ANR010
R ANGE E STIMATOR

V ERSION 1.1
J ULY 19, 2023

WIRELESS CONNECTIVITY & SENSORSANR010 - Range Estimator

Contents
1 Introduction

3

2 Graphical User Interface

5

3 Fresnel zone

6

4 Calculation models
9
4.1
Friis transmission for free space . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.2
Two-ray ground reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
5 Conclusion

15

6 Important notes

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WIRELESS CONNECTIVITY & SENSORSANR010 - Range Estimator

Revision history
Document
Notes
versionDate

1.0• Initial version of this document

December2019

1.1• Updated Important notes, metadata and document style

July 2023

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WIRELESS CONNECTIVITY & SENSORSANR010 - Range Estimator

1 Introduction
When a radio connection is planned the given circumstances define largely the requirements
for radio range, operating temperature and available space. To ease the challenge of choosing
a suitable RF-module regarding the radio range Würth Elektronik eiSos makes freely available
the range estimator to find on the website http://www.we-online.com/redexpert. With this tool
the modules can be sorted and selected by their attributes. After selecting a module and maybe
changing the radio profile and antenna height it shows the calculated range for the Friis modeland for the two ray ground reflection model. This application note explains the theory behind
the two models, the requirements, differences and the reasonable use.

Figure 1: RedExpert

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Figure 2: Range Estimator Overview

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2 Graphical User Interface
In order to use the Range Estimator properly, a basic understanding of the selectable attributes
is required. The first step is to select a module which is suitable for the application. This will
preconfigure the input boxes to a default set of values for the Range Estimator Tool corresponding to the specific datasheet. These presets are typical conditions, and may need to be
adjusted by the user.
For example, the antenna height has to be adjusted to the utilized height, as this impacts thetwo ray radio range. Equally the use of an other radio profile with for example a higher data
rate would degrade the receiver sensitivity and consequently the radio range.
Label

Description

Nr.

Antennaenables switching troughradio profiles

1

Antennaabove groundselect antenna heights fortransmitter/receiver

2

TX Power

maximum power output of
the transmitter

3

RX Sensitivity

sensitivity of the receiver

4

Link Margin

power margin of thetransmission link

5

ModuleInformationshows used protocol andorder code of the selected
module6RFFrequencyshows operating
frequency of the selected
module7

Data Rate

specific data rate of theselected module in theselected radio profile

8

Link Budget

is the value of maximum
loss in the link withacceptable radio
connection

9

2-way Ground
Refelction
Modelshows the range
estimation calculated bythis model

10

Free Space
Range Estim.
(Friis Model)shows the range
estimation calculated bythis model

11

Figure 3: Range Estimator GUI

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3 Fresnel zone

Figure 4: Fresnel zone ideal simplified

Character

Description

Unit

c0

speed of light in vaccum[m/s]dtotaldistance from transmitter to receiver[m]f

the frequency of the transmitted
signal[Hz]Fnradius of the n-th Fresnel zone

[m]

Fnmax

maximum radius of the n-th Fresnel
zone between transmitter andreceiver[m]

λwavelength of the transmitted signal[m]nnumber of the Fresnelzonex

point on the line of sight between
transmitter and receiver[m]

The Fresnel zones are ellipsoids around the line of sight between the transmitter Tx and thereceiver Rx with the antennas in its focal point. There are multiple Fresnel zones around theline of sight. If an object is within the Fresnel zone in a matter, that a 2-segment path fromTx to Rx deflects off a point within that border. This corresponds to a time-of-arrival difference
between the line of sight and the reflected signal from objects, for the primary Fresnel zone of
between 0° and 90°, for the second between 90° and 270°, for the third between 270° and 450°
and so on. The primary Fresnel zone is the most important to keep free, because most of thesignal power will be transmitted in this area.
The radius of the any Fresnel zone at any chosen point on the line of sight x is calculated by

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WIRELESS CONNECTIVITY & SENSORSANR010 - Range Estimatorthe equations
Fn (x) =nλx(dtotal − x)=dtotals

nc0 x(dtotal − x)dtotal fso the equation for the radius on any chosen point on the line of sight isss
λx(dtotal − x)c0 x(dtotal − x)=
F1 (x) =dtotaldtotal f(1)(2)

this formula makes the assumption, that x and dtotal − x both are much longer than n · λ, for the
first Fresnel zone this means that x and dtotal − x have to be much longer than the wavelengthof the signal.
Due to this restriction the radius will not be accurate for distances close to the Tx- or Rxantenna.

