LOW FREQUENCY RADIO FREQUENCY IDENTIFICATION ANTENNA DESIGN
Walter Joseph Imfeld IV
B.S., DeVry University of Technology, 1999
PROJECT
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
ELECTRICAL AND ELECTRONICS ENGINEERING
at
CALIFORNIA STATE UNIVERSITY, SACRAMENTO
SPRING
2011
© 2011
Walter Joseph Imfeld IV
ALL RIGHTS RESERVED
ii
LOW FREQUENCY RADIO FREQUENCY IDENTIFICATION ANTENNA DESIGN
A Project
by
Walter Joseph Imfeld IV
Approved by:
__________________________________, Committee Chair
Milica Markovic, Ph.D.
____________________________
Date
iii
Student: Walter Joseph Imfeld IV
I certify that this student has met the requirements for format contained in the University format
manual, and that this project is suitable for shelving in the Library and credit is to be awarded for
the project.
__________________________, Graduate Coordinator
Preetham Kumar , Ph. D.
Department of Electrical and Electronic Engineering
iv
___________________
Date
Abstract
of
LOW FREQUENCY RADIO FREQUENCY IDENTIFICATION ANTENNA DESIGN
by
Walter Joseph Imfeld IV
Statement of Problem
Many household pets today have a radio frequency identification chip implanted by their
owners. These devices operate as a passive device in the low frequency range, because they are
passive the power received back is very small and utilize inductive coupling to power them. The
distance at which these devices can be read effectively is very small because they are operating in
low frequency range and require inductive coupling. Increasing the range these radio frequency
identification devices can be effectively read will open up many types of automated applications
to work with existing technology implanted in household pets. This project will explore the
parameters of a loop antenna in the operation of activating and reading a low frequency radio
frequency identification device with the intent of maximizing the effective range trying to reach a
range of nine inches or more.
Sources of Data
Most of the back ground and history of radio frequency identification technology was
researched from online journals and articles. As more detailed information was obtained, iEEE
v
articles and industry techniques were researched. Antenna theory and operation were pulled from
industry leading text books imploring antenna concepts and electromagnetic signal transmissions.
Conclusions Reached
The resulting antenna created through this project did exceed the effective read range and
area of the existing premade antenna. However the effective read distance did not exceed the
previous set goal of nine inches. Other techniques and antenna designs are described but not
detailed within this project.
, Committee Chair
Milica Markovic, Ph. D.
______________________
Date
vi
TABLE OF CONTENTS
Page
List of Tables ............................................................................................................................... ix
List of Figures .............................................................................................................................. x
Chapter
1. INTRODUCTION ................................................................................................................. 1
2. HISTORY OF RFID TECHNOLOGY ................................................................................. 2
Uses of RFID .................................................................................................................. 3
Types of RFID ................................................................................................................ 4
3. TECHNOLOGY USED IN PROJECT ................................................................................. 8
Low Frequency RFID Microstrip ................................................................................... 8
Protocols ......................................................................................................................... 9
Low Frequency RFID Reader ......................................................................................... 11
Transmitter ............................................................................................................... 11
Receiver .................................................................................................................... 11
Micro Processor........................................................................................................ 12
Transceiver Antenna................................................................................................. 12
4. PASSIVE LOW FREQUENCY RFID ANTENNA DESIGN .............................................. 13
Electrically Small Antenna Definition ............................................................................ 13
Near-Field and Far-Field................................................................................................. 13
Electric and Magnetic Field Strengths ............................................................................ 14
Wave Impedance............................................................................................................. 22
Radiation Pattern............................................................................................................. 24
vii
Directivity ....................................................................................................................... 26
Antenna Resistance ......................................................................................................... 26
Antenna Inductance ........................................................................................................ 29
Electrical Model .............................................................................................................. 31
FCC and iEEE Regulations for Radio Frequency Transmissions................................... 38
5. ANTENNA CREATION AND ACTUAL DATA ................................................................ 41
Designing Antenna for Application ................................................................................ 41
Creation of the Antenna Based on Inductance Chosen ................................................... 44
Measured Antenna Physical Parameters ......................................................................... 46
Fine-tuning the Operation Frequency ............................................................................. 47
Actual Measurements ..................................................................................................... 49
Measuring Activation Distance....................................................................................... 52
Field Measurements ........................................................................................................ 54
6. POSSIBLE APPLICATIONS ............................................................................................... 59
7. CONCLUSION ..................................................................................................................... 60
Appendix A. Field Equation Conversion Math ........................................................................... 61
Appendix B. MatLab Code .......................................................................................................... 64
Appendix C. Excel Design Model ............................................................................................... 68
References .................................................................................................................................... 69
viii
LIST OF TABLES
Page
1.
Table 1Types of RFID technology ..................................................................................... 5
2.
Table 2 Passive low frequency RFIDs for animal identification ....................................... 10
3.
Table 3 Field strengths at r = 3.146 inches ........................................................................ 18
4.
Table 4 Calculated antenna resistances .............................................................................. 28
5.
Table 5 Calculated versus measured antenna inductance .................................................. 30
6.
Table 6 FCC Maximum Permissible Exposure (MPE) [20] .............................................. 38
7.
Table 7 FCC Power thresholds for routine evaluation [27] ............................................... 38
8.
Table 8 Very low frequency common appliances electromagnetic field strengths [27] .... 40
9.
Table 9 Measured antenna inductance ............................................................................... 46
10.
Table 10 Measured antenna resistance ............................................................................... 47
11.
Table 11 Antenna tuning capacitance ................................................................................ 48
12.
Table 12 Measured values of operating circuit .................................................................. 51
13.
Table 13 Distance and field measurements ........................................................................ 52
14.
Table 14 Measured H and E fields ..................................................................................... 56
15.
Table 15 Calculated and actual H-field, r=3.146 inches .................................................... 58
ix
LIST OF FIGURES
Page
1.
Figure 1 Microchip compared with a grain of rice............................................................. 8
2.
Figure 2 Close-up of microchip ......................................................................................... 9
3.
Figure 3 Field magnitude θ = 0 degrees, taken at arbitrary t=1 ......................................... 17
4.
Figure 4 Antenna field strength plot (near-field), taken at arbitrary t=1 ............................ 19
5.
Figure 5 Field strength comparison (far-field), taken at arbitrary t=1 ............................... 20
6.
Figure 6 Field strength comparison at θ = 90 degrees, taken at arbitrary t=1 .................... 21
7.
Figure 7 Close up of normalized E and H-fields, taken at arbitrary t=1 ............................ 22
8.
Figure 8 Wave impedance (1λ) .......................................................................................... 23
9.
Figure 9 Radiation pattern loop antenna ............................................................................ 25
10.
Figure 10 Radiation pattern of a small loop antenna obtained from Matlab created by
Milica Marcovic, Ph. D. and used with permission ........................................... 25
11.
Figure 11 Network analyzer 300kHz to 20MHz, loop antenna ......................................... 31
12.
Figure 12 Network analyzer setup ..................................................................................... 32
13.
Figure 13 ADS model loop antenna ................................................................................... 33
14.
Figure 14 ADS magnitude frequency response, loop antenna 300kHz to 2MHz .............. 35
15.
Figure 15 ADS Smith Chart loop antenna 300kHz to 2MHz............................................. 35
16.
Figure 16 ADS model tuned loop antenna ........................................................................ 36
17.
Figure 17 ADS magnitude frequency response, tuned loop 300kHz to 2MHz .................. 37
18.
Figure 18 ADS Smith Chart tuned loop antenna 300kHz to 2MHz ................................... 37
19.
Figure 19 iEEE safety levels for electromagnetic fields [27] ............................................ 39
20.
Figure 20 Schematic of RFIDRW-E-232 for tuning the EM4095 ..................................... 41
21.
Figure 21 Using a CD spindle to hold the circular shape of the antenna ........................... 44
22.
Figure 22 Measuring the first antenna................................................................................ 45
x
23.
Figure 23 RFID reader measuring tuned frequency ........................................................... 48
24.
Figure 24 Frequency test point measurement of second antenna....................................... 50
25.
Figure 25 Vr measurement while adjusting Rs .................................................................. 50
26.
Figure 26 Measurement of Va............................................................................................ 51
27.
Figure 27 Device Measurement Test Setup ....................................................................... 53
28.
Figure 28 Electric field test probe (top left), Magnetic field test probe for (bottom left),
Combined probes (right) .................................................................................... 54
29.
Figure 29 Field measurement test setup ............................................................................. 55
30.
Figure 30 Measured field strengths of second antenna at activation r = 3.148" ................ 56
xi
1
Chapter 1
INTRODUCTION
Radio Frequency Identification (RFID) is a way of identifying an item or animal from a
distance using electro-magnetic waves. This project explores one such application that will allow
an application to utilize the existing household pet passive low frequency RFID microchip that
veterinarians implant today. Critical to the implementation of the passive low frequency RFID
technology is the distance at which such a device can be activated and deciphered. This project
will modify an existing passive low frequency RFID antenna design and increase the effective
distance at which an RFID reader can be used. Increasing the effective range will allow this
technology to open up a variety of new applications that would utilize the existing passive low
frequency RFID implants in household pets.
2
Chapter 2
HISTORY OF RFID TECHNOLOGY
Passive RFID in its most basic form was first used in world war 2 when the Germans
discovered that if their pilots would do a barrel roll as they came flying back to base the radar
pings would show a change in the blip. This was how the Germans began to detect friend from
foe plane coming back to base. When the radar ping would be sent out, the reflection received
would show a different result for an aircraft doing a barrel roll versus one that was not [1].
The British first used active RFID in World War when Sir Robert Alexander Watson-Watt
created the Identification Friend or Foe (IFF) transponder. When the radar ping was sent out it
would initiate the transponder on the aircraft to send a specific signal back not only identifying
the aircraft as British, but which aircraft it was [1], [2].
Through the 1950’s and 1960’s RFID was fine-tuned and first used as theft detection in
department stores. Using a 1-bit passive RFID tag attached to the merchandise, a activation field
at the exit would activate the RFID tag. After the RFID tag is activated it would reflect a
frequency representing logic 1 or a slightly different frequency representing logic 0. If a logic 1
was detected the alarm would sound because the security tag was still active [1].
In 1973 the first actual patent was issued to Mario W. Cardullo for an RFID device with
memory that would identify a user that passed the device over a door pad [3]. The addition of
memory to the RFID technology allowed the same device template to be programed with many
different identification codes.
Also in the 1970’s the United States Department of Energy contracted Los Alamos National
Laboratory to create a device to identify nuclear materials in transit. Los Alamos designed a
3
passive RFID tag that would be activated by electromagnetic field created by the entry gate. This
system of tracking vehicles was mass marketed in the mid 1980’s and utilized where tracking
vehicles were required such as told roads and bridges [1].
With Los Alamos National Laboratories success of the vehicle RFID tracking, the United
States Department of Agriculture (USDA) requested Los Alamos National Laboratories to create
and RFID tag for tracking livestock. USDA had a growing concern of ill livestock getting double
the dosage of medication or hormones then allowed [1]. In 2003 the USDA began a program to
require all farms in the United States to utilize RFID tags with their livestock by 2009. In 2007
however, the USDA has changed the program from required to voluntary due to the quantity of
livestock in the United States [4].
Once RFID was commercialized into the agriculture area, RFID technology moved from ear
tags on livestock to glass capsules injected under the skin. This advancement paved the way for
more and more companies to create RFID devices. These applications and advancements
contributed to lowering the cost of what we see today being used in household pets.
Uses of RFID
Today RFIDs are used across our society in such fields as agriculture, research, security,
operations, and personal use by consumers. Similar to how agriculture management of livestock
was used in both controlling medication and hormone doses via RFID Animal Identification
Numbers (AIN), researchers frequently use RFID AINs to track wild animals for migration
patterns. The unique AIN can provide correct tracking of the research data to a particular animal.
