Intermodulation

INTERMODULATION 

1. Introduction

The INTMOD program performs harmonic and intermodulation analysis of 2 and/or 3 signals of 3^rd, 5^th or 7^th order mixing.  The user enters the transmitter and receiver frequencies in MHz with their corresponding bandwidths in kHz.  The user may enter the lists interactively or use a database built from a previous run.

2. Harmonics and Intermodulation analysis

            Background

Mutual interference may occur between two circuits operating at different frequencies because of radiation at frequencies other than the operating frequencies.  A transmitter may radiate harmonics of its operating frequency, which may affect a receiver tuned to one of the harmonics.

Intermodulation products result in interference, when two or more signals combine in a nonlinear device and produce an undesired signal on or near the tuned frequency of the victim receiver.  The combination process can occur in the final stage of a transmitter or in the RF of first mixer circuitry of a receiver.

When the number of transmitters is increased, the number of possible intermodulation frequencies increases rapidly.  The most serious of these frequencies are the third order products of the form 2f₁ – f₂ or f₁ + f₂ – f₃, where f₁, f₂ and f₃ are operating frequencies of the transmitters.  The interference will be most serious when all or several of the frequencies, both transmitting and receiving, are in close proximity.  To minimize intermodulation, frequencies should be selected such that the frequency difference between any pair of frequencies is unlike the difference between any other pair.  In some cases, the specific operating frequencies can be chosen so that no third order product frequency coincides with a receiving channel frequency at the same or a nearby site.

Harmonic Analysis Equation

The mixing of frequencies whereby the largest frequency is greater than twice the smallest frequency is not analyzed.  Harmonic interference is defined below.

A f_t = f_r ± BW                                                             (2.1)

where, A is either 1 or 2, f_t is the transmitter frequency, f_r is the receiver frequency and BW is the receiver bandwidth.

Intermodulation Analysis Equations

The interference due to intermodulation is defined by the following equations.  The analysis only considers in-band modulation products.

Two Signal Case

3^rd order:                            2 f_t1 – f_t2 = f_r ± BW                                                     (2.2)

5^th order:                          3 f_t1 – 2 f_t2 = f_r ± BW                                                    (2.3)

7^th order:                          4 f_t1 – 3 f_t2 = f_r ± BW                                                    (2.4)

Three Signal Case

3^rd order:                        f_t1 – f_t2 + f_t3 = f_r ± BW                                                    (2.5)

5^th order:                    2 f_t1 - 2f_t2 + f_t3 = f_r ± BW                                                    (2.6)

                                   3 f_t1 – f_t2 – f_t3 = f_r ± BW                                                     (2.7)

7^th order:               2 f_t1 – 3 f_t2 + 2 f_t3 = f_r ± BW                                                    (2.8)

                                3 f_t1 – 3 f_t2 + f_t3 = f_r ± BW                                                    (2.9)

                                4 f_t1 – 2 f_t2 – f_t3 = f_r ± BW                                                     (2.10)  

        

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Line of sight antenna coverage Model (Shado)

Line of sight antenna coverage Model (Shado)

1. Introduction

The SHADO program is a line-of-sight antenna coverage model, which can handle up to two antennas. It generates a plot of a specified area and will shade the areas that are within the line-of-sight of either antenna or both antennas. SHADO uses terrain/topographic database.

2. Analysis

Terrain profiles are generated for each antenna site. Profile analysis is then performed to determine whether the end point of each profile is in the radio line-of-sight (LOS) or it lies within the earth’s shadow (Figure 1). In Figure 1, q_n is the radio horizon elevation angle to n^th profile point. Primary objective is to determine the elevation that constitutes the limiting LOS along each profile.

Figure 1. A profile path from an antenna site

Two factors must be taken into consideration: the bending of radio waves as they propagate through the atmosphere due to refractivity and the effects of earth’s curvature with respect to the elevations. The program uses the user specified refractivity value to compute the amount of ray bending. If the default refractivity of 301 is used, a 4/3 radius earth is assumed to be correct for ray bending. Radio horizon angles are then calculated from the beginning of the profile to the end-point, which represents a grid point coordinate. The rays representing waves from the antenna site along the profile to the end point are represented as straight lines for a 4/3 earth’s radius.

