[rev 09.17.09.00.10]

VHF - UHF basics by KE9SE

Introduction:

This page is intended to be an introduction to and provide a basic understanding of VHF and UHF radio communications. The information was compiled from many sources and a bibliography will be included at the end. Although the information is directly related, it was discovered that a lot of hunting was required to bring it all together. So the second purpose of this page is to be a one stop information resource, one which hopefully you will find to be convenient and helpful. All of the math used in these examples is simple and can be solved using the Windows calculator in the scientific mode. Care must be taken to solve the operations within the parenthesis, a scratch pad helps keep things in order. Because of a likeness for RPN and the convenience of the stack, I prefer to use an HP-48.

This page is not complete and probably never will be. It will however be updated and corrected as time permits. If a listed topic has not been developed yet, it eventually will be. Please feel free to email any suggestions, improvements or hate mail to me:

ke9seradio@gmail.com

Temperature conversion:

Kelvin to Celsius  C° = K° - 273.15

Celsius to Fahrenheit  F˚ = ( 9 / 5  • C˚ ) + 32

Fahrenheit to Celsius C˚ = 5 / 9 • ( F˚ - 32 )

The decibel:

The decibel is logarithmic in nature and represents a ratio. The dB is a convenient way to sum losses and gains.

dBW = a value relative to 1 watt    0 dBW = 30 dBm

dBm = a value relative to 1 milliwatt    0 dBm = -30 dBW

Examples:

-10 dBm = 1/10 of a milliwatt

-20 dBm = 1/100 of a milliwatt

-30 dBm = 1/1000 of a milliwatt

S9 +60dB = 1/20 of a milliwatt

dBi = gain relative to an isotropic antenna model

dBd = gain relative to a half wave dipole antenna

0 dBd = 2.14 dBi

An isotropic radiator has a spherical radiation pattern, it will transmit an equal amount of energy to all points within a sphere. The isotropic radiator is a purely mathematical construct and is presently not possible to build. So why bother referencing to it? It is an absolute platform of reference which gives it scientific value.

Some antenna manufacturers inflate their gain claims by using dBi rather than dBd and others will even include fresnel ground reflection (ground bounce) as a function of antenna gain, this is not a lie but is misleading. The effects of the ground on an antenna pattern vary with terrain, antenna height, ground conductivity and dielectric constant. Ground bounce characteristics change with local climate, it is difficult to predict or model these effects with absolute accurately (unless you live on a flat metal surface, many wavelengths in radius).

Decibel Table:

Most of what we will be dealing with here will use the power ratio.

Receiving:

Noise:

Noise is what places a limit on how weak of a signal we can detect, the signal to noise ratio or noise temperature is inversely proportional to sensitivity.

Thermal noise:

Thermal noise is the limiting factor of weak signal detection, it is a function of molecules in motion which can easily be calculated and because it is effected by bandwidth, an understanding of thermal noise (the theoretical noise floor) is useful. kTB is the formula used for determining the noise floor.

Pn = kTB

Pn = noise power in watts

k = Boltzman's constant (do not confuse with K)

k = 1.38 times 10 to the minus 23 joule per degree Kelvin

k = 1.38 x 10^-23

T = temperature in degrees Kelvin (K)

B = bandwidth in hertz

T is typically seen as 290 degrees K in most examples, this corresponds to 17 degrees C which is about 62 degrees F

Therefore, a 1 hertz bandwidth has a noise floor of:

Pn = ((1.38 x 10^-23) x 290) x 1

Pn = 0.000000000000000000004002 a rather useless number to me until it has been converted to a decibel

10 x (Log 0.000000000000000000004002) = -203.977 dBW (-204 dBW is close enough)

When referring to noise floor it is more customary to use dBm so simply subtract a minus 30 (change the sign of the subtrahend and add)

(-204) - (-30) = -174 dBm (per hertz)

How bandwidth is related to noise floor:

The width of the received pass band will have an effect upon the noise floor. There are two easy ways to derive the thermal noise floor for a given bandwidth. The first is to recalculate using the kTB formula and the second to "10 Log" the difference between two bandwidths.

