Category Archives: IQ-IR-SSB Mixers
For many years Marki Microwave has sold Image Reject and Single Sideband Mixers to both laboratory/research customers and industrial/military customers. Due to the advancement of digital to analog and analog to digital converters, significantly better image rejection and sideband suppression is now possible by connecting the IQ mixer directly to the ADC/DAC. Therefore, the industrial and military customers have migrated towards using IQ mixers without hybrids. Following this trend, and to facilitate maximum flexibility, Marki offers its new line of MLIQ mixer primarily without an IF hybrid, requiring the user to select their own hybrid to create an IR/SSB mixer. While we sell many of these, the bad news is that we do not offer quadrature hybrids below 700 MHz as a strategic decision.
The good news is that we don’t offer them because they are offered by so many different companies. Quadrature hybrids are required to make quadrature balanced amplifiers, one of the most common amplifier topologies. There is a cottage industry in supplying these quadrature splitters at low frequencies, and so there are many, many options available to the user looking to buy an IF hybrid to match with an MLIQ mixer. The sortable and filterable table below is an incomplete list of models below 2 GHz that can be used as IF hybrids. For frequencies above 2 GHz we recommend our own very well balanced quadrature hybrids.
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.
Sometimes you need a mixer; sometimes you need an IQ mixer. How do you know which one to buy? Before answering this question, I recommend reading the Mixer Basics Primer to get a good understanding of the fundamentals of mixers, the blog post ‘IQ, Image Reject, and Single Sideband-Mixers’ for and introduction to these mixers, and ‘How to think about IQ mixers’ if you want a deeper physical understanding of the mechanisms of IQ, image reject (IR), and single sideband (SSB) mixers.
We’ve talked a lot about IQ mixers in the last few posts, about their theoretical underpinnings and applications as a phase detector and phase modulator. In upcoming posts we will discuss applications of image reject and single sideband mixers as well. The key to all of these circuits is the quadrature phase shift, both at the LO side for an IQ mixer, and at the LO and IF side for an image reject or single sideband mixer.
Remember: a phase shift is not the same as a time shift. This is one of the most difficult concepts to grasp in RF, microwaves, and optics. We will begin with the trivial example of a time delay, just to show that this doesn’t work for anything but the most simple circumstances. We go on to show how different techniques can be used to create more flexible and useful quadrature phase shifts to ultimately realize our goal of an ideal, broadband IQ/image reject/single sideband mixer.
In our last post we showed the physical basis for how mixers are used as phase detectors, concluding by showing that IQ mixers make ideal phase detectors due to their ability to unambiguously identify the relative phase between two signals at any power level. In this post we examine the opposite: how to use mixers as phase modulators. It seems like you should be able to use them in exactly the opposite way, which is to apply a DC voltage to get a linear phase shift. Unfortunately, it’s not that simple.
Note: as with mixers as phase detectors, we as the manufacturers are not the best experts, but our users are. In this case I would recommend Kratos General Microwave, whose application notes I used in preparation of this blog post.
Why phase modulators?
Before examining how to get a phase modulator, let’s look at why you might need one. The main applications are communications and electronic warfare.
Communications: Phase modulation (mathematically identical to frequency modulation) has been used since very early in radio communications, due to FM communications having constant amplitude, better spectral/power efficiency, and convenience. The most common way of understanding phase modulation is with binary phase shift keying (BPSK), or quadrature phase shift keying (QPSK) if both orthogonal components are used. All modern communication systems use these techniques, so they have been written about very extensively, and we will assume that you are familiar with them.
Electronic Warfare: Here it gets interesting. If you have a phase modulator in a jammer, you can trick an enemy radar system into thinking that your plane/boat/tank is not where it actually is. You do this by listening to their radar pulses and responding with frequency shifted radar pulses, making it appear that you are moving at a different speed. This is the classic decoy technique. Modern jammer systems employ much more advanced, exotic, and classified schemes than this that I hope I never have the classification level to learn about. The principles, however, are the same.
