Editor’s note: I am pleased to bring you this month’s author for Texas Instruments’ ongoing series of Signal Chain Basics: Dean Banerjee, Applications Engineer, Texas Instruments
When the phase noise performance is just not good enough, one possibility is to combine two or more signals that are in phase to generate a better phase noise signal. This concept applies to the scenario of combining two sides of a differential output to form a single-ended output or the combination of signals from two semiconductor chips of the same type and configuration. The general concept is that the output power theoretically increases 6 dB while the uncorrelated noise only increases 3 dB, for a net gain of 3 dB. Although the combination circuit may have losses, as in the case of a balun or a splitter, the phase noise is not impacted by this as it applies equally to both the signal and the noise. Some other considerations are how to know if noise is uncorrelated, dealing with phase error between the signals, and getting some actual measured data using this approach.
Correlated and uncorrelated noise
Two sources of noise can be thought to be uncorrelated if they are independent. In Figure 1 , the voltage controlled oscillator (VCO), divider, and buffer for each signal is completely independent. Hence, these noise sources are uncorrelated and the combined signal has 3 dB higher noise power. However, the signal is 6 dB higher, translating into a 3 dB improvement in phase noise for a noiseless combination circuit.
Combination of two independent sources.
In Figure 2 , we see the divider and VCO are common to both signals and only the output buffers after the divider is different. In this case, the noise contribution of the VCO and divider is correlated so there is a 6 dB noise power. However, the output buffers are not correlated and this is only a 3-dB noise power. So the net effect is that the phase noise normalized to carrier of the VCO and divider are unimproved by this combination, but the output buffer noise contribution are decreased 3 dB. This scenario is typical of two sides of a differential output being combined with a balun to form a single-ended output. In this case, the close-in phase noise is likely unaffected, but the far-out noise floor is improved.
Combination of a differential output.
The uncorrelated noise of two sources is 3 dB higher, while it is 6 dB higher for correlated sources relates to the fact that noise power at any given offset is related to the variance of the noise voltage at that offset frequency. The variance of the sum of two random variables is:
If X and Y are perfectly correlated, then ρ = 1 and the sum will be four times, which is 6 dB power. If X and Y are uncorrelated, then ρ = 0 and the sum will be twice, or 3 dB power.
Impact of phase error on output power
As long as the phase is reasonably close, the output power and phase noise benefit will be close to the maximum value. To illustrate this, consider the combination of two signals of equal amplitude, A, and phase error of φ.
The power of the combined signal relative to just one of the signals can be found by looking at the square of the RMS voltage.
This verifies the expected result that there is a 6 dB increase in power for signals that are perfectly in phase and that, if they are 180 degrees in phase, they are canceled out. Figure 3 shows what the output power will be for an arbitrary phase error between the two signals.
Phase error between signals.
This curve shows that the phase does not need to be perfect to get the benefit of the higher output power. For instance, if the phase error is less than 50 degrees, the power benefit is within 1 dB of the maximum possible value.
In the following example, two LMX2582 phase-locked loops (PLLs) were combined for better phase noise. They were driven by a 100 MHz Wenzel crystal, which is lower than the noise of the PLLs themselves. The LMX2582 has no phase synchronization pin or bit and the VCO was divided by two, which creates an ambiguous phase. In order to achieve the phase alignment, the phase of one of the PLLs was adjusted with the MASH_SEED bit until the optimal output power was found. This combination also corresponds to the optimal phase noise and optimal jitter of 37 fs.
Combination of two LMX2582 devices.
In this case, we indeed see an improvement in the noise for the combination of the two signals. The individual signal sources were about 50 fs and the combined signal source achieved a jitter of 37 fs.
Jitter plot of combined signals.
Stay tuned for the next Signal Chain Basics article with advice on working with data converters, amplifiers, interface or other analog design challenges.