__POWER
AND POWER MEASURING TECHNIQUES__

**When you have finished,
press the "Technical" button on the left to return to the Main Page,
or press an appropriate button to go to a different section.**

**If there are no buttons
on the left, you probably got directly to this page via a search engine. Select
normal access to go to the G3NPF/M1AIM home page.**

**Before considering how to measure power, we should consider what power is
and the different ways of specifying power. Power is the rate at which work
is done or at which energy is transferred. This is true for all types of power,
including mechanical and electrical power.**

** The SI unit of power is
the watt (W) or joule per second (J/s). Horsepower is a unit of power in the
British system of measurement and is equal to 746W.**

** Mechanical work is defined
as the distance of displacement caused by applying a force to a body, multiplied
by the force itself.**

**W = F s
where W is work, F is force, and s is the displacement**

** The SI units of work are
the joule (J) or the newton-meter (Nm). The joule is also the SI unit of energy.**

** Energy is the capacity
of a physical system to perform work. Energy exists in several forms, such as
kinetic or mechanical energy, potential energy, electrical energy, heat and
light. Sound is a longitudinal pressure wave, not a transverse electro-magnetic
wave but the same basic principles apply.**

** According to the law of
conservation of energy, the total energy of a system remains constant, though
energy may transform into another form. For example, two billiard balls colliding
will come to rest displaced from their original positions, with some of the
original energy becoming sound and a small amount of heat at the point of collision.**

** There are several ways
of specifying electrical power and different methods are used to measure them.**

** Mathematical Analysis**

** To understand power measurement
techniques fully, a mathematical analysis of the waveforms is necessary but
such an analysis of modulated waveforms, especially frequency modulated waveforms,
is extremely complicated and involves the use of calculus. It is therefore beyond
the scope of this tutorial.**

** There are many textbooks
available on the subject and a wealth of information is available on the Internet
should it be necessary to study the subject in greater depth.**

** DC Power**

** When a DC voltage is applied
across a resistance, a DC current will flow and the temperature of the resistance
will rise due to the power being dissipated.**

**P = E I
and by Ohms Law:- P = E²/R and P = I****²****
R**

** Low Frequency AC Power**

** When a sinusoidal AC voltage
is applied across a resistance, an AC current will flow and the temperature
of the resistance will rise due to the power being dissipated. If the resistance
is "pure" i.e. there is no reactive element, the same formulae as used for the
DC condition apply but if there is a reactive element, either XL or XC, the
current will consist of two orthogonally displaced vector quantities. The "in-phase"
component will be the current flowing in the purely resistive part of the load
and will produce heat but there will be a lagging or leading component flowing
in the reactive part of the load but this will not produce heat as a pure reactance
cannot absorb power.**

** The power in an AC circuit
is expressed in terms of the RMS (root-mean-square) voltage and current and
the power factor:-**

** P = E I
cos φ**

**Where: P
= RMS power
**

I = RMS current

φ = The phase angle between the voltage and current

** The product of the voltage
and current E I (usually called VA) is often quoted together with the "real"
power P. VA relates to the voltage and current actually supplied by the power
source, whereas P is the useful power consumed by the load.**

** If VA and P are not equal,
the power factor cannot be unity. When the circuit is purely resistive, the
phase angle is zero. Therefore cos φ = 1 and P = E I. However, if the
circuit is purely inductive, the phase angle is -90° (lagging power factor),
cos φ = 0 and therefore P = 0, although E I has a finite value. Similarly,
if the circuit is purely capacitive, the phase angle is +90° (leading power
factor), cos φ = 0 and P = 0, with E I again having a finite value. Clearly,
a device with a leading power factor can be used to compensate for one having
a lagging power factor and vice versa.**

** A power factor of one,
or "unity power factor", is the goal of any electric utility company since if
the power factor is less than one, they have to supply more current to the user
for a given amount of useful power consumed (VA is greater than P).**

**As stated previously, a
pure reactance cannot absorb power. It can be seen from the above
diagram that when the load is a pure resistance, all the power is "positive"
and therefore the average power has a finite value. However, for
purely reactive loads, there are equal amounts of "positive" and "negative"
power, resulting in the average power being zero. Obviously
there is no such thing as "negative" power but this is a convenient
way of explaining why a reactance does not absorb power, as the power stored
in the reactance during one quarter cycle has the opposite "polarity"
to that stored during the following quarter cycle, resulting in a net zero power
absorption over any given half cycle. There is, however, instantaneous
power during a cycle, except at "cross-over points" where either the
voltage or the current is zero.**

