Phase coherence, that is a stable phase relationship between signals, is essential when making measurements that require more than one RF output. While this was once primarily required when evaluating the performance of phased-array antennas in military applications, it has become more and more important now that wireless systems are using MIMO and beamforming techniques to increase network performance.
It is particularly important when evaluating the performance of algorithms used in MIMO receivers to compensate for defined phase differences between antennas as well as when testing modules that use differential amplifiers. To make phase adjustments between two signal sources and to make measurements on multi-output subsystems, it is essential to understand the fundamental characteristics of phase coherence.
Phase Relationship Between Two Sources
In the signal-generation chain within a signal source, a modulation coder creates a digital baseband signal whose phase can be offset (Figure 1). Two DACs deliver the analog in-phase/quadrature (I/Q) signal to the I/Q modulator, which mixes the complex input signal to the RF domain using the LO signal from the synthesizer. The I/Q modulator’s output incorporates the correct RF frequency but must be leveled to the desired value by either amplifying or attenuating it. The resulting output signal then is fed to the RF output connector.
Most synthesizers have their own reference oscillator and can use an externally generated reference signal. In both cases, the resulting LO signal is generated in several steps from the 10-MHz signal using a PLL-based design. If two signal generators are coupled via their 10-MHz reference, they will generate the same frequency. However, a closer look at the instantaneous differential phase of these two RF signals shows that this phase is rather unstable. There are several reasons for this:
• The phase noise of the two synthesizers.
• Weak coupling at 10 MHz, which requires a long synthesis chain to arrive at the RF domain. If phase drifts 0.1 degree in the 10-MHz reference loop, such as from phase detector offset drift, the RF phase at 1 GHz will drift 10 degrees.
• Other sources of drift in the DACs, I/Q modulator, power amplifier, and electronic attenuator.
• Thermal expansion of conducting paths or cables. This changes the electrical length of the signal path. For example, at 6 GHz, the wavelength is 3.3 cm, and adding only 1 mm more cable produces a phase shift of 11 degrees.
Thermal expansion is calculated for coaxial cables where the velocity of propagation is approximately two-thirds that of free space. Consequently, the wavelength will be two-thirds that in free space and the electrical length approximately 1.5 times the physical length. For a 1-m copper cable (coefficient of thermal expansion 16.4 x 10-6/K), a 10K temperature change leads to a 0.164-mm change in length or about 2 degrees of phase drift.
Weak coupling, the second effect, is most dominant, so it is imperative to use a common synthesizer/LO source to stabilize the phase between two signal generators. This also eliminates phase noise, and the third and fourth effects can be minimized by internal adjustment and temperature compensation, respectively.
Factors That Influence Phase Measurement
RF Frequency
When the RF frequency of both signal generators is changed, phase also changes, sometimes dramatically depending on frequency. While a common LO source is vital to achieve phase stability, the phase itself is primarily determined by the different electrical lengths of both RF paths. Generally speaking, frequency is the most important parameter for phase measurement.
RF Level
The RF level of a signal generator is determined by the power amplifier and switching in the step attenuator, and both have an effect on phase. The amplifier drive level may change the phase by 1 degree/dB. The step attenuator switches several paths whose length may vary by several centimeters, which will cause large phase changes.
To achieve the lowest noise and minimize harmonic content, the amplifier usually is driven in its sweet spot, and the attenuator is frequently switched. Attenuator switching can be avoided by setting the attenuator to a fixed level and operating within a fixed power level range. Even in this fixed mode, in practice you can expect 3 degrees of phase drift when changing the level by 20 dB, depending on instrument specifications.
Temperature
If the temperature of the signal generator is changed, phase will change as the result of component drift and thermal expansion of cables and conductor paths. Although these effects typically are less than 0.1 degree/K, it is highly recommended to follow the manufacturer’s guidelines for warm-up time, which may be on the order of 30 minutes. The influence of time also is very small, and the instrument’s drift and aging can be reduced by internal adjustment.
We have looked into the causes of phase instability and the key factors influencing phase measurements, but what mechanism can we use to offset one signal generator’s phase relative to another? Those familiar with frequency synthesizer concepts may know about the presence of a phase shifter in typical synthesizer architectures; however, we’ve already determined that each signal generator should use a common synthesizer/LO source to minimize phase instability. Accordingly, using the phase shifter in the common LO will shift each generator’s phase by equal amounts, getting us nowhere.
Fortunately, many vector signal generators allow the signal’s phase to be varied in the digital baseband domain. The phase offset is very precise and not affected by temperature, time, or level. This means that we also must use the baseband section of a vector signal generator if we wish to generate phase coherent signals between two or more sources—even for simple CW signals.
For CW signals, the simplest method is to use a binary phase shift keying (BPSK) signal with each data bit set to zero, which equates to a DC signal from the baseband. Referring to Figure 1, the DC signal input to the I/Q modulator is mixed with the synthesizer/LO signal to generate an RF output with frequency equal to that of the LO.
Manual Phase Adjustment
Now that we know to use a vector signal generator equipped with a digital baseband module, we are ready to consider the test setup for phase coherent applications. We eventually will need to dial in the phase of each generator in the setup, but first we must figure out how to properly measure the phase so we know to what extent each phase must be adjusted.