Double Balanced Mixers as Phase Modulators
Let us start by running a phase detector in reverse. Instead of a DC output, lets input a DC signal to the IF port and a CW signal to the LO port and see what comes out of the RF port. If the device is reciprocal, then a small DC voltage/current should induce a small phase change, and a larger voltage should create a larger phase change. Here is what happens:
So this is nothing like what we expected. Why? I don’t really know. Somewhere the hand waving ‘superposition’ argument I gave in the last blog post breaks down, and something is not reciprocal. The above behavior makes sense from what we know about double balanced mixers. Namely that with no voltage applied, the LO-RF isolation prevents any signal from passing through. As the DC voltage is applied, it breaks down the symmetry of the diode quad, reducing the isolation and allowing more of a signal to pass through, although without a phase change. Now here is what happens when we apply a negative voltage:
So at least with a negative voltage you can get a 180° phase flip. So a double balanced mixer does give you phase modulation, but only between two different options. This makes it suitable as a BPSK modulator (emphasis on the word binary), but not for much else.
IQ Mixers as Phase Modulators
IQ mixers worked great as phase detectors, will they work great as phase modulators? Only one way to find out:
This picture is a little confusing, but the idea is that it works out mostly okay. As with the double balanced mixer, you see no signal pass through with 0 voltage applied. If you manipulate the DC voltage applied to the I and Q port, then you will see the phase rotate around the complete circle as expected. When you only have one voltage applied you will be almost at 0°, 90°, 180°, or 270°. There are some phase errors, I would imagine due to the non-ideality of the components, but this can probably be accounted for. There is also a non-uniformity to the amplitude due to the isolation being degraded differently in the different mixers.
So what is going on here, how can you achieve an arbitrary phase with an IQ mixer when you can only get two phases with the double balanced mixers that make them up? This is the following trigonometric identity:
a cos(x) + b sin(x) = R cos(x-theta)
where R2=a2 + b2 and tan(theta) = b/a. This means that by simply changing the values of the input signals (in this case by modulating the isolation of the mixers) you can achieve any phase within the range of the tangent function (-90° to 90°), and then by flipping the value to negative you can achieve any value in the phase circle.
Is this a good idea?
Just because you can do something doesn’t mean you should, you can drive a car with your feet if you want to but that doesn’t make it a good idea.
The short answer is yes and no. Using an IQ mixer is an easy way to achieve an arbitrary phase modulator, definitely useful if you are in the lab. A few problems though:
- The isolation change with applied DC voltage is non-linear, and the whole structure has to be carefully characterized to achieve repeatable results.
- All non-idealities are frequency dependent, so this characterization has to take place at each point in the system. Further, if you are modulating a broadband or multitone signal you won’t be able to correct for the system errors at all frequencies.
- The insertion loss when used in this way will look very little like the insertion loss shown in the datasheet for the IQ mixer. For example, here is the MLIQ-0416 datasheet conversion loss:
Nice and flat across the band around 8 dB. Now here is the same mixer as a phase modulator:
This starts out strong, but then falls off at higher frequencies. This is because the second plot is of an insertion loss instead of a conversion loss. The difference is subtle but important. In the first case the LO is only used to turn on the diodes, so the losses that it takes passing through the LO quad hybrid don’t matter very much. In the second case, the LO is the signal, so any loss that it takes shows up as an insertion loss.
Those are the main problems, and if these can be overcome, then you may be in business.
Single Sideband Mixer as a Phase/Frequency Modulator
There is another way to use an IQ mixer as a phase or frequency modulator, and this involves creating quadrature CW signals into the IF port of the mixer, effectively using the IF port as the LO, and varying the frequency of this LO signal to change the frequency offset. We will examine this, and other use cases, in our next blog post on using IQ mixers as single sideband upconverters and image reject downconverters.
