Advanced compact model and processing circuit for integrated magnetic sensor systems

Kỹ thuật điện tử 
D. D. Ha, T. T. Trung, “Advanced compact model  integrated magnetic sensor systems.” 196 
ADVANCED COMPACT MODEL AND PROCESSING CIRCUIT 
FOR INTEGRATED MAGNETIC SENSOR SYSTEMS 
Dao Dinh Ha
1*
, Tran Tuan Trung
2
Abstract: The generalized electric model of the Hall sensor, which is designed 
for circuit simulation, is taken into account the features of its design and used for 
manufacturing materials. The model of the Hall sensor is implemented in the 
language Verilog-A, has a simple structure and allows to accurately describe its 
performance characteristics. The equivalent circuit of the sensor is built on the 
basis of standard subcomponents and does not use complex equations to describe 
the physical processes in its structure. A circuit and topological solution consisting 
of Hall sensor, differential amplifier and 10-bit successive approximation register 
analog-to-digital converter and other components integrated on a single chip using 
the TSMC 0.18 μm CMOS MS/RF 1,8/3,3V PDK design library, allowing to receive 
and process data of sensor devices. 
Keywords: Hall sensor; Compact Model; Verilog-A; Signal processing circuit; Analog-to-digital converter. 
1. INTRODUCTION 
In modern electronics sensors for measuring the induction of a magnetic field, 
contactless determination of mechanical and electrical influences is widely used. 
This type of sensor is used in the automotive, mobile and consumer segments, 
medicine, aerospace and marine industries, power engineering – as sensors for 
cameras and displays, electronic compasses, etc. [1]. For practical applications, the 
Hall sensor (HS) is usually placed with a signal processing circuit on a single chip. 
However, the constructive implementation of such a system remains a problem, 
because the sensor models are not included in the design library provided by the 
chip manufacturer. Standard models for describing the electrical characteristics of 
HS are too complex [2] or idealized [3]. 2D or 3D physical models described by 
FEM simulators for integration with circuit simulation programs require significant 
computational costs [3], but are useful for analyzing the effect of geometric 
parameters on the behavior of a sensor. To improve design efficiency and system 
performance, it is necessary to have an electrical (SPICE) model that adequately 
describes the characteristics of the sensor element. Such a model describes the 
behavior of the sensor using a set of equations obtained by means of adequate 
assumptions and simplifications. 
Another important task in the field of sensor design is the development of 
systems that provide accurate processing of input data, as well as their conversion 
to a digital signal. The latter would greatly simplify the process of further analysis 
of the results of measurements. These tasks can be solved by sharing amplifiers 
and analog-to-digital converters, which enable the transition to a digital 
representation of the original analog signal with small amplitude. 
The paper presents the results of the development of a unified compact model of 
a Hall sensor fabricated both by standard silicon technology and based on wide-
gap semiconductors. The model also provides the ability to account for the 
material and geometry of the integrated magnetic concentrator (IMC) designed to 
increase the sensitivity of the sensor. A circuit-based solution consisting of a low-
Nghiên cứu khoa học công nghệ 
Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san Viện Điện tử, 9 - 2020 197 
noise amplifier and an analog-to-digital converter, which allows receiving and 
processing of sensor data, is developed and topologically realized. 
2. SIMULATION TOOLS, INVESTIGATED SENSOR CONSTRUCTIONS 
AND COMPACT MODEL DESCRIPTION 
2.1. Investigated Hall Sensor designs 
In the calculations presented below, the simulation of the electric characteristics 
of the Hall sensor was carried out in the Silvaco software environment [4], the 
IMC parameters were calculated in the FEMM program [5], the Verilog-A [6] 
language was used to develop the electrical model, and the compact model and 
circuit solutions were designed and tested using Cadence software [7]. 
Fig. 1 shows the HS designs that are being investigated. The design presented 
on the left is a sensor manufactured using standard silicon technology [8], the 
design on the right is a sensor based on gallium nitride [9]. 
L
W
Sapphire (0001)
contact
AlxGa1-xN
GaN
AlN
Ti/Al/Ni/Au
L
W
n-well
depletion layer
p-substrate
contact
n+ n+
oxide
t
Figure 1. Investigated Hall Sensors designs. 
1
2
2
3
θ
l
d
D
4
Figure 2. Modeling determining the parameters of material sample by CST. 
