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CC430的433M天线

CC430的433M天线
CC430的433M天线

Antenna Selection Guide

By Richard Wallace

Keywords

?

Antenna Selection ?

Anechoic Chamber ?

Antenna Parameters ?

169 MHz (136 – 240 MHz) Antenna ? 315 MHz (273 – 348 MHz) Antenna ? 433 MHz (387 – 510 MHz) Antenna ? 868 MHz (779 – 960 MHz) Antenna ? 915 MHz (779 – 960 MHz) Antenna ? 2.4 GHz Antenna ? CC-Antenna-DK

1 Introduction

This application note describes important

parameters to consider when deciding

what kind of antenna to use in a short

range device application.

Important antenna parameters, different

antenna types, design aspects and

techniques for characterizing antennas are

presented. Radiation pattern, gain,

impedance matching, bandwidth, size and

cost are some of the parameters

discussed in this document.

Antenna theory and practical

measurement are also covered.

In addition different antenna types are presented, with their pros and cons. All of the antenna reference designs available on https://www.wendangku.net/doc/59688310.html,/lpw are presented including the Antenna Development Kit [29]. The last section in this document contains references to additional antenna resources such as literature, applicable EM simulation tools and a list of antenna manufacturer and consultants. Correct choice of antenna will improve system performance and reduce the cost.

Figure 1. Texas Instruments Antenna Development Kit (CC-Antenna-DK)

Table of Contents

KEYWORDS 1 1INTRODUCTION 1 2ABBREVIATIONS 3 3BRIEF ANTENNA THEORY 4 3.1D IPOLE (Λ/2)A NTENNAS4 3.2M ONOPOLE (Λ/4)A NTENNAS5 3.3W AVELENGTH C ALCULATIONS FOR D IPOLE IN F REE S PACE5 3.4M AXIMUM P OWER T RANSFER (VSWR) 6 3.5A NTENNA P ERFORMANCE C ONSIDERATIONS7 3.6F RIIS T RANSMISSION E QUATION7 4ANTENNA TYPES 8 4.1PCB A NTENNAS 10

4.1.1TI Antenna Reference Designs 10

4.1.2IP Based 10 4.2C HIP A NTENNAS 11 4.3W HIP A NTENNAS 11 4.4W IRE A NTENNAS 11 5ANTENNA PARAMETERS 12

5.1R ADIATION P ATTERNS 12

5.1.1Polarization 15

5.1.2Ground Effects 16 5.2D IRECTIONAL A NTENNAS 17 5.3S IZE,C OST AND P ERFORMANCE 17 6ANTENNA MEASUREMENTS 18

6.1M EASURING B ANDWIDTH WITH A S PECTRUM A NALYZER 18 6.2M EASURING RL,I MPEDANCE AND B ANDWIDTH WITH A N ETWORK A NALYZER 19

6.2.1Mounting of cable for S11 measurements 19

6.2.2Calibration 20

6.2.3Placement of the Device under Test 21

6.2.4Interpreting Measurement Results 21

6.2.5Antenna Matching 23 6.3O VER-T HE-A IR (OTA)M EASUREMENTS 24 7ANTENNA REFERENCE DESIGNS AVAILABLE ON https://www.wendangku.net/doc/59688310.html,/LPW 26

7.1CC-A NTENNA-DK R EFERENCE D ESIGNS 26 7.2 2.4GH Z A NTENNA R EFERENCE D ESIGNS 27

7.2.1Single Ended Antennas 27

7.2.2Differential Antennas 29

7.2.3YAGI PCB Directional Antenna 30 7.3S UB 1GH Z A NTENNA R EFERENCE D ESIGNS 31

7.3.1Reference Designs for 868/915/955 MHz Antennas 31

7.3.2Reference Designs for 433 MHz Antennas 35

7.3.3Reference Designs for 315 MHz Antennas 36

7.3.4Reference Designs for 169 MHz Antennas 37 8ADDITIONAL ANTENNA RESOURCES 37 8.1A NTENNA L ITERATURE 37 8.2EM S IMULATION T OOLS 37 8.3S MITH C HARTS –A NTENNA M ATCHING 38 8.4G ERBER V IEWERS 38 8.5E2E C OMMUNITY 38 8.6A NTENNA S UPPLIERS AND C ONSULTANTS 38 9SUMMARY 39 10REFERENCES 42 11GENERAL INFORMATION 44 11.1D OCUMENT H ISTORY 44

2 Abbreviations

Note

Application

AN

Test

Under

AUT

Antenna

Materials

Of

BOM

Bill

Bandwidth

BW

CT I A Cellular Telecommunications Industry Association

Wave

CW

Carrier

Board

Demonstration

DB

Development

Kit

DK

Note

Design

DN

Test

Under

Device

DUT

Board

EB

Evaluation

EIRP Effective Isotropic Radiated Power

EM

Magnetic

Electro

Evaluation

Module

EM

Inverted-F

Antenna

IFA

Property

IP Intellectual

Scientific,

Medical

Industrial,

ISM

of

Sight

Line

LOS

Inverted-F

Antenna

Meandered

MIFA

Connected

Not

NC

NHPRP Near Horizon Partial Radiated Power

NHPRP45 Near Horizon Partial Radiated Power within 45 degrees angle

Air

The

OTA

Over

Board

Circuit

Printed

PCB

Radio

Frequency

RF

Loss

Return

RL

Device

Range

SRD

Short

Ratio

Wave

Standing

SWR

Instruments

TI Texas

TRP

Power

Radiated

Total

Market

To

Time

TTM

VSWR Voltage Standing Wave Ratio

Antenna

YAGI

Directional

3 Brief Antenna Theory

The antenna is a key component for reaching the maximum distance in a wireless communication system. The purpose of an antenna is to transform electrical signals into RF electromagnetic waves, propagating into free space (transmit mode) and to transform RF electromagnetic waves into electrical signals (receive mode).

Figure 2. Maximum Power Delivered at Quarter Wavelength

A typical antenna is basically an air core inductor of defined wavelength. As can be seen in Figure 2, the AC current through an inductor lags the voltage by 90 degrees so the maximum power is delivered at ? wavelength. The λ/2 dipole produces most power at the ends of the antenna with little power in the centre of the antenna.

(λ/2) Antennas

3.1 Dipole

A dipole antenna most commonly refers to a half-wavelength (λ/2). Figure 3 shows the typical emission pattern from a dipole antenna. The antenna is standing in the Z plane and radiating energy outwards. The strongest energy is radiated outward in the XY plane, perpendicular to the antenna.