** From the vector diagram
for AC impedance, it can be seen that the power factor (cos φ) is R/Z
(resistance divided by impedance). For a purely resistive AC circuit, X = 0,
φ = 0 and therefore R = Z and cos φ = 1.****
**

**
**

__High Frequency
AC Power__

** All the statements made
in respect of low frequency AC power apply equally to high frequency AC power
except that the concept of power factor is seldom relevant at frequencies above
those used for domestic, industrial or military mains supplies. Consequently,
above (say) 500Hz, although in-phase and out-of-phase currents still exist,
the actual phase angle is a more meaningful parameter than power factor. At
RF and microwave frequencies, neither the phase angle nor the power factor,
of a given signal have any real significance, although the phase angle between
a given signal and another, completely separate signal, may be highly important.**

** Also, high frequency circuits
often involve tuned circuits which further complicate the situation and parameters
such as coupling factor and Q must be considered.**

** RMS Power**

** As stated above, AC power,
at any frequency, is normally expressed as an RMS value. This is true regardless
of waveform but is most relevant when the waveform is repetitive. If the waveform
is random or contains spikes and transients, it is normal to consider average
and peak powers separately, as being more meaningful. When considering amplitude
modulated waveforms, it is more meaningful to use peak envelope power. Music
power is more a concept than a measurable quantity.**

** Instantaneous power**

** Instantaneous power is
the RMS power in a circuit at any given instant of time.**

** Average Power**

** The average power supplied
in a given period is the arithmetic mean of the RMS powers supplied in the period.
In a steady state condition, e.g. when a fixed voltage is applied across a fixed
load, the average power will equal the RMS power. If the voltage varies over
the period, time and the instantaneous RMS powers must be taken into consideration.
Obviously, if the voltage was applied for half the period, the average power
would be half the value of that obtained when the voltage was present for the
entire period. The situation becomes more complicated if the voltage varies
in a random manner over the period as the value of RMS voltage over the period
is not obvious. For this reason, average power is normally only used when considering
steady state conditions.**

** Peak Power**

** Peak power is the instantaneous
power level at the highest amplitude of the power waveform. When considering
pulsed transmissions of radio frequency power, such as in radar applications,
the peak power can be hundreds of kilowatts, whereas the average power may only
be hundreds of watts, depending on the pulse width and repetition rate of the
signal.**

**For a sinusoidal voltage
to produce heat equivalent to that produced by a DC voltage, the peak AC power
required is twice the DC power. Therefore the average AC power equivalent to
a corresponding DC power is half the peak AC power.**

**DC equivalent power = (Vpk/√2)
x (Ipk/√2) = Ppk/2. In other
words, RMS power is the product of RMS voltage and RMS current, as stated earlier.**

** Peak Envelope Power**

** Peak envelope power (PEP)
is a term used to describe the power contained within the highest peak of a
modulated waveform and is most useful when considering a single sideband signal,
although it is relevant to any amplitude modulated signal. It is not relevant
to CW, frequency or phase modulated signals where the peak power equals the
average or RMS power. PEP is not normally used to quantify pulse modulated signals
where the pulses all have similar characteristics of amplitude, width and repetition
rate. Peak power and average power are normally used for this type of signal.**

** Various types of modulation,
using a single modulating frequency, can be represented in the frequency domain
although, perversely, frequency modulation is best illustrated in the time domain.
The comparison between amplitude and frequency modulation is shown below.**

**The amount the carrier
deviates (Δf) from its nominal frequency (fc) is determined by the amplitude
of the modulating waveform whereas the rate at which it deviates is determined
by the frequency of the modulating waveform. The corresponding frequency domain
diagrams are shown below and assume the modulating signal to be a single frequency
tone.**

**The first diagram represents
the case of a single CW carrier. If this carrier is 100% amplitude modulated,
the carrier power remains unaltered but two sidebands appear on either side
of the carrier, displaced by the frequency of the modulating waveform, as shown
in the second diagram. Obviously, the total power of the resulting signal is
now increased. This is termed "incremental modulation" and the received signal
strength, as indicated on a receiver's S-meter, will rise slightly on speech
peaks. All too often, the power amplifier in the transmitter is not capable
of providing the extra power and the carrier will reduce on speech peaks. This
is termed "decremental modulation".**