[8],[10]
Almost every company with a large number of employees utilizes an identification badge
that has embedded RFID technology. This allows a company to control access to specific parts of
the building and monitor their employees movements. Similarly in an operations environment,
4
supply chain logistics began heavily using RFID on the packages to monitor the comings and
goings of packages starting in 2005. Within the supply chain environment however, RFID also
carries additional information about the product other than identification such as destination [6].
This helps expedite the identification of the package and what operation needs to be done to the
package.
Even though implanted RFID devices have been used in household pets since the early
1990’s, it wasn’t until 2007 that a worldwide standardized database was created that the United
States truly adopted RFID implants for household pets. With a standardized database pet owner
information could be recorded and retrieved anywhere by authorized officials who locate lost
pets. Veterinarians have started to offer this added lost and found feature to pet’s during routine
surgeries and checkups. In 2007 the USDA reported that about 5 percent of all household dogs
and cats in the United States had a low frequency RFID microchip implanted [7]. In the recent
USDA publication for “Official Animal Identification Number (AIN) Devices”, all of the
implanted RFID microchips following the AIN standards operated at 134.2 kHz compared to the
125 kHz RFID microchips popular in Europe [8].
Types of RFID
RFIDs have a wide variety of uses as well as a wide range of operating frequencies. Table 1
shows a list of the types of RFIDs on the market today.
5
Table 1 Types of RFID technology
RFID Type
Frequency
Range
Microwave
and UHF
Typical Market
Pros
Cons
All Listed for
UHF and
Microwave
Greater Distance
(20-100M), Can hold
additional
information
Passive
All Above
All Listed
Microwave
2.45 GHz
Toll Collection,
Airline Luggage
UHF
868 ~ 956
MHz
HF
13.56 MHz
Logistics,
Supply chain,
Livestock
Warehouse
Inventory,
Livestock
Requires no
maintenance,
Inexpensive, Small
in size
Fastest Read Rates,
Good Read
Distance,
Good Read Distance,
Faster Read Rate
Requires power,
typical battery life is
10 years, Devices
are larger than the
size of a coin
Limited Distance
(up to 10M), Only
holds unique ID
LF
125kHz and
134.2 kHz
Active
Animal
Identification
Very Expensive,
Most energy is
absorbed by water
FCC Restrictions
Apply, energy is
absorbed by water
Good Read Distance, Devices are external
Inexpensive,
tags to avoid high
Fast Read Rate
water content
absorbing energy
Very Small devices
Limited read
can be implanted
distance, possible up
to about 0.5m, Slow
Read Rate
Active RFIDs is used with the UHF or microwave frequency ranges and because the device
is self-powered the transponder signal sent back to the reader will have a stronger signal allowing
a read distance of up to 300 meters. This read distance is the biggest benefit to active devices.
The down side is that the power source can be bulky and has a finite life span which means it will
require some maintenance [9].
Passive RFIDs can be used with any of the RFID frequency ranges, are not self-powered, are
much smaller than active devices and are inexpensive. The deterrent for using passive RFID is
the limited read distance of only 10M. With passive devices the frequency range the RFID is
operating in really determines the application the RFID is used for.
6
Microwave RFIDs have the best advantage of being used in a high velocity application,
because passive RFID devices utilize the operating frequency as the device clock, the faster the
clock the faster the transmission. With microwave RFID devices operating in the gigahertz
range, transactions can be processed fast enough to capture the RFID’s information even if the
RFID is moving at 80 MPH. Passive microwave RFIDs still only have about a 3 meter read
distance. Used as with active RFID technology, microwave devices are used up to 100 meters.
With the extremely fast read rate a microwave RFID implores, these devices can easily read a
passive transponder of a moving motor vehicle and is why it is commonly used in toll collection
booths. Microwave RFIDs do have a couple negatives [9].
Due to the frequency range, the size of the device, and sensitivity to design tolerance,
microwave RFID readers are more expensive than the other types of RFID readers. Also due to
the high frequency when the microwave signal passes through water content, most of the energy
is absorbed into the water and does not reach the RFID device. Since animals consist of mostly
water, passive microwave RFIDs are not typically used with tracking animals and never used as
an implant without an external antenna [9].
Ultra High Frequency (UHF) RFID devices are much like the microwave devices with a few
key differences; they are not as expensive and UHF devices do not have as quick a read rate as
compared to the microwave devices. Even though UHF RFIDs do not operate in the gigahertz
ranger, they still loose energy when transferring through a water medium. Passive UHF RFIDs
do have a read range up to 10 meters, fast read rate, and are inexpensive. This makes UHF
RFIDs a great choice for supply chain logistics tracking merchandise without liquid content.
Passive UHF RFIDs are utilized on many farms tracking livestock via ear tags, because the tags
are external to the animal most of the energy is received by the transponder [6],[9],[10].
7
High Frequency (HF) RFID devices operate in the low megahertz frequency range and are
not as sensitive to water mediums. HF devices don’t have a nanosecond read rate or the read
distance of UFH and microwave devices, but they can be used with animals better than the UHF
RFID devices can. HF devices are still loose energy when penetrating water, so they cannot be
used as implants, however, they are used as tags external to an animal. Farms use HF RFID ear
tags often to track livestock. This identifies the animals without having to brand them and can
record electronic tracking when administering medication or hormones. Both UHF and HF are
used in the implantation of ear tags, with the difference being the size. A UHF ear tag is the size
of a nickel, were as a HF ear tag is a rectangular tag about one and a half inch by 2 inches. It is
preference of the farmer as to the type of RFID technology used. [9]
Low frequency (LF) RFID devices operate in the kilohertz range. This lower range has the
slowest read rate and smallest read distance, however, LF RFID’s energy does not get absorbed
by water. LF RFIDs are the only type of RFIDs used as animal implants because of this reason
[9].
Due to the small size, the ability to work as an implant and the low cost; passive LF RFIDs
are what are used today by the pound or veterinary office. With household pet identification
using passive LF RFID device, this is the technology focused on with thought this project.
8
Chapter 3
TECHNOLOGY USED IN PROJECT
Low Frequency RFID Microchip
LF Passive devices are used for the implantation of household pets. These are used
because they use less power, are the size of a grain of rice (figure 1), inexpensive, and can be
implanted. The LF passive RFID microchip uniquely fits all these qualifications.
LF Passive RIFD operates in either 125 kHz or 134.2 kHz. According to the USDA in
2007, five percent of all household pets in the United States had been implanted with a LF RFID
microchip and out of those implanted a 125 kHz LF RFID was used [7]. Current trend of official
RFID devices listed by USDA today are passive LF RFIDs operating at 134.2 kHz. [8]
Figure 1 Microchip compared with a grain of rice
9
In 2011 it was discovered that 125 kHz are sold in the European and Asia regions but in the
United States today 134.2 kHz Schering-Plough are used by veterinaries through HomeAgain Pet
Recovery Systems [11]. HomeAgain and AVID are the two leading distributors for household
pet microchip implants in the United States today [12]. Figure 2 shows the LF RFID device that
was purchased through HomeAgain for this project.
Figure 2 Close-up of microchip
Protocols
The transmission standards for passive LF RFID devices are outlined in ISO standards
11784 & 11785 [13],[5]. These standards describe the types of protocols used to communicate to
a LF RFID device. The initiating activation field is a resonating frequency that will interact with
the tuned antenna on the microchip. The resonating frequency will cause a capacitor to charge
and once enough power is built up to power the transmitter, a burst of data will be sent. Because
the resonating frequency is low, the charging of this capacitor is longer than it would take other
devices operating at higher frequencies but even with the LF the charge time is only 50ms before
a the RFID transmits back [13],[14],[5].
ISO Standards 117784 & 11785 discusses the protocol standards for these LF devices.
The 2 protocols published in these standards are HDX and FDX-B [13],[5].
10
Table 2 Passive low frequency RFIDs for animal identification
Protocol
FDX-B
HDX
Activation
Field
134.2 kHz
or 125 kHz
134.2kHz
or 125 kHz
Modulation ID Code
Pros
Cons
AM-PSK
10/12 Bit
Full Duplex
FSK
12 Bit
FSK Modulation
Cleaner Signal
AM modulation is
susceptible to noise
Requires addition
demodulation
FDX-B is a full duplex activation signal. This means that the transceiver is able to read the
signal coming from the microchip at the same time it is transmitting the activation field. The
return signal of the device uses amplitude modulation to send the signal back with phase shift
keying. The RFID reader uses the phase shift key to distinguish between activation field
frequency and the modulated signal coming back from the device [13],[5]. To acquire the
amplitude modulation, the microchip simply accesses two different points on the antenna coil.
Changing the amount of turns that are used in the RFID antenna, will alter the amplitude being
sent back because the amount of turns is directly related to the power transmitted. When shorting
out a few of the turns in the coil, a smaller amplitude will be transmitted thus representing a logic
0. By utilizing the full amount of turns, the full amplitude will be transmitted, representing a
logic 1 [14].
HDX is Half Duplex, which means the transmitter has to rest the transmission of the
activation field long enough to read the response. This pause is can be up to 20ms. The
disruption in the activation field signals the HDX device to transmit back a burst of information.
If no signal is received within 3ms, the activation signal will resume. If there is a signal detected,
the activation field will stay off for 20ms waiting for the HDX signal to be completely received.
The modulation used is Frequency Key Shifting (FSK), which changes the frequency to
142.2kHz to represent a logic 0 and 134.2 kHz to represent a logic 1. Using FSK, noise is less of
a factor than it is for AM-PSK used by FDX-B [13],[5].
11
Because of the size of modulation circuitry required, the transponders that utilize HDX are
too large for implants but are still very useful in external tags such as ear tags on live stock.
Transponders used in household pet implants use FDX-B protocol and will be the focus of this
paper.
Low Frequency RFID Reader
The LF RFID reader that was chosen to be used in this project was sold by Priority 1 Design,
model number RFIDRW-E-232. This LF RFID reader is inexpensive and can read a variety of
LF RFID devices [14]. The most important component in reference to LF RFID on this device is
the EM4095 by EM Microelectonics [15]. The EM4095 uses the ISO standards 11784 & 11785
to communicate with LF RFID devices and demodulate the burst transmission received back.
The main operation blocks of the RFIDRW-E-232 are briefly described in the following sections.
Transmitter
The transmitter is a voltage controlled oscillator (VOC) that generates a frequency
corresponding with the activation field frequency of the device used. This is done with a tuned
LC circuit made of the loop antenna and tuning capacitor in series. The signal is pushed through
a power amplifier transmitted on the loop antenna [15].
Receiver
The receiver consists of a phase lock loop (PLL), a voltage divider circuit, and demodulator.
The PLL is used to capture the phase and locking it to the transmitting phase. The received signal
is then run through a capacitive voltage divider to lower the signal from transmitting power to a
level below 5 Volts peak to peak (Vp-p). The DC offset is 2.4 so the signal being sent into the
AM demodulator needs to be less than 4 V p-p so that it will not clip distorting the AM envelope.
12
The reduced signal is passed through a 2 stage band pass filter to remove as much noise as
possible and then applied to a comparator that will measure the levels of the signal and
distinguish between a logic high and logic low. The output of the comparator is buffered and sent
out on the digital demodulated line to be interpreted by the microprocessor using the protocols
defined in ISO 11784 & 11785 [15].
Micro Processor
The output of the comparator is buffered and sent out on the digital demodulated line to be
interpreted by the microprocessor using the protocols defined in ISO 11784/11785. The
information is decoded and transmitted serially to PC hosting software that will process and
display the information from the microchip for the user [14].