Figure 3. Emission Pattern of a Dipole Antenna

Given these antenna patterns, you can see that a dipole antenna should be mounted so that it is vertically oriented with respect to the floor. This results in the maximum amount of energy radiating out into the intended coverage area. The null in the middle of the pattern will point up and down.

3.2 Monopole

(λ/4) Antennas

A monopole antenna most commonly refers to a quarter-wavelength (λ/4). The antenna is constructed of conductive elements whose combined length is about quarter the wavelength at its intended frequency of operation. This is very popular due to its size since one antenna element is one λ/4 wavelength and the GND plane acts as the other λ/4 wavelength which produces an effective λ/2 antenna. Therefore, for monopole antenna designs the performance of the antenna is dependent on the ground size, refer to Figure 4. All small antennas are derivatives of a simple dipole where one element is folded into the GND and serves as the second radiator.

Figure 4. Monopole Antenna Utilizing GND Plane as an Effective λ/4 Antenna Element

3.3 Wavelength Calculations for Dipole in Free Space

For the same output power, sensitivity and antenna gain; reducing the frequency by a factor of two doubles the range (line of sight). Lowering the operating frequency also means that the antenna increases in size. When choosing the operating frequency for a radio design, the available board space must also accommodate the antenna. So the choice of antenna, and size available should be considered at an early stage in the design.

λ meters = 2.99792458E8 m/sec

f (GHz)

Equation 1. Wavelength Equation

Frequency λ / 4 (cm) λ / 4 (inch) λ(cm) λ (inch)

GHz 3.1 1.2 12.5 4.9

2.4

955 MHz 7.8 3.1 31.4 12.4

915 MHz 8.2 3.2 32.8 12.9

868 MHz 8.6 3.4 34.5 13.6

MHz

17.3 6.8 69.2 27.3

433

169 MHz 44.3 17.5 177.4 69.8

MHz 277.6 109.3 1110.3 437.1

27

Table 1. Various Wavelengths for Several Frequency Ranges

3.4 Maximum Power Transfer (VSWR)

Moritz Von Jacobi’s maximum power theory states that maximum power transfer happens when the source resistance equals the load resistance. For complex impedances, the maximum power delivered from a transmission line with impedance Z0 to an antenna with impedance Z a, it is important that Z0 is properly matched to Z a. If a signal with amplitude V IN is sent in to the transmission line, only a part of the incident wave will be transmitted to the antenna if Z0 is not properly matched to Z a, refer to Equation 2.

Z0 = Z a′

Equation 2. Maximum Power Transfer Theorem

The complex reflection coefficient (Γ) is defined as the ratio of the reflected waves’ amplitude to the amplitude of the incident wave. Γ can be calculated from the impedance of the transmission line and the impedance of the antenna, as shown in Equation 3.

Equation 3. Complex Reflection Coefficient (Γ)

The reflection coefficient is zero if the transmission line impedance is the complex conjugate of the antenna impedance. Thus if Z0 = Z a′ the antenna is perfectly matched to the transmission line and all the applied power is delivered to the antenna.

Antenna matching typically uses both the Return Loss and the Voltage Standing Wave Ratio (VSWR) terminology. VSWR is the ratio of the maximum output (Input + Γ) to the minimum waveform (Input – Γ), refer to Equation 4.

Equation 4. Voltage Standing Wave Ratio

The power ratio of the reflected to the incident wave is called Return Loss; this indicates how many decibels the reflected wave power is below the incident wave. Refer to Equation 5.

Equation 5. Return Loss (dB)

With antenna design, VSWR and Return Loss are a measure of how well the antenna is matched. Refer to Table 2, for the conversions between Return Loss, VSWR and percentage of power loss.

When matching an antenna a VSWR of 1.5 (RL = 14 dB) is a good match, when the VSWR is > 2.0 (RL = 9.5 dB) then the matching network should be reviewed. VSWR of 2.0 (RL = 9.5 dB) is usually used as the acceptable match level to determine the bandwidth of the antenna. Mismatching of the antenna is one of the largest factors that reduce the total RF link budget. To avoid unnecessary mismatch losses, it is recommended to add a pi-matching network so that the antenna can always be matched. If the antenna design is adequately matched then it just takes one zero ohm resistor or DC block cap to be inserted into the pi-matching network.

Table 2. VSWR Chart

3.5 Antenna Performance Considerations

There are a numerous issues to consider when selecting the antenna:

? Antenna

placement

?Ground planes for ? wavelength antennas

?Undesired magnetic fields on PCB

?Antenna mismatch (VSWR)

?Objects that alter or disrupt Line of Sight (LOS)

?Antenna gain characteristics

? Antenna

bandwidth

?Antenna Radiation Efficiency

3.6 Friis Transmission Equation

Friis equation is the primary math model to predicting Line of Sight communication links. This is a very elementary equation and has been expanded to include height of antenna above ground and difference in TX and RX antennas. The formula is very accurate once all the constants have been entered. Please refer to [28] for further information concerning “Range Measurements in an Open Field Environment”.

Equation 6. Friis Transmission Equation

λ = Wavelength in Meters

P r = Received Power in dBm

P t = Transmit Power in dBm

G t = Transmit Antenna Gain in dBi

G r = Receive Antenna Gain in dBi

R = Distance between Antennas in Meters

4 Antenna Types

There are several antenna types to choose from when deciding what kind of antenna to use in an RF product. Size, cost and performance are the most important factors when choosing an antenna. The three most commonly used antenna types for short range devices are PCB antennas, chip antennas and wire antennas. Table 3 shows the pros and cons for several antenna types.

Antenna types Pros Cons

PCB antenna ?Very low cost

?Good performance at

> 868 MHz

?Small size at high

frequencies

? Standard design

antennas widely

available ?Difficult to design small and efficient PCB antennas at < 433 MHz

?Potentially large size at low frequencies

Chip antenna ? Small size

?Short TTM since

purchasing antenna

solution ? Medium performance ? Medium cost

Whip antenna ? Good performance

?Short TTM since

purchasing antenna

solution ? High cost

?Difficult to fit in many applications

Wire antenna ? Very cheap ?Mechanical manufacturing of

antenna

IP based antenna

?Support from IP

company

?High cost compared to standard

free PCB antenna designs.