** The third diagram shows
frequency modulation, where the amplitude of the carrier remains constant but
its frequency shifts anywhere between the dotted lines, depending on the amplitude
of the modulating waveform. The rate of this frequency shift depends on the
frequency of the modulating waveform.**

** The fourth diagram shows
an upper sideband, suppressed carrier signal. The carrier is reduced to an extremely
low level which could actually be zero and the sideband consists of a single
signal, the amplitude of which depends on the amplitude of the modulating waveform
and the frequency depends on the frequency of the modulating waveform as with
the amplitude modulation example. A lower sideband signal is similar except
the sideband frequency is below the carrier frequency.**

** The following diagrams
illustrate the differences between amplitude modulation and single sideband
modulation in the time domain. The diagrams depicting amplitude modulation show
100% modulation and it is obvious that the instantaneous power output rises
during modulation.**

** The diagrams depicting
single sideband modulation show that the power output remains constant during
a single tone transmission but can be instantaneously higher or lower than this
value when the modulating waveform is complex, such as in speech.**

** Music Power**

** The term "music power"
is used in relation to both amplifiers and loudspeakers. When live music is
recorded without amplitude compression or limiting, the resulting signal contains
brief peaks of very much higher amplitude (20 dB or more) than the mean. True
reproduction would require an amplifier capable of providing peaks of power
around a hundred times greater than the average level. Thus the ideal 100 watt
audio system would need to be capable of handling peaks of 10,000 watts in order
to avoid clipping.**

** An amplifier can be designed
with audio output circuitry capable of generating brief peak power levels, but
with a power supply only able to sustain these for a very short time, and with
heat sinking that would overheat dangerously if full peak output power were
to be maintained for long periods. Modern recordings tend to be heavily compressed
and so can be played at high mean levels without the obvious distortion that
would result from an uncompressed recording causing the amplifier to clip.**

** This makes good technical
and commercial sense, as the amplifier can handle music with a relatively low
mean power, but with brief peaks. A high "music power" output can be advertised
and money saved on the power supply and heat sink. Program sources that are
significantly compressed are more likely to cause trouble, as the mean power
can be much higher for the same peak power. Circuitry which protects the amplifier
and power supply can prevent equipment damage in the case of sustained high
power operation.**

** Most loudspeakers are
in fact capable of withstanding peaks of several times their continuous rating
(although not a hundred times), since thermal inertia prevents the voice coils
from burning out on short bursts. It is therefore acceptable to drive a loudspeaker
from a power amplifier with a higher continuous rating several times the steady
power that the speaker can withstand, but only if care is taken not to overheat
it.**

** Field Strength and
Power Density**

** Electromagnetic field
strength is normally measured in "volts-per-metre", which is the voltage induced
in a non-resonant, 1 metre long conductor at the measuring location. This term
is used to define the signal strength of a radiated RF signal at a point remote
from the transmitter. Obviously, if the frequency of the signal being
measured is such that 1 metre is an exact number of quarter-waves, a different
length must be used and the induced voltage calculated from the actual conductor
length.**

** Power density is normally
measured in "watts-per-square metre" and is used where a strong and often focused,
electromagnetic field exists, such as the output of a laser or the near field
associated with a highly directional antenna.**

**Reference field strength
levels for the UK Amateur Radio bands are given on the Health
Protection Agency’s web site.**

** Measurement of Power**

** When measuring the power
consumed by a load connected to the supply mains or to a DC power supply, "in-line"
measuring techniques are used. The output impedance of the supply is normally
very low and can often be regarded as zero, whereas the load is a relatively
large finite value. The load is not matched to the output impedance of the supply.
If very accurate measurements are to be made, the power consumed by the measuring
instruments must be allowed for, as volts will be dropped across ammeters and
voltmeters consume current. However, with modern measuring instruments, these
effects can normally be ignored and even with older, "traditional", instruments
the power consumed by them is usually a tiny fraction of the power being measured.
The amount of power available is determined by the load characteristics, rather
than by the capabilities of the supply.**

