Graphical method for designing a PLL frequency synthesizer to meet a phase
noise specification
- a simple graphical and understandable approach to understanding where
phase noise is generated within a PLL frequency synthesizer and designing it to
meet a requirement
Phase noise in PLL frequency synthesizers if of great
importance because it determines many factors about the equipment into which it
is incorporated. For receivers it determines the reciprocal mixing performance,
and in some circumstances the bit error rate. In transmitters the phase noise
performance of the frequency synthesizer determines features such as adjacent
channel noise and it contributes to the bit error rate for the whole system.
Phase noise in a synthesizer loop
Phase noise is generated at different points around the
synthesizer loop and depending upon where it is generated it affects the output
in different ways. For example, noise generated by the VCO has a different
effect to that generated by the phase detector. This illustrates that it is
necessary to look at the noise performance of each circuit block in the loop
when designing the synthesizer so that the best noise performance is obtained.
Apart from ensuring that the noise from each part of the
circuit is reduced to an absolute minimum, it is the loop filter which has the
most effect on the final performance of the circuit because it determines the
break frequencies where noise from different parts of the circuit start to
affect the output.
To see how this happens take the example of noise from the
VCO. Noise from the oscillator is divided by the divider chain and appears at
the phase detector. Here it appears as small perturbations in the phase of the
signal and emerges at the output of the phase detector. When it comes to the
loop filter only those frequencies which are below its cut-off point appear at
the control terminal of the VCO to correct or eliminate the noise. From this it
can be seen that VCO noise which is within the loop bandwidth is attenuated, but
that which is outside the loop bandwidth is left unchanged.
The situation is slightly different for noise generated by
the reference. This enters the phase detector and again passes through it to the
loop filter where the components below the cut-off frequency are allowed through
and appear on the control terminal of the VCO. Here they add noise to the output
signal. So it can be seen that noise from the reference is added to the output
signal within the loop bandwidth but it is attenuated outside this.
Similar arguments can be applied to all the other circuit
blocks within the loop. In practice the only other block which normally has any
major effect is the phase detector and its noise affects the loop in exactly the
same way as noise from the reference. Also if multi-loop synthesizers are used
then the same arguments can be used again.
Effects of multiplication
As noise is generated at different points around the loop it
is necessary to discover what effect this has on the output. As a result it is
necessary to relate all the effects back to the VCO. Apart from the different
elements in the loop affecting the noise at the output in different ways, the
effect of the multiplication in the loop also has an effect.
The effect of multiplication is very important. It is found
that the level of phase noise from some areas is increased in line with the
multiplication factor (i.e. the ratio of the final output frequency to the phase
comparison frequency). In fact it is increased by a factor of 20 log10 N where N
is the multiplication factor. The VCO is unaffected by this, but any noise from
the reference and phase detector undergoes this amount of degradation. Even very
good reference signals can be a major source of noise if the multiplication
factor is high. For example a loop which has a divider set to 200 will multiply
the noise of the reference and phase detector by 46 dB.
From this information it is possible to build up a picture of
the performance of the synthesizer. Generally this will look like the outline
shown in Fig. 6. From this it can be seen that the noise inside the loop
bandwidth is due mainly to components like the phase detector and reference,
whilst outside the loop the VCO generates the noise. A slight hump is generally
seen at the point where the loop filter cuts off and the loop gain falls to
unity.
By predicting the performance of the loop it is possible to
optimise the performance or look at areas which can be addressed to improve the
performance of the whole synthesizer before the loop is even built. In order to
analyse the loop further it is necessary to look at each circuit block in turn.
Voltage controlled oscillator
The noise performance of the oscillator is of particular
importance. This is because the noise performance of the synthesizer outside the
loop is totally governed by its performance. In addition to this its performance
may influence decisions about other areas of the circuit.
The typical noise outline for a VCO is flat at large
frequency offsets from the carrier. It is determined largely by factors such as
the noise figure of the active device. The performance of this area of the
oscillator operation can be optimised by ensuring the circuit is running under
the optimum noise performance conditions. Another approach is to increase the
power level of the circuit so that the signal to noise ratio improves.