?Similar cost to Chip antenna Table 3. Pros and Cons for Different Antenna Solutions

It is also common to divide antennas into single ended antennas and differential antennas. Single ended antennas are also called unbalanced antennas, while differential antennas are often called balanced antennas. Single ended antennas are fed by a signal which is referenced to ground and the characteristic input impedance for these antennas is usually 50 ohms. Most RF measurement equipments are also referenced to 50 ohms. Therefore, it is easy to measure the characteristic of a 50 ohm antenna with such equipment.

However many RF IC’s have differential RF ports and a transformation network is required to use a single ended antenna with these IC’s. Such a network is called a balun since it transforms the signal from balanced to unbalanced configuration. Figure 5 shows a single ended antenna and a differential antenna.

Single Ended

Antenna Differential Antenna

Figure 5. Single Ended and Differential Antenna

The antennas presented in this document are for the license free world wide band 2.4000 GHz - 2.4835 GHz band and the all the standard frequency bands at sub 1 GHz. For the sub 1 GHz bands; there is usually a “low“ sub 1 GHz band and a “high” sub 1 GHz band.

The “high” sub 1 GHz band in Europe covers 863-870 MHz, the US covers 902-928 MHz band and the Japanese band 955 MHz. The European band is usually referred to as the “868 MHz band” and the US band is commonly designated the “915 MHz band”. It is often possible to achieve good performance with the same antenna for both the European 868 MHz, US 915 MHz and Japanese 955 MHz bands by tuning the antenna length or changing the values of the matching components. Such antennas are called “868/915/955” MHz antennas” in this document.

The “low” sub 1 GHz band in Europe covers 433.050 - 434.790 MHz, the US covers 300-348 MHz band. The European band is usually referred to as the “433 MHz band” and the US

band is commonly designated the “315 MHz band”.

Antennas

4.1 PCB

Our ambition is to provide excellent antenna reference designs and application notes so the design-in process will be easier and quicker. With RF designs, the antenna design is a critical stage to be able to achieve the best possible link budget for a specific application. As previously mentioned in 3.5, there are many considerations when choosing the type of antenna.

The antenna application notes are updated on a regular basis with new designs. The TI antenna designs that are released are free of charge and can be used directly in the final application design. In addition to these free TI antenna designs, we also have specific antennas designs that are IP based. The antenna IP company usually has a specific design profile such as directivity or compact design for example.

The antenna in the basic form, PIFA, patch, spiral etc is generally free from patent infringement because these are well known designs that have been around for many years. When the antenna is adapted from the "standard format"; then the antennas are more than likely protected through patents. It is important to keep this in mind when developing a new antenna. Many antenna patents collide with each other and which company had the original IP, and if the IP is valid can be a long discussion. It is advisable to keep the standard text book antenna designs when developing an antenna to avoid any legal discussions.

4.1.1 TI Antenna Reference Designs

Designing a PCB antenna is not straight forward and usually a simulation tool must be used to obtain an acceptable solution. In addition to deriving an optimum design, configuring such a tool to perform accurate simulations can also be difficult and time consuming. It is therefore recommended to make an exact copy of one of the reference designs available at https://www.wendangku.net/doc/59688310.html,/lpw, if the available board space permits such a solution. See section 7 for a description of the available reference designs.

The CC-Antenna-DK [43] contains 13 low cost antennas and 3 calibration boards. The antennas cover the frequency range as low as 136 MHz to 2.48GHz; refer to Figure 1. The antenna designs from the CC-Antenna-DK are summarized in 7.1.

If the application requires a special type of antenna and none of the available reference designs fits the application, it could be advantageous to contact an antenna consultant or look for other commercially available solutions. Table 8 lists a few companies that can offer such services.

Based

4.1.2 IP

There are many IP antenna design companies that sell their antenna design competence through IP. Since there is no silicon or firmware involved; the only way for the antenna IP companies to protect their antenna design is through patents. Purchasing a chip antenna or purchasing an IP for the antenna design is similar since there is an external cost for the antenna design.

IP based antennas from Pinyon are specifically designed for directional operation (5.2) and Fractus is targeting compact designs as well as sales of their standard chip antennas.

An alternative to the IP Pinyon antenna reference designs [20], [21], [22] & [23] can be a standard patch antenna or YAGI antenna (refer to Section 7.2.3) which will also give directivity but with no IP cost attached. A 2.4 GHz patch antenna will be released as a reference design. The patch antenna mainly radiates in just one direction (one main lobe) whereas the IP Pinyon antenna has two lobes, similar to a figure eight. The YAGI antenna usually has a higher gain than the patch antenna and is typically larger in size as well.

4.2 Chip

Antennas

If the available board space for the antenna is limited a chip antenna could be a good solution. This antenna type allows for small size solutions even for frequencies below 1 GHz. The trade off compared to PCB antennas is that this solution will add BOM and mounting cost. The typical cost of a chip antenna is between $0.10 and $0.50. Even if manufacturers of chip antennas state that the antenna is matched to 50 ohms for a certain frequency band, it is often required to use additional matching components to obtain optimum performance. The performance numbers and recommended matching given in data sheets are often based on measurements done with a test board. The dimensions of this test board are usually documented in the data sheet. It is important to be aware that the performance and required matching will change if the chip antenna is implemented on a PCB with different size and shape of the ground plane.

Antennas

4.3 Whip

If good performance is the most important factor, size and cost are not critical; an external antenna with a connector could be a good solution. If a connector is used then to pass the regulations, conducted emission tests must also be performed. The whip antenna should be mounted normally on the ground plane to obtain best performance. Whip antennas are typically more expensive than chip antennas, and will also require a connector on the board that also increases the cost. Notice that in some cases special types of connectors must be used to comply with SRD regulations. For more information about SRD regulations please refer to [1] and [2].

Antennas

4.4 Wire

For applications that operate in the lower bands of the sub 1 GHz such as 315 MHz and 433 MHz; the antenna is quite large, refer to Table 1. Even when the earth plane is utilized for half of the antenna design; the overall size can be large and difficult to put onto a PCB. What can be done for this frequency range which is practical and cheap; a wire can be used for the antenna and the wire can be formed around the mechanical housing of the application.

The pros of such a solution are the price and good performance can be obtained. The cons are the variations of the positioning of the antenna in the mechanical housing will have to be controlled so that the antenna will not vary too much during volume production.