** Different conditions apply
when measuring the power output from an amplifier or a transmitter. Here, the
output impedance of the source is usually a finite, if rather low, value and
is often comparable to the impedance of the load. Power is often fed to the
load via a transmission line, which will have a characteristic impedance, usually
equal to the load impedance, and the amount of power available is usually determined
by the capabilities of the source, rather than the by the value of the load.
In-line measuring instruments are often used and these instruments are designed
to operate with characteristic impedances equal to the more common transmission
line impedances of 50ohms or 75ohms. Absorption power meters having an internal
fixed load impedance equal to the impedance that the source is intended to drive
are often employed. RF power meters of this type usually have load impedances
of 50ohms, 75ohms or 600ohms, whereas LF and AF power meters are usually capable
of being set to have load impedance values in the range 1ohm to about 5000ohms.**

** DC Power Measurement**

** The simplest arrangement
for measuring DC power is to use an ammeter to measure the current flowing through
the load and a voltmeter to measure the voltage across the load. These two readings
are multiplied together to give the power:-**

** W = V A**

** If E is measured in volts
and I is measured in amps, P will be in watts. Obviously, if the current were
to be in milliamps, then the power would be in milliwatts. The two diagrams
below show the alternative methods of connecting the measuring instruments.**

** The first diagram shows
a connection in which the voltmeter reads the actual voltage across the load
but the ammeter reads the current in the load plus the current drawn by the
voltmeter and hence the calculated power will be slightly higher than the true
value. The second diagram shows a connection where the ammeter reads the actual
current drawn by the load but the voltmeter reads the voltage across the load
plus the voltage dropped across the ammeter. It therefore follows that the actual
voltage across the load will be lower than that indicated by the voltmeter and
the calculated power will be slightly lower than the true value. In practice,
these errors are usually very small and are often ignored.**

** A single scale instrument,
called a dynamometer wattmeter, is very versatile as it can be switched to read
either voltage, current or true wattage. This type of instrument is described
in the following section.**

** Low Frequency Power
Measurement**

** The dynamometer wattmeter
is an electrodynamic instrument for measuring electric power in a circuit and
consists of a pair of fixed coils, known as current coils, and a moving coil,
known as the potential coil, to which is attached a pointer. This pointer moves
over a scale that is calibrated in amps, volts and watts corresponding to the
switched ranges of the instrument.**

** The current coils are
connected in series with the circuit, while the potential coil is connected
in parallel. A current flowing through the current coil generates an electromagnetic
field around the coil. The strength of this field is proportional to the line
current and is in phase with it. The potential coil usually has a high-value
resistor connected in series with it to reduce the current that flows through
it.**

** The result of this arrangement
is that on a DC circuit, the deflection of the pointer is proportional to both
the current and the voltage, thus conforming to the equation W = V A. On an
AC circuit the deflection is proportional to the average instantaneous product
of voltage and current, thus measuring true power, and possibly, if the power
factor is not unity, showing a different reading to that obtained by simply
multiplying the readings that would be obtained from a stand-alone voltmeter
and a stand-alone ammeter in the same circuit. These readings are subject to
the same errors caused by the connection criteria discussed in the DC power
measurement section above. The illustration below shows such an instrument in
which the voltage measuring circuit consumes 6 VA and the current measuring
circuit consumes either 1.2 VA when measuring only current or 0.8 VA when measuring
watts.**

** Discrete meters and dynamometer
wattmeters are only used at frequencies up to about 500Hz and are intended for
the measurement of powers in the range 1W to many kilowatts.**

** Obviously, if the load
is purely resistive and of known value, a calibrated oscilloscope can be used
measure the voltage across it and hence calculate the power. Remember that oscilloscopes
indicate peak-to-peak voltage and accurately determining the equivalent RMS
value is only possible if the waveform is sinusoidal. The RMS value of a sinusoidal
waveform is 0.3535 x the peak-to-peak voltage.**

** High Frequency Power
Measurement**

** For the purposes of this
tutorial, high frequencies include audio frequencies between 10Hz and 30kHz,
RF frequencies between 30kHz and 1000MHz and microwave frequencies above 1000MHz.
Each of these frequency ranges require different power measuring techniques.**

** AF Power Meters**

** As stated earlier, audio
frequency power meters are usually absorption instruments that include a resistive
load, selectable in value over a wide range of about 1ohm to 5000ohms. They
are not intended for "in-line" measurements. Since the load resistance is known
and the signals to be measured are nominally sinusoidal, the voltage developed
across the load is full-wave rectified and the resulting DC voltage is applied
to an integral meter, calibrated in watts (or milliwatts). The illustration
below shows a vintage (circa 1939) AF power meter of this type. Modern meters
make use of sophisticated solid state circuitry and digital displays but the
basic principles are the same as with traditional meters.**