If the elevation angle of the profile end-point, with respect to the antenna site, is less than the calculated radio horizon angle, then the grid point coordinate lies within the earth’s shadow (Figure 2).

Figure 2. Profile path with an end-point within earth’s shadow

For an end-point within the LOS, the radio horizon angle is that formed by a direct ray from the antenna site to the profile end-point (Figure 3).

Figure 3. Profile path with an end-point within LOS

Plots are generated where each grid point is shaded to indicate whether it is within the LOS with respect to each antenna site (Figures 4 and 5). The program generates 3721 (61 X 61) profiles along a number of equally spaced radials emanating from each antenna site to each grid point on the plot as an extension of the PROFILE program. These sites do not have to be within the area of the overlay.

Figure 4. Path 1 shows a radial with Figure 5. Path 1 end-point within

end-point within LOS, Path 2 with LOS and is clear at bin 3,7, path 2

end-point within earth’s shadow. End-point within earth’s shadow

and is black at bin 5,9.

Analysis of the profiles makes it possible to determine the grid coordinates at which signals approaching or emanating from the site will be detected on a LOS basis. This information is consolidated to produce LOS shading contours around the site, which provide a composite of the sites’ coverage, as determined by terrain features. The engineer can determine a site location with the best use of the terrain characteristics by locating the proposed antenna at each point on the grid.

3. Input Parameters

The input parameters are the latitudes and longitudes of the southwest and northeast corners of the plot area, the latitude(s) and longitude(s) of antenna(s), surface refractivity, the antenna height(s), and optionally the antenna site elevation(s). The latitudes and longitudes are expressed in degrees North and West respectively. The default site elevation is calculated from the terrain profile. The antenna heights and the site elevation can be in English or Metric units.

4.Output

The output from the program SHADO is a map, which shows the location(s) of one or two antennas and the LOS coverage by the antenna(s)

Single Emitter analysis Model

1.Introduction

The single-emitter analysis model (SEAM) estimates the signal levels received at a specified propagation distance in terms of the field strength or emitter power of a single emitter. The estimated signal levels are field strength, power flux density, power and voltage. An inverse computation estimates the propagation distance required for the received signal level to meet a threshold value specified by the user.

A propagation model option is included in the package as a subroutine for path loss versus distance determination as a function of emission frequency in both direct and inverse modes. The user selects free-space or smooth-earth propagation, with the Integrated Propagation System (IPS) model representing the smooth-earth option.

The user also selects the computation mode: Direct or Inverse and the user is prompted only for those input parameters needed for the selected computation mode. In the Direct mode, the received signal parameters, such as, propagation loss L_p in dB, field strength in mV/m and dBmV/m, power density P_d in mW/m² and dBm/m², received power P_r in mW and dBm and received voltage V_r in mV and dBmV, are computed and displayed for specified emission frequency, emission level and propagation distance. In the Inverse mode, propagation loss L_p in dB and the propagation distance D in km are computed and displayed for specified emission frequency and received signal threshold selected by the user.

The user can also select Field strength E₀ at reference distance D₀ or the emitter power to specify the emission level in either direct or inverse mode. The emitter can be expressed in either equivalent isotropic radiated power (EIRP) or the transmitter power P_t and transmitter antenna gain G_t, where EIRP = P_tG_t.

In the inverse mode, the received signal threshold can be specified in terms of one of the following: received voltage threshold V_rt, received power threshold P_rt, power density threshold P_dt or field strength threshold E_t.

2. Input parameters

The input parameters for direct mode are emission frequency F in MHz, EIRP and transmitter power P_t in W, mW, nW, dBm or dBW, transmitter and receiver antenna gains G_t and G_r respectively in dBi, field strength E₀ in mV/m or mV/m, receiver antenna diameter D_r in m, and, reference and propagation distances D₀ and D respectively in m.

