# Patent

## Title
Systems and methods using single antenna for multiple resonant frequency ranges

## Abstract

A radio frequency device utilizing an antenna having a single antenna structure resonant on multiple resonant frequency ranges. The antenna can be configured to operate within multiple frequency ranges for communication according to respective protocols associated with the respective frequency ranges.

## Background
RELATED APPLICATIONS
The present application is a continuation application of U.S. patent application Ser. No. 14/183,240, filed Feb. 18, 2014, which is a continuation application of U.S. patent application Ser. No. 12/123,826, filed May 20, 2008, issued as U.S. Pat. No. 8,712,334 on Apr. 29, 2014 and entitled “RFID Device Using Single Antenna for Multiple Resonant Frequency Ranges”, the entire disclosure of which is hereby incorporated herein by reference.


BACKGROUND
The present invention relates to a radio frequency identification (RFID) device using a single antenna for multiple resonant frequency ranges. RFID is a technology that incorporates the use of electromagnetic or electrostatic coupling in the radio frequency (RF) portion of the electromagnetic spectrum to uniquely identify and communicate with a device attached to an object, animal, or person. With RFID, the electromagnetic or electrostatic coupling in the RF portion of the electromagnetic spectrum is used to transmit signals.
A typical RFID system includes a reader (interrogator) and a plurality of tags. A reader includes an antenna and a transceiver, and transmits a radio frequency signal to a tag to initiate a response from the tag. The tag (RFID device) contains an antenna, circuitry, and information to be transmitted to the reader. The tag antenna enables the circuitry to transmit its information to the interrogator, which converts the radio waves reflected back from the RFID device into digital information that can then be passed on to computers that can analyze the data.
Conventional RFID devices are typically designed for use in a particular frequency range, and according to a single communication protocol. Modifying the RFID devices to operate in additional frequency ranges, and with additional communication protocols, requires significant and costly modifications.
In current EPCglobal® passive device architecture, the amount of time that an RFID device can receive and transmit data per session is limited, due to the minimal amount of charge that the RFID passive device can store. In addition, the communication link between interrogator and RFID device in current RFID systems is limited in range due to constraint distance parameters of powering the RFID device.
SUMMARY OF THE DESCRIPTION
In one aspect, the present disclosure includes a radio frequency device utilizing an antenna having a single antenna structure resonant on multiple resonant frequency ranges. The antenna can be configured to operate within multiple frequency ranges for communication according to respective protocols associated with the respective frequency ranges.
In another aspect, the present disclosure provides a radio frequency identification (RFID) device using a single antenna for multiple resonant frequency ranges.
For example, an embodiment of the invention features an RFID system that includes an RFID interrogator having an interrogator antenna configured to operate within multiple frequency ranges. The system also includes an RFID device having an RFID circuit, and a device antenna coupled to the RFID circuit. The RFID device antenna can be configured to operate within multiple frequency ranges that match at least those of the interrogator antenna(s) for communicating with the RFID interrogator according to respective protocols associated with each respective frequency range.
In another aspect, an embodiment of the invention features an RFID device including an RFID circuit, and an antenna coupled to the RFID circuit. The antenna can be configured to operate within multiple frequency ranges for communicating with at least one RFID interrogator, according to respective protocols associated with each respective frequency range.
In another aspect, an embodiment the invention provides a method that includes 1) receiving radio frequency (RF) signals having different frequency ranges on an antenna coupled to an RFID device and tuned to the different frequency ranges, 2) selecting protocols, such that each protocol is associated with only one of the frequency ranges of the received signals, and 3) processing the received signals according to the protocols associated with the frequency ranges.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of an RFID system linked to a network.
FIG. 2 is a block diagram of an exemplary RFID system.
FIG. 3 is a block diagram of an exemplary RFID device.
FIG. 4 is a block diagram of an exemplary RFID device antenna.
FIG. 5A is a graphical representation of primary and secondary resonant frequencies of an exemplary RFID device antenna.
FIG. 5B is a block diagram of an exemplary RFID device.
FIG. 6 is a block diagram of an exemplary RFID device.
FIG. 7 is a block diagram of an exemplary RFID device.
FIG. 8 is a flow diagram.