We have several methods at our disposal, and they are compared in Table 1. For general purposes, the method using an RF combiner and spectrum analyzer is most appropriate, and this is the method we will use here.
The test setup requires two signal generators, a spectrum analyzer, and RF combiner as well as cables and connectors. Figure 2 shows an example that includes two R&S SMBV100A Vector Signal Generators, one R&S FSU Spectrum Analyzer, and one Weinschel Resistive Power Divider/Combiner Model 1506A. The gray cables in Figure 2 are used during phase adjustment. After adjustment, the same two cables shown in dotted blue between RF outputs and the combiner connect to the DUT. This can be a MIMO receiver, two antennas, or any other two-port device.
The adjustment plane is the input of the power combiner so the cables must be equal in length. These same cables must be used during both adjustment and testing and should be highly phase-stable over temperature and with flexing. The connectors on the combiner should either be the same type as on the DUT or converted using very small, precision adapters.
The combiner/divider determines the phase uncertainty that can be achieved and should be of the resistive type with excellent temperature stability and phase tracking. Its symmetric construction allows it to be used in both directions to divide or combine the RF power. A power splitter is not suitable for this application because it can only be used in one direction: to split the power.
With the right instruments and components in place, we are ready to begin taking measurements. It is important to remind ourselves that we are trying to establish a precise phase relationship between the two RF signals. Once established, we will note the conditions that give rise to the precise phase relationship and use this information to adjust the phase differential to any arbitrary value we want. We can extend this to as many phase coherent signals as needed for the application.
For the case with two signal generators, the phase of one signal generator is shifted so both signals have 180 degrees phase relation. At that point, also known as destructive interference, the combined RF output power is zero.
Figure 3 shows the gain of the combined signal as a function of phase, which is symmetric about 180 degrees. This curve allows us to understand to what precision we are able to make our two signals phase coherent.
Table 2 lists values of gain or RF carrier suppression corresponding to various phase distances from 180 degrees. For 1-degree phase uncertainty, we must achieve around 40-dB carrier suppression relative to the signal generator’s set output level and including the loss of the resistive combiner and cables. To improve our precision by a factor of 10, we must suppress the signal by an additional 20 dB.
This assumes both signals are at exactly the same level into the combiner, but in the real world, this is not the case. Two signal generators with equal level setting and external cabling typically will exhibit a level mismatch of around 0.2 dB.
How does this affect the resultant combiner output in our setup? The difference will remain as a residual signal in the combiner output, and the effect on additional phase uncertainty may be quantified by plotting the residual gain as a function of level mismatch between the combiner inputs (Figure 4).
Table 3 lists the gain values for particular level differences, showing that the 0.2-dB mismatch equates to around -30-dB gain. Referring back to the gain vs. phase plot in Figure 3, we see that typical level mismatch in this setup will lead to 2 degrees of phase uncertainty. So as a rule of thumb, level adjustment is required if we wish to reduce phase uncertainty to 1 degree or less.
Start by adjusting the phase of the first signal generator’s baseband until the RF level of the combiner output is minimal, typically around -40 dBm. At this point, we are at around 1 degree phase uncertainty, and for higher precision, we now must adjust the level of the first signal generator. This should require adjustments in 0.01-dB steps until the carrier is suppressed down to -60 dBm. We now have phase uncertainty of approximately 0.1 degree.
It is possible to go back to the phase setting in the baseband and adjust in 0.01-degree increments to further suppress the carrier down to -80 dBm. We now have achieved a 180-degree phase relation between the two generators with a phase uncertainty of 0.01 degree. At this point, we are well within typical requirements for phase coherency in MIMO applications.
The last step is to establish an arbitrary phase relationship between the two signal generators to meet the needs of the relevant application. Since we now have a 180-degree relationship between the two generators, if we simply add 180 degrees additional offset in the first signal generator’s baseband, we will have a zero degree phase difference. Lastly, we adjust the phase of the second signal generator’s baseband by any desired phase offset.
The same approach may be used for any number of desired phase coherent signals. Simply choose one generator as the reference and repeat the process for each of the other generators. In the end, we can achieve zero phase difference with known uncertainty between all generators and arbitrarily adjust the phase offset of each nonreference generator to the desired values relevant to the application.
Summary
Adjusting the phase of multiple RF signals and maintaining coherence between these signals over time and temperature are becoming increasingly important in modern wireless communications. The inherent phase instability among multiple signal generators is mostly overcome by using a common synthesizer/LO source for each generator.
For phase, it is necessary to use the digital baseband of vector signal generators to adjust phases prior to mixing the baseband signal with the common LO signal. Using a high-quality RF combiner and an appropriate spectrum analyzer with enough dynamic range for the application, it is possible to establish the desired phase relationship—with known uncertainty—among the multiple generators.
About the Author
Justin Stallings is a senior product manager at Rohde & Schwarz in Columbia, MD. He has more than 10 years experience in the field of RF communications and received a B.S.E.E. from the University of Illinois and an M.B.A. from the University of Florida. Rohde & Schwarz, Signal Generators and Power Meters, 443-691-0871, e-mail: [email protected]
March 2009