Some of the most common questions we receive here are about using mixers as phase detectors. We previously discussed this topic in the post, “DC Offset and Mixers as Microwave Phase Detectors”. In this post we will go into much further depth about the physical mechanisms by which mixers act as phase detectors, and what is important for engineers trying to accomplish this in the lab. First a warning though: we’re just showing experimental results here. The real experts in phase detectors, phase noise, and all things related to phase are the people that do this every day at Holzworth Instrumentation.
Double Balanced Mixers as Phase Detectors
Much has been written about how double balanced mixers work as phase detectors (for example, see this article from Watkins Johnson about the subject). As with most circuit topics the descriptions in the literature are based in math rather than physical principles, so we’ll now consider the physical mechanisms in play when a double balanced mixer is used as a phase detector. Let’s look at what happens when we apply two in phase (frequency matched) voltage signals to an ideal double balanced ring mixer1:
The phases correspond to the phase of each signal as it appears at the diodes. Only two are show, but take my word that superposition works here and every other in between state produces the same effect. For current to flow, two conditions must be met. First there must be a voltage differential across the diode. Second is that the diode has to be pointed in the correct direction. The red arrows indicate where those conditions are met and current will flow. As you can see, when the signals are in-phase current will flow into the IF balun, creating a positive DC voltage at the IF port. Now out of phase signals:
The situation is similar for out of phase signals, except that current is always pulled out of the IF balun, thus creating a negative DC voltage at the IF port. For quadrature signals, there is equal current flowing both into and out of the IF balun. This means that no net DC current is created, no net voltage is apparent. The IF port is essentially always a DC virtual ground. This is the physical basis for why a double balanced mixer will show no DC voltage for two signals in quadrature2.
With these principles understood, let’s go in the lab and see what happens when we actually apply these signals to double balanced mixers. First we create two signals and use an oscilloscope to verify that they are in quadrature:
At 10 GHz the period is 100 ps, so 25 ps out of phase is in quadrature. Now we apply these voltages to the input of a ML1-0220LS mixer, and what do we find? Nonzero voltage! In fact, here is what the DC output voltage (taken with a terminated bias tee, this is very important) looks like a function of phase between the two input signals:
Now we would expect this to be a peak at 0°, and the minimum to be at 180°. What is going on? This is a phenomenon that is documented by Stephan Kurtz in the previously referenced WJ app note. In modern double balanced mixers the RF and LO baluns are not identical. In fact, they are not even close. One side is built as a magic tee, where the IF is removed, and the other side has a return to ground on it. Even though the LO and RF baluns traditionally cover identical frequency bands, there is no reason that they need to. They can be completely different! This means that they most likely have a different electrical transmission length and phase delay, which is why the peak of the voltage curve is not quite at 0°. Another effect highlighted in this app note is that there is a voltage offset that shifts the entire curve up (or down). As we detailed in our first post, the excellent balance and isolation of the ML1-0220 minimizes this DC offset and makes it not noticeable for this plot.
1 Note that the necessary DC current return to ground path is necessary but not illustrated for clarity.
2 It is easy to imagine how to extend these principles to the situation where the signals are not at their peak or zero values, and similarly to phases that are not either perfectly in phase or out of phase. While superposition does not strictly work in a nonlinear system such as this, the results one would expect from superposition are maintained qualitatively.
IQ Mixers as Phase Detectors
Now we can calculate the phase of the signal. Excellent. However, there are two ambiguities that we need to clear up. Since this is a sine wave instead of a sawtooth wave, there is some ambiguity about the phase. The same output voltage could be two different phases, except for the max and min. This is fine if you are doing phase noise testing, where you put the two signals in quadrature and just look at any voltage that comes out. For actually detecting the phase between two signals though, it isn’t enough information. The second ambiguity is that we need to know the max and min voltage levels, as well as the DC offset, to determine the phase. Since the DC offset in Microlithic mixers is small we can ignore this, but we still have a problem if the incoming signals change power at all.
