1. Rf Satellite Transmitter Power Supply

RF Satellite Link

Description: The 2408LT is an outdoor fiber optic transmitter for RF signals in the satellite L-Band or wider frequency range. It accepts a single RF input on coaxial cable and provides a single output for optical transmission.

This model shows a satellite link, using the blocks from the Communications Toolbox™ to simulate the following impairments:

• Memoryless nonlinearity

• Free space path loss

• Doppler error

• Receiver thermal noise

• Phase noise

• In-phase and quadrature imbalances

• DC offsets

The model optionally corrects most of these impairments.

By modeling the gains and losses on the link, this model implements link budget calculations that determine whether a downlink can be closed with a given bit error rate (BER). The gain and loss blocks, including the Free Space Path Loss block and the Receiver Thermal Noise block, determine the data rate that can be supported on the link in an additive white Gaussian noise channel.

Structure of the Example

The example highlights both the satellite link model and its signal scopes. The model consists of a Satellite Downlink Transmitter, Downlink Path, and Ground Station Downlink Receiver.

The blocks that correspond to each of these sections are

Satellite Downlink Transmitter

• Bernoulli Binary Generator - Creates a random binary data stream.

• Rectangular QAM Modulator Baseband - Maps the data stream to 16-QAM constellation.

• Raised Cosine Transmit Filter - Upsamples and shapes the modulated signal using the square root raised cosine pulse shape. Fallout new vegas gog.

• HPA Nonlinearity with Optional Digital Predistortion (High Power Amplifier) - Models a traveling wave tube amplifier (TWTA) using the Saleh model option of the Memoryless Nonlinearity and optionally corrects the AM/AM and AM/PM with a Digital Predistortion block.

• Gain (Tx Dish Antenna Gain) - Applies gain of the transmitter parabolic dish antenna.

Rf Satellite Transmitter Power Supply

Downlink Path

• Free Space Path Loss (Downlink Path) - Attenuates the signal by the free space path loss.

• Phase/Frequency Offset (Doppler Error) - Rotates the signal to model Doppler error on the link.

Ground Station Downlink Receiver

• Gain (Rx Dish Antenna Gain) - Applies gain of the receiver parabolic dish antenna.

• Receiver Thermal Noise (Satellite Receiver System Temp) - Adds white Gaussian noise that represents the effective system temperature of the receiver.

• Phase Noise - Introduces random phase perturbations that result from 1/f or phase flicker noise.

• I/Q Imbalance - Introduces DC offset, amplitude imbalance, or phase imbalance to the signal.

• LNA (Low Noise Amplifier)- Applies low noise amplifier gain.

• Raised Cosine Receive Filter - Applies a matched filter to the modulated signal using the square root raised cosine pulse shape.

• DC Blocking - Compensates for the DC offset in the I/Q Imbalance block.

• AGC - Sets the signal power to a desired level.

• I/Q Imbalance Correction - Estimates and removes I/Q imbalance from the signal by a blind adaptive algorithm.

• Doppler Correction - Uses the Carrier Synchronizer block to compensate for the carrier frequency offset due to Doppler.

• Rectangular QAM Demodulator Baseband - Demaps the data stream from the 16-QAM constellation space.

Exploring the Example

Double-click the block labeled Model Parameters to view the parameter settings for the model. All these parameters are tunable. To make changes to the parameters as the model is running, apply them in the dialog, then update the model via ctrl+d. The parameters are:

Satellite altitude (km) - Distance between the satellite and the ground station. Changing this parameter updates the Free Space Path Loss block. The default setting is 35600.

Frequency (MHz) - Carrier frequency of the link. Changing this parameter updates the Free Space Path Loss block. The default setting is 4000.

Transmit and receive antenna diameters (m) - The first element in the vector represents the transmit antenna diameter and is used to calculate the gain in the Tx Dish Antenna Gain block. The second element represents the receive antenna diameter and is used to calculate the gain in the Rx Dish Antenna Gain block. The default setting is [.4 .4].

Noise temperature (K) - Allows you to select from four effective receiver system noise temperatures. The selected noise temperature changes the Noise Temperature of the Receiver Thermal Noise block. The default setting is 20 K. The choices are

• 0 (no noise) - Use this setting to view the other RF impairments without the perturbing effects of noise.