Figure 5: The changing radius of the Fresnel zone for different frequencies with a dtotal of 1000
metersdtotal, which is actually right
The Fresnel zone shows the largest diameter for x = dtotal − x =2in the middle between Transmitter and Receiver.To get an impression on which objects may
cause power loss of the signal, it is often useful to know at least the maximum diameter of thefirst Fresnel zone. Which according to (1) is.
sp1
1 c0 dtotal
Fnmax =
λdtotal =(3)
22f
The dependency of the maximum radius from the frequency and the transmission distance isshown in this graph.

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Figure 6: Radius of the Fresnel zone
Obviously the radius of the Fresnel zone will increase for longer distances between Transmitterand Receiver. But also the frequency of the transmitted signals has a major influence to theradius of the Fresnel zone. A 2.44 GHz Signal will have an 8.5 meters maximum radius for aline of sight distance of 2350 meters. Will the signal be transmitted with a frequency of 868
MHz a maximum radius of 8.5 meters will only allow a line of sight distance below 850 meters.
As a short reminder, any object within the first Fresnel zone will damp the transmitted signal
and reduce the range of the transmission.

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4 Calculation models
Depending on the application it is often not possible to keep the Fresnel zone free of objects.
So it is essential to understand, that this has high influence on damping of the transmission
and therefore maintaining the range of a RF-module. But to estimate its range, a look on thespecific data-sheet is mandatory. There are several methods to calculate the range of a RFtransmission, but these equations are often very complex and unhandy for practical usage,
so simplification is needed. The results of the simplified equations are only approximations,but experience shows that the discussed equations are able to deliver reliable estimations forthe transmission range, when applied correctly. As a convention all symbols are in metricunits, if not otherwise declared. To improve understanding of basic equations metric units aremandatory, but because logarithmic values are commonly used in radio communication, it ispurposeful to also use the logarithmic units for the range calculation.
Character

Description

Unit

λ

wavelength of the signal

[m]

2RP L

path losses of the 2-ray ground reflection model

[dB]

c

speed of light in vacuum (299 792 458)

[m/s]

d

distance from transmitter to receiver[m]ffrequency of the signal

[m]

hT x

height of the transmitter antenna over ground

[m]

hRx

height of the receiver antenna over ground[m]

F SP L

path losses of the free space model

[dB]

LM

link margin (safety to ensure a received signal)

[dB]

PT x

total power emitted by the transmitting antenna[W] or [dBm]PRxtotal power received by the receiving antenna[W] or [dBm]

Rxsenssensitivity of the receiving RF module

[dB]

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4.1 Friis transmission for free space

Figure 7: Free space model
Friis transmission for Free Space is a model to calculate the path loss, to estimate the range ofa radio link in a free space environment.

Free field condition: The first Fresnel zone is free of objects

This model makes the assumption, that the emitted power is radiated equally in every direction(isotropic) and calculates the power loss only taking into account the decreasing power densityof the wavefront with increasing distance to the origin, without any reflection, absorption or
attenuation.
λ 2) ∗ PT x
4πd

(4)

PT x
4πd 2
4πd f 2
=(
) =(
)
PRx
λ
c

(5)

PRx = (
this leads to the free space path loss
F SP L =expressed in decibel this means,

F SP L[dB] = 10 log10 ((4πd f 2))c

F SP L[dB] = 20 log10 (

4πd f
)
c

4π
) + 20 log10 (d) + 20 log10 (f )c
To determine the maximum range of a Wurth Elektronik eiSos RF-module, the path losses of
F SBL[dB] = 20 log10 (10Version 1.1, July 2023

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Figure 8: Wave amplitude depending on the distance to the Tx antenna
the transmission are equaled to the ratio of the received power to the emitted power:
F SBL[dB] =PT x= PT x [dBm] − PRx [dBm]
PRx

(6)

4π
) + 20 log10 (d) + 20 log10 (f ) = PT x [dBm] − Rxsens [dBm] − LM [dB]c4πPT x [dBm] − Rxsens [dBm] − LM [dB] − 20 log10 ( ) − 20 log10 (f )c20
d = 1020 log10 ((7)

The calculated range depends on the frequency.

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Figure 9: Path losses for different frequencies

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4.2 Two-ray ground reflection

Figure 10: Two ray ground model
The two-ray ground reflection model is applied, when transmitter and receiver are in line ofsight but the first Fresnel zone is not free ob objects. So the calculation consideres the received
power of the direct line of sight path and in addition the power of the reflection path with slightphase difference. In the following a simplified formula is shown, giving suitable results forthe precondition of long distance between receiver and transmitter compared to their antennaheights, d » ht + hr .:
h2 h2
(8)
PRx = PT x T x 4 Rx
dWhich translates to
PT x
d4
= 2 2
(9)
2RP L =PRx
hT x hRx
and in decibel
2RP L[dB] = 40 log10 (d) − 20 log10 (hT x hRx )A very interesting aspect now is, that the formula depends on the heights of both antennas but
not on the frequency.