How do we resolve this? One way is to use two mixers as phase detectors and deliberately introduce a phase shift between the two inputs (RF and LO). 180° is no good, because the phase ambiguity remains, so a balun is out. A length of line changes phase with frequency, so that is out too. The other broadband phase shifting options we have are a Schiffman phase shifter or a quadrature hybrid. The quad hybrid is much more common and easy to build3, so what would a structure with a quadrature hybrid introduced on one side look like?
That’s right: the structure is exactly an IQ mixer. Since I and Q are in quadrature, it is easy to calculate the phase between the two signals as
after making a small correction to scale the I and Q values by their peak output level and DC offset4. Let’s look at the same plot of voltage vs. phase for the IQ mixer, along with the calculated phase:
As expected, the calculated phase is almost linear with input phase after the correction factors. This is a significant improvement over the double balanced mixer, since we don’t need to know the input power levels and there is never any phase ambiguity. But how close is the IQ mixer to invariant with input power? When the two signals are at 0/90/180/270 degrees to each other, there is obviously very little variation in calculated phase with power since one of the voltages doesn’t change. If we pick a phase in the middle (135°)5, this is what it looks like:
As you can see the power levels the agreement to 135° is excellent. As we increase to higher power levels, one of the mixers compresses sooner than the other mixer, and the phase is thrown off. Up to 0 dBm, however, the agreement with the real phase is excellent. This does not address what happens when one of the signals is significantly higher than the other one, nor with double balanced mixers when you are just trying to detect phase changes, where high powers are desirable to increase sensitivity.
Now that we have examined the physical mechanisms of how mixers work as phase detectors, we can do the reverse and see how they work as phase modulators. This is the subject we will tackle in our next post, “All About Mixers as Phase Modulators”.
3Quad hybrids are easier than Schiffman phase shifters, but still ridiculously difficult to build broadband. You don’t have to trust me, you can try yourself, and then buy ours when it takes you 6 months.
4You also have to convert to a -180 to +180 phase range, or 0 to 360, or whatever. Arctangent only gives you values from -90 to +90, so you have to use the sign of the signals to figure out where exactly you are.
5How do we know the phase is 45 degrees? Because we put the signals in quadrature (which is the same at any power levels), and then moved them 12.5 ps on the oscilloscope, equivalent to 45° at 10 GHz.
There are many ways to think about IQ modulation, and all of them rely on math. This is because ‘quadrature’ modulation is a mathematical construct, a way of thinking about how time domain signals can be manipulated more than a physical reality. In this blog post I will describe how I think of IQ modulation, which is as the cancellation of a signal through two 90° phase shifts that create a 180° phase shift, which is the negative of the original signal. The negative and positive versions of the signals cancel, resulting in suppression of the other signal. This is identical to the math that governs image cancellation in image reject and single sideband mixers, the only difference is that one of the 90° phase shifts occurs at the transmitter in an IQ scheme, while they are both at the receiver in the image reject/single sideband scheme.
The easiest way to see this is with a combination of a trigonometric derivation and graphics. I will try to make the math as straightforward as possible, since I don’t speak math well.
We’ll use the following trigonometric identities:
Consider a single sided downconversion imagining the mixer as a perfect frequency multiplier. The output at the RF will be given (ignoring the 2πt terms) by
The same math works for an upconversion:
It is irrelevant whether we use an in phase (cosine) or out of phase (sine) LO for a double sided downconversion on a single tone, other than a phase shift of the output (90° from the input and 180° between the two products) for a downconversion:
Or an upconversion:
Now consider following the double sided upconversion with a double sided downconversion. We’ll multiply the original output by an in phase LO
Where we use the identities given above. Clearly it can be seen that the desired IF frequency is present along with the undesired 2*LO terms. However, if we attempt to perform a downconversion with an out of phase LO, the following results:
As you can see from the math and the diagram, the two sidebands compete at the downconverted sideband, canceling each other out. For this reason a double sided upconversion followed by a double sided downconversion is not recommended. If the phase of the LO is set correctly the signal will be reconstructed with twice the amplitude of a single sided downconversion, but if it isn’t phased correctly the two sidebands will cancel each other.
