,598,063 
0.25 
11 
563K (56nF 10%) 
52.7006 
0,0576 
52.6150 
0,0948 
3,255,986 
0.16 
12 
633J (63nF 5%) 
69.0542 
0,1407 
68.8577 
0,0623 
4,272,470 
0.28 
13 
104K(100nF 10%) 
94,3276 
0,1942 
94,4634 
0,1975 
5,891,775 
0,14 
14 
104J(100nF 5%) 
98.5234 
0,0575 
98.5654 
0,2419 
6,128,104 
0.04 
CX
measurement results (columns 2 and 4 in Table 1) are the average of 5 measurements using LCR 821 and using capacitance measuring system. The % error (column 8) value is calculated using equation (8).
4. Discussion
Referring to equation (7), there are 2 variables that affect the measurement results of capacitance: (1) stability of the
Δt
; and (2) stability of the
R CHARGE
. Because
Δt
is generated from the function of micros
()
which has a
4μS
resolution [12] so that it is assumed that it does not affect the measurement results, the change in the
RCHG
value will cause a change in the value of the
CX
measurement. If the
R CHARGE
value rises, then the
CX
measurement value will decrease and vice versa. The average
R CHARGE
value is
89.7MΩ
with standard deviation 121 (measured 5 times using LCR821, so it can be concluded that there is a correlation between the % error value of the measurement ofthe capacitance measuring system and the instability of the
R CHARGE
value.
5. Conclusion
An Arduinobased capacitance measuring system uses the technique of calculating the charging time of the capacitor voltage in the RCseries circuit has been successfully made to measure the capacitance of 14 ceramicdisk capacitors with a measurement error rate
<±
0.7% (compared to LCR 821.
Funding
This capacitance measurement system research can be completed with research funds from the Faculty of Engineering, Universitas Negeri Jakarta (based on PPK Decree Faculty of Engineering, Universitas Negeri Jakarta, number 461.a/SP/20l8 May 23, 2018.
Acknowledgement
The researchers thanked many colleagues in the Laboratory of Instrument & Control of the Faculty of Engineering, Universitas Negeri Jakarta for their contributions and support for this research. The researcher also thanked all the reviewers who provided valuable input and helped complete this article.
Conflict of Interest
The researcher does not have a conflict of interest related to the completion ofthis article.