Kỹ thuật điện tử 
D. D. Ha, T. T. Trung, “Advanced compact model  integrated magnetic sensor systems.” 198 
Fig. 2 shows the sensor system design, which includes an IMC. It consists of 
four HS (2) and an IMC (3) formed on a silicon substrate (1). Four HS are 
perpendicular to each other along the edges of the IMC. Between the IMC and the 
HS there is a dielectric layer (4) of thickness d. The IMC is a disk of a 
ferromagnetic material with a diameter D, a thickness l, and a deflection angle θ. 
Supermindur which has a high induction of magnetic saturation was used as the 
IMC material. Earlier studies were carried out to optimize the design and 
technology, electrical and operational characteristics of presented sensors types 
within the device-technological simulation [8-10, 12]. 
2.2. Advanced compact model of the Hall Sensor 
Fig. 3 shows an equivalent circuit describing the HS compact. For an ideal 
design (no technological discrepancy and mechanical stress in the system), the van 
der Pauw method is used to measure the surface resistance of the RS layer. Since 
the device is symmetrical, it is necessary to determine the values of the two 
resistances between the contacts: RD for the resistance between the two opposite 
and RH for the two adjacent contacts [11]. In comparison with the existing 
solutions [12], this scheme provides the possibility of taking into account the 
galvanomagnetic and temperature effects. 
INPUT
CCVS1
CCVS4
CCVS3
CCVS2
RH RD
-
+
- +
-
+
-+
INPUT
OUTPUTOUTPUT
RD RD
RD
RH RH
RH
2
1
4
3
5
B
R
Figure 3. Equivalent circuit describing the basic HS compact model. 
The proposed equivalent circuit has 4 electrical outputs and one external source 
as input (B) and includes the following components: 8 non-linear resistors 
designed to describe the dependences of the characteristics of the HS from the 
magnetic field and temperature; 4 current-controlled voltage sources, which allow 
estimating the contributions to the Hall voltage of currents flowing through 
nonlinear resistances; 4 interface blocks for the simulation of series resistances. 
The parameters of the silicon-based HS compact model [11] are given in Table 1. 
Nghiên cứu khoa học công nghệ 
Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san Viện Điện tử, 9 - 2020 199 
The last two lines contain the parameters typical for the hall sensor made on the 
basis of wide-gap semiconductors. The names of electrical model parameters used 
in the text are shown in parentheses. To simulate the magnetosensitive sensor with 
IMC, added the parameters presented in Table 2. 
Table 1. Silicon based hall sensor model parameters. 
Parameter Description Unit Value range 
TEMP Ambient temperature K 248–398 
L Length of active area m (30–120)×10-6 
W Active Area Width m (10–40)×10-6 
S (s) Size of the contact electrode M (9–39)×10-6 
TETA (θ) Hall angle radians 0–0.45 
RH (rH) The Hall Scattering Coefficient 0.2–1.7 
GH (GH) Correction geometric coefficient 0,5–1 
NDNW (ND,NW) 
Concentration of charge carriers in 
the active region 
m
-3
 10
21–1023 
NSUB (NSUB) 
Concentration of charge carriers in a 
substrate 
m
-3
 5×10
20–1021 
DEFF (deff) Effective depth of active area m (0.5–5)×10
-6
MOBN (µn) 
Mobility of electrons in the active 
region 
m
2/V∙s 0.072–0.141 
MOBH (µh) 
Mobility of holes in the active 
region 
m
2/V∙s 0.032–0.047 
RSS (RS) Surface resistance of silicon Ohm 100–15×10
3
RDD (RD) 
Resistance between two opposite 
contacts 
Ohm 650–120×103 
RHH (RH) 
Resistance between two neighboring 
opposites 
Ohm 1100–200×103 
BBR1 
The first coefficient of resistance 
versus voltage 
V
-1
 0–0.01 
BBR2 
The second coefficient of resistance 
versus voltage 
V
-2
 -0.005–0 
BBS1 
The first coefficient of sensitivity 
versus voltage 
V
-1
 0–0.01 
BBS2 
The second coefficient of sensitivity 
versus voltage 
V
-2
 -0.005–0 
RTC1 
The first temperature coefficient of 
resistance 
V
-1
 0–0.01 
RTC2 
The second temperature coefficient 
of resistance 
V
-2
 0–0.0005 
ALPHA (αSI) 
Temperature coefficient of 
sensitivity 
V
-1
 0–0.001 
NSS (NS) 
Concentration of charge carriers in 
2DEG 
m
-2
 10
16–1018 
MOBN (µS) Mobility of electrons in 2DEG m
2/V∙s 0.01–1.0 
Kỹ thuật điện tử 
D. D. Ha, T. T. Trung, “Advanced compact model  integrated magnetic sensor systems.” 200 
Table 2. The compact model parameters of the magnetosensitive sensor with IMC. 