Like reference numbers and designations in the various drawings indicate like elements.
DETAILED DESCRIPTION
The following description and drawings are illustrative and are not to be construed as limiting. Numerous specific details are described to provide a thorough understanding. However, in certain instances, well known or conventional details are not described in order to avoid obscuring the description. References to one or an embodiment in the present disclosure are not necessarily references to the same embodiment; and, such references mean at least one.
Certain terms are used throughout the following description and claims to refer to particular system components. As one skilled in the art will appreciate, design and manufacture companies may refer to a component by different names. This disclosure does not intend to distinguish between components that differ in name but not in function.
In the following discussion and in the claims, the terms “including” and “comprising” are used in an open-ended fashion, and thus should be interpreted to mean “including, but not limited to . . . ” Also, the term “couple” or “couples” is intended to mean an indirect or direct connection. Thus, if a first device couples to a second device, that connection may be through a direct connection or through an indirect connection via other intermediate devices and connections. Moreover, the term “system” is understood to include “one or more components” combined together. Thus, a system can include an “entire system,” “subsystems” within a system, a radio frequency identification (RFID) tag, a reader circuit, or any other devices including one or more components.
In general, various embodiments of the present invention configure RFID devices with single antenna structures, for instance, multiband resonant antennas that are designed to operate at multiple carrier frequency ranges. A different communication protocol is utilized with each frequency range, and power can be received by RFID devices over multiple frequency ranges.
FIG. 1 illustrates an exemplary RFID system 10 that includes a computer 3 coupled to a network 2 and to an RFID interrogator 4. The RFID interrogator 4, which may sometimes be referred to as an RFID reader, includes a processor 5, a transceiver 6, a memory 7, a power supply 8, and an antenna 9. The RFID interrogator 4 is programmable and performs transmitting and receiving functions with the transceiver 6 and antenna 9. Alternatively, multiple antennas may be connected to transmitters and receivers. Through antenna 9, the RFID interrogator 4 can communicate with one or more RFID devices 11 that are within communication range of the RFID interrogator 4. Data downloaded from an RFID device 11 can be stored in memory 7, or transferred by the processor 5 to computer 3. Thereafter, this transferred data can be further processed or distributed to network 2.
The exemplary RFID device 11 includes device antenna 16 and RFID circuit 17. The RFID circuit 17 can include a transceiver 12, a processor 13, memory 14, and depending on whether or not RFID device 11 is active, semi-active or passive, a battery 15. Any RF interrogation signal 18 transmitted by the RFID interrogator 4 to the RFID device 11 is received by the antenna 16, and passed to transceiver 12 in RFID circuit 17. When triggered by the transceiver 12, processor 13 fetches the data (e.g., time stamp, unique RFID code, and so forth) from memory 14 and transmits a return signal 19 through antenna 16 to RFID interrogator 4, as multiplexed data packets from transceiver
As shown in FIG. 2, in an exemplary system 20, the RFID interrogator 4 can be configured with antenna 9 that is designed to operate within multiple frequency ranges. Antenna 9 can be a multiband resonant antenna. Another RFID interrogator 25 may be configured with multiple antennas 21, 26 that can be tuned to different respective frequencies or frequency ranges. For example, antenna 21 may operate in a 100 MHz wide frequency range centered at 900 MHz, and antenna 26 may operate in a 100 MHz wide frequency range centered at 2.45 GHz.
The RFID device 11 can be configured with an antenna 16, such as a multiband resonant antenna, that is designed to operate at multiple frequency ranges. Some antenna designs have a primary resonance and secondary resonances, which enable the use of one antenna 16 for multiple carrier frequencies. Another option is to implement antenna 16 as a single antenna structure, such as a patch antenna array, which includes multiple antennas and is resonant on multiple frequency ranges. A single antenna is desirable where space and antenna size are limited. The antenna 16 on device 11 is coupled to the RFID circuit 17, and tuned to frequencies or frequency ranges that match at least those of the corresponding antennas 9, 21, 26 on RFID interrogators 4, 25. For example, antenna 16 on RFID device 11 may operate in a 100 MHz wide frequency range centered at 900 MHz to correspond to antenna 21 on RFID interrogator 25, and antenna 16 on device 11 may also operate in a 100 MHz wide frequency range centered at 2.45 GHz to correspond with antenna 26 on RFID interrogator 25. Such a configuration allows antenna 16 to receive multiple signals 18, 23, 27 from the antennas 9, 21, 26 on RFID interrogators 4, 25, and to respond by transmitting signals 19, 24 on respective frequency ranges that match those of antennas 9, 21, 26.