This same phenomenon can easily be shown to occur if a sine wave LO is used as the upconverting LO and a cosine is used as the downconverting LO. This raises an interesting possibility, however. If a phase coherent LO is available, then we can upconvert one signal into a sideband and downconvert it with the same phase LO (with some gain). We can also upconvert a separate signal using a 90° out of phase LO and transmit across the same medium, downconverting it with the same LO but again 90° out of phase. The sidebands of the signal will cancel each other out for the out of phase signal while adding constructively for the in-phase signal. This is called quadrature modulation, and is the basis for such modern signaling techniques as quadrature amplitude modulation (QAM), which is the how all modern wireless communications systems operate.
Here is what the math looks like (it gets a little messy, you can just look at the conclusions):
Combined upconverted signal, with signals added:
Now multiply by an in-phase LO:
After low pass filtering we recover:
The in-phase components add constructively, while the quadrature components add destructively. It can be similarly shown for a quadrature (sine wave) downconverting LO, we will only recover the b(t) signal. Graphically this appears like this:
At this point we can see everything that we need to make an IQ modulator: 2 matched mixers, a device to separate the LO into in-phase and quadrature signals (called a quadrature hybrid coupler) and a device to add the two signals together (an in-phase power combiner).
Before we move on from the IQ modulator, consider what would happen if we eliminated one of the sidebands after the upconversion and try to downconvert:
After low pass filtering, this becomes:
That is, both versions of the signal are present without cancellation or suppression, and neither can be recovered without the information present in the second sideband. There are many more advanced modulation techniques using DSP that may offer quadrature information transmission in a single sideband, but this cannot be achieved using conventional analog components.
IQ and Image Reject or Single Sideband mixers use similar circuitry to solve two different fundamental problems in communications and signal processing. IQ mixers address the problem of maximizing information transmission by allowing the user to modulate both the in-phase and quadrature components of a carrier simultaneously, multiplexing two signals onto the carrier*. Image Reject (IR) mixers allow a user to select a signal in a crowded signal environment while suppressing the adjacent image signal, relaxing receiver filtering requirements. Single Sideband (SSB) mixers allow a user to upconvert a signal onto a carrier while suppressing the same image frequency signal, relaxing transmitter filter requirements.
By using quadrature hybrid couplers to manipulate the phase of a signal during conversion, IQ, Image Reject (IR) and Single-Sideband (SSB) mixers enable advanced signal processing capabilities. An IQ mixer allows a system to send twice the information content in a double sideband transmission without using any more bandwidth by using ‘quadrature’ modulation. An IR mixer allows the selection of only one of either the LO + IF frequency or the LO – IF frequency while rejecting the other ‘image’ frequency. This allows for unambiguous signal detection in a crowded signal environment without a tunable RF filter. The SSB mixer is the same structure as the IR mixer and allows the upconversion of an IF signal to only one of the LO + IF or LO – IF frequencies without creating an image of the signal at the other frequency. These mixers are particularly useful when using low IF frequencies, making preselection filtering difficult.
IQ Mixer Operation and Structure
The IQ mixer is the basic building block for higher order IR and SSB mixers. The structure is shown below:
An IQ mixer is actually two mixers with an LO that is shifted by a quadrature hybrid coupler by 90° to each other. In a normal downconversion the phase of the LO is irrelevant because the data is single sided. The IQ mixer requires transmission of both sidebands for accurate reconstruction of the original signal.
An IQ mixer operates on the basis of quadrature modulation, two signals are upconverted into the same block of spectrum in the frequency domain using one LO with either a 0 or 90° phase shift. When the same operation is performed at the receiver in a downconversion, the addition of an extra 90° phase shift will create a complete 180° phase shift, leading to the inversion of one of the original signal components. This will cause the cancellation of one component of the signal, while the other component is reinforced. When an IQ mixer is used as a downconverter it allows both of the original data signals to be retrieved with an appropriately phased LO signal.
IR/SSB Mixer Operation and Structure