• 20 (very low noise level) - Use this setting to view how easily a low level of noise can, when combined with other RF impairments, degrade the performance of the link.

• 290 (typical noise level) - Use this setting to view how a typical quiet satellite receiver operates.

• 500 (high noise level) - Use this setting to view the receiver behavior when the system noise figure is 2.4 dB and the antenna noise temperature is 290K.

HPA backoff level - Allows you to select from three backoff levels. This parameter is used to determine how close the satellite high power amplifier is driven to saturation. The selected backoff is used to set the input and output gain of the Memoryless Nonlinearity block. The default setting is 30 dB (negligible nonlinearity). The choices are

• 30 dB (negligible nonlinearity) - Sets the average input power to 30 decibels below the input power that causes amplifier saturation (that is, the point at which the gain curve becomes flat). This causes negligible AM-to-AM and AM-to-PM conversion. AM-to-AM conversion is an indication of how the amplitude nonlinearity varies with the signal magnitude. AM-to-PM conversion is a measure of how the phase nonlinearity varies with signal magnitude.

• 7 dB (moderate nonlinearity) - Sets the average input power to 7 decibels below the input power that causes amplifier saturation. This causes moderate AM-to-AM and AM-to-PM conversion, which is correctable with digital predistortion.

• 1 dB (severe nonlinearity) - Sets the average input power to 1 decibel below the input power that causes amplifier saturation. This causes severe AM-to-AM and AM-to-PM conversion, and is not correctable with digital predistortion.

Doppler error - Allows you to select one of two values of Doppler. The selection updates the Phase/Frequency Offset (Doppler Error) block. The default setting is 0 Hz. The choices are

• 0 Hz - No Doppler on the link.

• 3 Hz - Adds 3 Hz carrier frequency offset.

Phase noise - Allows you to select from three values of phase noise at the receiver. The selection updates the Phase Noise block. The default setting is Negligible (-100 dBc/Hz @ 100 Hz). The choices are

• Negligible (-100 dBc/Hz @ 100 Hz) - Almost no phase noise.

• Low (-55 dBc/Hz @ 100 Hz) - Enough phase noise to be visible in both the spectral and I/Q domains, and cause bit errors when combined with thermal noise or other RF impairments.

• High (-48 dBc/Hz @ 100 Hz) - Enough phase noise to cause errors without the addition of thermal noise or other RF impairments.

I/Q imbalance and DC offset - Allows you to select from five types of in-phase and quadrature imbalances at the receiver. The selection updates the I/Q Imbalance block. The default setting is None. The choices are

• None - No imbalances.

• Amplitude imbalance (3 dB) - Applies a 1.5 dB gain to the in-phase signal and a -1.5 dB gain to the quadrature signal.

• Phase imbalance (20 deg) - Rotates the in-phase signal by 10 degrees and the quadrature signal by -10 degrees.

• In-phase DC offset (1e-8) - Adds a DC offset of 1e-8 to the in-phase signal amplitude. This offset changes the received signal constellation diagram, but does not cause errors on the link unless combined with thermal noise or other RF impairments.

• Quadrature DC offset (5e-8) - Adds a DC offset of 5e-8 to the quadrature signal amplitude. This offset causes errors on the link even when not combined with thermal noise or another RF impairment. This offset also causes a DC spike in the received signal spectrum.

Digital predistortion - Allows you to enable or disable the Digital Predistortion subsystem. The default setting is Disabled.

DC offset correction - Allows you to enable or disable the DC Blocking subsystem. The default setting is Disabled.

Doppler correction - Allows you to enable or disable the Doppler Correction subsystem. The default setting is Disabled.

I/Q imbalance correction - Allows you to enable or disable the I/Q Imbalance Correction subsystem. The default setting is Disabled.

Results and Displays

When you run this model, the following displays are active:

Power Spectrum - Double-clicking this Open Scopes block enables you to view the spectrum of the modulated/filtered signal (yellow) and the received signal before demodulation (blue).