A standard cable can be used as an antenna if cut to the right length, refer to Table 1. The performance and radiation pattern will change depending on the position of the cable. If this type of antenna is used then it is good practice to keep the first part of the cable which is closest to the feed point into a more controlled position so the matching will not be affected too much when the remaining cable antenna changes positions when touched or moved.

5 Antenna Parameters

There are several parameters that should be considered when choosing an antenna for a wireless device. Some of the most important things to consider are how the radiation varies in the different directions around the antenna, how efficient the antenna is, the bandwidth which the antenna has the desired performance and the antenna matching for maximum power transfer. Sections 5.1 and Section 6.3 give an explanation on how these properties are defined and how they should be evaluated. Since all antennas require some space on the PCB, the choice of antenna is often a trade off between cost, size and performance.

Patterns

5.1 Radiation

Antenna specs from the majority of suppliers will reference their designs to an ideal Isotropic antenna. This is a model where the antenna is in a perfect sphere and isolated from all external influences. Most of the measurements of power are done in units of dBi where “i” refers to the condition of isotropic antenna. Power measurements for a theoretical isotropic antenna are in dBi. Dipole Antenna Power is related to an isotropic antenna by the relationship 0 dBd = 2.14 dBi.

The radiation pattern is the graphical representation of the radiation properties of the antenna as a function of space. i.e. the antenna's pattern describes how the antenna radiates energy out into space (or how it receives energy). It is common, however, to describe this 3D pattern with two planar patterns, called the principal plane patterns. These principal plane patterns can be obtained by making two slices through the 3D pattern through the maximum value of the pattern or by direct measurement. It is these principal plane patterns that are commonly referred to as the antenna patterns.

Principal plane patterns or even antenna patterns, you will frequently encounter the terms azimuth plane pattern and elevation plane pattern. The term azimuth is commonly found in reference to the horizontal whereas the term elevation commonly refers to "the vertical". When used to describe antenna patterns, these terms assume that the antenna is mounted (or measured) in the orientation in which it will be used.

The azimuth plane pattern is measured when the measurement is made traversing the entire XY plane around the antenna under test. The elevation plane is then a plane orthogonal to the XY plane, say the YZ plane (φ = 90 deg). The elevation plane pattern is made traversing the entire y-z plane around the antenna under test. θ is associated with elevation plane and φwith azimuth plane. The antenna patterns (azimuth and elevation plane patterns) are frequently shown as plots in polar coordinates.

The azimuth plane pattern is formed by slicing through the 3D pattern in the horizontal plane, the XY plane in this case. Notice that the azimuth plane pattern is directional, the antenna does not radiate its energy equally in all directions in the azimuth plane.

The elevation plane pattern is formed by slicing the 3D pattern through an orthogonal plane (either the XZ plane or the YZ plane).

Figure 6. 3D Radiation Pattern from a YAGI Directional Antenna

It is also important to be able to relate the different directions on the radiation pattern plot to the antenna. With the 3D plots; the XYZ coordinates are usually documented with a picture of the AUT; this is required since the orientation of the AUT in the anechoic chamber usually changes depending on the physical size and the possibility to position the AUT on the turn

arm. This can be seen in Figure 7 which is board 6 from the CC-Antenna-DK.

Figure 7. 3D Coordinates AUT Example

Prior to the availability of 3D radiation patterns, the AUT was typically measured in three

orthogonal planes, XY, XZ and YZ. Another way of defining these three planes is by using a

spherical coordinate system. The planes will then typically be defined by θ = 90°, φ = 0° and

φ = 90°. Figure 8 shows how to relate the spherical notation to the three planes. If no

information is given on how to relate the directions on the radiation pattern plot to the

positioning of the antenna, 0° is the X direction and angles increase towards Y for the XY

plane. For the XZ plane, 0° is in the Z direction and angles increase towards X, and for the y-

z plane, 0° is in the Z direction and angles increase towards Y.

Figure 8. Traditional Spherical Coordinate System for Radiation Patterns

A dipole antenna radiates its energy out toward the horizon (perpendicular to the antenna). The resulting 3D pattern looks like a donut with the antenna sitting in the hole and radiating energy outward. The strongest energy is radiated outward, perpendicular to the antenna in the XY plane. Given these antenna patterns, you can see that a dipole antenna should be mounted so that it is vertically oriented with respect to the floor or ground. This results in the maximum amount of energy radiating out into the intended coverage area. The null in the middle of the pattern will point up and down.

Figure 9 shows how the radiation from the PCB antenna shown in Figure 7 varies in different directions. Several parameters are important to know when interpreting such a plot. Some of these parameters are stated in the top right portion of Figure 9.

With the AUT coordinate description in Figure 7 and the measured radiated pattern in Figure 9, the radiation pattern can be related to the AUT. The peak signal strengths can be observed and taken into account when radiated power from a given angle. This is useful information for the positioning of the AUT when performing range tests, calculating link budgets and determining the expected range.

Figure 9. Radiation Pattern from board 6 (868 MHz) from the CC-Antenna-DK

The gain or the reference level is usually referred to an isotropic radiating antenna which is an ideal antenna that has the same level of radiation in all directions. When such an antenna is used as a reference, the gain is given in dBi or specified as the Effective Isotropic Radiated Power (EIRP) [6.3].

The Transmitted Radiated Power (TRP) is shown in Figure 9 as -0.43 dBm. Standard CTIA OTA reports usually nominate the TRP with respect to an input of 0 dBm. The colour scale notation in the top right of Figure 9 illustrates the specific span of the TRP. A peak gain of 5.16 dB has been recorded with the lowest level at -12.81dB. This means that compared to an isotropic antenna the PCB antenna in Figure 7 will have 5.16 dB higher radiated power in the direction where the TRP was recorded at 5.16dB; this looks like this is in the “Z” direction according to Figure 9.

5.1.1 Polarization

Polarization describes the direction of the electric field. All electromagnetic waves propagating in free space have electric and magnetic fields perpendicular to the direction of propagation. Usually, when considering polarization, the electric field vector is described and the magnetic field is ignored since it is perpendicular to the electric field and proportional to it. The receiving and transmitting antenna should have the same polarization to obtain optimum performance. Most antennas in SRD application will in practice produce a field with polarization in more than one direction. In addition reflections will change the polarization of an electric field. Polarization is therefore not as critical for indoor equipment, which experiences lots of reflections, as for equipment operating outside with Line of Sight (LOS). Some antennas produce an electrical field with a determined direction, it is therefore also important to know what kind of polarization that was used when measuring the radiation pattern. It is also important to state which frequency the measurement was done at. Generally the radiation pattern does not change rapidly across frequency. Thus it is usual to measure the radiation pattern in the middle of the frequency band in which the antenna is going to be used. For narrowband antennas the relative level could change slightly within the desired

frequency band, but the shape of the radiation pattern would remain basically the same.

