HD Radio Digital Carrier Power Calculations



With all the discussion regarding the true RMS power in the digital
sidebands for the iBiquity AM IBOC system, I decided I needed to conduct
some research.  It has taken me a while to post because I needed to
consult with some experts and run some tests to verify our findings.  To
me this is basically an academic exercise, albeit a valuable one: the AM
IBOC system will work, or not, regardless of our calculations or
discoveries here.


I have learned that calculating the "total true RMS digital power" in
the AM sidebands utilizing the iBiquity IBOC digital transmission scheme
is more complex than it first appears.  The reason for this is the
presence of the multiple OFDM carriers within the measured passband.
Typically we deal with a single carrier, or compare a single signal to
another single signal and express that as a ratio in dB.  A spectrum
analyzer will conveniently display the relationship between signals in
dB, making this a fairly simple matter.  However for the purposes of
calculating the total true RMS digital power, given the multiple
individual OFDM carriers involved, it is necessary to calculate the
aggregate power of the multiple carriers, integrated across their full
passband.  This is NOT the power you will observe directly on a spectrum
analyzer display when setting up the system, or measure directly in the
field with a field intensity meter (which is a voltage device not a
power meter).


The NRSC and iBiquity standards give the maximum AM digital sideband
power as 27.8 dB below unmodulated carrier (dBc).  When we set up our AM
HD transmitters we adjust the digital sidebands so that they fall at
least 27.8 dB below the carrier as measured on a spectrum analyzer with
300 Hz resolution bandwidth, as per the iBiquity spec.  This is the
figure we have been concerned with in the "real world" when deploying
these systems, since this is the spec we need to meet.  And we always
certify that with a spectrum analyzer each time we launch a system.  We
have purchased quite a few spectrum analyzers for the purpose of setting
up AM and FM digital systems.  They are also helpful of course for
verifying occupied bandwidth and looking at spurious emisisons.


But in the case of "total true digital RMS power" these numbers, and the
spectrum analyzer display, don't tell the whole story.  To compensate
for the difference in the 300 Hz measurement bandwidth used for spectrum
analysis versus the total bandwidth occupied by all the digital carriers
in the sidabands, a "Bandwidth Correction Factor" must be employed to
integrate the power across the band of interest.

The Bandwidth Correction Factor ("BWC") can be expressed as 10
log(4360.5 Hz / 300 Hz), or +11.6 dB.  This represents integration of
the power of the static, individual OFDM digital carriers across 4360.5


So we add the BWC of 11.6 dB to the measured (required) digital sideband
signal level of -27.8 dBc (what we read on our spectrum analyzers) and
we get a total sideband power (for the upper or lower digital sidebands)
of -16.2 dBc.   Given this fact, the interfering true RMS power/energy
of the IBOC digital sideband to a first adjacent station for a 50 KW AM
station is 1200 watts, which comports closely with Barry McLarnon's
figure for true RMS power of the combined digital carriers, not 500
watts as I stated in an earlier post (the 500 watts was not integrated
or bandwidth corrected).  There was no deception intended.  It's all a
matter of calculations that are applied to the observed measurements,
taking into account the nature of the signal we're measuring and the
bandwidth of the tools we're using.

Self interference to the host analog station is 3 dB worse, since both
sidebands are present within the host envelope.  The total RMS energy in
the two digital sidebands, combined, is 13.2 dB below unmodulated
carrier within the host channel envelope, or 2400 watts for the 50 kW AM


But iBiquity says each sideband is 27.8 dB below carrier.  Accounting
for both digital sidebands, the digital signal is still only spec'd at
-24.8 dBc.  What's wrong here?  Are we all exceeding legal power?  No.
-27.8 dBc is the correct level observed on a spectrum analyzer for each
of the primary digital sidebands when setting up the system.  It's not
the total true RMS power integrated across all the digital carriers,
which is what is being discussed here.  It's also worthwhile to note
that when we speak of a 50 KW analog station, that too is not the power
integrated across the full audio passband when modulated with a complex
waveform.  Additionally, with 100% modulation the analog power will
actually be 75 kW (150% of unmodulated power), but the digital power
never changes.  What does all this mean?  It means both numbers (-24.8
dBc and -13.2 dbC) are correct.  This is just about definitions and
measurement methodology.


Ok, this is a lot of theory.  To confirm these numbers, a transmitter
manufacturer conducted a test at my request.  Using a waveform
independent, true-RMS power meter, total power in a properly adjusted
IBOC AM transmitter was measured with unmodulated carrier and all
digital carriers turned OFF, and again with all digital carriers turned
ON.  The tests confirmed the math above: RMS power on either sideband
was 16.2 dB below unmodulated carrier, and RMS power within the full
band was 13.2 dB below unmodulated carrier.  This was also repeated
using a calorimeter, which is truly bandwidth agnostic, and the same
results were observed.  So I'm fairly confidant that -13.2 dBc for on
band digital to analog, and -16.2 dBc for first adjacent digital to
analog, are the right numbers for true RMS power of the digital carriers
in a properly adjusted AM IBOC system.  Just remember these refer to an
unmodulated carrier.  Also all of this is for the HYBRID mode, that is,
analog and digital co-existing on channel.  Pure digital transmission is
another matter.


None of this guarantees that AM IBOC signals won't create interference
to other AM analog stations in the field, nor does it guarantee that
they will.  While the system authorized by the FCC today has been
extensively tested and verified by the system designers and the NRSC,
I'll be the first to admit that those were for the most part (except for
some field tests) laboratory conditions.  As they say "the proof of the
pudding is in the eating."  Over 750 AM and FM stations have been
converted to digital as of today.  For the reasons I and others have
mentioned in previous posts such as array and amplifier nonlinearities,
pattern bandwidth, and impedance asymmetry, it is certain that there
WILL be cases of interference.  This will be something we as engineers
will be asked to correct.  And the transmission system designers and
receiver manufacturers will also continue to work to improve the system.
As the owner of more AM radio stations, in markets large and small, than
any other broadcaster, you can rest assured that Clear Channel is very
concerned about the potential for interference in the AM band.  Whether
our stations are the cause, or the victims of interference, we will work
diligently to correct it.  We have more to lose than most.


Steve Davis
Senior Vice President, Engineering
Clear Channel Radio