Comparing the two spectra allows you to view the effect of the following RF impairments:

• Spectral regrowth due to HPA nonlinearities caused by the Memoryless Nonlinearity block

• Thermal noise caused by the Receiver Thermal Noise block

• Phase flicker (that is, 1/f noise) caused by the Phase Noise block

HPA AM/AM and AM/PM - Double-clicking this Open Scopes block enables you to view the AM/AM and AM/PM conversion after the HPA. These plots enable you to view the impact that the Digital Predistortion block and HPA have on the linearity of the signal.

Constellation Before and After HPA - Double-clicking this Open Scopes block enables you to compare the constellation of the transmitted signal before (yellow) and after (blue) the HPA. The amplifier gain causes the HPA Output signal to be larger than the HPA Input signal. This plot enables you to view the combined effect of both the HPA nonlinearity and digital predistortion.

End to End Constellation - Double-clicking this Open Scopes block enables you to compare the reference 16-QAM constellation (red) with the received QAM constellation before demodulation (yellow). Comparing these constellation diagrams allows you to view the impact of all the RF impairments on the received signal and the effectiveness of the compensations.

Bit error rate (BER) display - In the lower right corner of the model is a display of the BER of the model. The BER computation can be reset manually by double-clicking the green 'Double-click to reset BER' button. This allows you to view the impact of the parameter changes as the model is running.

Experimenting with the Example

This section describes some ways that you can change the model parameters to experiment with the effects of the blocks from the RF Impairments library and other blocks in the model. You can double-click the block labeled 'Model Parameters' in the model and try some of the following scenarios:

Link gains and losses - Change Noise temperature to 290 (typical noise level), 0 (no noise) or 500 (high noise level). Change the value of the Satellite altitude (km) or Satellite frequency (MHz) parameters to change the free space path loss. In addition, increase or decrease the Transmit and receive antenna diameters (m) parameter to increase or decrease the received signal power. You can view the changes in the received constellation in the received signal constellation diagram scope and the changes in received power in the spectrum analyzer.

Raised cosine pulse shaping - Make sure Noise temperature is set to 0 (no noise). Turn on the Constellation Before and After HPA scopes. Observe that the square-root raised cosine filtering results in intersymbol interference (ISI). This results in the points being scattered loosely around ideal constellation points, which you can see in the After HPA constellation diagram. The square-root raised cosine filter in the receiver, in conjunction with the transmit filter, controls the ISI, which you can see in the received signal constellation diagram.

HPA AM-to-AM conversion and AM-to-PM conversion - Change the HPA backoff level parameter to 7 dB (moderate nonlinearity) and observe the AM-to-AM and AM-to-PM conversions by comparing the Transmit RRC filtered signal constellation diagram with the RRC signal after HPA constellation diagram. Note how the AM-to-AM conversion varies according to the different signal amplitudes. You can also view the effect of this conversion on the received signal in the received signal constellation diagram. In addition, you can observe the spectral regrowth in the received signal spectrum analyzer. You can also view the phase change in the received signal in the received signal constellation diagram scope.

Digital predistortion With the Digital predistortion checkbox checked, change the HPA backoff level parameter to 30 dB (negligible nonlinearity), 7 dB (moderate nonlinearity), and 1 dB (severe nonlinearity) to view the effect of digital predistortion on the HPA nonlinearity.

Phase noise plus AM-to-AM conversion - Set the Phase Noise parameter to High and observe the increased variance in the tangential direction in the received signal constellation diagram. Also note that this level of phase noise is sufficient to cause errors in an otherwise error-free channel.

DC offset and DC offset compensation - Set the I/Q imbalance and DC offset parameter to In-phase DC offset (1e-8) and view the shift of the constellation in the received signal constellation diagram. Set DC offset correction to Enabled and view the received signal constellation diagram to view how the DC offset block estimates the DC offset value and removes it from the signal. Set DC offset compensation to Disabled and change I/Q imbalance to Quadrature DC offset (5e-8). View the changes in the received signal constellation diagram for a large DC offset and the DC spike in the received signal spectrum. Note that the LNA amplifies the small DC offsets so that they are visible on the constellation diagram with much larger axis limits. Set DC offset compensation to Enabled and view the received signal constellation diagram and spectrum analyzer to see how the DC component is removed.

