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.