## All About Mixers as Phase Modulators

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.

Recommended Posts

• […] 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 […]

Start typing and press Enter to search