Amplitude imbalance - With the I/Q imbalance correction disabled, set the I/Q Imbalance and DC offset parameter to Amplitude imbalance (3 dB) to view the effect of unbalanced I and Q gains in the received signal constellation diagram. Enable the I/Q imbalance correction to compensate for the amplitude imbalance.

Doppler and Doppler compensation - Disable Doppler correction by unchecking the Doppler correction check box. Set Doppler error to 3 Hz to show the effect of uncorrected Doppler on the received signal constellation diagram. Enable Doppler correction to show that the carrier synchronizer restores the received constellation. Repeat the exercise with different I/Q imbalance and DC offsets.

Selected Bibliography

[1] Saleh, Adel A.M., 'Frequency-Independent and Frequency-Dependent Nonlinear Models of TWT Amplifiers,' IEEE® Transactions on Communications, Vol. COM-29, No. 11, November 1981.

[2] Kasdin, N.J., 'Discrete Simulation of Colored Noise and Stochastic Processes and 1/(f^alpha); Power Law Noise Generation,' The Proceedings of the IEEE, Vol. 83, No. 5, May, 1995.

[3] Kasdin, N. Jeremy, and Todd Walter, 'Discrete Simulation of Power Law Noise,' 1992 IEEE Frequency Control Symposium.

[4] Sklar, Bernard, Digital Communications: Fundamentals and Applications, Englewood Cliffs, N.J., Prentice Hall, 1988.

Effective radiated power (ERP), synonymous with equivalent radiated power, is an IEEE standardized definition of directional radio frequency (RF) power, such as that emitted by a radio transmitter. It is the total power in watts that would have to be radiated by a half-wave dipole antenna to give the same radiation intensity (signal strength in watts per square meter) as the actual source at a distant receiver located in the direction of the antenna's strongest beam (main lobe). ERP measures the combination of the power emitted by the transmitter and the ability of the antenna to direct that power in a given direction. It is equal to the input power to the antenna multiplied by the gain of the antenna. It is used in electronics and telecommunications, particularly in broadcasting to quantify the apparent power of a broadcasting station experienced by listeners in its reception area.

An alternate parameter that measures the same thing is effective (or equivalent) isotropic radiated power (EIRP). Effective isotropic radiated power is the total power that would have to be radiated by a hypothetical isotropic antenna to give the same signal strength as the actual source in the direction of the antenna's strongest beam. The difference between EIRP and ERP is that ERP compares the actual antenna to a half-wave dipole antenna, while EIRP compares it to a theoretical isotropic antenna. Since a half-wave dipole antenna has a gain of 1.64, or 2.15 decibels compared to an isotropic radiator, if ERP and EIRP are expressed in watts their relation is

${\displaystyle \mathrm{E}\mathrm{I}\mathrm{R}\mathrm{P}(\mathrm{W})=1.64\cdot \mathrm{E}\mathrm{R}\mathrm{P}(\mathrm{W})}$

If they are expressed in decibels

${\displaystyle \mathrm{E}\mathrm{I}\mathrm{R}\mathrm{P}(\mathrm{d}\mathrm{B})=\mathrm{E}\mathrm{R}\mathrm{P}(\mathrm{d}\mathrm{B})+2.15}$

• 5FM example

Definitions[edit]

Effective radiated power and effective isotropic radiated power both measure the amount of power a radio transmitter and antenna (or other source of electromagnetic waves) radiates in a specific direction: in the direction of maximum signal strength (the 'main lobe') of its radiation pattern.^[1][2][3][4] This maximum radiated power is dependent on two factors: the total power output and the radiation pattern of the antenna – how much of that power is radiated in the desired direction. The latter factor is quantified by the antenna gain, which is the ratio of the signal strength radiated by an antenna to that radiated by a standard antenna. For example, a 1,000-watt transmitter feeding an antenna with a gain of 4 (6 dBi) will have the same signal strength in the direction of its main lobe, and thus the same ERP and EIRP, as a 4,000-watt transmitter feeding an antenna with a gain of 1 (0 dBi). So ERP and EIRP are measures of radiated power that can compare different combinations of transmitters and antennas on an equal basis.

