Decibels
Decibels are used extensively in electronics and communications. The dB is a logarithmic ratio, for ERCES the reference is typically milliwatts = dBm. Where the power is measured in dBm, the ratio is the gain or loss in dB. For example a BDA receiving a signal at -70dBm and transmitting a +20dBm into the DAS would have a gain of 90dB. The math would be 10 times the log base 10 of the power output divided by the power input. dB = 10x log(P1/P2)
P1 is always the output
P2 is always the input
+3dB is a doubling of power
-3dB is a halving of power
Decibels
dB is a ratio
- it is a way to notate change
- 0 dB means no change in power
- the suffix is what it is in reference to
- dBm = decibels in reference to milliwatts
- 0 dBm is 1 milliwatt
- 3 dBm is 2 milliwatts
- 10 dBm is 10 milliwatts
- these are the rules of 3s and 10s
- -3 dBm 0.5 milliwatt
- -10 dBm 0.01 milliwatt
- Power in Watts will never be negative
- Power in dBm is a ratio in reference to a milliwatt so values less than 1 milliwatt will be negative
Antenna gains
- dBi = decibels in reference to an isotropic antenna
- dBd = decibels in reference to a dipole antenna *this is what you will use in calculations for gain in your antennas
- Antennas will not have a negative gain value
dB is logarithmic and allows large and small values in more recognizable and easy numbers
Effective Radiated Power (ERP)
When working with transmitters and their antennas, an important concept to know s effective radiated power or ERP. This is a theoretical measurement of RF energy emitted by an antenna system. You cannot directly measure ERP, rather its a math problem. It is derived by adding the system gains and subtracting the system losses from the measured transmitter output. System losses include the transmission line or coaxial cable loss due to attenuation and the coupling or connector losses, while system gain is antenna gain.
FCC rules limit the ERP for ERCES to +37dBm
Free Space Path Loss
IEEE Std 145-1993, defines free-space loss as "The loss between two isotropic radiators in free space, expressed as a power ratio." Basically, how much power is lost between the transmitter and the receiver due to the signal travelling through the air.
To calculate Free Space Path Loss (FSPL) in miles and Megahertz, you can use the following formula
FSPL (dB) = 20log(d) + 20log(f) +36.6
Where:
- d = distance in miles
- f = frequency in MHz
- FSPL is in decibels (dB)
At a frequency of 806MHz the FSPL is
10 feet ~ -40 dB
20 feet ~ -46 dB
1/2 mile ~ -89 dB
1 mile ~ -95 dB
2 miles ~ -101 dB
Notice the 2x distance results in a 1/4 power.
Antennas
The antenna is the most important factor in determining range and system performance. Antennas come in many sizes, shapes and form factors. Antennas can be used to enhance or restrict coverage in certain directions.
Polarization
Polarization is the orientation of the transmitting and receiving elements. These must be orientated in the same plane for maximum performance. Cross polarization results in a signal loss of around 18dB. Two-way radio systems typically use vertically polarized elements.
Resonance
Resonance is the point where an antenna's length and frequency match to produce maximum signal radiation. Antennas can be resonant at more than one frequency.
Match
Match is where the impedance of the transmitter, cable and antenna are equal. Typically at 50 ohms in LMR systems.
Bandwidth
Bandwidth is the range of frequencies from lowest to highest where the antenna produces acceptable performance. In some cases, an antenna may have a bandwidth of a few kilohertz (KHz) or hundreds of megahertz (MHz).
Beamwidth
Excluding an omni directional antenna, beamwidth is the width in degrees from one extreme angle to the other where the focused signal exists.
3 dB Points
3 dB or half power points represent where the signal is at half the power of the main lobe. They are found on both the + and - axis.
Gain
Gain is achieved by redirecting the signal from non-useful directions to more useful ones. Gain is a measure of the signal power compared to a dipole (dBd) or an isotropic antenna (dBi). to convert dBi to dBd subtract 2.1dB. For frequencies below 900MHz always use the dBd value to calculate system gain.
Front-to-Back Ratio
Front-to-Back ratio is the amount of signal expressed in dBd between the forward direction and 180 degrees to the rear.
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Yagi
Yagi antennas are dipole antennas with 2 or more elements added at specific spacing to direct signal and provide gain. These are typically used as the donor antenna for ERCES.
Omnidirectional
Omnidirectional means the signal radiates equally in a 360 degree pattern. They have a major lobe that is perpendicular to the antenna's vertical plane. Typically there is also a reduced power area directly above and below. These types of antenna make up the distributed antenna system.
Pass-Band Filter
Filters are devices that allow some frequencies to pass through and other frequencies to be attenuated. BDAs use filters to eliminate unwanted frequencies, allowing only certain frequencies to be enhanced. Most BDAs use band pass filters to allow a range of frequencies to pass through while rejecting the frequencies above and below the band-pass frequencies. The bandwidth of a filter is based on the frequencies where the attenuation is 3 dB or greater from the peak frequency. Frequencies whose attenuation is less than 3 dB are in the pass range.
RF Signal Loss over coax
Signal loss in a cable is normally measured in dB per 100 feet. Transmitter loss can be measured and calculated by comparing the output power to the input power using the formula for dB loss. Receiver loss can be measured by injecting a signal at the receiver input and measuring it at the end of the cable. This can be accomplished with a frequency domain reflectometer (FDR) by measuring the return loss of an off resonant frequency. FDRs use velocity factor, frequency, and impedance to determine distance to faults or impedance mismatches.
Equal Power Dividers
Power dividers evenly split the power between 2,3 or 4 output ports. They are either Wilkinson style or reactive style. Wilkinson style have better port to port isolation and may be used in low power combining.
Directional Couplers
The directional coupler is one form of unequal splitter. Most of the power passes through the devices with a smaller fraction sent to the coupled port. They are typically available in values from 5 dB to 30 dB, meaning the coupled port power is reduced by this value. Power in the reverse direction does is attenuated far more to the coupled port maintaining most of the signal on the through port. This makes installation direction critical.
Tappers
Tappers are similar to directional couplers; they are also unequal splitters but without the directionality. Power and losses will be the same in both directions. Typically they are smaller and less expensive than directional couplers and are rated on insertion loss to the coupled port.
Modulation and Demodulation
Modulation is the process of adding intelligence to an RF carrier. Demodulation is the process of separating the intelligence from the RF carrier. The intelligence could be voice traffic, location information, status bits, or pretty much any data. Modulation takes place in the transmitter and demodulation takes place in the receiver. Modulation modes can vary in analog or digital and amplitude, frequency, phase and combinations of these. Typical public safety LMR systems will be P25.
Bit Error Rate (BER)
When demodulating any difference between the transmitted signal and the received signal is called distortion. In a digital system, this can be detected and is called bit error rate (BER). Distortion or degradation in analog systems should be below 5%. P25 Phase 1 systems should be below 2.6% and below 3.1% in P25 Phase 2 to achieve a DAQ of 3.0.