The input parameters for the inverse mode include the received signal threshold instead of the propagation distance. The threshold values of either the received voltage V_rt in dBmV/m or received power P_rt in dBm or power flux density P_dt in dBm/m² or field strength E_t in dBmV/m.

The IPS model also requires transmitter and receiver antenna heights, transmitter antenna polarization and environmental data as input parameters, which are entered through a dedicated screen that includes parameter ranges and helpful suggestions. The environmental data needed are ground conductivity (0.0001– 5.0 mho/m), ground dielectric constant (1.00–81.00) and atmospheric refractivity (200.00 – 450.00). The suggested values of electrical ground constants are given below.

Conductivity (mho/m) Dielectric Constant

Average ground 0.005 15.0

Poor ground 0.001 4.0

Good ground 0.020 25.0

Fresh water 0.010 81.0

Sea water 5.000 81.0

3. Analysis

The input/output computations are performed with a set of standard units and formulas. Any unit conversion is done before or after the input/output formulas are applied. This permits the potential modification of the input and output units without affecting the set of input/output formulas implemented in the package. The EIRP is automatically derived if the transmitter power and antenna gain are specified. The receiver antenna gain is automatically derived if the receiver antenna diameter is specified, assuming a parabolic dish with an efficiency factor n = 0.55. If neither the receiver gain nor the receiver antenna diameter is given, a default value of G_r = 0.0 dBi is provided.

The input/output formulas employed in the direct and the inverse mode computations are summarized in Tables 1 and 2 respectively. Each table consists of two sets of formulas, with one set corresponding to the field strength input option and the other to the emitter power input option. The formulas assume a medium characteristic impedance of 377 ohms and a receiver load impedance of 50 ohms.

The IPS propagation model is hard wired to its envelope mode (minimum path loss magnitude) and median signal attenuation (50% path loss percentile).

TABLE 1

SEAM DIRECT MODE INPUT/OUTPUT FORMULAS

Case of Field Strength (E₀, D₀) Input Parameter

E (dBmV/m) = -27.6 + E₀ (dBmV/m) + 20 log D₀ (m) + 20 log F (MHz) – L_p (dB)

V_r (dBmV) = 2.2 + E₀ (dBmV/m) + 20 log D₀ (m) + G_r (dBi) - L_p (dB)

P_r (dBm) =-104.8+ E₀ (dBmV/m) + 20 log D₀ (m) + G_r (dBi) - L_p (dB)

P_d (dBm/m²) =-143.3+ E₀ (dBmV/m) + 20 log D₀ (m) + 20 log F (MHz) – L_p (dB)

L_p (dB) = Propagation Model evaluated at D (m) in Direct Mode

Case of EIRP Input Parameter

E (dBmV/m) = 77.2 + EIRP (dBm) + 20 log F (MHz) – L_p (dB)

V_r (dBmV) =107.0 + EIRP (dBm) + G_r (dBi) – L_p (dB)

P_r (dBm) = EIRP (dBm) + G_r (dBi) – L_p (dB)

P_d (dBm/m²) = -38.5 + EIRP (dBm) + 20 log F (MHz) – L_p (dB)

L_p (dB) = Propagation Model evaluated at D (m) in Direct Mode

Note: The conversion algorithm between the two cases above is

EIRP (dBm) = -104.8 + E₀ (dBmV/m) + 20 log D₀ (m),

based on free space propagation at the reference distance D₀ (m)

TABLE 2

SEAM INVERSE MODE INPUT/OUTPUT FORMULAS

Case of Field Strength (E₀, D₀) Input Parameter

L_p (dB) = -104.8 + E₀ (dBmV/m) + 20 log D₀ (m) + G_r (dBi) – P_rt (dBm)

= -143.3 + E₀ (dBmV/m) + 20 log D₀ (m) + 20 log F (MHz) – P_dt (dBm/m²)

= -27.6 + E₀ (dBmV/m) + 20 log D₀ (m) + 20 log F (MHz) – E_t (dBmV/m)

= 2.2 + E₀ (dBmV/m) + 20 log D₀ (m) + G_r (dBi) – V_r (dBmV)