5.1.2 Ground Effects

The size and shape of the ground plane will affect the radiation pattern. Figure 10 shows an example of how the ground plane affects the radiation pattern. The radiation pattern in the upper left corner is measured with the small antenna board plugged in to the SmartRF04EB, while the pattern in the upper right corner of Figure 10 is measured with the antenna board used as stand alone board. SmartRF04EB has a solid ground plane. By plugging the antenna board into this, the effective ground plane seen by the antenna is increased; this effects the antenna match and also the SmartRF04EB ground plane restricts emissions compared to using the antenna board as stand alone. The change in size and shape of the ground plane not only changes the gain but the radiation pattern. Since many SRD applications are mobile, it is not always the peak gain that is most interesting. The TRP and antenna efficiency gives a better indication on power level that is transmitted from the AUT.

CC-Antenna-DK Board 6 on SmartRF04EB

CC-Antenna-DK Board 6 as stand alone

Figure 10. Influence on Shape and Size of the Ground Plane on Radiation Pattern

5.2 Directional

Antennas

High gain does not automatically mean that the antenna has good performance. Typically for a system with mobile units it is desirable to have an omni-directional radiation pattern such that the performance will be approximately the same regardless of which direction the units are pointed relative to each other.

Applications environments such as corridor coverage, metering surveillance, and maximum range distance between two fixed devices can be ideal applications for the directional type of antennas. One advantage of using a directional antenna is the PA power can be reduced due to the higher gain in the antenna between two devices for a given distance so that current consumption can be reduced. Another advantage is that the antenna gain can be utilized to achieve a greater range distance between two devices.

However, a disadvantage of using directional antennas is that the positioning of the transmitter and receiver unit must be known in detail. If this information is not known then it is best to use a standard omni-directional antenna design such as described in DN007 [4].

5.3 Size, Cost and Performance

The ideal antenna is infinitely small, has zero cost and has excellent performance. In real life this is not possible. Therefore a compromise between these parameters needs to be found. By reducing the operating frequency by a factor of two, the effective range is doubled. Thus one of the reasons for choosing to operate at a low frequency when designing an RF application is often the need for long range. However, most antennas need to be larger at low frequencies in order to achieve good performance, Table 1.

In some cases where the available board space is limited, a small and efficient high frequency antenna could give the same or better range than a small an inefficient low frequency antenna. A chip antenna is a good alternative when seeking a small antenna solution. Especially for frequencies below 433 MHz, a chip antenna will give a much smaller solution compared to a traditional PCB antenna. The main draw backs with chip antennas are the increased cost and often narrow band performance.

Figure 11. Size v Performance Example using Boards 6 & 14 from CC-Antenna-Kit Figure 11 shows the layout of board 6 (868 MHz) and board 14 (169 MHz) from the CC-Antenna-Kit [29]. Both board size and area allocated for the antenna are identical for these two boards. Board 6 has been tuned for 868 MHz and Board 14 tuned for 169 MHz. The antenna efficiency of board 6 was recorded at 91% efficiency; board 14 antenna efficiency is very low at 7%. For the efficiency of the board 14, 169 MHz antenna to be increased; the antenna and GND size has to be physically increased. By using the meandering layout techniques on the PCB antenna, the total size can be reduced, refer to Table 1.

6 Antenna Measurements

6.1 Measuring Bandwidth with a Spectrum Analyzer

Using a spectrum analyzer, the bandwidth of the antenna can be observed by measuring the radiated power when stepping a carrier across the frequency band of interest. This can be easily done with the SmartRF Studio version 7, refer to Figure 12 for the screen dump of SmartRF Studio whilst performing a frequency sweep on CC1110.

Figure 12. Using SmartRF Studio to Perform a Frequency Sweep

The screen shot of the spectrum analyzer can be seen in Figure 13 whilst frequency sweeping to determine the bandwidth for a 2.4 GHz radio. For the 2.4 GHz frequency sweep measurement, a 2.4 GHz antenna must be connected to the spectrum analyzer so the radiated power can be measured from the AUT. The results show that the antenna has approximately 2 dB variation in output power across the 2.4 GHz frequency band and max radiation at the centre of this band.

Such measurements should ideally be performed in an anechoic chamber to obtain a correct absolute level. This kind of measurement can however also be very useful even if an anechoic chamber is not available. Performing such a measurement in an ordinary lab environment will give a relative result, which shows whether the antenna has optimum performance in the middle of the desired frequency band. The performance of the antenna connected to the spectrum analyzer will affect the result. Thus it is important that this antenna has approximately the same performance across the frequency band being used. This will ensure that the result gives a correct view of the relative change in performance across the measured frequency band.

Figure 13. Bandwidth of a 2.4 GHz Antenna.

6.2 Measuring RL, Impedance and Bandwidth with a Network Analyzer

The optimum method to characterize the antenna is to use a Network Analyzer so the Return Loss, Impedance and Bandwidth can be determined. This is done by disconnecting the antenna from the radio section and connecting a semi-rigid coax cable at the feed point of the antenna.

6.2.1 Mounting of cable for S11 measurements

It is invaluable to have semi-rigid cables in the lab for debugging RF. Solder first shielding onto an earth plane and then solder the 50 ohm connection. Minimize risk for ripping off tracks when connecting to the semi-rigid cable. Ready made semi-rigid cables are quite expensive but can be re-used again. A semi rigid coax cable is useful when performing measurements on prototypes. The outer of the cable should be soldered to ground while the inner conductor is soldered to the feed line of the antenna. It is important that the antenna is disconnected from the rest of the circuitry when this measurement is performed. The unshielded part of the inner conductor should be as short as possible to avoid introducing extra inductance when measuring and the outer should be soldered to ground as close as possible to the end of the cable.To avoid that the presence of the cable is affecting the result, the cable should be placed as far away from the antennas as possible

Figure 14. Mounting of Semi-Rigid Cable to Measure Antenna Characteristics

6.2.2 Calibration

It is important to calibrate the network analyzer before doing measurements. The network analyzer should be calibrated for a suitable frequency range containing the band where the antenna will operate. Typically network analyzers have a cable with SMA connector in the end. Calibration is performed by connecting three known terminations, 50 ohm load, short, and open, to this SMA connector. After calibration the reference plane will be at the connection point of the SMA connector. To measure the reflection at the feed point of the antenna, a semi rigid coax cable with SMA connector in one end, can be used. This cable is soldered to the feed point of the antenna and the connector is connected to the network analyzer. Return Loss is only dependent of the absolute value of the reflection coefficient and hence there is no need to move the reference plane to the feed point to make a correct measurement.