Transceiver Antenna
The transceiver antenna has a basic but very important function. The antenna will be
transmitting the activation field and be receptive enough to receive the response back from the
transponder. The most typical design of a LF RFID antenna is a small loop antenna. There are
other types that can be used, such as a ferrite rod stick antenna, Helmholtz coil antenna, or a
folded loop antenna. For this project we will be focusing on the small loop antenna to allow for
a direct comparison to the remanufactured antenna that was received with the RFIDRW-E-232.
13
Chapter 4
PASSIVE LOW FREQUENCY RFID ANTENNA DESIGN
Electrically Small Antenna Definition
A small loop antenna means that the total length of conductor used in the loop is
electrically small compared to the wave length of the operating frequency being transmitted. An
electrically small antenna is defined as the total conductor length being less than 1/10th of the
𝑐
wave length (λ). The wavelength of a frequency is defined by 𝜆 = 𝑓. As 0.1 𝜆 is the true
definition in practice, 0.085 𝜆 is used as the maximum length of conductor to be considered
electrically small for a loop antenna [17,18].
In the design for this application the operating frequency is 134.2 kHz which in turn has a
3∗108 𝑚/𝑠
wave length of 𝜆 = 134.2∗103 𝑝𝑒𝑟𝑖𝑜𝑑/𝑠 = 2.2 ∗ 103 𝑚/𝑝𝑒𝑟𝑖𝑜𝑑 [21]. To be a small loop antenna
the total conductor length use cannot exceed 0.85 𝜆 = 0.085 ∗ (2.2 ∗ 103 𝑚) = 187𝑚.
Near-Field and Far-Field
The distance from the antenna can be broken into three regions, which are defined by the
way the signal responds at those distances. Antenna radiation has a quick power fall off and then
stabilizes farther away [17].
Reactive near-field is the area closest to the antenna, and is where the reactive (magnetic)
𝐷3
field supersedes the electric field strength. This region ends at a distance of 0.62√ 𝜆 were D is
the largest dimension of the antenna in question and is in the same units as λ. Signals within this
range are not ideal for transmitted signals but works well for coupled signals. For electrically
small antennas this distance is approximated with
𝜆
2𝜋
= 0.16 𝜆 [17].
14
Radiating near-field is the region between the reactive near-field and the far-field. In this
region the angular signal strength of the electric and magnetic field varies based on distance,
which makes compensation difficult as you need to know the distance from the antenna at any
given time. If the antenna dimension is smaller than the wave length (𝐷 < 𝜆) this region may
not exist [17].
Far-field is the region beyond the outer boundary of the near-field and where the angular
field strength is only slightly affected by distance from the antenna. Transmitting towers sending
radio frequency signals operate in this range and is why radio frequency books discuss everything
in far-field. The equations deciphering field strength, power, and other antenna properties can be
simplified since they do not vary on distance from the antenna as much [17].
Due to the LF RFID requiring inductive coupling to power the microchip, the reactive
near-field region is the area that will be focused on. With the λ = 2200 m/period, the outer
boundary of the reactive near-field can be estimated at 0.16 λ = 352 meters away from the
antenna.
Electric and Magnetic Field Strength
With the loop antenna being strongly magnetic compared to other dipole antennas, the
reactive near-field is larger than that of a dipole. It is this that makes the loop antenna a good
candidate for inductive coupling needed to transfer power to the transponder.
Infinitesimal Small Dipole Phasor Equations [17]:
k = Phase Constant =
2𝜋
𝜆
Io = Current through the antenna
l = Length of dipole antenna
a = Area of the loop antenna
15
r = Distance from the center of the antenna
θ = Angle from the z-axis perpendicular to the center of the antenna
𝐻𝑟 = 𝐻𝜃 = 𝐸𝜙 = 0
𝐻𝜙 = [𝑗𝜔
𝐸𝑟 = [𝜂
𝑘𝐼𝑜 lsin(𝜃)
1
] [1 + 𝑗𝜔𝑘𝑟] 𝑒 −𝑗𝜔𝑘𝑟
4𝜋𝑟
𝐼𝑜 𝑙𝑐𝑜𝑠(𝜃)
] [1
2𝜋𝑟 2
𝐸𝜃 = [𝑗𝜔𝜂
1
+ 𝑗𝜔𝑘𝑟] 𝑒 −𝑗𝜔𝑘𝑟
𝐼𝑜 𝑙𝑠𝑖𝑛(𝜃)
1
] [1 + 𝑗𝜔𝑘𝑟
4𝜋𝑟
1
− (𝑘𝑟)2 ] 𝑒 −𝑗𝜔𝑘𝑟
(1)
(2)
(3)
Reviewing the infinitesimal small dipole field equations the first thing observed is there
is only one H-field vector and two E-field vectors. The next item is at θ = 0 degrees only Er has
any magnitude. This shows that with a dipole antenna the E-field is the strongest component
strait out from the dipole antenna.
When comparing the dipole phasor equations 1- 3 to the equations 4 - 6 for a small loop
antenna, the primary component shown for the loop antenna is the H-field and the primary
component for the dipole is the E-field. Due to the requirement of inductive coupling using a
magnetic field the small loop antenna is required.
Small Loop Antenna Phasor Equations [17]:
k = Phase Constant =
2𝜋
𝜆
Io = Current through the antenna
Nt = Number of turns in the loop antenna
a = Area of the loop antenna
r = Distance from the center of the antenna
θ = Angle from the z-axis perpendicular to the center of the antenna
16
𝐸𝑟 = 𝐸𝜃 = 𝐻𝜙 = 0
𝐸𝜙 = [𝜂
(𝑘𝑎)2 𝐼𝑜 𝑁𝑡 sin(𝜃)
1
] [1 + 𝑗𝜔𝑘𝑟] 𝑒 −𝑗𝜔𝑘𝑟
4𝑟
(4)
𝑘𝑎 2 𝐼𝑜 𝑁𝑡 𝑐𝑜𝑠(𝜃)
1
] [1 + 𝑗𝜔𝑘𝑟] 𝑒 −𝑗𝜔𝑘𝑟
2𝑟 2
(5)
𝐻𝑟 = [𝑗𝜔
𝐻𝜃 = [−
(𝑘𝑎)2 𝐼𝑜 𝑁𝑡 sin(𝜃)
1
] [1 + 𝑗𝜔𝑘𝑟
4𝑟
1
− (𝑘𝑟)2 ] 𝑒 −𝑗𝜔𝑘𝑟
(6)
From the field vector equations for the small loop antenna it is observed that when θ = 0
degrees only Hr is present. Through this experiment the activation distance will be measured off
of the z-axis directly out from the loop antenna meaning θ will be 0 degrees. Only the H-field
should be seen on this axis.
Before these equations can be plotted in the time domain they must first find the
magnitude and phase and then these equations need to be converted to the time domain. To do
this first a constant is defined to simply the equation, for Hr is (7).
𝐴𝑟 =
𝑎 2 𝐼𝑜 𝑁𝑡 cos(𝜃)
2
(7)
With (7) defined, (5) can be simplified to:
𝐴
𝐻𝑟 = [𝑟3𝑟 + 𝑗
𝜔𝐴𝑟 𝑘
] 𝑒 −𝑗𝜔𝑘𝑟
𝑟2
(8)
Once the vector equation has been simplified, the real and imaginary parts can be isolated and
used to find the magnitude and angle equations shown in (9) and (10).
|𝐻𝑟 | =
𝐴𝑟
1
√
𝑟2 𝑟2
2
+ 𝜔 2𝑘 [𝑒 −𝑗𝜔𝑘𝑟+∠𝐻𝑟 ]
∠𝐻𝑟 = arctan(𝜔𝑘𝑟)
(9)
(10)
Now using the phasor to time converting tables the time domain equivalent equations are derived
[19].
|ℎ𝑟(𝑡) | =
𝐴𝑟
1
√
𝑟2 𝑟2
+ 𝜔 2 𝑘 2 cos(𝜔𝑡 − 𝜔𝑘𝑟 + ∠ℎ𝑟(𝑡) )
∠ℎ𝑟(𝑡) = arctan(𝜔𝑘𝑟)
(11)
(12)
17
The same derivation to convert the magnitude and angle from the phasor equation is
done to the other field vector equations shown in (13 - 16).
|ℎ𝜃(𝑡) | =
𝐴𝜃
√( 12
𝑟
𝑟
2
𝑘2
− 𝑘 2 ) + 𝜔2 𝑟 cos(𝜔𝑡 − 𝜔𝑘𝑟 + ∠ℎ𝜃(𝑡) )
(13)
𝑘
∠ℎ𝜃(𝑡) = arctan ( 1 𝜔𝑟 2 )
|𝑒𝜙(𝑡) | =
𝐴𝜙 𝑘
𝑟
√𝑘 2 +
∠𝑒𝜙(𝑡) = − arctan (
(14)
−𝑘
𝑟2
1
cos(𝜔𝑡
𝜔2 𝑟 2
− 𝜔𝑘𝑟 + ∠𝑒𝜙(𝑡) )
1
)
𝜔𝑘𝑟
(15)
(16)
Now that the equations are created the field vectors can be plotted with respect to
distance. In figure 3 the project antenna operation parameters are plotted and θ = 0 degrees.
Figure 3 Field magnitude θ = 0 degrees, taken at arbitrary t=1
18
Due to θ = 0 degrees the Eϕ and Hθ vectors zero out and only Hr is present. Due to Hr
being the only H-field component present the total magnitude of the H-field is equal to
the magnitude of the Hr vector.
Using the parameters from the created antenna and actual readings of the amount of current
found the plots shows little difference in magnitude but show the same trend at close proximity to
the antenna, where the magnetic field is stronger than the electric field shown in figure 4. As you
move away from the antenna the electric field takes over and becomes prominent in the far-field,
seen in figure 5.
Figure 6 displays a comparison of the 3 vectors when the approaching the antenna from the
side. This figure shows that Hθ is much stronger than Hr and dominates the overall magnitude of
the H-field.
Table 3 Field strengths at r = 3.146 inches
Theta (degrees)
0
45
90
E-field (V/m)
0
6.4 ∗ 10−6
9 ∗ 10−6
H-field (A/m)
84.68
59.88
0.3953
Also plotted is the power density, which works on the knowledge that the wave impedance
in the far-field is the same for both the electric and magnetic fields so the relationship equation
can be derived [20].
S = Power density (mW/cm2)
E = Electric field strength (V/m)
H = Magnetic field strength (A/m)
𝑆=
𝐸2
3770
= 37.7𝐻 2
19
Figure 4 Antenna field strength plot (near-field), taken at arbitrary t=1
20
Figure 5 Field strength comparison (far-field), taken at arbitrary t=1
21
Figure 6 Field strength comparison at θ = 90 degrees, taken at arbitrary t=1
22
By plotting the power density both the electric and magnetic field strengths could be
normalized and compared in the same units. This shows that in the reactive near-field the
magnetic power density is stronger but as you move out towards 0.1λ to 0.2 λ the power densities
of both fields coverage. This convergence is also highlighting were the far-field region begins
and the values are not affect by distance from the antenna.
Figure 7 Close up of normalized E and H-fields, taken at arbitrary t=1
Wave Impedance
As shown in the field stregth equations above the E-field and H-field have the same parameters
with the exception of there being a polynomial in the H-field equation and the intrinsic
impedance in the E-field equation. As the distance grows the polinomial in these equations
becomes neglegible compared to the intrinsic impedance, which only leaves η which for free
space is 377Ω [17].
Zw = Wave impedance
23
η = Intrinsic impedance of free space
𝑍𝑤 =
𝐸𝜙
≃𝜂
𝐻𝜃
Plotting the wave impedance shown in figure 8, the three radiation regions clearly appear.
As distance dramitically changes the power radiated is the near-field range. As the wave
impedance settles into the intrinsic impedance of free space this identifies the far-field range.