Closer in the noise starts to rise, initially at a rate of 20
dB per decade. The point at which this starts to rise is determined mainly by
the Q of the oscillator circuit. A high Q circuit will ensure a good noise
performance. Unfortunately VCOs have an inherently low Q because of the Q of the
tuning varactors normally employed. Performance can be improved by increasing
the Q, but this often results in the coverage of the oscillator being reduced.
Still further in towards the carrier the noise level starts
to rise even faster at a rate of 30 dB per decade. This results from flicker or
1/f noise. This can be improved by increasing the level of low frequency
feedback in the oscillator circuit. In a standard bipolar circuit a small
un-bypassed resistor in the emitter circuit can give significant improvements.
To be able to assess the performance of the whole loop it is
necessary to assess the performance of the oscillator once it has been designed
and optimised. Whilst there are a number of methods of achieving this the most
successful is generally to place the oscillator into a loop having a narrow
bandwidth and then measure its performance with a spectrum analyser. By holding
the oscillator steady this can be achieved relatively easily. However the
results are only valid outside the loop bandwidth. However a test loop is likely
to have a much narrower bandwidth than the loop being designed the noise levels
in the area of interest will be unaltered.
Reference
The noise performance of the reference follows the same
outlines as those for the VCO, but the performance is naturally far better. The
reason for this is that the Q of the crystal is many orders of magnitude higher
than that of the tuned circuit in the VCO.
Typically it is possible to achieve figures of -110 dBc/Hz at
10 Hz from the carrier and 140 dBc/Hz at 1 kHz from a crystal oven. Figures of
this order are quite satisfactory for most applications. If lower levels of
reference noise are required these can be obtain, but at a cost. In instances
where large multiplication factors are necessary a low noise reference may be
the only option. However as a result of the cost they should be avoided wherever
possible. Plots of typical levels of phase noise are often available with
crystal ovens giving an accurate guide to the level of phase noise generated by
the reference.
Frequency divider
Divider noise appears within the loop bandwidth. Fortunately
the levels of noise generated within the divider are normally quite low. If an
analysis is required then it will be found that noise is generated at different
points within the divider each of which will be subject to a different
multiplication factor dependent upon where in the divider it is generated and
the division ratio employed from that point.
Most divider chains use several dividers and if an
approximate analysis is to be performed it may be more convenient to only
consider the last device or devices in the chain as these will contribute most
to the noise. However the noise is generally difficult to measure and will be
seen with that generated by the phase detector.
Phase detector
Like the reference signal the phase detector performance is
crucial in determining the noise performance within the loop bandwidth. There
are a number of different types of phase detector. The two main categories are
analogue and digital.
Mixers are used to give analogue phase detectors. If the
output signal to noise ratio is to be as good as possible then it is necessary
to ensure that the input signal levels are as high as possible within the
operating limits of the mixer. Typically the signal input may be limited to
around -10 dBM and the local oscillator input to +10 dBm. In some instances
higher level mixers may be used with local oscillator levels of +17 dBm or
higher. The mixer should also be chosen to have a low NTR (noise temperature
ratio). As the output is DC coupled it is necessary to have a low output load
resistance to prevent a backward bias developing. This could offset the
operation of the mixer and reduce its noise performance.
It is possible to calculate the theoretical noise performance
of the mixer under optimum conditions. An analogue mixer is likely to give a
noise level of around -153 dBc/Hz.
There are a variety of digital phase detectors which can be
used. In theory these give a better noise performance than the analogue
counterpart. At best a simple OR gate type will give figures about 10 dB better
than an analogue detector and an edge triggered type (e.g. a dual D type or
similar) will give a performance of around 5 dB better than the analogue
detector.
These figures are the theoretical optimum and should be
treated as guide although they are sufficient for initial noise estimates. In
practice other factors may mean that the figures are different. A variety of
factors including power supply noise, circuit layout etc. can degrade the
performance from the ideal. If very accurate measurements are required then
results from the previous use of the circuit, or from a special test loop can
provide the required results.