To measure the impedance of the antenna it is necessary to move the reference plane from the SMA connector to the feed point of the antenna. This must be done to adjust for the phase change caused by the semi rigid coax cable. On most network analyzers it is possible to choose an electrical delay to compensate for this phase change. The correct delay can be found by watching how the impedance varies, in the Smith Chart, when measuring the impedance with an open and shortened end of the coax cable.

With the end of the coax cable short circuited, the electrically delay should be varied until the impedance is seen as a point to the left in the Smith Chart. Theoretically the same electric delay should result in a point to the right in the Smith Chart when the end is left open. If there is a small difference between the optimum electric delay for the opened and short circuited case, the averaged value should be chosen. When the correct electric delay is found, a correct measurement of the impedance can be performed.

It is ideal to have dedicated boards that are specifically used just for calibration purposes. In the CC-Antenna-DK, there are three boards dedicated for calibration purposes, refer to

CC-Antenna-DK Using a semi-rigid cable

1. OPEN Board 9 end connection in air

2. SHORT Board 1 end connector to closest GND; shield connected

to GND

3. LOAD (50ohm) Board 2 useful to use two 100ohm parallel resistors

assembled at the end connection point; shield

connected to GND

Table 4. Calibration with CC-Antenna-DK Boards or Usage of Semi-Rigid Cable

By performing these steps then the antenna feed track or semi-rigid cable is also taken care of during the calibration. By just using the network analyzer calibration kit; then the semi-rigid cables will be a part of the measurements.

Keep the cables in a constant direction and it is good practice to use cable ties to maintain cables including network analyzer cables in a fixed position. The placement of the cable can affect the measurement result, especially if there are strong currents traveling back and forth on the ground plane.

Ferrites can be used to reduce the influence from currents running at the outer of the cable. PCBs which have a ground plane with dimensions that are a fraction of a wavelength tend to have larger currents running on the ground plane. This could potentially cause more unstable results when trying to measure the reflection at the feed pint of antennas implemented on such PCBs, refer to Figure 15. The placement of the ferrite along the cable will also affect the result. Thus it is important to understand that there is a certain inaccuracy when performing this kind of measurement.

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标之一,它表示天线在某一方向能量集中的能力。表示天线增益的单位通常有两个:dBi、dBd。两者之间的关系为:dBi=dBd+2.17 dBi定义为实际的方向性天线(包括全向天线)相对于各向同性天线能量集中的相对能力,“i”即表示各向同性——Isotropic。 dBd定义为实际的方向性天线(包括全向天线)相对于半波振子天线能量集中的相对能力,“d”即表示偶极子——Dipole。 两种增益单位的关系见图1: 图1 dBi与dBd的关系 天线增益不但与振子单元数量有关,还与水平半功率角和垂直半功率角有关。 2.天线方向图 天线辐射的电磁场在固定距离上随角坐标分布的图形,称为方向图。用辐射场强表示的称为场强方向图,用功率密度表示的称之功率方向图,用相位表示的称为相位方向图。 天线方向图是空间立体图形,但是通常用两个互相垂直的主平面內的方向图来表示,称为平面方向图。一般叫作垂直方向图和水平方向图。就水平方向图而言,有全向天线与定向天线之分。而定向天线的水平方向图的形状也有很多种,如心型、8字形等。 天线具有方向性本质上是通过振子的排列以及各振子馈电相位的变化来获得的,在原理上与光的干涉效应十分相似。因此会在某些方向上能量得到增强,而某

天线设计毕业论文

第一章绪论 一、绪论 1.1 课题的研究背景及意义 自古至今,通信无时无刻不在影响着人们的生活,小到一次社会交际中的简单对话;大到进行太空探索时,人造探测器与地球间的信息交换。可以毫不保留地说,离开了通信技术,我们的 生活将会黯然失色。近年来,随着光纤技术越来越成熟,应用范围越来越广。在广播电视领域, 光纤作为广播电视信号传输的媒体,以光纤网络为基础的网络建设的格局已经形成。光纤传输系统 具有的传输频带宽,容量大,损耗低,串扰小,抗干扰能力强等特点,已成为 城市最可靠的数字电视和数据传输的链路,也是实现直播或两地传送最经常使用的电视传送 方式。随着全球通信业务的迅速发展,作为未来个人通信主要手段的现代通信技 术引起了人们的极大关注,我国在移动通信技术方面投入了巨大的人力物力,我国很多地区的电力通信专用网也基本完成了从主干线向光纤过度的过程。目前,电力系统光纤通信网已成为我国规模较大,发展较为完善的专用通信网,其数据、语音,宽带等业务及电力生产专业业务都是由光纤通信承载,电力系统的生产生活,显然,已离不开光纤通信网。 无线通信现状另一非常活跃的通信技术当属,无线通信技术了。无线通信技术包括了移动通信技术和无线局域网( WLAN )技术等两大主要方面。移动通信就目前来讲是 3G时代,数字化和网络化已成为不可逆转的趋势。目前,移动通信已从模拟通信发展到了数字移动通 信阶段。无线局域网可以弥补以光纤通信为主的有线网络的不足,适用于无固定场所,或有线局域网架设受限制的场合,当然,同样也可以作为有线局域网的备用网络系统。WLAN ,目前广泛应用 IEEE802.11 系列标准。其中,工作于 2.4GHZ频段的 820.11可支持 11Mbps 的共享接入速率;而802.11a 采用 5GHZ 频段,速率高达 54Mbps ,它比802.11b 快上五倍,并和 820.11b兼容。给人们的生活工作带来了很大的方便与快捷。 在整个无线通信系统中,用来辐射或接收无线电波的装置成为天线,而通信、雷达、导航、广播、电视等无线电技术设备都是通过无线电波来传递信息的,均 需要有无线电波的辐射和接收,因此,同发射机和接收机一样,天线也是无线电技术设备的一个重要组成部分,其性能的优良对无线通信工程的成败起到重要作用。天线的作用首先在于辐射和接收无线电波,但是能辐射或接收电磁波的东西不一定都能作为天线。任何高频电路,只要不被完全屏蔽,都可以向周围空间或多或少地辐射电磁波,或从周围空间或多或少地接收电磁波,但是任意一个高频电路并不一定能用作天线,因为它的辐射或接收效率可能很低,要能够有效地辐射或接收电磁波,天线在结构和形式上必须满足一定的要求。快速发展的移动通信系统需要的是小型化、宽频带、多功能 (多频段、多极化 )、高性能的天线。微带天线作为天线 家祖的重要一员,经过近几十年的发展,已经取得了可喜的进步,在移动终端中采用内置微带天线,不但可以减小天线对于人体的辐射,还可使手机的外形设计多样化,因此内置微带天线将是未来天线技术的发展方向之一,设计出具有小型化的微带天线不但具有一定的理论价值而且具有重要的应用价值,这也成为当前国际天线界研究的热点之一。

