5 Ways to Compensate for Passive IQ Mixer Imbalance
The IQ mixer is the backbone of modern communications architectures, as well as advanced vector signal analyzers for electronic warfare and test and measurement receivers. The backbone of the IQ mixer is vectorial cancellation based on phase an amplitude balance. Any imperfection in the phase and amplitude balance of the baluns that constitute the double balanced mixer cores of the IQ mixer will lead to increased LO feedthrough, RF/IF feedthrough, and spurious products. Any imperfection in the phase balance of the LO or the amplitude or phase balance of the I/Q channels will lead to imperfect cancellation of the sidebands in a single sideband (SSB) or image reject (IR) mixer, or imperfect rejection of the unwanted channel in an IQ mixer.
In this blog post we will examine various ways to compensate for the fact that these structures are built with real components with imperfect phase and amplitude balance. In general we will focus on this situation:
Here we are performing a single sideband upconversion where the desired sideband signal is corrupted by LO feedthrough, the suppressed sideband, and spurious products. In this blog post we will not address compensation for spurs, although this is possible. First we need to answer the question, can IQ imbalance be compensated? If we consider a basic IQ transmission where arbitrary signals I and Q are upconverted by quadrature phase signals with phase error θ and φ, and then downconverted by quadrature LO signals with phase errors ε and γ, then it can be shown that after lowpass filtering the I (or Q) output will be the desired I (or Q) signal contaminated by the undesired Q (or I) signal in proportion to sin (φ- ε) (or sin(θ- γ)), as shown below.
This has the profound implication that by correcting the phase of the LO signal driving the receiver side mixer, we can compensate for any imperfections in the transmitting side mixer. The only penalty is a reduction in the desired signal amplitude by a small amount, so long as the error correction is small (an error of less than 25˚ will have a power penalty below 10%). A similar calculation can be performed on an image reject/single sideband structure.
This is a little dense, so we’ll take a second to analyze it. The output is given by the sum of the top two terms, where the first is the desired sideband (low side in this case) and the second term is the undesired or suppressed sideband. The first part of the cosine is just the time variance at the RF frequency, and the second part (atan2(C2,C1)) is a phase offset that goes to zero with perfect error terms (φ, ε, θ, γ = 0, A=B=1). The constants in front of the two terms show the magnitude of the conversion loss (ideally) and the sideband suppression. The latter term goes to 0 with perfect error terms, while the former goes to 1.
Once again the profound implication is that if we control the IF but not the LO, then errors in φ can be compensated with θ, and errors in γ can be compensated in ε, and the only penalty is a small reduction in the desired sideband power. If we control the LO but not the IF, then an amplitude error is more serious, since it causes the C3 constant to not cancel. This can be corrected, however, by adjusting φ and ε. It may be possible to show that any error in A or B can be compensated with phase terms, but we will not show that here. Below we assume that the upper half of the circuit is perfect, there is a phase error of 10˚ in ε, and we try to compensate it with B and γ.
As you can see, the cancellation becomes very good when γ is equal to -10˚ (-.17 radians). If γ is slightly off, however, the amplitude B will still be set to the correct value if it is swept while monitoring the sideband suppression.
Now that we have established that IF or LO amplitude and phase errors can be compensated, let us discuss the various ways in which this can be accomplished.
- DC offsets
The application of a DC voltage to the IF port of a double balanced mixer will change the bias conditions of the diode rings inside. Specifically, two of the diodes will turn on at a higher voltage, and two of them will turn off at a higher voltage. Below is a screenshot of the output of an ML1-0732LS with no DC bias and a 0.5 V DC bias as measured with an oscilloscope triggered by an MM1-0726HSM.
As you can see the application of a DC voltage will degrade the conversion loss without changing the phase, allowing you to easily vary the amplitude balance of one side of an IQ mixer.
Unfortunately there is a tradeoff. As we showed in All About Mixers as Phase Modulators, the application of a DC voltage will degrade the LO-RF isolation, meaning that as you are improving the sideband suppression, you will be reducing the LO suppression. Since the LO is always closer than the sideband, this doesn’t make much sense for a single sideband mixer, as shown below.
In the chart above sideband suppression is increased from about 19 dB to 23 dB by adding an offset voltage, and then again to 50 dB or so by combining phase manipulation with the DC offset. The penalty, as you can see, is an increase in the LO feedthrough from -30 dBm to -3 dBm, overpowering even the desired sideband. This technique can be used without penalty for image reject mixers, however, since the LO is out of band of the IF output. Without phase compensation the possible improvements can be severely limited, depending on how close the phase balance is to start with.
2) LO Phase Manipulation
The error terms for sideband elimination are all dependent on φ and ε, meaning that the LO phase can be manipulated to completely eliminate the erroneous sideband. This can be done without the penalty to LO feedthrough that comes with DC biasing, since the phase of the incoming LO does not affect the LO-RF isolation. The problem, however, is that this cannot be done in a convenient way. If the IQ mixer is built as a bolt-together solution, then the phase can be manipulated by varying line lengths or with a phase trimmer. If the IQ mixer is integrated, however, it is more difficult. In MLIQ mixers in chip form, the LO phase can be trimmed by applying ceramic, absorber, or other microwave tuning elements (familiar to the microwave black magicians out there) to the LO quad hybrid in a certain way while observing the sideband suppression. Since some of this is proprietary I will leave it at that and say that you should contact support at Marki for more information.
3&4) ADC/DAC Phase and Amplitude Correction Registers
This is the big daddy when it comes to analog IQ compensation methods. Amplitude and offset correction registers are generally built into DACs that are designed for communications, arbitrary waveform generation, and software defined radio applications. This makes them readily accessible for IF amplitude and phase manipulation. The phase can also be manipulated in digital implementations. Since the amplitude and phase terms are sufficient to completely eliminate the sideband error terms, the only limit to the achievable sideband suppression is the quantization noise of the DAC and the time/temperature/frequency variation between the calibration point and the transmitted signal.
Some ADCs are also designed to receive I/Q data, and perform another downconversion stage, particularly those designed for software defined radios. The phase control in these ADCs may be performed on the internal oscillator. For more information consult the (usually very detailed) datasheet of a dual channel high speed ADC.
5) Digital Compensation
This is the ultimate in IQ compensation techniques. As we have seen with fiber optic links, wireless links, and any other modern data standard, it is easier and cheaper to use millions of transistors to digitally compensate for a bad signal than to create the analog channel necessary for a good signal. Any deterministic impairment can be pre- or post-compensated, and sideband suppression is definitely deterministic. The most basic approach for sideband suppression is to simply receive both I and Q channels, and estimate the distortion coming from the Q channel in the I channel, and subtract your received estimate of the Q channel from the I channel.
There are myriad methods to perform this digital compensation, with different cost tradeoffs. For example, some techniques are ‘blind’, meaning that they do not require a separate receiver to estimate the error vector magnitude, some require training sequences while others do not, and some are capable of compensating for other errors in addition to IQ imbalance such as fading and DC offset. There are easily 150 references for this topic, including several books, and most are full of dense math and advanced digital signal processing. My favorite, though, is Marcus Windisch’s thesis Estimation and Compensation of IQ Imbalance in Broadband Communications Receivers, in particular Chapter 4.