D (m) = Propagation Model evaluated at Lp (dB) in Inverse Mode

Case of EIRP Input Parameter

L_p (dB) = EIRP (dBm) + G_r (dBi) –P_rt (dBm)

= -38.5 + EIRP (dBm) + 20 log F (MHz) - P_dt (dBm/m²)

= 77.2 + EIRP (dBm) + 20 log F (MHz) + E_t (dBmV/m)

=107.0 + EIRP (dBm) + G_r (dBi) –V_r (dBmV)

D (m) = Propagation Model evaluated at L_p (dB) in Inverse Mode

Note: The conversion algorithm between the two cases above is

EIRP (dBm) = -104.8 + E₀ (dBmV/m) + 20 log D₀ (m),

based on free space propagation at the reference distance D₀ (m)

4. Output

The direct mode outputs are Propagation Loss L_p in dB, Field Strength E in mV/m or dBmV/m, Power Flux Density P_d in mW/m² or dBm/m², Received Power P_r in mW or dBm and Received Voltage V_r in mV or dBmV.

The inverse mode outputs are Propagation Loss L_p in dB and Propagation Distance D in km.

Land Mobile Service : Okumura Hatta Models

Land Mobile Services

1. PROGRAM REQUIREMENTS

To begin the program, select LMS - Land Mobile Services from the Propagation menu

On program startup, an information dialog box is displayed describing the overall models and suggestions on selecting a model based on the input parameters. The dialog box also contains a checkbox option for not displaying on subsequent runs. Pressing the OK button will close the information dialog box and proceed to the main program.

The program is used to calculate and display loss and field strengths for the following models: ITU 529, Okumura-Hata-Davidson, and Cost 231. Chart 1 depicts the main functions.

2. CALCULATIONS

2.1 Single Calculations

Initially the user is presented with a dialog box containing input and output values (see Figure 1). To calculate model values, the user enters the following parameters:

Table 1 – Input Parameters

Parameter Range

Frequency Range 30 MHz to 2000 MHz

Distance Range 0 to 300 Km

Area Type Urban, Suburban, Rural

City Size Small / Medium, Large

Base Antenna Height 1m to 2500m

Mobile Antenna Height 1m to 10m

Power Enter in Watts or kW

Percent of Time 1% to 99%

Precent of Location 1% to 99%

If parameters are entered that fall out of the allowable range, a dialog box appears informing the user of the correct range, and the parameter is then set to a default value.

2.2 Units

Parameters can be entered using either English or Metric units. To specify the units select Units then either English or Metric.

2.3 Calculate

Pressing the calculate button causes the program to update the dB Loss and Field strength values. Values that are out of range for a model will appear with a red background. To have the out of range values blacked out, the user selects Hide out of range values from the calculate menu. To have out of range values appear in red again, select Show Out of Range Values from the calculate menu.

Table 2 – Model Ranges

Valid Model Ranges are as follows:

Model	Distance (Km)	Frequency (MHz)	Base Antenna Height (m)	Mobile Antenna Height (m)
ITU 529	+= 100	150 to 1500	30 to 200	1 to 10
Davidson	+=300	30 to 1500	20 to 2500	1 to 10
Cost 231	+=100	1500 to 2000	30 to 200	1 to 10

Every time new values are calculated with the calculate button, the new model values are updated on the screen and also saved to a report log. The report log maintains a table of values that can be viewed, printed and stored. The report can also be cleared. To view the Report Calculation Log, select Calculations, then View Output Report from the main menu.

2.4 Out of Range Parameters

To determine if the parameters entered are in a valid range for a particular model, click on the model name on the lower half of the display using the left mouse button. Text will appear below the input parameters describing the valid range for that model. In addition, the parameters that fall out of range for the model will appear with a red background. When the left mouse button is released, the display will return to normal.

2.5 The Report Calculation Log

The Report Calculation Log displays the calculation history in a scrollable list (see Figure 5). Selections are provided below the log to Clear, Print and Save the Log to a file. When saving the report log, you can choose a file type of .txt or .rtf. Selecting type .txt will save the report log as straight text loosing all formatting including underlines. Selecting the .rtf format will save the file as a rich text file that preserves all formatting. The .rtf file can be read directly into Microsoft Word. Note that values falling out of range for a model, as specified in Table 2, are displayed with an underline.