天线选型

短波无线电通信天线选型 短波通信是指波长100-10米(频率为3-30MHz)的电磁波进行的无线电通信。短波通信传输信道具有变参特性,电离层易受环境影响,处于不断变化当中,因此,其通信质量,不如其它通信方式如卫星、微波、光纤好。短波通信系统的效果好坏,主要取决于所使用电台性能的好坏和天线的带宽、增益、驻波比、方向性等因素。近年来短波电台随着新技术提高发展很快,实现了数字化、固态化、小型化,但天线技术的发展却较为滞后。由于短波比超短波、卫星、微波的波长长,所以,短波天线体积较大。在短波通信中,选用一个性能良好的天线对于改善通信效果极为重要。下面简单介绍短波天线如何选型和几种常用的天线性能。 一、衡量天线性能因素: 天线是无线通信系统最基本部件,决定了通信系统的特性。不同的天线有不同的辐射类型、极性、增益以及阻抗。 1.辐射类型:决定了辐射能量的分配,是天线所有特性中最重要的因素,它包括全向型和方向型。 2.极性:极性定义了天线最大辐射方向电气矢量的方向。垂直或单极性天线(鞭天线)具有垂直极性,水平天线具有水平极性。 3.增益:天线的增益是天线的基本属性,可以衡量天线的优劣。增益是指定方向上的最大辐射强度与天线最大辐射强度的比值,通常使用半波双极天线作为参考天线,其它类型天线最大方向上的辐射强度可以与参考天线进行比较,得出天线增益。一般高增益天线的带宽较窄。 4.阻抗和驻波比(VSWR):天线系统的输入阻抗直接影响天线发射效率。当驻波比(VSWR)1:1时没有反射波,电压反射比为1。当VSWR大于1时,反射功率也随之增加。发射天线给出的驻波比值是最大允许值。例如:VSWR为2:1时意味着,反射功率消耗总发射功率的11%,信号损失0.5dB。VSWR为1.5:1时,损失4%功率,信号降低0.18dB。 二、几种常用的短波天线 1.八木天线(YagiAntenna)八木天线在短波通信中通常用于大于6MHz以上频段,八木天线在理想情况下增益可达到19dB,八木天线应用于窄带和高增益短波通信,可架设安装在铁塔上具有很强的方向性。在一个铁塔上可同时架设几个八木天线,八木天线的主要优点是价格便宜。 2.对数周期天线(LogPeriodicAntenna)对数周期天线价格昂贵,但可以使用在多种频率和仰角上。对数周期天线适合于中、短波通信,利用天波信号,效率高,接近于发射期望值。与其它高增益天线相比,对数周期天线方向性更强,对无用方向信号的衰减更大。 3.长线天线(Long-WireAntennas)长线天线优点是结构简单,价格低,增益适中。与八木天线和对极周期天线比,长线天线长度方向性和增益低。但其优势在于,由于其增益与线长度有关,用户可以找到最佳接收线的长度和角度。通过比较信号波长,计算出线的长度,非常适合于远距离通信。当线长4倍波长在仰角为25度时与双极天线比增益高3dB,当线长8倍于波长时,增益高6dB,仰角下降到18度,图1为长线天线增益示图。

HFSS 天线设计实例

HFSS 天线设计实例 这是一种采用同轴线馈电的圆极化微带天线 切角实现圆极化 设计目标!(具体参数可能不精确,望大家谅解)主要讲解HFSS操作步骤! GPS微带天线:介质板:厚度:2mm,介电常数:2.2,大小:100mm*100mm 工作频率:1.59GHz,圆极化(左旋还是右旋这里不讲了哈),天线辐射在上半平面覆盖! 50欧同轴线馈电, 1、计算参数 首先根据经验公式计算出天线的基本参数,便于下一步建立模型。 贴片单元长度、宽度(正方形贴片长宽相等)、馈电点位置,分离单元长度.下表是经HFSS分析后选择的一组参数:

2、建立模型 首先画出基板50mm*50mm*2mm 的基板 起名为substrate 介电常数设置为如图2.2的,可以调整color颜色和transparent透明度便于观察 按Ctrl+D可以快速的使模型全可见!按住Ctrl+Alt键,拖动鼠标可以使3D模型自由旋转同理,我们画贴片:

1、在基板上画出边长65mm(假设用公式算出的是这么多)的正方形 2、起名为patch,颜色选绿色,透明度设为0。5 画切角是比较麻烦的 1、用画线条工具,画三线段,坐标分别是0.5.0, 5.0.0, 0.0.0 2、移动三角形,选中polyline1,选菜旦里edit\Arrange\move,先确定坐标原点或任一点为基准点,将三角形移动到左上角和贴片边沿齐平。 3、复制三角形,选中polyline1,选菜单里edit\arrange\duplicate\around axis,相对坐标轴复制,角度换成180,然后在右下角就出现了相对称的另一个三角形。 4、从patch上切掉对角上的分离单元polyline1和polyline1_1: 选中patch、polyline1和polyline1_1,选菜单里3D modeler\Boolean\Subtract 把polyline1和polyline1_1从patch上切掉最后剩下 先在介质板底面画一个100mm*100mm的正方形作为导电地板。起名为 ground 下面就是画馈源了:我们采用同轴线馈电,有两种建模方法: 1、在馈电点画一0.5mm的铜柱代表同轴线内导体,起名为feed 2、在介质板底面馈电点处画一1.5mm的圆,起名为port 3、复制port为port1,复制feed为feed1 4、复选port和feed1,执行菜单里3D Modeler\Boolean\Subtract,使port成为一个内径0.5mm外径1.5mm

