System Phase Noise Calculation and Measurement Techniques
By Joseph D. DiBona, Senior Engineer, Spectrum Microwave

Correlated and Uncorrelated Components
When calculating the phase noise of a system, there are many considerations. The following illustrates phase noise calculations of a system and the effects of correlated components versus uncorrelated components. Following these calculations there is an illustration showing consideration of absolute power levels and how they affect the phase noise of a system.

Let us assume the phase noise for each component at a single offset frequency, say 100 kHz is the following in dBc/Hz:

We will start off with a doubler and an amplifier. (See Equation 1).

If we have a component preceding a doubler or any multiplier, its phase noise will be degraded by 20 log of the multiplication factor. (See Equation 2).

Let’s consider a mixer. If we have two uncorrelated sources with the same phase noise characteristics conditioned by these components and fed into a mixer, the calculations and result is shown in Equation 3.

When the output of a single source is split, conditioned and mixed, it is considered correlated. This would also be true if the two sources above were phase locked to each other. The calculations for the source would be correlated while the other components are not. The result would be higher phase noise. (See Equation 4).

One can also conclude from this that the phase noise of a doubler made by splitting a source and then combining it in a mixer will be the same as using a passive doubler. (See Equation 5).

Thermal Noise Floor
If the phase noise measurement of a component is made at the same power levels that will exist in the system, the thermal noise floor is already in the result. If the data is recorded at much higher power levels than components will experience in the system or if the engineer would like to know what the power levels must be to maintain a particular phase noise result, then the thermal noise floor must be a consideration. The thermal noise floor or kTB is approximately -174 dBm/Hz. This is based on Boltzmann’s constant, the temperature, and the bandwidth of the signal.

Thermal noise is specified in dBm. If the phase noise of a component comes close to this power level, it will be degraded and there is no method to correct the situation short of filtering for phase noise.

The same rules for calculating correlated and uncorrelated components apply as before, so let us consider the performance of the following cascade. (See Equation 6).

Therefore, if the source in this system was ideal, it would have a phase noise of –189 dBc/Hz (-174 minus 15). Allowing the power level to drop significantly degrades the system noise performance.

Frequency Source Measurement Techniques
There are two basic methods for measuring the phase noise of a frequency source: the Phase Locked Loop method and the Delay-Line Frequency Discriminator method. After a basic description of each method, the critical considerations will be discussed and comparisons of the two methods will be summarized.

The basic block diagram of this technique is shown in Figure 1. Two sources are phase locked together and their outputs are presented to a double-balanced mixer acting as a phase detector. With the signals at identical frequencies and in phase quadrature, the output of the phase detector is a fluctuating voltage which is proportional to the instantaneous phase difference between the two signals. This fluctuating output voltage represents the combined phase noise sidebands of the two input signals.

Critical Calibration / Setup Requirements
The phase noise of the reference source as well as that of the Unit Under Test (UUT) contributes to the output noise from the phase detector. If the noise of the reference source is equal to that of the UUT, the measurement results will be 3 dB higher than the noise of the UUT. To ensure that this noise “bump” due to the reference source is less than 0.5 dB, the noise of the reference must be at least 10 dB below that of the UUT.

If the reference source and the UUT are not well isolated from each other, there will be a tendency for the two sources to “injection lock,” which will cause measurement errors because of the uncertainty of the loop characteristics. Combinations of isolators, pads, and amplifiers are often used on each source output to defeat injection locking. It may also be necessary to power the two sources from separate supplies.

Within the bandwidth of the phase locked loop, the noise is suppressed; therefore the loop must be characterized carefully so the suppression can be corrected for in the measurement results. An alternative is to narrow the loop and only consider the noise far outside of the loop bandwidth, which may not be practical.

Power levels within the measurement setup must also be considered relative to the noise floor. For example, with a thermal noise floor of -174 dBm/Hz and an RF power of 0 dBm, noise sidebands at -160 dBc/Hz will be bumped by about 0.2 dB.

Calibration at any one offset frequency can be obtained by phase-modulating one of the two sources, noting the sideband level on an RF analyzer, and equating that level with the resultant baseband signal produced at that offset.

Delay-Line Discriminator Method
The basic block diagram of the Delay-Line Discriminator is shown in Figure 2. In this method, the output of the test source is split into two signals. One of the two resulting signals is delayed and it and the undelayed signal are presented to a phase detector (as before, a double-balanced mixer). The fixed time delay causes a phase shift in the delayed signal which is proportional to the frequency. When compared to the undelayed signal from the other path, frequency fluctuations on the original signal are converted to phase fluctuations. These phase fluctuations are converted by the phase detector into amplitude (voltage) fluctuations. As in the phase locked loop method, the phase detector output is proportional to the input phase differences of two signals in phase quadrature at the input. The transfer response is

Critical Calibration / Setup Requirements
Since the output is proportional to both the phase detector constant and the delay, it is desirable to make both large for maximum sensitivity. However, the presence of the (sin x) / x component introduces peaks and nulls into the response which complicates matters. For offsets less than 1/(2π τ) this effect can be neglected. For offsets greater than 1/(2π τ), a correction for the response must be made. Also, there are nulls in the response at even multiples of n/(2π) where the system sensitivity degrades and cannot be corrected for. Here the only option is to reduce the amount of delay to push the null out beyond the frequency of interest.