The reactive near-nield and radiating near-field are better demonstrated by figure 7
showing the comparison of the H-field vs E-field where the H-field is of greater strength. The
range for a loop atenna is about 0.16λ and with figure 7 it is observed that the field strengths
measured in power (mW/cm2) do begin to cross over in this range allowing the E-field to take
presedance over the H-field.
Figure 8 Wave impedance (1λ)
24
From the reactive near-field the transition begins to the radiated near-field as the H and Efield settle into the same power, which defines the far-field. Due to the dyamanic nature of the
field strengths between both the H and E-fields most texts prefere to operate in the far field while
deriving equations.
Radiation Pattern
The radiation pattern is the intensity that the power is radiated in watts per meter squared
from the antenna. This plot is derived to demonstrate the power intensity in the Far-Field range.
As radiated power is in all directions, the representation of the radiated power is usually plotted
three dimensionally to show the full dissipation pattern of the specific antenna.
The radiation pattern creates a donut like shape, where most of the power is radiated around
the coil. The direction of the loop turns determines which direction the field is radiating but
simply flipping the coil over reverses the direction.
The radiation pattern in figure 9 shows the far-field representation and demonstrates how the
radiated power stays near the antenna coil and creates a null in the middle of the antenna. In the
reactive near-field however, the magnetic field is stronger extending out from the coil and will
merge in the middle of the antenna. Since the loops are all in the same direction, all the flux of
the magnetic field is also in the same direction. As they merge in the middle they add to each
other’s strength. Thus in the reactive near-field a spike of magnetic field strength is observed in
the middle coming from the 0 degree and 180 degree. This will be the area of test for measuring
the effective read distance of the RFID device further on.
25
Figure 9 Radiation pattern loop antenna
Figure 10 Radiation pattern of a small loop antenna obtained from Matlab created by Milica
Markovic, Ph. D. and used with permission
26
Directivity
If the radiation pattern shows the power intensity in 3 dimensions, the directivity plot shows
in which direction the power is maximized. This plot gives a quick review of which direction the
majority of the power is dissipated.
With antennas this defines the transmission pattern of the antenna and helps identify if the
antenna is right for your application. Loop antennas have a focused uniform pattern. This is why
loop antennas are generally used in direction finding applications like radar or signal location.
When turning the antenna towards the signal, the full strength is observed but turning the antenna
by 90 degrees a null in signal strength is seen.
Antenna Resistance
To identify the current that will be flowing through the loop antenna, the resistance of the
antenna needs to be found. There are two different resistances that need to be taken into account;
radiation resistance and loss resistance, Rt = RL + RR.
Radiation resistance is used to represent the antenna’s resistance to radiating power, and is
often referred to as AC resistance. Based on the antenna design this parameter is defined in
different ways. For a small loop antenna the radiation resistance can be found with (17)[17].
Nt = Number of turns in the loop antenna
a = Area of the loop
λ = Wave length
𝑎2
𝑅𝑅 = 31,171 𝑁𝑡2 (𝜆4 )
(17)
The other resistance is conductor loss due to the current flowing through it. DC resistance
is very straight forward. Based on the size of the conductor and the conductivity (σ), the
27
resistance per meter can be computed. Once the conductivity is obtained, multiply it by the
length of the conductor in meters to get the DC resistance.
R = Resistance in ohms per foot
f = Frequency in hertz
d = Conductor diameter in inches
𝑅=
0.996∗10−6 ∗√𝑓
𝑑
(18)
R = Resistance in ohms per foot
f = Frequency in hertz
d = Conductor diameter in inches
works for a single loop antenna to estimate the total conductor loss but when there are
multiple loops resistance due to skin and proximity effect, needs to be taken into account. Skin
effect is a bit more complicated, and is an added resistance, because as higher frequencies are
applied to the conductor the current density through the conductor begins to change. This is
because when you have alternating current passing through a conductor, not only is an external
inductance observed but there is also an internal inductance to the conductor. This internal
inductance causes impedance in the conductor where the flux lines are densest As electrons
move through the area with least impedance the current density migrates to the outer edges of the
conductor. This reduces the surface area for current to move through causing resistance [23].
Skin depth and skin effect can be determined using (19) [26] and (20) [17].
2
𝛿𝑠 = √𝜔𝜇𝜎
𝜔𝜇
𝑅𝑠 = √ 2𝜎
(19)
(20)
Proximity effect is a main contributor to loss resistance of the conductor in the loop.
Because the loop has multiple turns and is tightly wound, you have mutual inductance induced on
28
one wire from the neighboring wires [26],[23]. This causes the current density to be pushed away
from the outer edge of the conductor. There is self-inductance, which pushes the current density
from the middle of the conductor to the outer edges and mutual inductance that is pushing the
current density away from side with a neighboring conductor. When there are multiple turns and
multiple layers most of the conductors have mutual inductance from all sides. This makes it very
difficult to calculate loss resistance in multi-turn multi-layer loop antennas.
There have been few experimental methods for deciphering the loss resistance of an electrically
small loop antenna. In a iEEE published paper by Glenn Smith [23], is one method outlined
below.
Rp = resistance due to proximity effect
𝑁𝑅
𝑅0 = 2𝜋𝑏𝑠
𝑅
𝑁𝑡 𝑎
) 𝑅𝑠 ( 𝑝
𝑏
𝑅0
𝑅𝑜ℎ𝑚𝑖𝑐 = (
+ 1)
(21)
Through multiple experiments it was found that as the number of turns in the loop increases
𝑅𝑝
𝑅𝑝
0
0
the 𝑅 ratio increases. At 2 turns the 𝑅 ratio is 0.3 and at 8 turns it is greater than 2.4. As you
increase the number of turns the ratio begins to converge at about 2.5 for small number of turns
(2-8). With this trend and the number of turns being 82 or more for the antennas in this project
𝑅
the 𝑅𝑝 ratio that will be used is 3.
0
Table 4 Calculated antenna resistances
Antenna
Loop
Radius
(a)
Manufactured 22.9mm
First Ant
63.5mm
Second Ant
63.5mm
Wire
Radius
(b)
0.030mm
0.065mm
0.163mm
𝑅𝑝
𝑅0
Turns
(Nt)
158
90
82
3
3
3
Rr
(nOhm)
RL
(Ohm)
Rdc
(Ohm)
Rtot
(Ohm)
0.027
1.35
1.35
45.41
33.32
12.08
11.50
8.44
3.06
56.91
41.76
15.14
29
Antenna Inductance
Inductance of a loop antenna is the most important parameter that needs to be followed since
it is used when tuning the antenna to the operating frequency of the device. Without knowing the
inductance of the antenna a tuning capacitor cannot be chosen to create a resonance at the
operating frequency.
Initially the equation that was used to determine the inductance of the antenna was [17].
a = Radius of loop in meters
b = Radius of conductor in meters
Nt = Number of turns in the loop
8𝑎
𝐿𝐴 = 𝜇0 𝑎𝑁𝑡2 [ln ( 𝑏 ) − 2]
(22)
When this equation was used to determine the inductance against the manufactured antenna,
the values did not compare to the inductance the manufacturer stated or were measured by a
4251A LRC meter, manufactured by Hewlett Packard.
Researching the equation of antenna inductance uncovered that much like multiple turns
and multiple layers that makes finding the conductor loss complicated due to proximity of other
conductors nearby, the inductance is just as complicated. Searching for another method to
calculate antenna inductance while taking into consideration the multiple rows and multiple
layers an online calculator was discovered with the following (23) [22]:
a = Loop radius in inches
Nt = Number of loops in the antenna
l = The thickness of the antenna coil from back to front
d = The thickness of the antenna coil from outside to inside
0.8(𝑎 2 ∗𝑁2 )
𝑡
𝐿𝐴 = 6𝑎+9𝑙+10𝑑
(23)
30
While trying to use this equation with the manufactured antenna parameters it was soon
learned that the number of turns was not documented. The cross section of the coil was
determined and the cross section of the wire was measured and calculated to obtain an estimate of
how many conductors are in one cross section of coil. Once the two cross sectioned areas were
found, it was then calculated how many conductors would fit into the coil cross section. This
resulted in 766 turns in the manufactured coil and applying that along with the other physical
parameters into (23), the inductance result was 59mH. This was much higher than the 2.8 mH
specified by the manufacture.
After this experiment did not yield solid evidence for a functional equation, it was decided
to create an antenna that would have similar inductance. The (23) determined the parameters
required to get 2.54 mH. After the antenna was created with a known number of turns and
measured dimension, the resulting measured inductance was 2.65 mH.
These results were satisfactory to use in the equation to determine the antenna inductance
and from the measured inductance of the manufactured antenna of 1.316mH, the number of turns
was calculated to be 158 and will be the value used for the manufactured antenna from here on.
Two other antennas were created and using this inductance equation they both demonstrated
similar results further proving the inductance equation being used.
Table 5: Calculated versus measured antenna inductance
Antenna
Dia.
(In)
Loop
Radius
(In)
Depth
(In)
Len
(In)
Manufactured
1.802 0.9295
0.057
First Ant
Second Ant
Experiment
5.017 2.5385
5.017 2.5985
5.017 2.626
0.06
0.18
0.235
Conductor
Radius (In)
Calculated
Inductance
(uH)
Measured
Inductance
(uH)
0.053 0.00118
2605
2540
0.068 0.00255
0.32 0.0064
0.169 0.00255
2540
1792
56918
2650
1316
59300
31
Electrical Model
A loop antenna has an interesting frequency response. As expected at lower frequencies a
loop antenna which is essentially a coil of wire is inductive. When the frequency expands across
the threshold in to the higher frequencies it becomes capacitive.
Below is a plot on the smith
chart of the second antenna, which is the antenna used for this project. Unfortunately the network
analyzers available did not go below 300kHz, so the frequency response of the antenna at the
operating frequency could not be read.
Figure 11 Network analyzer 300kHz to 20MHz, loop antenna
The setup of the network analyzer was a 50Ω connector cable that connected to a SMB
connector that was plugged into a breadboard for ease of switching antennas. The test cable was
calibrated at the point where it connected to the breadboard. This took the test cable out of the
frequency response of the antenna due to the length of the transmission line.
Both the smith chart showing input impedance versus frequency response and the reflection
magnitude versus frequency where observed using the network analyzer. The network analyzer
32
was not made to test very low frequencies (VLF) or LF ranges, the bandwidth could not be
obtained using this device. What was seen however was this antenna had a natural frequency
response at about 11MHz. This is where the large dip in reflection occurs in figure 12 and in
figure 11 were the frequency response nearly reaches the middle of the smith chart. This means
the antenna resistance at 11 MHz is nearly 50Ω, which matches the transmission line delivering
the power and will allow the loop antenna to accept the most power.
Figure 12 Network analyzer setup
The reading shown in figure 12 was done with the antenna by itself and not with the tuning
capacitor in series. With a tuned capacitor in series the antenna response will tune to the operating
frequency and matching the antenna to the circuit.
Based on the frequency response observed from the network analyzer a ADS model was
created to attempt to simulate the same frequency response in the lower frequency ranges and
show the response for the operating frequency.
33
Because the response shows the impedance crossing the infinite impedance side of the smith
chart, a inductor and capacitor in parallel were used. This also aligns with what is known about
inductors and capacitors, being that LF inductors are a short and capacitors are an open. For HF
inductors are an open and capacitors are a short. If there is a capacitor and inductor in series at a
low frequency this would be seen as an open. A coil of wire at low frequency is measured as a
short, so this would not be the case and aligns with the inductor and capacitor in parallel.
The series resistor is the DC resistance of the loop antenna as measured by a 37XR-A digital
multi meter. The inductor, resistor, and capacitor (LRC) circuit is designed by the antenna
inductance. The resistance seen as the impedance plot cross the real axis of the smith chart, and
the capacitance is derived from the 𝑓 = 2𝜋
impedance cross the real axis.
