ACE9030
Iprop(0) = 250 µA
ACC x
0.125 ns
φ DOWN due to
phase error
COMPENSATION
PULSE
156 ns
Icomp(0) = 0.2 µA x ACC
10 µs
Fig. 28 Fractional-N Phase Error And Compensation Pulse
calculationof± 92 Hzandthelevelofthefundamentalisagain
(2/π) x peak level, giving 102 Hz deviation at a frequency now
of1/8 xfCOMP (12·5 kHz).β thenbecomes102/12500=0·00816,
giving sidebands at up to 0·00408 times or – 47 dBc.
Compensation pulses are used to cancel the effect of the
unwanted phase corrections, and if these match to within
10 % they should give a reduction of 20 dB in the fundemental
sideband levels, down to a worst figure of – 67 dBc. The low
harmonics will also be adequately cancelled but higher har-
monics will be left to the loop filter to remove, and as the
bandwidth is set by the comparison frequency at only 8 times
the Fractional-N fundamental these harmonics will always be
well attenuated.
A typical system specification (AMPS) is – 60 dBc so the
harmonic spectrum of the modulation needs to be considered
to find the manufacturing margins but if the Fractional-N
system is only used to help achieve correct lock times and
spuriouslevels(ratherthansolveallloopproblemsonitsown)
then this example suggests that the compensation is not
critical and can give a performance advantage at little cost.
More critical compensation is needed if NTOT is less or if
the comparison period is longer, but these cancel if the VCO
stays at the same frequency, equation (4). Changing only the
comparison frequency in the above example would then give
the same 184 Hz deviation. In practice the loop filter capacitor
value is likely to also change to match the new comparison
frequencygivingapeakdeviationproportionaltothecompari-
son frequency. The modulation index is inversely proportional
to the comparison frequency so the final sideband level is not,
in practice, much affected by the comparison frequency
choice, but the separation from the carrier is affected. This all
suggeststheaboveexampleisnotjustaspottypicalresultbut
will apply over a broad range of systems and allow Fractional-
N to be used whenever desired.
not ramp in size and that the loop somehow stays on the
correct frequency:
Average phase error:
= mid-range ACC x 0·125 ns
= 4 x 0·125 ns = 0·5 ns
Charge into filter: QERR = 0·5 ns x 250 µA
= 125 fC per pulse
VERR = QERR ÷ CPROP
= 125 fC ÷ 6·8 nF = 18·4 µV
Voltage step:
Frequency step:
FERR = VERR x VCO gain
= 18·4 µV x 10 MHz/V = 184 Hz
This gives a signal with a modulation frequency of
100 kHz with a step deviation of 184 Hz and if the loop is to
stay on frequency the waveform must ramp back between
steps, giving a sawtooth with an amplitude of ± 92 Hz. Fourier
analysis gives the level of the fundamental as (2/π) x peak
level, to give 58·6 Hz deviation and hence a modulation index
β (peak deviation ÷ modulation frequency) of only 0·000586,
puttingitwellintothenarrowbandf.m. category. Atsuchsmall
deviations the sideband amplitude is β/2 of the carrier, giving
0·000293timesor– 71 dBc.Therewillalsobehigherharmon-
ics present but these will all be at lower levels.
This calculation assumed all phase error pulses are the
same, but in reality the size varies in a pattern determined by
the fractional numerator (0 to 7) with a period equal to the
demoninator (8) times the comparison period. The fractions
that give the highest level of output at 1/8 x fCOMP are 1/8 and 7/8
and with these the phase error changes in seven steps of a
staircase waveform until the eighth cycle, when the phase
resets and the pattern starts again. The loop will settle to the
correct average frequency by adding a d.c. offset for the mean
level of the staircase, leading to an error waveform which is
approximately a sawtooth wave with a step size of 7 in units of
ACC value. The peak deviation is then 7/4 times the previous
33
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