LMX2531
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SNAS252S –OCTOBER 2005–REVISED DECEMBER 2014
The fractional word, NFractional , is a fraction formed with the NUM and DEN words. In the example used here with
the fraction of 61/100, NUM = 61 and DEN = 100. The fractional denominator value, DEN, can be set from 2 to
4,194,303. The case of DEN = 0 makes no sense, because this would cause an infinite N value; the case of 1
makes no sense either (but could be done), because integer mode should be used in these applications. All
other values in this range, like 10, 32, 42, 734, or 4,000,000 are all valid. Once the fractional denominator, DEN,
is determined, the fractional numerator, NUM, is intended to be varied from 0 to DEN-1.
In general, the fractional denominator, DEN, can be calculated by dividing the phase detector frequency by the
greatest common divisor (GCD) of the channel spacing (fCH) and the phase detector frequency. If the channel
spacing is not obvious, then it can be calculated as the greatest common divisor of all the desired VCO
frequencies.
FDEN = k × fPD / GCD (fPD , fCH) k = 1, 2, 3 .. (3)
For example, consider the case of a 10 MHz phase detector frequency and a 200 kHz channel spacing at the
VCO output. The greatest common divisor of 10 MHz and 200 kHz is just 200 kHz. If one takes 10 MHz divided
by 200 kHz, the result is 50. So a fractional denominator of 50, or any multiple of 50 would work in this example.
Now consider a case with a 10 MHz phase detector frequency and a 30 kHz channel spacing. The greatest
common divisor of 10 MHz and 30 kHz is 10 kHz. The fractional denominator therefore must be a multiple 1000,
because this is 10 MHz divided by 10 kHz. For a final example, consider an application with a fixed output
frequency of 2110.8 MHz and a OSCin frequency of 19.68 MHz. If the phase detector frequency is chosen to be
19.68 MHz, then the channel spacing can be calculated as the greatest common multiple of 19.68 MHz and
2110.8 MHz, which is 240 kHz. The fractional denominator is therefore a multiple of 41, which is 19.68 MHz /
240 kHz. Refer to AN-1865 Frequency Synthesis and Planning for PLL Architectures (SNAA061) for more details
on frequency planning.
To achieve a fractional N value, an integer N divider is modulated between different values. This gives rise to
three main degrees of freedom with the LMX2531 delta-sigma engine including the modulator order, dithering,
and the way that the fractional portion is expressed. The first degree of freedom is the modulator order, which
gives the user the ability to optimize for a particular application. The modulator order can be selected as zero
(integer mode), two, three, or four. One simple technique to better understand the impact of the delta-sigma
fractional engine on noise and spurs is to tune the VCO to an integer channel and observe the impact of
changing the modulator order from integer mode to a higher order. The higher the fractional modulator order is,
the lower the spurs theoretically are. However, this is not always the case, and the higher order fractional
modulator can sometimes give rise to additional spurious tones, but this is dependent on the application. The
second degree of freedom with the LMX2531 delta-sigma engine is dithering. Dithering is often effective in
reducing these additional spurious tones, but can add phase noise in some situations. The third degree of
freedom is the way that the fraction is expressed. For example, 1/10 can be expressed as 100000/1000000.
Expressing the fraction in higher order terms sometimes improves the performance, particularly when dithering is
used. In conclusion, there are some guidelines to getting the optimum choice of settings, but these optimum
settings are application specific. Refer to AN-1879 Fractional N Frequency Synthesis (SNAA062) for a much
more detailed discussion on fractional PLLs and fractional spurs.
8.3.5 Partially Integrated Loop Filter
The LMX2531 integrates the third pole (formed by R3 and C3) and fourth pole (formed by R4 and C4) of the loop
filter. The values for C3, C4, R3, and R4 can also be programmed independently through the MICROWIRE
interface and also R3 and R4 can be changed during FastLock, for minimum lock time. The larger the values of
these components, the stronger the attenuation of the internal loop filter. The maximum attenuation can be
achieved by setting R3 = R4 = 40 kΩand C3 = C4 = 100 pF while the minimum attenuation is achieved by
disabling the loop filter by setting EN_LPFLTR (R6[15]) to zero. Note that when the internal loop filter is disabled,
there is still a small amount of input capacitance on front of the VCO on the order of 200 pF.
Because that the internal loop filter is on-chip, it is more effective at reducing certain spurs than the external loop
filter. The higher order poles formed by the integrated loop filter are also helpful for attenuating noise due to the
delta-sigma modulator. This noise produced by the delta-sigma modulator is outside the loop bandwidth and
dependent on the modulator order. Although setting the filtering for maximum attenuation gives the best filtering,
it puts increased restrictions on how wide the loop bandwidth of the system can be, which corresponds to the
case where the shunt loop filter capacitor, C1, is zero. Increasing the charge pump current and/or the phase
detector frequency increases the maximum attainable loop bandwidth when designing with the integrated filter. It
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