Figure 13 ADS model loop antenna
1
√𝐿𝐶
equation, taken at the frequency were the
34
Figure 13 shows the ADS model created and will be used to simulate the frequency response
by mimicking the plots shown on network analyzer but trying to show the lower frequency range.
Since the lower frequencies are what needs to be plotted, the simulation is going to about were
the impedance is expected to cross the real axis on the smith chart. With the project antenna this
point was about 1.2MHz and so 2MHz was chosen for the S-parameter simulation frequency
response range.
Figure 14 is the magnitude plot of the reflection and shows a drop off at about 60 kHz. This
does not support the application as a operating frequency of 134.2kHz is needed. Shown on the
smith chart in figure 15, the frequency that is crossing the real axis aligns with the LC circuit
chosen and has the real impedance of 32.046*50 = 1.6 kOhm. This demonstrates the higher
frequency response found with the network analyzer and by applying R1 in series provides the
DC resistance at the lower frequency response. The entire response between 0Hz and 1.2MHz is
inductive but 134.2 kHz appears very close to the to the real axis which does not match the
network analyzer plot in figure 11 showing 300kHz higher on the impedance curve. This implies
that there are other elements not taken into consideration that would cause a loop to appear on the
smith chart in lower frequency response ranges. This is difficult to model without a full
frequency response obtained from the network analyzer.
35
Figure 14 ADS magnitude frequency response, loop antenna 300kHz to 2MHz
Figure 15 Smith Chart loop antenna 300kHz to 2MHz
Continuing with the same model but applying the tuning capacitor into the circuit to mimic
the resonating operating frequency being used, the plots set a better example.
36
Figure 16 ADS model tuned loop antenna
The magnitude plot in figure 17 shows a dip at the frequency range of 134.1kHz which is the
operating frequency needed for the application. A tuning capacitor of 1.3 nF was put in series
with the antenna to obtain these results. With the capacitor in series the lower frequencies will
show as an open and is why the smith chart in figure 18 shows the impedance response bunched
up near the open circuit side of the chart.
The real part of impedance seen at 134.2kHz continues to be the same with and without the
tuning capacitor and is 10.642*50 = 532.1 Ohms which does not follow suite with the calculated
and measured impedance of the antenna at the operating frequency.
Even though the model did not accurately depict the antenna being used, by reviewing the
network analyzer response and the ADS plots information was gathered as to how a loop antenna
would respond. The theory of operation is still held with this simulation.
37
Figure 17 ADS magnitude frequency response, tuned loop 300kHz to 2MHz
Figure 18 ADS Smith Chart tuned loop antenna 300kHz to 2MHz
38
FCC and iEEE Regulations for Radio Frequency Transmissions
Due to this project transmitting electromagnetic waves at an increased power the FCC and
iEEE regulations needed to be observed for maximum emissions exposure.
The FCC does not have any regulations for maximum exposure levels below 300 kHz and
because our operating frequency range is 124 ~ 135kHz there are no restrictions applied. Table 6
shows the maximum allowed exposure for an expressed period of 6 minutes. The FCC also does
not require routine evaluations for LF transmitters. The lowest frequency range that the FCC will
require routine evaluations on is 1.857 MHz transmitting at more than 500 watts.
Table 6 FCC Maximum Permissible Exposure (MPE) [20]
Table 7 FCC Power thresholds for routine evaluation [27]
39
In reviewing the iEEE standards, the plotted chart extends to the 3kHz range. Highlighted in
red are the maximum levels for the operating frequency range applied in this project. The H-field
cannot exceed about 200 A/m and the E-field cannot exceed 600 V/m. These values are well
above the transmitted power shown in the previous section for the E and - field strengths.
Figure 19 iEEE safety levels for electromagnetic fields [27]
Table 8 is just an example of some every day products that consumers use, exposing
themselves to magnetic fields. The RFID reader in this project will be operating at its optimum
performance, emitting approximately 2000 milligauss, which is the same as blow drying your hair
in the morning.
40
Table 8 Very low frequency common appliances electromagnetic field strengths [27]
41
Chapter 5
ANTENNA CREATION AND ACTUAL DATA
Designing Antenna for Application
The RFID reader design chosen to be used for this project was RFIDRW-E-232 made by
Priority 1 Design. There are 3 basic parts to this device; the EM4095 by EM Microelectronic, a
Atmel microprocessor FPGA to process the signal and control logic, and a 95ALRA4M by Texas
Instruments to uplink with a RS232 serial port [15].
Figure 20 Schematic of RFIDRW-E-232 for tuning the EM4095
42
The EM4095 is the primary component focused on for this project. The EM409 is the
transceiver chip for LF RFID devices and follows the ISO standards 11784 & 11785 protocols
[16]. Figure 20 shows a simple circuit for this component and the outside factors that need to be
applied for the specific type of RFID devices being read. The EM4095 is configured in the
read/write mode with the option for low or high Q external antenna.
There are three parameters that need to meet specification. The current cannot exceed
200mA peak, Va cannot exceed 250V p-p, and Vr Vp-p cannot exceed 2 * the common mode
voltage of Vr. The equations to calculate Va and Vr are shown in (24) and (25) [15].
𝑉𝑎(𝑝−𝑝) = 𝑓 𝐶
2
(24)
0 𝑅 (𝑅𝐴𝑛𝑡 +6
𝑉𝑟(𝑝−𝑝) = 𝑉𝑎(𝑝−𝑝) ∗ (𝐶
(𝐶𝑑𝑣1 +𝐶𝐷 )
𝑑𝑣1 +𝐶𝐷 )+𝐶𝑑𝑣2
(25)
The higher the current, the stronger the field radiated from the antenna, maximizing the
effective read distance. In the RFIDRW-E-232 datasheet circuit equations were simplified [15].
𝑅𝐴𝑛𝑡 = 𝑅 𝑅 + 𝑅𝐿 + 𝑅𝑠
𝐼𝑎 (𝑝𝑒𝑎𝑘) = 𝑅
6.37
𝐴𝑛𝑡 +6
(26)
(27)
The total resistance of the antenna is calculated from (26) and is described in the antenna
resistance section shown in (17) thru (21). Rs is external resistance applied in series and is only
used if the antenna resistance is not high enough to keep Va within 250Vp-p so the EM4095 is
not being over driven. Ideally, there would be no external resistance used when applying an
antenna.
The first parameter that is required is the operating frequency of the RFID device being read
which 134.2kHz is what is used for this project. This is determined by (28) [15]:
𝑓𝑜 =
1
2𝜋√𝐿𝐴 𝐶𝑅
(28)
43
The design of this device seen in figure 20 is made to put external capacitance in parallel
with the internal capacitance already in the circuit. This means that the capacitance can only be
raised not decreased. To decrease the capacitance, external capacitance will have to be added in
parallel, which will reduce the power delivered to the antenna and is not desirable. With 517pF
being the minimum capacitance available the maximum inductance in the antenna is 2.72mH.
The magnetic field strength identified in Equations 4 thru 6 can be increased in three ways;
increasing current, increasing number of turns, or increase the area of the loop.
The area of the loop is squared compared to the current and the number of turns. The first
parameter will be increasing the area of the loop but not so large that it will not be practical in an
end application. A 5 inch diameter loop was chosen because it doubles the size of the
manufactured antenna. It is still a reasonable size antenna to use in most reader applications and
a CD spindle case will work nicely to use as a circular surface to wrap the wire around to keep the
antenna’s form.
With the current dependent on the total resistance which is directly related to the number of
turns and increasing inductance. It was difficult to take into account all the parameters to define
an optimum antenna. An excel spreadsheet model was created to link all of these factors together
using the equations shown in this project, this excel model can be located in appendix C. This
allows the manipulation of the various values that can be modified and view what impacts the
changes will have in the end result.
After modifying the values keeping the radius of the loop at 2.5 inches, 2.5mH was chosen
because it is below the 2.72mH maximum; given the internal capacitance stated by the data sheet
will have a tolerance of error [15]. This inductance required a 90 turn 2.5 inch radius antenna and
was created out of 32 gauge wire. The 32 gauge wire was used at first because the smaller the
44
wire the less effect the skin effect would have due to the skin depth being greater than the radius
of the wire.
Creation of the Antenna Based on Inductance Chosen
The first antenna attempt was using the 2.5mH design parameters obtained from the excel
model located in appendix C. To do this, the length and depth of the antenna need to be
approximate to the design parameters if the correct inductance is going to be obtained. A rubber
PVC pipe fitting was used to create a channel for the wire to be guided along and this channel
was measured with a micrometer to achieve the best results.
Figure 21 Using a CD spindle to hold the circular shape of the antenna
After the antenna was wound, the rubber fitting was removed. The shape of the antenna
shifted subtly but still would be considered a multiple layer multiple row coil.
45
Figure 22 Measuring the first antenna
Before the antenna was completely removed from the spindle the inductance was read. The
design was created for a 2.5mH and the inductance measured was 2.595mH. This demonstrated
that the inductance equation used was correct. This experiment was done before the excel model
was finalized to validate the inductance equation being used. The loop antenna was slid off the
spindle but because the wires were so thin it became very flexible and the loops did not hold the
uniform shape as it did on the spindle. Tape was used approximately every inch around the loop
to hold the shape for further testing.
The resulting first antenna was very close to the maximum inductance, so another antenna
was designed. This time 2mH was targeted and to have variation to the measurements 24 gauge
wire was chosen instead of 32 gauge wire. This was done to observe the difference in design but
also to create greater stability and hold less conductor resistance, as the skin effect shown was
very minimal compared to the proximity effect caused resistance. Less total resistance means
more current allowed through the antenna.
Learning from the first antenna in how it did not hold its shape, in creating the second
antenna only one layer was done at a time and a layer of nail polish was used to hold them
46
together. Nail polish was chosen because it would not stick to the rubber, the space it would
leave between the conductors is negligible, and it dries quickly. Once all the turns were complete
the antenna was left to dry and then removed from the mold the next day.
Measure Antenna Parameters
First the inductance was calculated based on the physical parameters measured with a
micrometer after the final product was created. These measurements were recorded in inches
because the inductance found using (23) is calculated using inches for the different dimensions.
Table 9 Measured antenna inductance
Radius
Avg
Antenna
(Inch)
Manufactured 0.9295
First Ant
2.5385
Second Ant
2.5985
Depth
(Inch)
0.057
0.06
0.18
Length
(Inch)
0.053
0.068
0.32
Conductor
Radius (inch)
0.001181102
0.002546479
0.006398781
Turns
158
90
82
Calculated
Inductance
(uH)
2605
2540
1792
Measured
Inductance
(uH)
2540
2650
1316
Due to the parameters not being exact for the second antenna, after it was removed from the
spindle the physical measurements of the depth and length were a slightly different. This caused
the calculated inductance to be 1.8 mH instead of 2 mH after true measurements were taken using
a micrometer.
Using the 4261A LRC meter to measure the inductance at 1kHz, the measured inductance
was found to be close to the calculated inductance based on the physical parameters of the
antenna. There was no measurable capacitance at 1kHz which aligns with the models shown in
figure 11 thru 18. A small loop antenna will not exhibit capacitance until the frequency reaches
in the megahertz range.
The DC resistance was measured for each of the antennas, which highlights the point that the
radiation resistance is negligible compared to the total loss resistance of the antenna. The
operating frequency being only 134.2kHz, the radiation resistance is not a factor.