Thermal noise floor for common bandwidths:

It would be nice if all receiving equipment was capable of receiving into the thermal noise floor. Unfortunately that's not the way the world works, there are many more sources of noise that we have to deal with.

Sky noise

Galactic noise

Sun noise

Antenna noise

Noise figure:

Conversion from noise figure to noise temperature:

TE (expressed in degrees Kelvin) = 290 ( Antilog₁₀ ( NF / 10 ) -1 )

TE = noise temperature

NF = noise figure

K degrees Kelvin

Noise temperature:

Conversion from noise temperature to noise figure:

NF (expressed in dB) = 10 x Log₁₀ ( 1 + ( TE / TO ))

NF = noise figure

TE = noise temperature

TO = 290 K ( degrees Kelvin )

Noise factor:

The noise factor of a system or component is the ratio, a number greater than one,  which corresponds to the equivalent noise figure. The noise figure is divided by 10 because we are dealing with a power ratio ( Pn ).

The preamplifier:

The purpose of the preamplifier is to increase the signal to noise ratio of the received signal. The preamplifier will possess some noise of its own, this is the noise figure of the amplifier. Generally for VHF a noise figure of 1 dB is more than adequate, for UHF a slightly lower noise figure may be needed to hear down into the ambient noise. The preamplifier gain needs only to overcome the downstream losses in the system. As an example, if the coaxial losses are equal to 2.5 dB and the selectivity device (cavity filter or whatever you prefer to use, if anything) has a loss of 1 dB and the front end of the receiver has a noise figure of 2 dB, then 5.5 dB gain will be all that is required of the preamplifier. This is called takeover gain. Any preamplifier gain beyond this point is called excess gain and will serve no purpose other than to inflate your receiver's S-meter, it will not increase the sensitivity of your receiver, lower the noise temperature of your system, or increase your signal to noise ratio (all one in the same).

Excess gain:

Excess gain can also degrade receiver performance from the effects of gain compression and third order IMD products. IMD will become a problem if there are strong signals within the passband of your preamplifier.

Noise amplification:

There is a source of noise that is often overlooked because it is relatively small, that noise is produced from the heat within the lossy system component (coax for instance). The amplification of noise will raise the overall system temperature (example to be given in the future)

Antenna mounted preamplifier:

Since the purpose of the preamplifier is to increase the signal to noise ratio, it becomes obvious that it should have a low noise figure and it should be the first component after the antenna. By placing the preamp at the antenna feedpoint (or common connection to a stacking manifold) the noise barrier imposed by the coax losses and the amplified noise temperature derived from the lossy device itself is excluded. The only thermal noise that we have to contend with is the noise figure of the preamp itself. A coaxial relay is used to bypass the amplifier during transmission and to ground the input when not in use for static protection. The relay is best inserted into a logical "and" loop so that the transmitter will only key after all positive conditions have been met.

Resonant cavity filters:

A resonant cavity filter at the input of the receiver can be used to clean up the preamplifier and protect the front end of the receiver from overloading and third order intermodulation products. The insertion loss of the pictured filter was measured using 100 watts at 146.475 MHz, a VHF watt/vswr meter and a 50 ohm dummy load.

The first measurement was made with the equipment in this order, ICOM 706, Mirage amplifier, VHF watt/swr meter, cavity filter, and dummy load. The cavity filter was tuned for minimum vswr and the power output adjusted to 100 watts.

The second measurement was made by placing the watt/swr meter between the cavity filter and the dummy load, a reading of 85 watts was observed. Interconnecting coaxial cables were kept as short as possible to reduce measurement errors due to lumped LC constants native to resonant lengths of coax.

The measured loss was 0.7 dB. The resulting signal-to-noise degradation (approximately the same as the loss 0.7dB) can be easily overcome by upstream takeover gain. The Q of the cavity is quite high so the receiver (Icom 706) is well protected from overloading. When transmitting, the missing 15 watts helps to heat the shack.

The pictured cavity filter, even though not 1/4 wavelength long, maintains a high Q through its gold plating both inside and out. Gold, although not quite as good of a conductor as silver or copper will not oxidize or corrode under normal use. Because of this, skin effect resistance remains low and will not degrade with age. The internal coupling loops are silver plated for highest efficiency and will not oxidize as long as the cavities remain assembled. The two filter sections are independently tunable and can be retuned when a frequency change of more than 300 KHz is made. These were purchased from Fair Radio Sales (Lima, Ohio). I do not know of the current availability.