2RP L = f unction(hT x , hRx ) 6= f unction(f ).

To determine the maximum range of a module, the path losses of the transmission are equaled
to the ratio of the received power to the emitted power:
2RP L[dB] =PT x= PT x [dBm] − PRx [dBm]
PRx

(10)

40 log10 (d) − 20 log10 (hT x hRx ) = PT x [dBm] − Rxsens − LM

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WIRELESS CONNECTIVITY & SENSORSANR010 - Range Estimator
PT x [dBm] − Rxsens [dBm] − LM [dB] + 20 log10 (hT x hRx )40
d = 10(11)

Figure 11: Path losses for different antenna heights

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5 Conclusion
In a lot of cases there is the need of long distances with regard to the antenna height, so usually
the two ray ground model is a good fitting estimation. Only for some special cases with the freespace condition fulfilled the Friis model is useful.
Having a closer look to the models there are several interesting points to mention.
• One point is the dependency of the frequency. Often it is mentioned in general, that thelower the frequency is, the higher the range is. We have learned, that this is only the casewhen free field conditions are met. But there other effects of the frequency, as the fact,that for higher frequencies smaller objects will cause reflections, or that for low frequencies it might be hard to find an antenna with acceptable size and efficiency.
• An other important point is the influence of the antenna height on the range. The higher
the antennas can be placed, the longer is the range that can be reached. Placing an antenna directly above ground reduces the range so radical, a layman could hardly imagine.
Often there is stated the free field range for radio modules. This might be useful to compare
modules as the two ray ground model would differ depending on the chosen antenna height.
But the risk is to underestimate the difference between this model and the practical reachedrange.
To illustrate, that the Friss model range can diverge extremely from the real accomplish able
range, we compare the range estimations of the 2 models. Therefore we pick a module, fromwhich we know, by empirical values and costumer feedback, that the 2-ray ground reflection
model is very close to the real accomplished range. Our pick is the Thebe-II, a proprietary radio
module at 869 MHz. We adjust the antenna heights to some realistic values, 6 m for the transmitter and 6m for the receiver and use radio profile 3, which is one of the long range modes ofThebe-II. In the following screen shot (figure 12) we can clearly see in this example, that therange estimation with the Friis model is almost up to twenty times higher, than the range thatwill be achieved in a real application.
Comparing the two models one point catching attention is the often large difference in the
resulting range. This is easy explained by the formulas, as in the Friis model the distance isentered by the power of two, in the two ray model by the power of four.
By using the the range estimator on Redexpert tool range calculations can be cut, because therange estimation of the 2 ray ground model is pretty accurate.

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Figure 12: Range estimations for Thebe-II