分形几何的应用

分形几何及其应用 【摘要】分形几何作为一门新兴的学科已经开始逐渐发展,分形研究深入到各学科领域。本文介绍了分形几何在地图学中、天线设计中的一些应用。 【关键词】分形几何;天线;研究 分形几何是美籍法国数学家芒德勃罗在20世纪70年代创立的一门数学新分支,它研究的是广泛存在于自然界和人类社会中一类没有特征尺度却有自相似结构的复杂形状和现象,它与欧氏几何不同。欧氏几何是关于直觉空间形体关系分析的一门学科,它研究的是直线、圆、正方体等规则的几何形体,这些形体都是人为的。但是,“云彩不是球体、山岭不是锥体、海岸线不是圆周”,自然界的众多形状都是如此的不规则和支离破碎。对这些形状的认识,欧几里得并未能给后人留下更多的启示,传统的欧氏几何在它们面前显得那样的苍白无力。对大自然的这种挑战,二千年来,激励着一代又一代的数学家上下求索,探寻从欧氏几何体系中解放出来的道路。终于在1975年,芒德勃罗发表了被视为分形几何创立标志的专著《分形:形、机遇和维数》。从此,一门崭新的数学分支——分形几何学跻身于现代数学之林。 一、分形几何学在地图中的应用 欧几里得几何在规则、光滑形状(或有序系统)的研究中相当有效。然而,现实世界中却有许多问题不能用欧氏几何去解决。英国

人l.理查森考察海岸线的长度问题,发现在西班牙、葡萄牙、比利时、荷兰等国出版的百科全书记录的一些海岸长度竟相差20%。法国数学家蒙德尔罗布采用瑞典数学家柯克发现的“柯克曲线”作为思考海岸线问题的数学模型,通过深入研究并引进了分数维概念,1977年正式将具有分数维的图形称为“分形”,并建立了以这类图形为对象的数学分支——分形几何。 现实空间和地图上有许多类似海岸线那样的不规则曲线,分形几何为这类曲线的度量提供了数学工具。 二、分形几何在天线设计中的应用 分形几何两个独特的特征:自相似性(或自仿射性)和空间填充性,结合天线的特征,使得分形几何在天线工程领域中的应用有了突破性的发展。分形天线的自相似性能减小分形天线元的整体宽度,同时和欧几里德几何天线元保持同样的性能,因为各个天线元具有同样的谐振频率和相同的辐射方向图。分形元能够改善运用欧氏几何天线元的线性天线阵列的设计,运用分形元来改善和提高天线阵列的性能。这里讨论两种方法: 一种方法就是减小天线元之间的相互耦合。因为线性阵列中天线元之间的相互耦合导致整个天线的辐射方向图性能下降。相互耦合还能改变天线元的激发电流。因此,如果在阵列天线的设计过程中忽略天线元之间的内部耦合作用,那么天线的辐射方向图就会受到影响,通常表现为副瓣电平的提高甚至导致零信号的填充。

2.4 GHz天线的选择和选择标准

Options and Selection Criteria for 2.4 GHz Antennas 2.4 GHz is a sweet spot for modern-day RF design can be demonstrated by mentioning a few well-known names: Bluetooth, ZigBee, Wi-Fi and WLAN. One can also toss cellular applications into the mix. Clearly, this unlicensed band allows a variety of handheld, mobile, and fixed base station designs that communicate either point-to-point, or are routed through a cellular or mesh network. Popularity, however, brings technical issues. Even with channel s egmentation, one standard’s signal can step on another and clog up throughput. Fortunately, frequency allocations, algorithms, time-slicing, and back-off timers, among other techniques, help let everyone share the band and play nicely together. Even so, achieving optimum performance and meeting reliability goals calls for superior antenna design and close attention to the associated components that keep everything resonant. What is more, whether balanced or single ended, the transmit gain and receive sensitivity depend on the physical nature of the antenna and its radiation pattern. This article takes a look at 2.4 GHz antennas and the coupling networks that make them work. It examines commercially available single-chip antennas that are designed to work in the 2.4 GHz ISM band. It discusses antenna types, RF distribution patterns, and range and design issues associated with using a single-chip antenna, as opposed to a connector- mounted external antenna or PCB antenna. All parts, datasheets, development kits and training modules referenced here are available on Digi-Key’s website. The signal path Key in making your antenna perform as desired is the signal path to the antenna. While most RF chips have good output stages, matching, filtering, and splitting still may be needed, especially if a single antenna is used for more than one communications standard. As such, the typical RF output stages must still connect to either a single ended, balanced, or diplexed matching network (Figure 1).

hfss设计天线范例

第二章创建项目 本章中你的目标是: √保存一个新项目。 √把一个新的HFSS设计加到已建的项目 √为项目选择一种求解方式 √设置设计使用的长度单位 时间:完成这章的内容总共大约要5分钟。 一.打开HFSS并保存一个新项目 1.双击桌面上的HFSS9图标,这样就可以启动HFSS。启动后的程序工作环境如图:

图2-1 HFSS工作界面 1.打开File选项(alt+F),单击Save as。2.找到合适的目录,键入项目名hfopt_ismantenna。 图2-2 保存HFSS项目 二.加入一个新的HFSS设计 1.在Project菜单,点击insert HFSS Design选项。( 或直接点击图标。)一个新的工程被加入到hfopt_ismantenna项目中,默认名为HFSSModel n。

图2-3 加入新的HFSS设计 2.为设计重命名。在项目树中选中HFSSModel1,单击鼠标右键,再点击Rename项,将设计重命名为hfopt_ismantenna。 图2-4 更改设计名

三.选择一种求解方式 1.在HFSS菜单上,点击Solution Type选项. 2.选择源激励方式,在Solution Type 对话框中选中Driven Mode项。 图2-5 选择求解类型图2-6 选择源激励方式 四.设置设计使用的长度单位

1.在3D Modeler菜单上,点击Units选项. 2.选择长度单位,在Set Model Units 对话框中选中mm项。 图2-5 选择长度单位图2-6 选择mm作为长度单位 第三章构造模型 本章中你的目标是: √建立物理模型。 √设置变量。 √设置模型材料参数 √设置边界条件和激励源 √设置求解条件 时间:完成这章的内容总共大约要35分钟。

天线设计毕业论文,DOC

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