Gain compression

Third order IMD products

dBc

RF selectivity

Detectors

SSB versus FM signal to noise ratio

S-meter / microvolt chart:

For a reference, here is a table which will help you to compare received signal strength. Your mileage may vary depending upon your radio manufacturer. In most receivers the voltage used to power the S-meter is scaled from the agc voltage via a buffer or amplifier circuit. Although care is taken to tailor the gain and linearity (or non linearity) of the circuit, no two S-meters seem to act alike..

uV = microvolts across 50 ohms (signal voltage at the receiver's antenna connector)

Sensitivity specifications:

dBf

dBu

SINAD

Signal + noise / noise ratio

Transmitting:

The decibel as an absolute unit:

Field intensity and power density:

uW / centimeter²  to uV / meter²  conversion

uV / meter²  to dBm conversion

Sometimes it is necessary to know the actual field intensity or power density at a given distance from a transmitter instead of the signal strength received by an antenna. Field intensity or power density calculations are necessary when estimating electromagnetic interference (EMI) effects, when determining potential radiation hazards, or in determining or verifying specifications.

Field intensity (field strength) is a general term that usually means the magnitude of the electric field vector, commonly expressed in volts per meter. At frequencies above 100 MHz, and particularly above one GHz, power density (P_D) terminology is more often used than field strength.

Power density and field intensity are related by equation [1]:

 1. P_D = E² / Z_o = E² / ( 120 ∙ pi ) = E² / 377

where P_D is in W/m², E is the RMS value of the field in volts/meter and 377 ohms is the characteristic impedance of free space. When the units of P_D are in mW/cm², then P_D (mW/cm²) = E²/3770.

Conversions between field strength and power density when the impedance is 377 ohms, can be obtained from Table 1. It should be noted that to convert dBm/m² to dBV/m add 115.76 dB. Sample calculations for both field intensity and power density in the far field of a transmitting antenna are in the Power Density Section which follows.

Note that the "/" term before m, m², and cm² in Table 1 mean "per", i.e. dBm per m², not to be confused with the division sign which is valid for the Table 1 equation P=E²/Z_o. Remember that in order to obtain dBm from dBm/m² given a certain area, you must add the logarithm of the area, not multiply. The values in the table are rounded to the nearest dBW, dBm, etc. per m² so the results are less precise than a typical handheld calculator and may be up to a dB off.

Table 1. Conversion Table - Field Intensity and Power Density P_D = E²/Z₀
( Related by free space impedance = 377 ohms )

Numbers in table are rounded off

Voltage measurements

Coaxial cable typically has input impedances of 50, 75, and 93, (nominal impedance) with 50 ohm being the most common. Other types of cabling include 300 ohm and 450 ohm twinlead.

In the 50 ohm case, power and voltage are related by:

 2. P = E² / Z_o = E² / 50 = 50 ∙ I²

Conversions between measured power, voltage, and current where the typical impedance is 50 ohms can be obtained from Table 2. The dBµA current values are given because sometimes a current probe is used  to determine the powerline input current to the system .

Matching cable impedance

In performing measurements, we must take into account an impedance mismatch between measurement devices (typically 50 ohms) and free space (377 ohms).

Field strength approach

To account for the impedance difference, the antenna factor (AF) is defined as: AF=E/V, where E is field intensity which can be expressed in terms taking 377 ohms into account and V is measured voltage which can be expressed in terms taking 50 ohms into account.

Power density approach

To account for the impedance difference , the antenna's effective capture area term, A_e relates free space power density P_D with received power, P_r , i.e. P_r = P_D A_e. A_e is a function of frequency and antenna gain and is related to AF

Examples:

Table 2. Conversion Table - Volts to Watts and dBµA

(P_x = V_x²/Z - Related by line impedance of 50 ohms)

Conversion Between Field Intensity (Table 1) and Power Received (Table 2).