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6 Important notes
The Application Note and its containing information ("Information") is based on Würth Elektronik eiSos GmbH & Co. KG and its subsidiaries and affiliates ("WE eiSos") knowledge andexperience of typical requirements concerning these areas. It serves as general guidance andshall not be construed as a commitment for the suitability for customer applications by WE
eiSos. While WE eiSos has used reasonable efforts to ensure the accuracy of the Information,
WE eiSos does not guarantee that the Information is error-free, nor makes any other representation, warranty or guarantee that the Information is completely accurate or up-to-date. The
Information is subject to change without notice. To the extent permitted by law, the Information
shall not be reproduced or copied without WE eiSos’ prior written permission. In any case,
the Information, in full or in parts, may not be altered, falsified or distorted nor be used for any
unauthorized purpose.
WE eiSos is not liable for application assistance of any kind. Customer may use WE eiSos’assistance and product recommendations for customer’s applications and design. No oral or
written Information given by WE eiSos or its distributors, agents or employees will operate tocreate any warranty or guarantee or vary any official documentation of the product e.g. data
sheets and user manuals towards customer and customer shall not rely on any provided Information. THE INFORMATION IS PROVIDED "AS IS". CUSTOMER ACKNOWLEDGES THATWE EISOS MAKES NO REPRESENTATIONS AND WARRANTIES OF ANY KIND RELATED
TO, BUT NOT LIMITED TO THE NON-INFRINGEMENT OF THIRD PARTIES’ INTELLECTUAL PROPERTY RIGHTS OR THE MERCHANTABILITY OR FITNESS FOR A PURPOSEOR USAGE. WE EISOS DOES NOT WARRANT OR REPRESENT THAT ANY LICENSE, EITHER EXPRESS OR IMPLIED, IS GRANTED UNDER ANY PATENT RIGHT, COPYRIGHT,
MASK WORK RIGHT, OR OTHER INTELLECTUAL PROPERTY RIGHT RELATING TO ANYCOMBINATION, MACHINE, OR PROCESS IN WHICH WE EISOS INFORMATION IS USED.
INFORMATION PUBLISHED BY WE EISOS REGARDING THIRD-PARTY PRODUCTS ORSERVICES DOES NOT CONSTITUTE A LICENSE FROM WE eiSos TO USE SUCH PRODUCTS OR SERVICES OR A WARRANTY OR ENDORSEMENT THEREOF.
The responsibility for the applicability and use of WE eiSos’ components in a particular customer design is always solely within the authority of the customer. Due to this fact it is up
to the customer to evaluate and investigate, where appropriate, and decide whether the device with the specific characteristics described in the specification is valid and suitable for therespective customer application or not. The technical specifications are stated in the current
data sheet and user manual of the component. Therefore the customers shall use the data
sheets and user manuals and are cautioned to verify that they are current. The data sheets
and user manuals can be downloaded at www.we-online.com. Customers shall strictly observe
any product-specific notes, cautions and warnings. WE eiSos reserves the right to make corrections, modifications, enhancements, improvements, and other changes to its products andservices at any time without notice.
WE eiSos will in no case be liable for customer’s use, or the results of the use, of the components or any accompanying written materials. IT IS CUSTOMER’S RESPONSIBILITY TO
VERIFY THE RESULTS OF THE USE OF THIS INFORMATION IN IT’S OWN PARTICULAR
ENGINEERING AND PRODUCT ENVIRONMENT AND CUSTOMER ASSUMES THE ENTIRERISK OF DOING SO OR FAILING TO DO SO. IN NO CASE WILL WE EISOS BE LIABLE FOR

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CUSTOMER’S USE, OR THE RESULTS OF IT’S USE OF THE COMPONENTS OR ANY ACCOMPANYING WRITTEN MATERIAL IF CUSTOMER TRANSLATES, ALTERS, ARRANGES,
TRANSFORMS, OR OTHERWISE MODIFIES THE INFORMATION IN ANY WAY, SHAPE OR
FORM.
If customer determines that the components are valid and suitable for a particular design andwants to order the corresponding components, customer acknowledges to minimize the risk ofloss and harm to individuals and bears the risk for failure leading to personal injury or death
due to customers usage of the components. The components have been designed and developed for usage in general electronic equipment only. The components are not authorized foruse in equipment where a higher safety standard and reliability standard is especially requiredor where a failure of the components is reasonably expected to cause severe personal injury
or death, unless WE eiSos and customer have executed an agreement specifically governing
such use. Moreover WE eiSos components are neither designed nor intended for use in areas
such as military, aerospace, aviation, nuclear control, submarine, transportation, transportation signal, disaster prevention, medical, public information network etc. WE eiSos must be
informed about the intent of such usage before the design-in stage. In addition, sufficient reliability evaluation checks for safety must be performed on every component which is used inelectrical circuits that require high safety and reliability functions or performance. COSTUMER
SHALL INDEMNIFY WE EISOS AGAINST ANY DAMAGES ARISING OUT OF THE USE OF
THE COMPONENTS IN SUCH SAFETY-CRITICAL APPLICATIONS.

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List of Figures
1
2
3
4
5
6
7
8
9
10
11
12

RedExpert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Range Estimator Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Range Estimator GUI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fresnel zone ideal simplified . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The changing radius of the Fresnel zone for different frequencies with a dtotal of1000 meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Radius of the Fresnel zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Free space model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Wave amplitude depending on the distance to the Tx antenna . . . . . . . . . . .
Path losses for different frequencies . . . . . . . . . . . . . . . . . . . . . . . . .
Two ray ground model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Path losses for different antenna heights . . . . . . . . . . . . . . . . . . . . . . .
Range estimations for Thebe-II . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3
4
5
6
7
8
10
11
12
13
14
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List of Tables

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Contact
Würth Elektronik eiSos GmbH & Co. KG
Division Wireless Connectivity & Sensors
Max-Eyth-Straße 174638 Waldenburg
Germany
Tel.: +49 651 99355-0
Fax.: +49 651 99355-69
www.we-online.com/wireless-connectivity