The difference between ERP and EIRP is that antenna gain has traditionally been measured in two different units, comparing the antenna to two different standard antennas; an isotropic antenna and a half-wave dipole antenna:

• Isotropic gain is the ratio of the power density ${\displaystyle S_{\text{max}}}$ (signal strength in watts per square meter) received at a point far from the antenna (in the far field) in the direction of its maximum radiation (main lobe), to the power ${\displaystyle S_{\text{max,isotropic}}}$ received at the same point from a hypothetical lossless isotropic antenna, which radiates equal power in all directions

${\displaystyle {\mathrm{G}}_{\text{i}}=\frac{S_{\text{max}}}{S_{\text{max,isotropic}}}}$

Gain is often expressed in logarithmic units of decibels (dB). The decibel gain relative to an isotropic antenna (dBi) is given by

${\displaystyle \mathrm{G}\text{(dBi)}=10\log \frac{S_{\text{max}}}{S_{\text{max,isotropic}}}}$

• Dipole gain is the ratio of the power density received from the antenna in the direction of its maximum radiation to the power density ${\displaystyle S_{\text{max,dipole}}}$ received from a lossless half-wave dipole antenna in the direction of its maximum radiation

${\displaystyle {\mathrm{G}}_{\text{d}}=\frac{S_{\text{max}}}{S_{\text{max,dipole}}}}$

The decibel gain relative to a dipole (dBd) is given by

${\displaystyle \mathrm{G}\text{(dBd)}=10\log \frac{S_{\text{max}}}{S_{\text{max,dipole}}}}$

In contrast to an isotropic antenna, the dipole has a 'donut-shaped' radiation pattern, its radiated power is maximum in directions perpendicular to the antenna, declining to zero on the antenna axis. Since the radiation of the dipole is concentrated in horizontal directions, the gain of a half-wave dipole is greater than that of an isotropic antenna. The isotropic gain of a half-wave dipole is 1.64, or in decibels 10 log 1.64 = 2.15 dBi, so

${\displaystyle G_{\text{i}}=1.64G_{\text{d}}}$

In decibels

${\displaystyle G\text{(dBi)}=G\text{(dBd)}+2.15}$

The two measures EIRP and ERP are based on the two different standard antennas above:^[1][3][2][4]

• EIRP is defined as the RMS power input in watts required to a lossless isotropic antenna to give the same maximum power density far from the antenna as the actual transmitter. It is equal to the power input to the transmitter's antenna multiplied by the isotropic antenna gain

${\displaystyle \mathrm{E}\mathrm{I}\mathrm{R}\mathrm{P}=G_{\text{i}}{P}_{\text{in}}}$

The ERP and EIRP are also often expressed in decibels (dB). The input power in decibels is usually calculated with comparison to a reference level of one watt (W): ${\displaystyle P_{\text{in}}(\mathrm{d}\mathrm{B}\mathrm{w})=10\log P_{\text{in}}}$. Since multiplication of two factors is equivalent to addition of their decibel values

${\displaystyle \mathrm{E}\mathrm{I}\mathrm{R}\mathrm{P}(\mathrm{d}\mathrm{B}\mathrm{w})=G\text{(dBi)}+P_{\text{in}}(\mathrm{d}\mathrm{B}\mathrm{w})}$

• ERP is defined as the RMS power input in watts required to a lossless half-wave dipole antenna to give the same maximum power density far from the antenna as the actual transmitter. It is equal to the power input to the transmitter's antenna multiplied by the antenna gain relative to a half-wave dipole

${\displaystyle \mathrm{E}\mathrm{R}\mathrm{P}=G_{\text{d}}{P}_{\text{in}}}$

In decibels

${\displaystyle \mathrm{E}\mathrm{R}\mathrm{P}(\mathrm{d}\mathrm{B}\mathrm{w})=G\text{(dBd)}+P_{\text{in}}(\mathrm{d}\mathrm{B}\mathrm{w})}$

Since the two definitions of gain only differ by a constant factor, so do ERP and EIRP

${\displaystyle \mathrm{E}\mathrm{I}\mathrm{R}\mathrm{P}(\mathrm{W})=1.64\cdot \mathrm{E}\mathrm{R}\mathrm{P}(\mathrm{W})}$