Power received (watts or milliwatts) can be expressed in terms of field intensity (volts/meter or µv/meter) using equation [3]:

3. Power Received ( P_r ) = ( E² / ( 480 ∙ pi² )) ∙ ( c² / f² ) ∙ G

or in log form:

4. 10 log P_r = 20 log E + 10 log G - 20 log f + 10 log (c²/480 ²)

Then

5. 10 log P_r = 20 log E₁ + 10 log G - 20 log f₁ + K₄

Where K₄ = 10 ∙ Log₁₀ [( c² / ( 480 ∙ pi² )) ∙ ( Watts to mW ) / (( volts to uV )² ∙ ( Hz to MHz or GHz )² ) ]

The derivation of equation [3] follows:

Equation	Terms
PD= E2/120	(v2/ohm)
Ae = 2G/4	(m2)
Pr = PDAe	(W/m2)(m2)
therefore: Pr = ( E2/120 )(2G/4)	(v2/m2ohm)(m2)
= c /f	(m/sec)(sec)
therefore: Pr = ( E2/480 2 )( c 2 G/f 2)	(v2/m2ohm)(m2/sec2)(sec2) or v2/ohms = watts

Bottom line here is to get close with the chart, use a little windage if necessary and call it good

Antennas

Common types - yagi, quad, quagi

Special - loop, double parallelogram rhombic

The rhombic antenna:

When we think of the rhombic antenna or any other type of traveling wave antenna, we generally picture its use on the HF bands. These high gain wire arrays can also be used at VHF and UHF frequencies and because of the shorter wavelength, wire antennas can be constructed in a limited amount of space. At UHF frequencies a wire array can easily be made to rotate. The antenna featured here is a particularly long (for its design frequency) and high gain rhombic array called the Double parallelogram rhombic antenna or LaPorte rhombic. It is claimed to have a free space gain of 27 dBi and in the UHF band it can be constructed on a supporting frame about 24 feet in length and 12 feet wide. (full details will be given in the future)

Rules of thumb:

Roughly estimating the (free space) gain of a yagi antenna when its active boom length is known.

The front to back ratio, swr bandwidth, and radiation resistance of a yagi antenna are dependent upon the number of elements used. Although gain is also effected, the primary factor in achieving gain is the length of the boom, from the reflector to the last director.

example: the KLM 2M-13LBA is a two meter 13 element yagi incorporating a dual driven element (for bandwidth) on a relatively long boom.

The boom length from the reflector to the last director is 21 feet 1 7/8 inches or close to 254 inches. One wavelength at 146 MHz is close to 81 inches.

254 / 81 = 3.1, multiply this by 10 and we now have 31, this is the power gain ratio, now convert it to a decibel, using the chart at the top of this page, we are real close to 15 dBi

This estimate is within a dB of  KLM's advertised gain for the antenna.

The Uzkov limit:

The Uzkov limit defines the maximum gain theoretically possible for an array of elements. The limit is 10.3 dBd for four dipole elements. This particular antenna uses 4 driven dipole elements on a 0.6 boom the 4 elements are fed (from back to front) at 0°, -172°, 16°, and -156°

Frequency scaling using proportion

Changing the element diameter of a yagi design:

When a design for a home made beam is chosen from a cookbook the author rarely uses the exact material that the builder has a surplus of. The diameter of a yagi element has great influence upon the reactance of the element at the design frequency. Arbitrarily making seemingly small changes in element diameter can ruin the performance of an antenna. Changing the diameter of a 2 meter driven element from 3/8 inch to 5/32 inch will increase its overall length by 1 inch. The 35 inch element now has to be a hair over 36 inches in order for the element to have the same reactance at 144 MHz (in this case -79.52 ohms).

The process may seem involved at first but the math is quite simple, if you use windows calculator you will need a scratch pad to keep things in order, if you use an HP-48 go with the stack.