Referring to FIG. 3, device antenna 16 is connected to the RFID circuit 17, which may include a respective transceiver 12 and a power supply 15. It should be noted that in place of transceiver 12, receivers such as a diode detectors and transmitters can be substituted and coupled to antenna 16. RFID processing circuitry 33 is coupled to the transceiver 12 and power supply 15, and processes a signal according to respective protocols.
Referring to FIG. 4, in an embodiment, a multiband (two-band) resonant antenna 40 can be constructed by coupling filter circuits 42, 43 (traps) to antenna 16. Filter circuit 42 includes inductor 45 connected in parallel with capacitor 46. Likewise, filter circuit 43 includes inductor 47 connected in parallel with capacitor 48. The value of inductors 45, 47 and capacitors 46, 48 are selected depending on the expected resonant frequency at which antenna 40 is to operate. The resonant frequency (or trapping frequency) of the filter circuits 42, 43 can be calculated by one divided by the square root of the product of the inductor times the capacitor (1/square root (L*C)). Antenna 16 can be a dipole antenna having a feedpoint 44. The two-band resonant antenna 40 can be constructed with off-the-shelf components, or fabricated using microstrip, stripline, copper etching on PC boards, films, etc.
It should be noted that although dipole antennas are specifically depicted in the figures, other antennas are possible, such as log periodic dipole array, triband Yagi antennas, multiple parallel antennas joined at a common feedpoint (dipoles, patches, etc.), multiple antennas connected serially, and quarter wave dipoles, monopoles and whips.
FIG. 5A shows a graphical representation 50 of two resonances, a primary 51 and secondary 52, which may be used to construct a multiband resonant antenna without the use of filter circuits 42, 43 in each arm of the dipole antenna 16. The secondary resonance 52 is usually not very pronounced, typically resulting in less than optimal performance at the secondary (higher) frequency. However, this antenna design may be useful where space is at a premium.
FIG. 5B shows an embodiment of the antenna graphically represented in FIG. 5A. Specifically, antenna 16 is coupled to two external filter circuits 42, 43. Filter circuit 42 may pertain to resonant frequency 51, and filter circuit 43 may pertain to resonant frequency 52. The filter circuits 42, 43 and antenna 16 are coupled to one or more RFID circuits 17 on RFID device 11. As discussed above, the RFID circuits 17 may include a power supply 15, receivers/transceivers 12, and a processor 13.
FIG. 6 shows an exemplary RFID device 11 configured with the two-band antenna structure 40 coupled to two additional respective filter circuits 61 and 62. Power supplies 15, transceivers 12, and additional circuitry 33 may be attached to the filter circuit outputs 63, 64 on RFID circuit 17, and configured to operate simultaneously or one at a time. Matching circuits or components may also be added. Multiple protocols, each carried at a different frequency, can be used simultaneously by connecting the appropriate protocol processing circuitry 33 in RFID circuit 17 to each filter circuit output 63, 64. Two different protocols can be used by connecting the appropriate processor 13, transceiver 12, (and even power supply 15) circuitry to the respective outputs 63, 64 of filter circuits 61, 62.
FIG. 7 shows exemplary RFID device 11 configured as a two frequency system in which one output 63 is used as a power supply, and the other output 64 is used for receiving, transmitting, and processing signals. In particular, RFID device 11 includes the two-band antenna structure 40 that is coupled to the two filter circuits 61 and 62. The output 63 of filter circuit 61 is connected to the RFID circuit 17 and used as a power supply. Specifically, a diode 72 is connected to output 63 and used as a half-wave rectifier to generate direct current (dc) voltage for powering processor 13 and the RFID circuit 17. A filtering capacitor 73 is coupled to the diode 72 to smooth out the dc voltage signal. The output 64 of filter circuit 62 is also connected to RFID circuit 17. Incoming signals from filter circuit 62 are passed through diode 74 and filtering capacitor 75 to the processor 13, which processes the received signals according to a protocol associated with the frequency range of the received signal. RFID circuit 17 can also include an automated voltage control 71 for modulating the frequency on which the processed data is to be transmitted.