47
Table 10 Measured antenna resistance
Antenna
Loop
Radius
(a)
Manufactured 22.9mm
First Ant
63.5mm
Second Ant
63.5mm
Wire
Radius
(b)
0.030mm
0.065mm
0.163mm
Turns
(N)
158
90
82
𝑅𝑝
𝑅0
7
10
18
Rr
RL
(nOhm) (Ohm)
Rdc
(Ohm)
Rtot
(Ohm)
0.027
1.35
1.35
62.3
20.2
2.6
153.11
121.84
59.99
90.81
91.64
57.39
After reviewing the peak current measured and working back to identify what the antenna
resistance should have been, a new
𝑅𝑝
𝑅0
ration was determined. The analysis done by Glenn Smith
𝑅
highlighted that as the number of turns of the antenna increases, the 𝑅𝑝 ratio should also increase
0
[23]. This was not observed by taking the current and backing out to the required antenna
resistance to achieve that current using the excel model. Which either means the peak current
measured by the 37XR-A multi-meter is not accurate or the experimental method used does not
apply for large winding antennas.
Fine-tuning the Operating Frequency
Once the antennas were created and the inductance measured the capacitance could be
derived to make the operating frequency of 134.2kHz. The RFID reader has a test point to
measure the operating frequency because this operating frequency is also the clock used for the
microprocessor in the circuit.
48
Figure 23 RFID reader measuring tuned frequency
Table 11 Antenna tuning capacitance
Antenna
Manufactured
First Antenna
Second Antenna
Measured
Inductance
(mH)
2.54
2.65
1.316
Calculated
External Tuning
Capacitance
(pF)
36.7
13.7
551.8
External
Capacitance
Series or
Parallel
N/A
Series
Parallel
Actual
External
Capacitance
(pF)
0
1007
430
Measured
Operating
Frequency
(kHz)
130.4
131.3
133.5
The calculated tuning capacitance predicted that both the manufactured and first antenna
would be able to obtain the correct operating frequency without external capacitance added. This
was true for the manufactured antenna but the first antenna’s inductance proved to be too large
for the built in capacitance and resonated at 113 kHz instead of the required 130+kHz. A
capacitor in series was needed with the first antenna, to obtain the correct operating frequency so
49
read distance performance could be compared. The second antenna was well below the
maximum inductance so adding external capacitance in parallel was easily done to obtain an
accurate resonating frequency. Figure 24 shows the operating frequency tested using the setup
shown in figure 23. Once the best frequency was obtained for each antenna the results were
recorded in table 11.
Actual Measurements
Once the operating frequency was obtained the next step was measuring the Va and Vr in the
circuit to optimize the power being delivered to the antenna. Vr has a common mode of 2.4V
which means that a signal carried on this common mode cannot exceed 2 times this value without
being in danger of clipping and cause the EM4095 to be unable to decipher the received signal.
The documentation from Priority 1 Design states not to exceed 4 Vp-p at Vr to be safe [15].
When using the test setup in figure 27 to measure Vr peak to peak, the external resister (Rs) was
replaced with a 100 Ω 20 turn potentiometer. This allowed for a small change in Rs to affect the
power being delivered to the antenna. By adjusting Rs to adjust Vr to a value of 4V p-p
(observed in figure 25), the maximum power will be delivered to the antenna for each design.
Both the manufactured and second antenna were adjusted to use the same value of Vr to help with
the comparison between the 2 antennas.
50
Figure 24 Frequency test point measurement of second antenna
Figure 25 Vr measurement while adjusting Rs
51
The results can be found in table 12 for all the measured parameters. Note that the first
antenna could not exceed 2.32 Vp-p at Vr because without Rs in the circuit the maximum power
was already being delievered for this antenna. The reason there was a lack of power pushed
through the first antenna is because to obtain the correct operating frequency a tuning capacitor
was required in series with the built in capacitor causing a decay of power delivered to the
antenna.
Table 12 Measured values of operating circuit
Antenna
Manufactured
First Antenna
Second Antenna
Ia Peak (mA)
48.26
61.56
87.74
Va (Vp-p)
196
180
204
Vr (Vp-p)
3.75
2.32
3.77
Rs (Ohm)
26
0
9.4
By adjusting Rs and focusing on Vr due to the fixed capacitor divider built into the circuit, a
4 Vp-p observed on Vr would be the maximum voltage output on Va allowed.
Figure 26 Measurement of Va
52
Measuring Activation Distance
Now that the circuit is tuned to the optimum operating effectiveness for each antenna, the
read distance is measured. The device has a bi-color LED installed to indicate when a passive LF
RFID device is recognized by the microprocessor. This LED does not stay green while a good
read is in place, instead it flashes green for 1 pause cycle of 20 ms. This is why the LED is
always observed as red in the figures shown.
By taking a LF RFID microchip and slowly lowering it in the middle of loop antenna until
the indicator flashes green, a activation distance can be read with the micrometer. This can be
observed in figure 27. Table 13 recorded the distance that each antenna obtained a verified read
from the RFIDRW-E-232.
Table 13 Distance and field measurements
Antenna
Manufactured
First Antenna
Second Antenna
Distance (Inch)
2.053
2.564
3.123
H-Field (mV)
70.4
68.6
108
E-Field(mV)
76
33
42
As the RFID microchip approached the antenna on the z-axis, the validation LED was
observed. With the activation and transmission time at 50ms, a slow approach must be made to
assure the maximum distance is recorded. As shown in figure 27, a read distance for the second
antenna was 3.086 inches. Measuring the distance was done multiple times to identify an average
read distance. A the RFID microchip was attached to a small piece of scotch tape and then when
the validation light would flash it was attached to the plastic stick. This was done so that accurate
measurements could be taken of the read distance.
53
Figure 27 Device Measurement Test Setup
Field Measurements
While the equipment was setup some electric and magnetic field measurement devices were
used to observe the magnetic and electric field strengths.
54
Figure 28 Electric field test probe (top left), Magnetic field test probe for (bottom left),
Combined probes (right)
To measure the H-field, a coax cable was used to create a loop, and the inside conductor
was grounded to the shielding of the cable to terminate the loop. To allow field measurements a
notch was cut in the dielectric half-way at the most extreme of the loop. To measure the E-field a
exposed oscilloscope probe was used to mimic a coax cable with ¼” of the conductor (probe tip)
exposed [28]. A close up of the probes used are shown in figure 28.
55
Figure 29 Field measurement test setup
56
Figure 30 Measured field strengths of second antenna at activation r = 3.148"
The 2 probes were put to channel 1 and 2 of the Oscilloscope so the fields could be
compared to each other at the same time. The E-field observed was capturing excessive
interference from surrounding equipment so markers were used to try and capture a more accurate
value from the screenshot.
Table 14 Measured H and E fields
Antenna
Distance (Inch)
Manufactured
First Antenna
Second Antenna
1
282
155
300
H Field (mV)
2
3
82.2
23.6
94
56.2
187
107
1
154
49
72
E Field (mV)
2
3
82
17.2
38
31
84
72
What was observed is that the E-field is stronger than the H-field in this reactive near-field.
This corresponds with the field plots in figure 3 thru 6, where the E-field did not over power the
H-field until greater than 5 inches. The H-field also does have a more dramatic fall then the E-
57
field does for all antennas, which also proves the field equations. These measurements are not
completely accurate because measuring the fields in this extreme reactive near-field is very
erratic and the probes used are not of industry quality. This experiment however does
demonstrate the field relationships between the H and E-field strengths.
The H-field probe loop will vary on the field strength obtained if the loop is rotated 90
degrees from the loop antenna and if the probe loop is flipped 180 degrees a 180 degree shift will
be observed on the oscilloscope compared to the E field probe. The measurements in figure 30
show that the E and H-fields are in phase. The phases plotted in figure 3 thru 6 shows that the E
and H-fields are 180 degrees out of phase. Due to how the H-field probe measures magnetic field
strength, the orientation of the loop in comparison to the antenna is very important. If the loop
probe is rotated so that the induced current is flowing in the opposite direction then that of the
antenna itself, a 180 degree phase shift will be seen on the H-field measurements. The E-field
probe is not affected as long as the probe is just rotated but stays parallel to the antenna. If the Efield probe is put on the z-axis the measurements observed would be much smaller.
Once the measurements are taken they need to convert to A/m and V/m to allow for a
comparison with the simulations plotted in figure 3 thru 6. The way to calculate the H-field
strength is to take the Vp-p received from the oscilloscope and find out how much magnetic field
was required to pass through the loop probe to induce such a voltage.
In (29) this method has been derived using [29]:
V0 = Peak to peak voltage seen on oscilloscope from loop probe
a = Area of the loop probe
Nt = Number of turns on the loop probe, the one created was only 1 turn
|𝐻𝑎𝑣 | =
𝑉0 ∗107
4𝜋𝑎𝑁𝑡 𝜔
(29)
58
Table 15 Calculated and actual H-field, r=3.146 inches
Second Antenna
Calculated
E-field (V/m)
H-field (A/m)
0
82.27
Measured
(mV)
42
108
Measured in correct
units (V/m, A/m)
N/A
52.18
Operating frequency
(kHz)
133.5
133.5
The E-field cannot be reliably measured in the near-field range and is calculated off Hfield measurements in the far-field using the intrinsic impedance relationship between the E and
H-field [29]. The measurements made by hand and that found in the plot in figure 3 came very
close. There are a lot of factors that would affect the reactive near-field measurements and the
results found are very good considering these hurdles.
59
Chapter 6
POSSIBLE APPLICATIONS
Maximizing the read distance for a low frequency RFID reader can be used for many
applications, such as in a veterinarian’s office. As the pets are brought into the waiting room
their RFID chip could be read, and the pet’s medical records and owner information could be
expedited for the receptionist. RFIDs have been used for security authorization for many years,
allowing authorized personnel into the appropriate buildings. Using existing RFIDs in household
pets, this technology could be applied to allowing authorized pets entrance through an exterior pet
door. For these applications to work correctly, a larger read distance would be required than the 3
inches obtained in this project.
60
Chapter 7
CONCLUSION
This project reviewed the history of RFID technologies and then specifically as it applies to
household pets. The original intent was to obtain a 6 to 9 inch activation distance by modifying
the design of a small loop antenna to maximize the read distance. As with the device selected this
was not achieved due to insufficient driving power, limited to built-in design values, complicated
operating resistance due to proximity and skin effects of the coil and the quick fall of observed
for the magnetic field strength.
Reviewing the device used, the EM4095 is a very good starting component for low
frequency RFID readers but in the future it would have been better to obtain the EM4095
separately and redesign the device. This would allow more freedom of design with the
inductance and tuning capacitance. A single layer multi turn antenna with a ferrite core would
strengthen and focus the magnetic field possibly allowing a farther reading distance to be
obtained. Also other antennas may be researched to help with the read distance like a folded
antenna or a Helmholtz coil antenna, both of which were not used in this project because of their
size not being practical for the application.
The value of this project was the knowledge gained testing the different antenna designs and
perfecting the models to help simulate small loop antenna designs in the future for any
application requiring this type of antenna.