In decibels

${\displaystyle \mathrm{E}\mathrm{I}\mathrm{R}\mathrm{P}(\mathrm{d}\mathrm{B}\mathrm{w})=\mathrm{E}\mathrm{R}\mathrm{P}\text{(dBw)}+2.15}$

Relation to transmitter output power[edit]

The transmitter is usually connected to the antenna through a transmission line. Since the transmission line may have significant losses ${\displaystyle L}$, the power applied to the antenna is usually less than the output power of the transmitter ${\displaystyle P_{\text{TX}}}$. The relation of ERP and EIRP to transmitter output power is

${\displaystyle \mathrm{E}\mathrm{I}\mathrm{R}\mathrm{P}(\mathrm{d}\mathrm{B}\mathrm{w})=P_{\text{TX}}(\mathrm{d}\mathrm{B}\mathrm{w})-L(\mathrm{d}\mathrm{B})+G\text{(dBi)}}$

${\displaystyle \mathrm{E}\mathrm{R}\mathrm{P}(\mathrm{d}\mathrm{B}\mathrm{w})=P_{\text{TX}}(\mathrm{d}\mathrm{B}\mathrm{w})-L(\mathrm{d}\mathrm{B})+G\text{(dBi)}-2.15}$

Losses in the antenna itself are included in the gain.

Dipole vs. isotropic radiators[edit]

Because ERP is calculated as antenna gain (in a given direction) as compared with the maximum directivity of a half-wave dipole antenna, it creates a mathematically virtual effective dipole antenna oriented in the direction of the receiver. In other words, a notional receiver in a given direction from the transmitter would receive the same power if the source were replaced with an ideal dipole oriented with maximum directivity and matched polarization towards the receiver and with an antenna input power equal to the ERP. The receiver would not be able to determine a difference. Maximum directivity of an ideal half-wave dipole is a constant, i.e., 0 dBd = 2.15 dBi. Therefore, ERP is always 2.15 dB less than EIRP. The ideal dipole antenna could be further replaced by an isotropic radiator (a purely mathematical device which cannot exist in the real world), and the receiver cannot know the difference so long as the input power is increased by 2.15 dB.

Unfortunately, the distinction between dBd and dBi is often left unstated and the reader is sometimes forced to infer which was used. For example, a Yagi-Uda antenna is constructed from several dipoles arranged at precise intervals to create better energy focusing (directivity) than a simple dipole. Since it is constructed from dipoles, often its antenna gain is expressed in dBd, but listed only as dB. Obviously this ambiguity is undesirable with respect to engineering specifications. A Yagi-Uda antenna's maximum directivity is 8.77 dBd = 10.92 dBi. Its gain necessarily must be less than this by the factor η, which must be negative in units of dB. Neither ERP nor EIRP can be calculated without knowledge of the power accepted by the antenna, i.e., it is not correct to use units of dBd or dBi with ERP and EIRP. Let us assume a 100-watt (20 dBW) transmitter with losses of 6 dB prior to the antenna. ERP < 22.77dBW and EIRP < 24.92dBW, both less than ideal by η in dB. Assuming that the receiver is in the first side-lobe of the transmitting antenna, and each value is further reduced by 7.2 dB, which is the decrease in directivity from the main to side-lobe of a Yagi-Uda. Therefore, anywhere along the side-lobe direction from this transmitter, a blind receiver could not tell the difference if a Yagi-Uda was replaced with either an ideal dipole (oriented towards the receiver) or an isotropic radiator with antenna input power increased by 1.57 dB.^[5]

Polarization[edit]

Polarization has not been taken into account so far, but it must be properly clarified. When considering the dipole radiator previously we assumed that it was perfectly aligned with the receiver. Now assume, however, that the receiving antenna is circularly polarized, and there will be a minimum 3 dB polarization loss regardless of antenna orientation. If the receiver is also a dipole, it is possible to align it orthogonally to the transmitter such that theoretically zero energy is received. However, this polarization loss is not accounted for in the calculation of ERP or EIRP. Rather, the receiving system designer must account for this loss as appropriate. For example, a cellular telephone tower has a fixed linear polarization, but the mobile handset must function well at any arbitrary orientation. Therefore, a handset design might provide dual polarization receive on the handset so that captured energy is maximized regardless of orientation, or the designer might use a circularly polarized antenna and account for the extra 3 dB of loss with amplification.