** AF power meters are primarily
used in the testing and calibration of audio amplifiers, 600ohm line drivers,
radio receivers and similar equipment and are intended for the measurement of
powers from a few milliwatts up to several hundred watts over a frequency range
of about 10Hz to 30kHz. They are normally calibrated to read RMS watts, assuming
a sinusoidal waveform and often incorporate a decibel scale.**

** RF Power Meters**

** There are many different
types of RF power meter, some being absorption types having integral load resistors
and some being designed for insertion into coaxial transmission lines. There
is no technical reason why an in-line power meter for 300ohm or 600ohm open
wire feeder could not be constructed but none is available commercially.**

** As stated above, if the
value of the load resistor is known, it is purely resistive and if the power
waveform is sinusoidal, a calibrated oscilloscope can be used to measure the
voltage across this load and hence the power may be calculated. The RMS value
of a sinusoidal waveform is 0.3535 x the peak-to-peak voltage. It is important
to use a low capacitance probe, X10 or even X100 if enough power is available,
so that the shunting effect of the oscilloscope probe does not adversely affect
the VSWR on the line.**

** The first instrument illustrated
is a laboratory absorption RF power meter having remote sensor heads, which
are connected to the indicator unit via a lead. The sensor heads contain the
integral load resistor and the power sensing components. The sensing head shown
is a 50ohm device fitted with an N-type connector. A range of heads is manufactured,
having various connector options, including waveguide flanges, and various load
values.**

** These instruments are
extremely accurate but the sensor heads are rather fragile and are easily damaged
by excessive power input (greater than 30mW). Higher powers are measured using
accurate attenuators between the power source and the sensor head. The sensor
head illustrated below has an operating frequency range of between 10MHz and
10GHz but other heads having an upper frequency limit of 18GHz are available.**

** Great care is taken in
the design of the sensor heads, such that a VSWR of less than 1.1 : 1 is achieved,
even at frequencies up to 18GHz. The instrument is calibrated to read RMS
power.**

** An older and less accurate
absorption power meter is shown in the next illustration. This particular device
uses a large 75ohm, 100W carbon resistor and a thermo-couple to sense the power
in the load. A 50ohm version was also manufactured. The instruments are calibrated
in RMS power and are far more robust than the laboratory instrument described
above but the usable frequency range is only DC to 150MHz.**

** Above 150MHz, the instrument
will still give an indication of power but the absolute accuracy is drastically
reduced due to reactive elements in the load resistor circuit resulting in incorrect
termination of the coaxial feeder resulting in high VSWR. However, comparative
measurements would still be valid.**

** All the above instruments
are intended to measure the RMS power of a constant, sinusoidal waveform. Amplifiers,
CW/FM transmitters and similar devices are usually adjusted and tested using
sinusoidal signals but when assessing the performance of SSB transmitters, different
techniques are necessary, especially when using speech as the modulating waveform.**

** These meters cannot accurately
measure peak envelope power under these conditions because of thermal inertia
in the thermo-couples or thermistors used and mechanical inertia in meter movements,
although this latter limitation does not apply to instruments using digital
LED or LCD displays. Also, the peaks would only be present for very short periods
of time, perhaps only a few milliseconds, and it would be virtually impossible
for a person to physically see and register the peak reading, even if the instrument
were capable of displaying it.**

** The solution is to use
an instrument that measures the instantaneous voltage and current on the transmission
line at any given point in time, processes the results to calculate the instantaneous
power and then displays and holds this reading on an indicating device, either
permanently, or for sufficient time to allow a person to register the result.
If a mechanical meter is used, the mechanical inertia of its pointer must be
compensated for electronically. Since no thermo-couples, thermistors or similar
devices are used, thermal inertia is not a problem. A current transformer feeding
a resistive load is used to monitor the line current and convert it into a voltage,
which is measured, together with the line voltage, by electronic means.**

** The above illustration
shows such an instrument. This particular device is home constructed and incorporates
two measuring circuits, one measuring forward power and the other reading reverse
or return power It is therefore possible to calculate the VSWR existing on the
line in addition to the peak envelope power. The instrument also incorporates
a bar-graph display which indicates approximate VSWR up to values of 3:1.**