System 20 can also be configured to utilize a different communication protocol (e.g., EPCglobal® protocol, EPC HF Class 1, EPC UHF Class 0, EPC UHF Class 1, EPC UHF Class 1 Gen 2) on each respective frequency range. Such a configuration permits the RFID interrogators 4, 25 to communicate with RFID device 11 simultaneously or serially over each respective frequency range. Using a different protocol on each frequency range also enables multiple RFID interrogators to communicate simultaneously or serially at the different frequency ranges with the same RFID device 11. More specifically, using multiple protocols enables a single RFID device 11 to perform different functions. For example, an EPC UHF Class 1 protocol may be used by RFID device 11 for identification of a hospital patient, and the same RFID device 11 using an entirely different protocol (e.g., EPC HF Class 1) on a different frequency range can be used for communicating with hospital equipment, monitoring patient data, or communicating with a nurse station to report patient status at a greater distance.
As a further example, tuning or selecting antenna 9 on RFID interrogator 4 and antenna 16 on the RFID device 11 to operate within a frequency range centered at 900 MHz, establishes a first communication link between the RFID interrogator 4 and RFID device 11. Similarly, tuning antenna 9 on RFID interrogator 4 and antenna 16 on the RFID device 11 to also operate within a frequency range centered at 2.45 GHz, establishes a second communication link between the RFID interrogator 4 and the RFID device 11. The 900 MHz frequency range can be used as a carrier for communications according to a first protocol, and the 2.45 GHz frequency range can be used as a carrier for communications according to a second protocol. The RFID interrogator 4 and device 11 can communicate simultaneously or serially over the two frequency ranges.
In another embodiment, the first frequency range may be used to provide power from the RFID interrogator 4 to the RFID device 11, and the second frequency range may be used for communication according to a particular protocol. Powering the passive device 11 on the first frequency range, while simultaneously communicating over the second frequency range, has the advantage of enabling the device 11 to stay energized longer, to receive or transmit more data per session and to extend processing time. The device 11 can also be configured to receive power from the RFID interrogators 4, 25 at multiple frequency ranges.
The powering of the RFID device 11, as opposed to commands or data sent to and from the RFID device 11, is typically a range-limiting factor in the communications link between RFID interrogators 4, 25 and RFID device 11. This is primarily due to free-space path loss, which tends to increase with frequency. Free-space path loss is the loss in signal strength of an electromagnetic wave that results from a line-of-sight path through free space, with no obstacles nearby to cause reflection or diffraction. Free-space power loss is proportional to the square of the distance between the transmitter and receiver, and also proportional to the square of the frequency of the radio signal. Therefore, when selecting a frequency range to power the device 11, it can be advantageous to utilize the lowest available frequency range to minimize the effects of free-space path loss and to extend the range of the device 11. Data can be sent at a higher frequency, which tends to balance the communication link.
In designing and implementing the antennas and system 20, frequency ranges are selected that are non-harmonic, non-integer multiple or non-integer-fraction frequencies relative to the other selected frequency ranges. For example, if a first frequency range is centered at 900 MHz, a subsequent frequency range should not be selected at 1800 MHz (the first harmonic of the first range). An advantage is if multipath interference exists at the first frequency range, such interference would be very unlikely at the second frequency range. Using this configuration, reliability and range can be improved by using redundant power transmissions at multiple frequency ranges, either simultaneously or multiplexed one at a time.
In embodiments, the RFID device 11 with antenna can be implemented as part of rigid (e.g., substrate-based) or flexible (e.g., RFID label) configuration. Depending on the application, printed or etched layout techniques including stripline, microstrip, organic or polymer semiconductors can be utilized for fabricating planar components or components on substrates that may be rigid or flexible.
FIG. 8 illustrates a method of operation 80 of an RFID device that is in accordance with an embodiment of the present invention. The method (80) starts (81) by receiving radio frequency (RF) signals (82) having different frequency ranges on an antenna tuned to the different frequency ranges. Once the signals are received, protocols are selected (83) so that each protocol is associated with only one of the frequency ranges of the received signals. The method (80) then processes (84) the received signals according to the protocols associated with the frequency ranges. Method (80) can then either end (85), or if implemented in an automated system e.g., firmware, the method (80) can proceed to step (82) and continue to repeat.