61
APPENDIX A
Field Equation Conversion Math
Small Loop Antenna:
Converting Hr to hr(t):
𝐴𝑟 =
𝑎 2 𝐼𝑜 𝑁𝑡 cos(𝜃)
2
𝐻𝑟 = [
𝐴𝑟
𝜔𝐴𝑟 𝑘
+ 𝑗 2 ] 𝑒 −𝑗𝜔𝑘𝑟
3
𝑟
𝑟
|𝐻𝑟 | =
𝐴𝑟 1
√ + 𝜔 2𝑘2 [𝑒 −𝑗𝜔𝑘𝑟+∠𝐻𝑟 ]
𝑟2 𝑟2
∠𝐻𝑟 = arctan(𝜔𝑘𝑟)
|𝒉𝒓(𝒕) | =
𝑨𝒓 𝟏
√ + 𝝎𝟐 𝒌𝟐 𝐜𝐨𝐬(𝝎𝒕 − 𝝎𝒌𝒓 + ∠𝒉𝒓(𝒕) )
𝒓𝟐 𝒓𝟐
∠𝒉𝒓(𝒕) = 𝐚𝐫𝐜𝐭𝐚𝐧(𝝎𝒌𝒓)
Converting Hθ to hθ(t):
𝐴𝜃 =
𝑎 2 𝐼𝑜 𝑁𝑡 sin(𝜃)
4
𝐴
𝐻𝜃 = [ 𝑟3𝜃 −
|𝐻𝜃 | =
𝐴𝜃 𝑘 2
𝑟
𝐴𝜃
√( 12
𝑟
𝑟
𝐴 𝑘
2
𝐴𝜃 𝑘 2
𝑟
𝐴 𝑘
+ 𝑗 𝜔𝑟𝜃 2 ] 𝑒 −𝑗𝜔𝑘𝑟
𝑘2
− 𝑘 2 ) + 𝜔2 𝑟2 [𝑒 −𝑗𝜔𝑘𝑟+∠𝐻𝜃 ]
∠𝐻𝜃 = arctan ( 1
𝑘
𝜔𝑟
𝑟2
|𝒉𝜽(𝒕) | =
𝐴
𝜃
−𝑗𝜔𝑘𝑟
− 𝑗𝜔𝑟
= [ 𝑟3𝜃 −
2] 𝑒
−𝑘 2
)
𝟐
𝑨𝜽
𝟏
𝒌𝟐
√( − 𝒌𝟐 ) +
𝐜𝐨𝐬(𝝎𝒕 − 𝝎𝒌𝒓 + ∠𝒉𝜽(𝒕) )
𝟐
𝒓
𝒓
𝝎𝟐 𝒓
∠𝒉𝜽(𝒕) = 𝐚𝐫𝐜𝐭𝐚𝐧 (
𝒌
𝝎𝒓
𝟏
− 𝒌𝟐
𝒓𝟐
)
62
Converting Eϕ to eϕ(t)
𝐴𝜙 = 𝜂
𝐸𝜙 = [
𝑎 2 𝐼𝑜 𝑁𝑡 sin(𝜃)
4
𝐴𝜙 𝑘 2
|𝐸𝜙 | =
𝑟
𝐴 𝑘
𝜙
−𝑗𝜔𝑘𝑟
+ 𝑗𝜔𝑟
=[
2] 𝑒
𝐴𝜙 𝑘 2
𝑟
𝐴 𝑘
𝜙
−𝑗𝜔𝑘𝑟
− 𝑗 𝜔𝑟
2] 𝑒
𝐴𝜙 𝑘
1
√𝑘 2 + 2 2 𝑒 −𝑗𝜔𝑘𝑟+∠𝐸𝜙
𝑟
𝜔 𝑟
∠𝐸𝜙 = − arctan (
|𝒆𝝓(𝒕) | =
1
)
𝜔𝑘𝑟
𝑨𝝓 𝒌
𝟏
√𝒌𝟐 + 𝟐 𝟐 𝐜𝐨𝐬(𝝎𝒕 − 𝝎𝒌𝒓 + ∠𝒆𝝓(𝒕) )
𝒓
𝝎 𝒓
𝟏
∠𝒆𝝓(𝒕) = − 𝐚𝐫𝐜𝐭𝐚𝐧 (
)
𝝎𝒌𝒓
Infinitesimal Dipole:
Converting Hϕ to hϕ(t)
𝐴𝜙 =
𝐼𝑜 lsin(𝜃)
4𝜋
𝐴𝜙
𝐴𝜙 𝜔𝑘 −𝑗𝜔𝑘𝑟
𝐻𝜙 = [
+𝑗
]𝑒
𝑟^2
𝑟
|𝐻𝜙 | =
𝐴𝜙 1
√ + 𝜔 2 𝑘 2 𝑒 −𝑗𝜔𝑘𝑟+∠𝐻𝜙
𝑟 𝑟2
∠𝐻𝜙 = arctan(𝜔𝑘𝑟)
|𝒉𝝓(𝒕) | =
𝑨𝝓 𝟏
√ + 𝝎𝟐 𝒌𝟐 𝐜𝐨𝐬(𝝎𝒕 − 𝝎𝒌𝒓 + ∠𝒉𝝓(𝒕) )
𝒓 𝒓𝟐
∠𝒉𝝓(𝒕) = 𝐚𝐫𝐜𝐭𝐚𝐧(𝝎𝒌𝒓)
63
Converting Er to er(t):
𝐼𝑜 𝑙𝑐𝑜𝑠(𝜃)
2𝜋
𝐴𝑟 = 𝜂
𝐸𝑟 = [
𝐴𝑟
𝐴𝑟
𝐴𝑟
𝐴𝑟
+
] 𝑒 −𝑗𝜔𝑘𝑟 = [ 2 − 𝑗
] 𝑒 −𝑗𝜔𝑘𝑟
2
3
𝑟
𝑗𝜔𝑘𝑟
𝑟
𝜔𝑘𝑟 3
|𝐸𝑟 | =
𝐴𝑟
1
√1 + 2 2 2 𝑒 −𝑗𝜔𝑘𝑟+∠𝐸𝑟
2
𝑟
𝜔 𝑘 𝑟
∠𝐸𝑟 = − arctan (
|𝒆𝒓(𝒕) | =
1
)
𝜔𝑘𝑟
𝑨𝒓
𝟏
√𝟏 + 𝟐 𝟐 𝟐 𝐜𝐨𝐬(𝝎𝒕 − 𝝎𝒌𝒓 + ∠𝒆𝒓(𝒕) )
𝟐
𝒓
𝝎 𝒌 𝒓
∠𝒆𝒓(𝒕) = − 𝐚𝐫𝐜𝐭𝐚𝐧 (
𝟏
)
𝝎𝒌𝒓
Converting Eθ to eθ(t):
𝐴𝜃 = 𝜂
𝐼𝑜 lsin(𝜃)
4𝜋
𝐸𝜃 = [𝑗
𝜔𝐴𝜃 𝐴𝜃
𝜔𝐴𝜃
𝐴𝜃
𝜔𝐴𝜃 𝜔𝐴𝜃
+ 2 − 𝑗 2𝑟3 ] 𝑒 −𝑗𝜔𝑘𝑟 = [ 2 + 𝑗 (
− 2 3 )] 𝑒 −𝑗𝜔𝑘𝑟
𝑟
𝑘𝑟
𝑘𝑟
𝑟
𝑘 𝑟
𝑘
|𝐸𝜃 | =
𝐴𝜃 1
𝜔 2
√ 2 + (𝜔 − 2 2 ) 𝑒 −𝑗𝜔𝑘𝑟+∠𝐸𝜃
𝑟 𝑟
𝑘 𝑟
∠𝐸𝜃 = arctan (𝜔𝑘𝑟 −
|𝒆𝜽(𝒕) | =
𝜔
)
𝑘𝑟
𝑨𝜽 𝟏
𝝎 𝟐
√ + (𝝎 −
) 𝐜𝐨𝐬(𝝎𝒕 − 𝝎𝒌𝒓 + ∠𝒆𝜽(𝒕) )
𝒓 𝒓𝟐
𝒌𝟐 𝒓𝟐
∠𝒆𝜽(𝒕) = 𝐚𝐫𝐜𝐭𝐚𝐧 (𝝎𝒌𝒓 −
𝝎
)
𝒌𝒓
64
APPENDIX B
Matlab Code
%Created By Walter Imfeld 5/2/11
%Thesis Project
%Signal Power requirement equations
clc
clear all
freq=134200 %Hz
I=0.08774%0.04823%0.08915%0.03129%
b=2.5*0.0254%0.023885%
Nt=82%90%Lamda*0.085/(2*pi*b)% Number of turns in the loop
len=Nt*(2*pi*b)%For dipole plot comparison, making dipole length same
as length of conductor in loop
PosAng = 0%0%pi/4% %Angle of position compared to center of loop
t=1 %time in seconds
Lamda=3*10^8/freq
r=[0:0.0001:0.5*0.0254];% Distance meters for near-field plot
r2=[0:1:Lamda];%12*0.0254]; %Distance in meters for far-field plot
Lamda is 1 wavelength in meters
Theta= -pi:pi/50:pi; %0 to pi elevation angle from y axis
%Constants%
Omega=2*pi()*freq
u0=4*pi*10^(-7)
e0=8.85*10^(-12)
n0=sqrt(u0/e0)
k= 2*pi*freq*sqrt((u0*e0*(sqrt(2)+1))/2)
%Estimated Field Distance
ReactiveNearField=(0.62*sqrt((2*b)^3/Lamda))/0.0254 %Found in Balini
Page 34
FarField=((2*(2*b)^2)/Lamda)/0.0254 %Found in Balini Page 34
%Loop Antenna Field Equations
%Hr
A = ((pi*b^2)^2*I*Nt*cos(PosAng))/2;
AngLHrt = atan(Omega*k.*r);
MagLHrt = A./(2.*r.^2).*sqrt(1./r.^2+Omega^2*k^2).*cos(Omega.*tOmega*k.*r+AngLHrt);
AngLHrt2 = atan(Omega*k.*r2);
MagLHrt2 = A./(2.*r2.^2).*sqrt(1./r2.^2+Omega^2*k^2).*cos(Omega.*tOmega*k.*r2+AngLHrt2);
%Htheta
A=((pi*b^2)^2*I*Nt*sin(PosAng))/4;
65
AngLHt=atan((k./Omega.*r)./((1./r.^2)-k^2));
MagLHt=A./r.*sqrt((1./r.^2-k^2).^2+k^2./(Omega^2.*r.^2)).*cos(Omega.*tOmega*k.*r+AngLHt);
AngLHt2=atan((k./Omega.*r2)./((1./r2.^2)-k^2));
MagLHt2=A./r2.*sqrt((1./r2.^2k^2).^2+k^2./(Omega^2.*r2.^2)).*cos(Omega.*t-Omega*k.*r2+AngLHt2);
%Ephi
A=(n0*(pi*b^2)^2*I*Nt*sin(PosAng))/4;
AngLEt=-atan(1./(Omega*k.*r));
MagLEt=(A*k)./r.*sqrt(k^2+1./(Omega^2.*r.^2)).*cos(Omega.*tOmega*k.*r+AngLEt);
AngLEt2=-atan(1./(Omega*k.*r2));
MagLEt2=(A*k)./r2.*sqrt(k^2+1./(Omega^2.*r2.^2)).*cos(Omega.*tOmega*k.*r2+AngLEt2);
%Infintesimal Dipole Antenna Field Equations
%Er
A = (n0*I*len*cos(PosAng))/(2*pi());
AngDErt = -atan(1./(Omega*k.*r));
MagDErt = A./r.^2.*sqrt(1+1./(r.^2.*Omega^2*k^2)).*cos(Omega.*tOmega*k.*r+AngDErt);
AngDErt2 = -atan(1./(Omega*k.*r2));
MagDErt2 = A./r2.^2.*sqrt(1+1./(r2.^2.*Omega^2*k^2)).*cos(Omega.*tOmega*k.*r2+AngDErt2);
%Etheta
A=(n0*I*len*sin(PosAng))/(4*pi());
AngDEt=atan(k.*Omega.*r-Omega./(k.*r));
MagDEt=A./r.*sqrt(1./r.^2+(Omega-Omega./(k^2.*r.^2)).^2).*cos(Omega.*tOmega*k.*r+AngDEt);
AngDEt2=atan(k.*Omega.*r2-Omega./(k.*r2));
MagDEt2=A./r2.*sqrt(1./r2.^2+(OmegaOmega./(k^2.*r2.^2)).^2).*cos(Omega.*t-Omega*k.*r2+AngDEt2);
%Hphi
A=(I*len*sin(PosAng))/(4*pi());
AngDHt=atan(Omega*k.*r);
MagDHt=A./r.*sqrt(1./r.^2+Omega^2*k^2).*cos(Omega.*tOmega*k.*r+AngDHt);
AngDHt2=atan(Omega*k.*r2);
MagDHt2=A./r2.*sqrt(1./r2.^2+Omega^2*k^2).*cos(Omega.*tOmega*k.*r2+AngDHt2);
66
%Total Magnitudes of E and H
TotMagLHt = sqrt(MagLHt.^2+MagLHrt.^2);
TotMagLEt = sqrt(MagLEt.^2);
TotMagDHt = sqrt(MagDHt.^2);
TotMagDEt = sqrt(MagDEt.^2+MagDErt.^2);
TotMagLHt2
TotMagLEt2
TotMagDHt2
TotMagDEt2
=
=
=
=
sqrt(MagLHt2.^2+MagLHrt2.^2);
sqrt(MagLEt2.^2);
sqrt(MagDHt2.^2);
sqrt(MagDEt2.^2+MagDErt2.^2);
SH = 37.7.*TotMagLHt.^2; % From FCC Regulation
SE = TotMagLEt.^2./3770; % From FCC Regulation
SH2 = 37.7.*MagLHt2.^2; % From FCC Regulation
SE2 = MagLEt2.^2./3770; % From FCC Regulation
WaveImp = -1.* MagLEt2./MagLHt2; %From Balini's 5-28
RadIntFunc = n0/2 * (k^2*b^2/4)^2*I^2.*(sin(Theta)).^2; %Radiation
DirectFunc = 1.5 .*(sin(Theta)).^2; %Directivity
%Deminsion conversions to plot in desired units
Ima=I*1000;%Making current in terms of mA for title
binch=b/0.0254;%Making loops radius in terms of inches for title
rin=r./0.0254; %Making near-field plot in terms of inches instead of
meters
rin2=r2./Lamda; %Making far-field plot in terms of wave length instead
of meters
thetadegree = PosAng*57.2957795; %Display theta in title in degrees
lenin=len/0.0254; %Display the length used in the dipole in inches
subplot(2,2,1)
semilogy(rin,TotMagLHt)
xlabel('Distance from Antenna (in)');
ylabel('Strength of Field');
title(['Instantaneous Fields: Theta =',num2str(thetadegree),' degrees
Radius= ' ,num2str(binch), 'in Current = ',num2str(Ima),'mA Number of
Turns= ',num2str(Nt)]);
grid on
hold all
%semilogy(rin,MagLHrt,'*')
%semilogy(rin,MagLHt,'+')
semilogy(rin,TotMagLEt, '-+')
Legend ('MagH A/m')%,'MagE V/m')%,,)%'SH mW/cm^2','SE mW/cm^2')
hold off
subplot(2,2,2)
semilogy(rin2,TotMagLHt2)
%semilogy(rin2,SH2,'+')
xlabel('Distance from Antenna (Wavelength)');
67
ylabel('Magnitude of Field');
title(['Instantaneous Fields: Theta =',num2str(thetadegree),' degrees
Radius= ' ,num2str(binch), 'in Current = ',num2str(Ima),'mA Number of