Parameter Description Unit Value range 
D Diameter of the concentrator m (50–500)×10-6 
t Thickness of concentrator m (5–20)×10-6 
Mu0 (µ0) Magnetic permeability (1–100)×10
3
BSAT (Bsat) Magnetic saturation induction Tesla 1–2.8 
N Demagnetization factor 0.015–0.15 
K Coefficient of magnetic flux 5–20 
3. SIMULATION RESULTS 
3.1. Device-technological vs. Schematic simulation 
Fig. 4 and 5 show the results of a comparison between data of device-
technological modeling in the software complex Silvaco and data of circuit 
simulation using the developed compact model a Hall sensor fabricated by 
standard silicon technology and based on wide-gap semiconductors, respectively. 
0 0,2 0,4 0,6 0,8 1,0
150
125
100
75
50
25
0
I , mA
V
H
 ,
 m
V
Device simulation 
B = 0.25 T
B = 0.1 T
B = 0.5 T
Compact Model
B = 0.25 T
B = 0.1 T
B = 0.5 T
Figure 4. The simulated and modeled output Hall voltage VH versus 
the biasing current at different magnetic field for Silicon Hall sensor. 
The analysis of the obtained results testifies to the high efficiency of the 
developed compact model. The error in the data of device-technological and circuit 
simulation does not exceed 5%. 
0,2 0,4 0,6 0,8 1,0
40
35
30
25
10
5
0
I , mA
V
H
 ,
 m
V
20
Device simulation 
B = 0.1 T
B = 0.5 T
Compact Model
B = 0.1 T
B = 0.5 T
B = 0.25 T
B = 0.25 T
15
Figure 5. The simulated and modeled output Hall voltage VH versus 
the biasing current at different magnetic field for GaN Hall sensor. 
Nghiên cứu khoa học công nghệ 
Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san Viện Điện tử, 9 - 2020 201 
3.2. Modeling of the sensor signal processing circuit 
Currently widely used multi-functional integrated sensor systems that are 
realized by combining the sensor (often multiple) and processing circuitry on a 
single chip. Such a system-on-chip (SoC) in which the data converter is integrated 
with the digital signal processing unit in one chip with integrated sensor may be a 
more effective solution. In comparison with optional discrete chip ADC, this 
approach can significantly improve the compactness and reduce the cost of 
production, which is a critical consideration for the sensitive region, medical, 
mobile, automotive, and other applications. 
The processing of the sensor signal can be widely classified in terms of signal 
bandwidth (the rate of change of the measured physical quantity) and the 
resolution necessary to obtain meaningful information. Typically, the required 
ADC can be built on the basis of one of two very efficient architectures: a 
sequential approximation register (SAR) and redundant discrete ADCs Sigma-
Delta (SD). Used in our case SAR ADC allows to effectively handle signals with a 
different frequency range – from a few Hz to hundreds of kHz with a high enough 
accuracy – 6-8 bits to 20 bits and higher, and also provides high versatility and low 
power dissipation, making it ideal for these systems. 
Table 3. 10-bit SAR ADC parameters. 
Parameter name Designation 
Value 
Unit 
Min Typical Max 
Temperature T -40 27 85 °C 
Supply voltage of analog blocks VDDA 1.62 1.8 1.98 V 
Supply voltage of digital blocks VDDD 1.62 1.8 1.98 V 
Resolution N 10 bit 
Clock frequency FCLK 160 MHz 
Sampling rate FS 10 MHz 
Sampling time TS ns 
Reference voltages 
VREFP 1.25 V 
VREFN 0.25 V 
DC level of input signal VCM 0.75 V 
Input capacitance CIN pF 
Spurious free dynamic range SFDR 63 dB 
Signal to noise ratio and distortion SINAD 57 dB 
Effective number of bits ENOB 9.2 bits 
Integral nonlinearity INL 1 LSB 
Differential nonlinearity DNL 0.7 LSB 
For this system, a topology which contains a system for receiving, amplifying, 
and sensory data processing based on the Hall sensor as an example on a single 
chip is developed using the TSMC 0.18 μm CMOS MS/RF 1.8/3.3V PDK. The test 
circuit used a 10-bit, own designed SAR ADC implemented in silicon using TSMC 
0.18 um CMOS MS/RF 1.8/3.3V technology. The topological implementation of 
the Hall sensor, differential amplifier and ADC are presented in Fig. 6. 
