ACE9030MSLASHIWSLASHFP2N datasheet(33/39 Pages) MITEL

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ACE9030

Fig. 28 Fractional-N Phase Error And Compensation Pulse

calculation of

± 92 Hz and the level of the fundamental is again

(2/

π) x peak level, giving 102 Hz deviation at a frequency now

of 1/8 x fCOMP (12·5 kHz). β then becomes 102/12500 = 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

spurious levels (rather than solve all loop problems on its own)

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 N

TOT 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

frequency giving a peak deviation proportional to the compari-

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

suggests the above example is not just a spot typical result but

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:

ERR = 0·5 ns x 250 µA

= 125 fC per pulse

Voltage step:

ERR = QERR ÷ CPROP

= 125 fC

÷ 6·8 nF = 18·4 µV

Frequency step:

ERR = 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,

putting it well into the narrow band f.m. category. At such small

deviations the sideband amplitude is

β/2 of the carrier, giving

0·000293 times or – 71 dBc. There will also be higher harmon-

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

8 and

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

φ DOWN due to

phase error

COMPENSATION

PULSE

156 ns

Icomp(0) = 0.2

µA x ACC

µs

Iprop(0) = 250

µA

ACC x

0.125 ns

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