Turns= ',num2str(Nt)]);
grid on
hold all
%semilogy(rin2,MagLHrt2,'*')
%semilogy(rin2,MagLHt2,'+')
semilogy(rin2,TotMagLEt2, '-+')
%semilogy(rin,MagDHt,'*')
%semilogy(rin,MagDEt,'+')
%semilogy(rin,MagDErt, 'x')
%semilogy(rin,TotMagDEt)
%semilogy(rin2,SE2,'x')
Legend('MagH A/m','MagE V/m')
%Legend ('SH mW/cm^2','SE mW/cm^2')
hold off
subplot(2,2,3)
plot(rin,AngLHrt,'*')
xlabel('Distance from Antenna (in)');
ylabel('Phase of Field');
title(['Instantaneous Fields: Theta =',num2str(thetadegree),' degrees
Radius= ' ,num2str(binch), 'in Current = ',num2str(Ima),'mA Number of
Turns= ',num2str(Nt)]);
grid on
hold all
plot(rin,AngLHt,'+')
plot(rin,AngLEt,'x')
%semilogy(rin,TotMagLHt)
Legend ('Hr A/m','H A/m','E V/m')%'SH mW/cm^2','SE mW/cm^2')
hold off
subplot(2,2,4)
%plot(rin,AngDHt,'*')
plot(rin2,AngLHrt2,'*')
xlabel('Distance from Antenna (Wavelength)');
ylabel('Phase of Field');
title(['Instantaneous Fields: Theta =',num2str(thetadegree),' degrees
Radius= ' ,num2str(binch), 'in Current = ',num2str(Ima),'mA Number of
Turns= ',num2str(Nt)])%'mA Length of Dipole= ',num2str(len),'m']);
grid on
hold all
plot(rin2,AngLHt2,'+')
plot(rin2,AngLEt2,'x')
%plot(rin,AngDErt,'+')
%plot(rin,AngDEt, 'x')
%semilogy(rin2,TotMagLHt2)
Legend ('Hr A/m','H A/m','E V/m')%'SH mW/cm^2','SE mW/cm^2')
hold off
68
APPENDIX C
Excel Design Model
U0
Ur
Frequency
Wavelength
WireGague
WireRadius (m)
WireRadius (In)
Nt
Radius
Area of Loop
Length of wire in loop
Length to Diameter ratio
1.25664E-06
0.999991
134.2E+3
2.2E+3
24
162.5E-6
6.4E-3
82
2.5
0.0127
32.717
257.6106
Sigma
AC
Resistance
of Coil
Inch
Meters
Meters
Depth
0.12 Inch
Length
Radius
0.12 Inch
2.56 Inch
Ant Inductance
Ant Radiation Resistance
Ant Loss Resistance
Ant DC Resistance
Ground Resitance
Ant Impedance
Ant Q
Ant Resistance
Antenna Effecency
Rs
2,005.55
1.3E-9
28.5E-3
3.06
33.00
1,691.09
23.45
72.12
0.0000000000371
9.4
Va Vp-p
VR V
Cdv1+CD
Cd
242.81
4
11.4E-12
389.8E-15
Hr dBuA/m
276.00
7.57
9.43E-05 Ohm
180.2E-6
10
107.338 Feet
187 m max
Number of
9 Layers
Number of
Turns per
10 Layer
Ohm
701.3E-12 F
184.3E-12 F
Range in
Hr A/m
Hr uA/m
Rohmic
Ro
Rskin
Skin Depth
Rp/Ro
uH
Ohm
Ohm/Ft
Ohm
Ohm
Ohm
Cr
Ce
Ia A
59600000 S/m
V p-p
V p-p
F
F
72.8E-3
Note: Can not Exceed 250 Vp-p
Note: Can not Exceed 4V
Note: Can not Exceed 200mA
6 Inches
2.673741723
2673741.723
128.542
Note:Must be greater then 126
69
REFERENCES
[1]
Mark Roberti. ( undated). The History of RFID Technology. [Online]. Available:
(http://www.rfidjournal.com/article/view/1338)
[2]
Wikipedia. (2011, April 24). Radio-frequency identification .[Online]. Viewed 2011 April
30. Availible: http://en.wikipedia.org/wiki/Radio-frequency_identification
[3]
Mario W. Cardullo, William L. Parks, III, “TRANSPONDER APPARATUS AND
SYSTEM,” U.S. Patent 3 713 148, January 23, 1973.
[4]
William Pentland and David E. Gumpert.(2007,December). USDA Bets the Farm on
Animal ID Program. [Online]. Available: http://www.thenation.com/article/usda-betsfarm-animal-id-program?page=0,0
[5]
Radio Frequency Identification of Animals-Technical Concept, ISO 11785, 1996.
[6]
Judith M. Myerson, RFID in the Supply Chain: A guide to Selection and Implementation,
Auerbach Publications: Taylor and Francis Group, 2007, pp 1-30.
[7]
R. Scott Nolen.(2007, Oct.). USDA:No authority to regulate pet microchips. Javma
News.[Online]. Available:
http://www.microchipidsystems.com/UserFiles/File/http%20%20%20www.avma.org%20o
nlnews%20javma%20oct07%20071015c.pdf
[8]
United States Department of Agriculture. (2011, March). “Official Animal Identification
Number (AIN) Devices”. [Online]. Viewed 2011 April 30. Available:
http://www.aphis.usda.gov/traceability/downloads/AIN_device_list.pdf
[9]
RFID Journal LLC. (undated). The Basics of RFID Technology. [Online]. Viewed 2011
April 30.Available: http://www.rfidjournal.com/article/view/1337/2.
[10] Mun Leng Ng, et al, “A SMALL PASSIVE UHF RFID TAG FOR LIVESTOCK
IDENTIFICATION,” Microwave, Antenna, Propagation and EMC Technology for
Wireless Commun.,Vol. 1, pp 67, Aug. 2005.
[11] Wikipedia. .(2011, February 10). Schering-Plough. [Online]. Viewed 2011 April
30.Available: http://en.wikipedia.org/wiki/Schering-Plough
[12] Home Again. (undated) [Online].Viewed 2011 April 30. Available:
http://public.homeagain.com/
[13] Radio Frequency Identification of Animals-Code Structure, ISO 11784, 1996.
[14] J.W. Bishop, et al, “ISO 11785 Transponder Performance Measurements,” JRC, Ispra
I(VA), Italy, Rep. 54745, 2009.
[15] Priority 1 Design, “Animal tag and RFID reader writer with external antenna,” RFIDRWE-232 data sheet, Oct. 2010
70
[16] EM Microelectroinc, “Read/Write analog front end for 125kHz RFID Basestation ,”
EM4095 data sheet, Sept. 2009
[17] C. A. Balanis, Antenna Theory; Analysis and Design, 3rd Ed., New Jersey: John Wiley &
Sons, 2005, pp 1-273.
[18] R. Dean Straw, Antenna Book, 21st Ed., Newington: ARRL, 2007-2009, pp 1-1 – 5-28.
[19] Fawwaz T. Ulaby, Fundamentals of Applied Electromagnetics, 2001 Media Ed., New
Jersey: Prentice Hall, 2001, pp 1-280.
[20] Evaluation Compliance with FCC Guidelines for Human Exposure to Radiofrequency
Electromagnetic Fields, OET Bulletin 65, 1997-2001.
[21] David M. Polzar, Microwave Engineering, 3rd Ed., New Jersey: John Wiley & Sons, 2005,
pp 1-160.
[22] 66Pacific.(undated).Coil Inductance Calculator.[Online].Viewed 2011 April 30.Availble:
http://www.66pacific.com/calculators/coil_calc.aspx.
[23] Glen S. Smith, “Radiation efficiency of electrically small multiturn loop antennas,” IEEE
Trans. On Antennas and Propagation, Vol. 20, No. 5, pp 656, Sep. 1972.
[24] Jane McGrath. (undated). How Pet Microchipping Works. [Online]. Viewed 2011 April
30.Availible: http://www.howstuffworks.com/pets/pet-travel/pet-microchip.htm.
[25] Radiofrequency Identification of Animals, advanced transponders-Air interface, ISO
14223-1, 2011
[26] Eric Bogatin, Signal Integrity Simplified, New Jersey: Prentice Hall, 2004, pp 1-330.
[27] R. Dean Straw, Antenna Book, 21st Ed., Newington: ARRL,” 2007-2009, pp 1-19 - 1-21.
[28] Martin Rowe. (2003, Aug.). Near-Field Probes Sniff Circuits. [Online]. Available:
http://www.tmworld.com/article/319170-Near_field_probes_sniff_circuits.php.
[29] Frank M. Greene, “NBS Field-Strength Standards and Measurements,” Proc. IEEE, Vol.
55, No. 6, pp 970, Jun. 1967.