2.6 Calculate Values over Distance

A set of values can be calculated for a range of distances. This is accomplished by selecting Report for Distance Range from the Calculations main menu choice. This will bring up a dialog box providing choices for entering the start distance, end distance and step rate (see Figure 6). The step rate specifies the increments taken, as the model values are calculated from the start to the end distance. This can also be used to have the values generated in descending order by having a larger end value than start value and specifying a negative step increment.

A check box is provided indicating whether to clear the log before updating it with the calculated values. Pressing the Begin Sending Distance Range to Log button will start the process. However, if invalid start, end or step values have been specified, a dialog box will be displayed indicating the problem and the values will be automatically corrected. As the values are calculated a progress bar indicates how far along the calculation process has gone. The routine can be exited early by pressing the Exit Calculations button. The values thus far calculated will still be saved to the Report Calculation Log. If calculations are allowed to run to completion, the log will be automatically displayed. Since this is the same log used to display all calculations, resulting values will be appended to the bottom of this list. To clear the log, press the Clear button from the Report Calculation Log dialog box.

2.7 Graphing the Results

A comparison of model calculations for loss (see Figure 2) and field strength (see Figure 3) over distance can be displayed from the Graph menu choice. In the case of field strength values, the user can also select to display results for individual models in addition to the comparison (see Figure 4).

The graph is display in the upper portion of the dialog box, with the lower portion showing input parameters. The user can change the input parameters, then have the graph recalculated by pressing the Update Graph button. Note that when values have been changed, the background of the Update Graph button will change from blue to red. This is to indicate the values have changed and the graph needs to be updated. Menu choices are provided for specifying the units, and selecting the maximum calculated distance of 100 km or 300 km. In the case of field strength, additional menu choices are provided for displaying individual models and for hiding or displaying measured data.

The graph can be printed in three ways:

• Double click on the graph. This will bring up the properties dialog box. From this select the print tab. Pressing the Printer Setup button will allow you to change the selected printer and the paper orientation. To send the graph to the printer press print from the print tab.
• Select Print from the File tab. This will bring up a Print Graph dialog box containing three buttons: Printer Setup, Print and OK. Selecting the Printer Setup button will allow you to specify a printer and page orientation, Print will print out the graph and OK will close the dialog box.
• Press the Print Graph button below the graph. This will cause the above-mentioned Print Graph dialog box to appear.

The X-Y axes can be modified by double-clicking on the graph, then selecting the axis from the properties dialog box.

The graph can be saved as a Windows Meta File. The .WMF file can be read directly into Microsoft Word by selecting Insert, then Picture, then From File from the MS Word main menu.

A menu selection has been added to plot measured data with the model data. Though the option exists, it is meant for future use.

3. HELP

A series of help screens have been created to explain how to run the program. To call up the main Okumura-Hata help screen select General from the Help menu choice. The help screens also provide information on the individual models and the calculations used in the code. Pressing the F1 key will also bring up the help screen. Under the Help menu choice the user can select About for information on the program authors, or How to Use Help for general information on how to use the windows help system.

An information screen is displayed at the initial program startup. This screen contains a checkbox option to not be displayed on subsequent runs. Selecting Hide Startup Help from the Help menu will also turn off the startup information screen. Once the startup information screen has been turned of, it can be turned back on by selecting Show Startup Help from the Help menu.

4. EXITING THE PROGRAM

To exit the program, select Exit from the File menu choice. The program will automatically save the parameters displayed on the screen and recall them the next time the program is run. The values are saved in the system registry.

Figure 1: Function diagram

Figure 2: Main screen

Figure 3: dB Loss Graph Screen

figure 4: Field Strength Comparison Graph

Figure 5: Field Strength Single Model Graph Screen

Figure 6: Report Calculation Screen

Figure 7: Report Distance Range Screen