In this description, various functions and operations may be described as being performed by or caused by software code to simplify description. However, those skilled in the art will recognize what is meant by such expressions is that the functions result from execution of the code by a processor, such as a microprocessor. Alternatively, or in combination, the functions and operations can be implemented using special purpose circuitry, with or without software instructions, such as using Application-Specific Integrated Circuit (ASIC) or Field-Programmable Gate Array (FPGA). Embodiments can be implemented using hardwired circuitry without software instructions, or in combination with software instructions. Thus, the techniques are limited neither to any specific combination of hardware circuitry and software, nor to any particular source for the instructions executed by the data processing system.
While some embodiments can be implemented in fully functioning computers and computer systems, various embodiments are capable of being distributed as a computing product in a variety of forms and are capable of being applied regardless of the particular type of machine or computer-readable media used to actually effect the distribution.
At least some aspects disclosed can be embodied, at least in part, in software. That is, the techniques may be carried out in a computer system or other data processing system in response to its processor, such as a microprocessor, executing sequences of instructions contained in a memory, such as ROM, volatile RAM, non-volatile memory, cache or a remote storage device.
Routines executed to implement the embodiments may be implemented as part of an operating system or a specific application, component, program, object, module or sequence of instructions referred to as “computer programs.” The computer programs typically comprise one or more instructions set at various times in various memory and storage devices in a computer, and that, when read and executed by one or more processors in a computer, cause the computer to perform operations necessary to execute elements involving the various aspects.
A machine readable medium can be used to store software and data which when executed by a data processing system causes the system to perform various methods. The executable software and data may be stored in various places including for example ROM, volatile RAM, non-volatile memory and/or cache. Portions of this software and/or data may be stored in any one of these storage devices. Further, the data and instructions can be obtained from centralized servers or peer to peer networks. Different portions of the data and instructions can be obtained from different centralized servers and/or peer to peer networks at different times and in different communication sessions or in a same communication session. The data and instructions can be obtained in entirety prior to the execution of the applications. Alternatively, portions of the data and instructions can be obtained dynamically, just in time, when needed for execution. Thus, it is not required that the data and instructions be on a machine readable medium in entirety at a particular instance of time.
Examples of computer-readable media include but are not limited to recordable and non-recordable type media such as volatile and non-volatile memory devices, read only memory (ROM), random access memory (RAM), flash memory devices, floppy and other removable disks, magnetic disk storage media, optical storage media (e.g., Compact Disk Read-Only Memory (CD ROMS), Digital Versatile Disks (DVDs), etc.), among others. The instructions may be embodied in digital and analog communication links for electrical, optical, acoustical or other forms of propagated signals, such as carrier waves, infrared signals, digital signals, etc.
In general, a machine readable medium includes any mechanism that provides (i.e., stores and/or transmits) information in a form accessible by a machine (e.g., a computer, network device, personal digital assistant, manufacturing tool, any device with a set of one or more processors, etc.).
In various embodiments, hardwired circuitry may be used in combination with software instructions to implement the techniques. Thus, the techniques are neither limited to any specific combination of hardware circuitry and software nor to any particular source for the instructions executed by the data processing system.
Although some of the drawings illustrate a number of operations in a particular order, operations which are not order dependent may be reordered and other operations may be combined or broken out. While some reordering or other groupings are specifically mentioned, others will be apparent to those of ordinary skill in the art and so do not present an exhaustive list of alternatives. Moreover, it should be recognized that the stages could be implemented in hardware, firmware, software or any combination thereof.
In the foregoing specification, the disclosure has been described with reference to specific exemplary embodiments thereof. It will be evident that various modifications may be made thereto without departing from the broader spirit and scope as set forth in the following claims. The specification and drawings are, accordingly, to be regarded in an illustrative sense rather than a restrictive sense.