Loop filter
There are a variety of parameters within the area of the loop
filter which affect the noise performance of the loop. The break points of the
filter and the unity gain point of the loop determined by the filter govern the
noise profile.
In terms of contributions to the noise in the loop the major
source is likely to occur if an operational amplifier is used. If this is the
case a low noise variety must be used otherwise the filter will give a large
contribution to the loop phase noise profile. This noise is often viewed as
combined with that from the phase detector, appearing to degrade its performance
from the ideal.
Plotting Performance
Having investigated the noise components from each element in
the loop, it is possible to construct a picture of how the whole loop will
perform. Whilst this can performed mathematically, a simple graphical approach
quickly reveals an estimate of the performance and shows which are the major
elements which contribute to the noise. In this way some re-design can be
undertaken before the design is constructed, enabling the best option to be
chosen on the drawing board. Naturally it is likely to need some optimisation
once it has been built, but this method enables the design to be made as close
as possible beforehand.
First it is necessary to obtain the loop response. This is
dependent upon a variety of factors including the gain around the loop and the
loop filter response. For stability the loop gain must fall at a rate of 20 dB
per decade (6 dB per octave) at the unity gain point. Provided this criterion is
met a wide variety of filters can be used. Often it is useful to have the loop
response rise at a greater rate than this inside the loop bandwidth. By doing
this the VCO noise can be attenuated further. Outside the loop bandwidth a
greater fall off rate can aid suppress the unwanted reference sidebands further.
From a knowledge of the loop filter chosen the break points can be calculated
and with a knowledge of the loop gain the total loop response can be plotted.
With the response known the components from the individual
blocks in the loop can be added as they will be affected by the loop and seen at
the output.
First take the VCO. Outside the loop bandwidth its noise
characteristic is unmodified. However once inside this point the action of the
loop attenuates the noise, first at a rate of 20 dB per decade, and then at a
rate of 40 dB per decade. The overall affect of this is to modify the response
of the characteristic as shown in Fig. 10. It is seen that outside the loop
bandwidth the noise profile is left unmodified. Far out the noise is flat, but
further in the VCO noise rises at the rate of 20 dB per decade. Inside the loop
bandwidth the VCO noise will be attenuated first at the rate of 20 dB per
decade, which in this case gives a flat noise profile. Then as the loop gain
increases at the filter break point, to 40 dB per decade this gives a fall in
the VCO noise profile of -20 dB per decade. However further in the profile of
the stand alone VCO noise rises to -30dB per decade. The action of the loop
gives an overall fall of -10 dB per decade.
The effects of the other significant contributions can be
calculated. The reference response can easily be deduced from the manufacturers
figures. Once obtained these must have the effect of the loop multiplication
factor added. Once this has been calculated the effect of the loop can be added.
Inside the loop there is no effect on the noise characteristic, however outside
this frequency it will attenuate the reference noise, first at a rate of 20 dB
per decade and then after the filter break point at 40 dB per decade.
The other major contributor to the loop noise is the phase
detector. The effect of this is treated in the same way as the reference, having
the effect of the loop multiplication added and then being attenuated outside
the loop bandwidth.
Once all the individual curves have been generated they can
be combined onto a single plot to gain a full picture of the performance of the
synthesizer. When doing this it should be remembered that it is necessary to
produce the RMS sum of the components because the noise sources are not
correlated.
Once this has been done then it is possible to optimise the
performance by changing factors like the loop bandwidth, multiplication factor
and possibly the loop topology to obtain the best performance and ensure that
the required specifications are met. In most cases the loop bandwidth is chosen
so that a relatively smooth transition is made between the noise contributions
inside and outside the loop. This normally corresponds to lowest overall noise
situation.
Summary
Although this approach may appear to be slightly "low tech"
in today's highly computerised engineering environment it has the advantage that
a visual plot of the predicted performance can be easily put together. In this
way the problem areas can be quickly identified, and the noise performance of
the whole synthesizer optimised before the final design is committed.
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