Formula 1 ( this will determine element reactance )

X = ((430.3 Log₁₀ ( 2 / D₁ )) - 320)  (( 2 L₁ / ) - 1) + 40

D_{1 =} original element diameter

L_{1 =} original element length

= wavelength ( of design frequency = 300 / MHz ) in same units as D₁ and L₁ ( m, mm, in )

Formula 2 ( this will determine the new element length )

L₂ = (( X - 40 ) / (( 430.3 Log₁₀ ( 2 / D₂ )) - 320) + 1 )  ( / 2 )

X = element reactance ( determined in previous formula )

D₂ = new element diameter

L₂ = new element length

= wavelength (of design frequency = 300 / MHz ) in same units as D₂ ( m, mm, in )

The effects of a conductive boom on element lengths:

The Boom Correction Factor

When modeling an antenna using highly developed computer algorithms, hundreds or even thousands of iterations later you have finally settled upon a yagi design that meets your needs. The only real problem is, that unless you use a non conductive boom such as fiberglass, all of your element lengths must be tweaked. This section will show you how to compensate for the effects of a conductive boom.

The method used to mount elements to a boom can affect antenna performance, particularly for Yagi arrays at VHF and UHF. Through-the-boom mounting on a conductive boom increases element effective diameter and raises the resonant frequency of the element. To compensate for this, the element lengths must be increased by a fraction of the boom diameter. This is referred to as the Boom Correction Factor.
 

When constructing a Yagi antenna with a conductive boom, use this formula to increase the calculated element lengths.

C = (25.195*B) - (229*B^2)

The formula is valid for booms with diameters less than .055 wavelength. At 446 MHz, a 1.5 inch boom slightly exceeds this limit.

C is the correction factor expressed as a fraction of boom diameter B in wavelengths.

C is the correction factor for non-insulated through-the-boom element mounting.

The correction factor for insulated through-the-boom mounting is approximately 50% of C.

For example, a .01-wavelength diameter boom requires an element-length correction of 23% of the boom diameter.

A 0.01 Wavelength boom diameter at 446 MHz is only 6.73mm (slightly over 1/4 inch) the next example will reflect something more realistic.

Example 1:

Frequency = 446 MHz   Wavelength = 673mm   (300/446)

Boom is 1" aluminum = 25.4mm   25.4/673 = .038 Wavelength

C = (25.195 * .038) - (229 * (.038 * .038))

C = 0.957 - 0.33

C = 0.627 or 63%

0.63 * 25.4 = 15.92 = 16mm

In this example 16 millimeters must be added to the total length of each element for conductive through-the-boom mounting, If insulated through-the-boom mounting is employed, only 8 millimeters must be added to the total length of each element. Make certain that you do not misinterpret the total length of each element with the element half-length.

Conductivity of common metals

Effects of conductivity on skin effect and efficiency

Dielectric constant of various insulators

Lossy dielectric materials

Numeric Electromagnetic Code (NEC) and computerized antenna design

Array gain

Pattern gain

Height gain

Ground reflection

Polarization: vertical, horizontal, omni, circular

Cross-polarization loss

The polarization of the antennas for any two stations in communication is generally the same, either horizontal or vertical. In some instances circular polarization is employed. The polarization is generally consistent with the mode of operation and the frequency sub-band. This rule is not necessarily cast in stone so contradictions will eventually arise.

Cross-polarization may be illustrated as one station transmitting on a vertically polarized antenna and the other receiving on a horizontally polarized antenna. Rule of thumb in this case is said to be 20 to 25 dB of loss due to 90 degree cross-polarization. This figure was obtained by experimentation but is not a truly accurate figure.

There is a formula which will give a "worst case" figure for this loss, by worst case we mean two antennas in free space, or more realistically in an RF Anechoic chamber, eliminating multipath reflections.

The formula (as entered into the HP-48) is: Loss = ( 10 * Log₁₀ ( sq ( Cos ( Theta ) ) ) )

Loss = dB

Theta = The angle of displacement (between two antennas in communication)

Example 1, one antenna is vertically polarized and the other is at a 45 degree angle: (work the formula backwards)

Theta = 45 degrees

Cos Theta = 0.707

Square of Cos Theta = 0.5

Log₁₀ of 0.5 = -0.3010

10 x -0.3010 = - 3.010

Loss = 3 dB

Example 2, one antenna is vertically polarized and the other is horizontally polarized:

Theta = 89 degrees ( We will fudge by one degree here because the Cosine of 90 degrees is 0, which causes heartburn with digital apparatus)

Cos Theta = 0.0174

Square of Cos Theta = 0.0003045

Log₁₀ of 0.0003045 = -3.516

10 x -3.516 = - 35.16

Loss = 35 dB

Simple Cross-polarization chart:

For argument's sake, presume 90 to be vertical and 0 to be horizontal. 45 is a 2 meter mobile whip on a vehicle at highway speeds.