Kỹ thuật điện tử 
D. D. Ha, T. T. Trung, “Advanced compact model  integrated magnetic sensor systems.” 202 
The results of computer simulation in the Cadence software package using the 
proposed signal processing circuit are presented in Fig. 7 and Table 3. During the 
simulation, developed and described above compact model was used to simulate 
the HS electrical characteristics. In Fig. 7 shows: B - magnetic field, VH+, VH- - hall 
voltage, code - DAC output signal, out - 10-bit ADC output signal. 
1 – Hall sensor
2 – Differential amplifier
3 – Voltage reference 
4 – ADC
4
31
2
1168 um
7
1
0
 u
m
Figure 6. Topological implementation of Hall sensor, 
differential amplifier and ADC. 
0
500
0
В
m
T
1,8
0,9V
730
770
750
VH+ VH-
m
V
0
1,5
0,8
refp refn vcm
V
data 
1,8
0
0,9
code
V
0,5
0
out
V
1,00,50 2,01,5 3,02,5 4,03,5 4,5
1,0
Time, us 
Figure 7. The «Hall Sensor – processing circuit» system simulation results. 
4. CONCLUSION 
The advanced compact model of Hall sensor presented in this paper has a simple 
structure which leads to fast simulations while allowing an accurate description of 
the behavior of the device. It is made of simple sub-components and does not 
involve any complex equation. The revision and expending of the model, primarily 
the mobility, provide the possibility of its use for simulation of Hall sensor based on 
other materials, for example wide-gap semiconductors and consider the impact of 
an integrated magnetic concentrator. The results of simulation of the "Hall sensor – 
processing scheme" system using the developed compact model and signal 
processing circuit demonstrate the high efficiency of the proposed solutions. 
Nghiên cứu khoa học công nghệ 
Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san Viện Điện tử, 9 - 2020 203 
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for SPICE simulations", ICECS, pp. 1-4 (2005). 
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[6]. K. Kundert, "The Designer's Guide to Verilog-AMS" Kluwert Academic 
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Heating Effect in AlGaN/GaN High Electron Mobility Transistor by Diamond 
Heat Sink Layers". ATC, Vietnam, pp. 264–267 (2016). 
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Characteristics with Various Geometry of the Active Area", Nano- i 
Mikrosistemnaya Tekhnika, vol.20, no.3, pp. 174-186 (2018). 
[11]. Y. Xu and H. Pan, "An Improved Equivalent Simulation Model for CMOS 
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TÓM TẮT 
MÔ HÌNH TỔNG QUÁT TIÊN TIẾN VÀ MẠCH XỬ LÝ TÍN HIỆU 
CHO HỆ THỐNG CẢM BIẾN TỪ TRƯỜNG TÍCH HỢP 
Đề xuất mô hình điện tổng quát của cảm biến Hall, được thiết kế cho mô 
phỏng mạch, có tính đến các tham số thiết kế và vật liệu sử dụng. Mô hình 
cảm biến được triển khai theo ngôn ngữ Verilog-A có cấu trúc đơn giản và 
cho phép mô tả chính xác các đặc tính của cảm biến. Mô hình tương đương 
được mô tả dựa trên các thành phần mạch điện tiêu chuẩn và không sử dụng 
các phương trình phức tạp để mô tả các quá trình vật lý diễn ra trong cấu 
trúc cảm biến. Thiết kế một cấu trúc mạch bao gồm cảm biến Hall, mạch 
khuếch đại và mạch chuyển đổi tín hiệu tương tự-số 10 bit tích hợp trên chip 
sử dụng thư viện thiết kế TSMC 0.18 um CMOS MS/RF 1,8/3,3V PDK cho 
phép nhận và xử lý tín hiệu của các thiết bị cảm biến. 
Từ khóa: Cảm biến Hall, Mô hình nhỏ gọn; Verilog-A; Mạch xử lý tín hiệu; Mạch chuyển đổi tương tự-số. 
Received 20
th
 April 2020 
Revised 21
th
 August 2020 
Published 28
th
 August 2020 
Author affiliations: 
1
Le Quy Don Technical University; 
2
Academy of Military Science and Technology. 
*Corresponding author: havixuly@gmail.com.