FM example[edit]

For example, an FMradio station which advertises that it has 100,000 watts of power actually has 100,000 watts ERP, and not an actual 100,000-watt transmitter. The transmitter power output (TPO) of such a station typically may be 10,000 to 20,000 watts, with a gain factor of 5 to 10 (5× to 10×, or 7 to 10 dB). In most antenna designs, gain is realized primarily by concentrating power toward the horizontal plane and suppressing it at upward and downward angles, through the use of phased arrays of antenna elements. The distribution of power versus elevation angle is known as the vertical pattern. When an antenna is also directional horizontally, gain and ERP will vary with azimuth (compass direction). Rather than the average power over all directions, it is the apparent power in the direction of the antenna's main lobe that is quoted as a station's ERP (this statement is just another way of stating the definition of ERP). This is particularly applicable to the huge ERPs reported for shortwave broadcasting stations, which use very narrow beam widths to get their signals across continents and oceans.

United States regulatory usage[edit]

ERP for FM radio in the United States is always relative to a theoretical reference half-wave dipole antenna. (That is, when calculating ERP, the most direct approach is to work with antenna gain in dBd). To deal with antenna polarization, the Federal Communications Commission (FCC) lists ERP in both the horizontal and vertical measurements for FM and TV. Horizontal is the standard for both, but if the vertical ERP is larger it will be used instead.

The maximum ERP for US FM broadcasting is usually 100,000 watts (FM Zone II) or 50,000 watts (in the generally more densely populated Zones I and I-A), though exact restrictions vary depending on the class of license and the antenna height above average terrain (HAAT).^[6] Some stations have been grandfathered in or, very infrequently, been given a waiver, and can exceed normal restrictions.

Microwave band issues[edit]

For most microwave systems, a completely non-directional isotropic antenna (one which radiates equally and perfectly well in every direction – a physical impossibility) is used as a reference antenna, and then one speaks of EIRP (effective isotropic radiated power) rather than ERP. This includes satellitetransponders, radar, and other systems which use microwave dishes and reflectors rather than dipole-style antennas.

Lower-frequency issues[edit]

In the case of medium wave (AM) stations in the United States, power limits are set to the actual transmitter power output, and ERP is not used in normal calculations. Omnidirectional antennas used by a number of stations radiate the signal equally in all directions. Directional arrays are used to protect co- or adjacent channel stations, usually at night, but some run directionally 24 hours. While antenna efficiency and ground conductivity are taken into account when designing such an array, the FCC database shows the station's transmitter power output, not ERP.

Related terms[edit]

Effective monopole radiated power (EMRP) may be used in Europe, particularly in relation to mediumwave broadcasting antennas. This is the same as ERP, except that a short vertical antenna (i.e. a short monopole) is used as the reference antenna instead of a half-wave dipole.

HAAT[edit]

The height above average terrain for VHF and higher frequencies is extremely important when considering ERP, as the signal coverage (broadcast range) produced by a given ERP dramatically increases with antenna height. Because of this, it is possible for a station of only a few hundred watts ERP to cover more area than a station of a few thousand watts ERP, if its signal travels above obstructions on the ground.

See also[edit]

References[edit]

1. ^ ^abJones, Graham A.; Layer, David H.; Osenkowsky, Thomas G. (2007). National Association of Broadcasters Engineering Handbook, 10th Ed. Elsevier. p. 1632. ISBN1136034102.
2. ^ ^abHuang, Yi; Boyle, Kevin (2008). Antennas: From Theory to Practice. John Wiley and Sons. pp. 117–118. ISBN0470772921.
3. ^ ^abSeybold, John S. (2005). Introduction to RF Propagation. John Wiley and Sons. p. 292. ISBN0471743682.
4. ^ ^abWeik, Martin H. (2012). Communications Standard Dictionary. Springer Science and Business Media. p. 327. ISBN146156672X.
5. ^Cheng, David K. (1992). Field and Wave Electromagnetics, 2nd Ed. Addison-Wesley. pp. 648–650.
6. ^47 CFR 73.211