** The measurement of forward
power has three modes of operation. One is "mean", where the instrument indicates
mean power, in a manner similar to those described earlier. The second mode
is "peak follow", where the peak power value is displayed for approximately
500mS before responding to subsequent peaks. The third operating mode is "peak
hold", where the meter indicates the peak value indefinitely, or until a higher
peak is detected, but does not respond to any lower peaks.**

** The reverse power measurement
mode is "mean". Peak power measurement is not necessary as VSWR is best measured
using a steady CW signal, rather than an SSB signal.**

** This meter is an "in-line"
instrument and has two power ranges. One is 1000W forward and 100W reverse,
while the other is 100W forward and 10W reverse. The frequency range over which
accurate measurements can be made is 1MHz to 30MHz.**

** When testing AM and SSB
transmitters, it is advisable to simultaneously monitor the output waveform
on an oscilloscope, as well as measuring the power output, to ensure that no
clipping or "flat-topping" is occurring.**

** Most commercially made
VSWR bridges intended for amateur use are advertised as being able to "measure
power" and some of the more expensive even claim to be able to measure PEP.**

** These claims should be
viewed with skepticism, particularly for those bridges intended for use at VHF
as these devices are often slightly frequency conscious and seldom use line
current and line voltage to determine the power. Also, they sometimes have an
adverse effect on the VSWR they are trying to measure. Those claiming to measure
PEP usually do no more than use a large capacitor across the detector output.
Although this has the effect of allowing signal peaks to build up charge on
the capacitor, it does, by definition, increase the time constant of the measuring
circuit such that it may "miss" very short peaks altogether.**

** Microwave Power Meters**

** Measurement of power at
microwave frequencies presents many problems not evident at lower frequencies.
Some commercial power meters, such as the HP 432A / HP748A described earlier,
are usable from very low frequencies to well into the microwave range but others
are only usable at microwave frequencies. Some of the more exotic microwave
power meters use techniques that are beyond the scope of this tutorial.**

** Power Density**

** Power density is extremely
difficult to measure directly. It is usually applicable to a focused radio signal,
such as that from a dish antenna, or focused light, such as that from a laser.
Power density is usually derived by measuring the total RF power being fed to
the antenna or the light emanating from the basic laser source, measuring the
area which the focused beam is illuminating and then calculating the "watts-per-square-metre"
from these figures.**

** As an example, the power
density of solar radiation, at the equator, is normally accepted to be approximately
1.4kW/m², dropping to about 1.0kW/m² at the latitude of northern Europe. It
therefore follows that in this country and ignoring losses, a 1 metre square
solar panel will provide 1.0kW of heating power. Now if that sunlight were focused
into a 1mm diameter spot (area =0.00785cm²) using a lens having an effective
diameter of 10cm (an area of 0.00785m²), the power in that focused spot of light
would be approximately 7.8W, which represents a power density of 1000W/cm² or
10MW/m², which would easily set fire to flammable materials such as wood or
paper.**

** Modern lasers can produce
power densities of around 1GW/cm², so it is obvious how they can be used for
cutting steel plate and shining focused spots of light onto the moon.**

__Field Strength__

** Field strength is related
to power density but is the parameter normally used to define the strength of
a radio signal at a point remote from a transmitter. The power densities of
signals impinging on a remote aerial are extremely small and difficult to measure,
whereas field strength is much easier to envisage and measure.**

** For example, if an aerial,
such as a dish or yagi with an effective aperture of 1m², is used to receive
a signal and the amplitude of that signal is 1μV into a receiver having
an input impedance of 50ohms, the power being input to the receiver will be
0.02pW. This implies that the power density of the original signal was 0.02pW/m².
It is virtually impossible to measure such miniscule powers directly.**

** Field strengths are measured
in volts/metre, which is the amplitude of signal that the incident field induces
into a non-resonant 1 metre long conductor. It is relatively easy to measure
sub-microvolt signal levels.**

**Concluding Remarks**

** As with most technical
subjects, there is more to power and power measurement than meets the eye. There
are many web-sites dealing with all aspects of this subject, some superficially
and some going to great lengths, with the mathematics to match. **

**Press the "Technical"
button on the left to return to the Main Page, or press an appropriate button
to go to a different section.**

**If there are no buttons
on the left, you probably got directly to this page via a search engine. Select
normal access to go to the G3NPF/M1AIM home page.**