RHCP = right hand circular polarization.

LHCP = left hand circular polarization.

AX = axial also called linear polarization where both horizontal and vertical elements are fed in-phase.

Phasing harness for the Cushcraft A148-20T
 

Parts needed:
A few feet of RG-8X Belden or equivalent 50 ohm coaxial cable.
A few feet of RG-6 type low loss 75 ohm coaxial cable. I prefer Belden 9248 because it has a tinned copper braid as opposed to the aluminum braid used in most RG-6 cable, also the center conductor is #18 solid copper opposed to copper coated steel which I avoid for reasons that are out of the scope of this article.
1 UHF Tee connector
1 UHF double female coupler
6 PL-259 connectors. Use silver/Teflon or silver/ceramic not the phenolic cheapies available at Radio Shack and other places. Phenolic is very lossy at VHF frequencies
6 UG-176 adapters

Description:
There are two parts to this harness, the phasing lines and the delay line.

Construction:
you will need to cut 3 pieces of coax, each will be 1/4 wavelength at the design frequency (times the velocity factor of the cable). 1/4 wave sections have a relatively low Q so the center of the two meter band was chosen. The lengths are not critical (within a quarter of an inch is ok)
 

For the two 75 ohm pieces;
(234/146) x 12 = 19.23 inches, the velocity factor for 9248 Belden is around 78% or .78 so 19.23 inches x .78 = about 15 inches
 

For the one 50 ohm piece;
(234/146) x 12 = 19.23 inches, the velocity factor for RG-8X Belden is around 75% or .76, so19.23 inches x .76 = about 14.6 (14 1/2) inches
 

Assembly: See diagram below
 

Changing polarization:
The illustration will yield RHCP or right hand circular polarization which is pretty much the standard. This can be changed if necessary however...
RHCP = delay line connected to the horizontal driven element.
LHCP = delay line connected to vertical driven element.
Axial Polarization, also called linear polarization = no delay line Just the 75 ohm phasing harness. Both sets of elements are fired at the same time, there is a loss of 3 db when talking to a vertical , horizontal or circularly polarized station.
 

These rules apply only to dual polarity beams which have the Horizontal and Vertical elements at the same spacing, some manufacturers 'stagger' the horizontal and vertical bays (like KLM) then things become very different

Effects of the mast (and feedline) on antenna performance (E plane distortion)

Pattern effects from stacking

Feeding stacked arrays

Coaxial phasing harnesses, impedance matching tricks

Power dividers

Baluns: 1/4 wave sleeve

Feed lines

Types of coaxial cables

Coax loss chart

Contamination

Water

Minimum radius

Tie wraps:

Avoid using tie wraps to secure coaxial cable to tower legs etc. The constant pressure will cause the coax to become pinched at each tie wrap. This in turn will create an impedance-bump at each tie wrap, increasing overall cable losses and degrading the noise figure of the system. I generally use good old Scotch 33 black electrical tape which is wider and spreads out the pressure as well as being flexible so it does not "dent" the coaxial cable over time. As an added bonus it eventually makes a black sticky mess on the coax, but does not effect the system electrically. When wrapping the tape do not stretch it too tightly, use a scissors or knife to cut the tape rather than stretching it until it breaks. This will reduce the number of tiny black flags flapping in the wind.

Un-rolling versus uncoiling:

Always unroll coaxial cable, as if reeling out thread from a spool. Uncoiling (like stretching a spring) will cause repeated twists in the cable, creating small but cumulative losses.

Combine uncoiling with tie wraps and with a bit of luck you won't hear anything.

Propagation

Path loss

Free space

Radio path horizon

Tropospheric ducting

Aurora

Meteor scatter

Backscatter

Lightning

Station capabilities (putting it all together)

Summing gains and losses (Link budget analysis)

Estimating station to station range and signal quality

The Passive Transfer of RF energy (Smoke and Mirrors, aka the repeater extender project)

Interference

KE9SE Home

Bibliography