The noise floor vs. signal level considerations that were described in the phase locked loop method also apply to the delay-line discriminator measurement method. This is also a consideration in selection of the amount of delay. For instance, 100 feet of .085 semi-rigid cable (150 nsecs delay) has about 2.5 dB loss at 50 MHz but about 12 dB loss at 1 GHz. Care must be taken when choosing the amount of delay to cover requirements for sensitivity as well as not overdriving components at lower frequencies or falling into the thermal noise floor at higher frequencies.

For maximum sensitivity, the two signals incident on the phase detector must be in quadrature. This is nominally at 0 volts output of the mixer. However, if AM noise is an issue, a more sensitive measure of quadrature is the phase at which the AM output of the mixer is at a minimum. Unfortunately, this is rarely at 0 volts and will also change with RF frequency.

As with the phase locked loop method, calibration at any offset frequency can be accomplished by phase modulating the source, noting the sideband level on an RF analyzer, and equating that level with the resultant baseband signal produced at that offset.

Comparison of the Two Methods
Phase Locked Loop Method

Advantages:
• Lower noise floor
• Good AM rejection

Disadvantages:
• Need second (reference) source at each frequency to be tested
• Reference source noise must be at least 10 dB below the noise of the unit under test to avoid significant distortion of the measurement
• One source must be voltage-tunable
• Tendency for injection-locking
• The phase locked loop parameters must be characterized for each measurement to insure accuracy
• Poor tolerance of frequency drift of source

Delay-Line Discriminator Method Advantages:
• Simpler setup
• Does not require reference source
• Easier calibration
• No possibility of injection locking
• Wide RF frequency coverage
• Less sensitive to source frequency drift

Disadvantages:
• Relatively poor noise floor
• Poor AM rejection

Considerations for Extending the Frequency Range of the Measurement
A method commonly used to extend the frequency range of a delay line discriminator noise measurement is downconversion. Figure 3 shows the basic functionality of a typical downconversion scheme. There are several considerations involved in designing this scheme. The goal is an intermod free downconverter, which causes no degradation in the noise floor of the frequency discriminator.

The noise floor is simply a function of the source that generates the LO. When a signal is passed through the mixer, the resulting noise is the sum of the two sources.

Therefore the same considerations that pertain to using two sources in the Phase Lock Loop method apply here.

The intermods are caused by different multiples of the LO mixing with different multiples of the RF. This causes mixer products to land in the measurement bandwidth. Quite often this causes a hole in the measurement abilities of the downconverter and delay line discriminator combination.

System Measurement Techniques
System or component measurements are accomplished using an additive measurement technique. This technique typically requires two units and the results assume the units exhibit the same phase noise. The results are then reduced by 3 dB to remove the additive effects of the measurement. Two units are required when there is frequency translation. The frequencies going into the mixer must be the same. If measuring an amplifier or other systems that do not change the input frequency, a single unit can be tested as long as one can maintain proper power levels in the mixer. If only one unit is tested, the 3 dB correction does not apply.

The basic block diagram of this technique is shown in Figure 5. A single source is used for this measurement. Ideally the noise of the source is cancelled, but in reality the noise is suppressed by approximately 30 dB. Depending on the expected results, this source can quite often be a synthesizer. Since this is a single frequency measurement, this allows for flexibility in frequency selection. The phase shifter is used to set the paths in quadrature for peak sensitivity in the mixer. This same phase shifter can also be used for calibration. One must also consider the power levels. The units should be tested at the power level expected in the system or when used at the next level.

Calibration Techniques
There are two techniques for calibrating this setup. One method requires that the phase shifter can vary the phase at least 180 degrees. This is required because the phase must be varied to achieve both the positive and negative DC peaks out of the mixer. One can assume the positive peak will be the same as the negative peak, but this can introduce error into the results. These values are then used to calculate the mixer’s sensitivity. With this information, the amplitude of the phase noise measured on the spectrum analyzer can be converted to actual power levels.

Another calibration technique is to introduce a sideband (single or double sided) onto the source. This can be accomplished by either frequency modulating the source or using a coupler to induce a sideband. This will require a second source very close in frequency to the source in the setup. The frequency of the modulation or sideband should relate to the frequency offset of the phase noise being measured. Therefore if the measurement is from 1 kHz to 1 MHz, the sideband should be at approximately 100 kHz. To be extremely rigorous one would calibrate at the offset being measured. This is required if the baseband amplifier does not have flat or calibrated gain over the measurement window. This sideband is set to an amplitude low enough not to saturate the baseband amplifier yet high enough to be easily measured over the noise in the system. For example, if the sideband is set for -50 dBc the system now knows the level it measures at baseband equates to -50 dBc, at RF. Knowing this allows the system to offset the results relative to the sideband measurement.

Conclusion
Many issues must be carefully considered when designing for phase noise. By using the proper measurement techniques and calculations, the phase noise of complex systems can easily be modeled and predicted.

Spectrum Microwave
www.spectrummicrowave.com
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