## Claims

1. A system, comprising:
a radio frequency communication apparatus configured to communicate wirelessly using multiple frequency ranges; and
a plurality of devices, each respective device of the plurality of devices having
a memory storing an identification number uniquely identifying the respective device among the plurality of devices during wireless communications with the radio frequency communication apparatus;
a device antenna having a single antenna structure resonant on the multiple frequency ranges,
a circuit coupled with the device antenna to communicate with the radio frequency communication apparatus wirelessly using the device antenna and the multiple frequency ranges, wherein the circuit is configured to use the single antenna structure to communicate with the communication apparatus simultaneously over the multiple frequency ranges; and
a processor;

wherein the circuit includes a first portion configured to receive first signals in a first frequency range and generate power from the first signals to power the processor; and
wherein the circuit further includes a second portion; and the processor is configured to use the power provided by the first portion of the circuit and use the second portion to communicate second signals in a second frequency range.

2. The system of claim 1, wherein the circuit is configured to use the single antenna structure to communicate, simultaneously over the multiple frequency ranges, with the communication apparatus according to different protocols.

3. The system of claim 2, wherein each protocol of the different protocols uses a respective frequency range of the multiple frequency ranges.

4. The system of claim 1, wherein the circuit is configured to use the single antenna structure to communicate wirelessly in a first protocol using a first frequency range of the multiple frequency ranges and simultaneously in a second protocol using a second frequency range of the multiple frequency ranges.

5. The system of claim 1, wherein the respective device is configured to receive the power in the device antenna using the first frequency range of the multiple frequency ranges and to communicate data with the radio frequency communication apparatus using the second frequency range of the multiple frequency ranges.

6. The system of claim 5, wherein the respective device is configured to receive the power using the first frequency range while simultaneously communicating data with the radio frequency communication apparatus using the second frequency range.

7. The system of claim 6, wherein the first frequency range used to receive the power is lower than the second frequency range used to communicate data.

8. The system of claim 1, wherein the multiple frequency ranges are non-harmonic, non-integer multiple, and non-integer-fraction with each other in frequency.

9. A device, comprising:
a memory storing an identification number of the device;
a radio frequency communication circuit;
at least one antenna coupled to the radio frequency communication circuit and having a single antenna structure resonant on multiple frequency ranges for communications in a first frequency range and a second frequency range different from the first frequency range; and
a processor;
wherein the radio frequency communication circuit includes
a first portion configured to receive first signals in the first frequency range and generate power from the first signals to power the processor, and
a second portion, wherein the processor is configured to use the power provided by the first portion and use the second portion to communicate second signals in the second frequency range different from the first frequency range; and

wherein the radio frequency communication circuit is configured to use the single antenna structure to communicate simultaneously in the first frequency range and the second frequency range.

10. The device of claim 9, wherein the antenna includes a first filter and a second filter to resonate on the first frequency range and the second frequency range respectively.

11. The device of claim 9, wherein the antenna is one of: a dipole antenna, a log periodic dipole array antenna, a triband yagi antenna, quarter wave dipole antenna, a monopole antenna, and a whip antenna.

12. The device of claim 9, wherein the antenna is configured to receive one power transmission from a remote communication apparatus.

13. The device of claim 12, wherein the power transmission is received via the first frequency range using a first protocol different from a second protocol used to communicate the second signals.

14. The device of claim 13, wherein the second frequency range used to communicate data is higher than the first frequency range.

15. The device of claim 9, wherein the multiple frequency ranges are non-harmonic, non-integer multiple, and non-integer fraction of each other in frequency.

16. A device, comprising:
a memory storing an identification number of the device;
a radio frequency communication circuit;
at least one antenna coupled to the radio frequency communication circuit and having a single antenna structure resonant on multiple frequency ranges for communications in a first frequency range and a second frequency range different from the first frequency range; and
a processor;
wherein the radio frequency communication circuit includes
a first portion configured to receive first signals in a first frequency range and generate power from the first signals to power the processor, and
a second portion, wherein the processor is configured to use the power provided by the first portion and use the second portion to communicate second signals in the second frequency range different from the first frequency range; and

wherein the radio frequency communication circuit is configured to use the single antenna structure to communicate simultaneously in the first frequency range and the second frequency range.

17. The device of claim 16, wherein the antenna includes a first filter and a second filter to resonate on the first frequency range and the second frequency range respectively.

18. The device of claim 16, wherein the antenna is one of: a dipole antenna, a log periodic dipole array antenna, a triband yagi antenna, quarter wave dipole antenna, a monopole antenna, and a whip antenna.

19. The device of claim 16, wherein the first frequency range used to communicate data is higher than the second frequency range to receive power.

20. The device of claim 16, wherein the multiple frequency ranges are non-harmonic, non-integer multiple, and non-integer fraction of each other in frequency.