## Top 7 Ways to Create a Quadrature (90˚) Phase Shift

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.

These techniques are ranked below from worst to best, where quality is roughly defined by phase and amplitude balance over bandwidth. Any of these techniques might be the correct one for your application, it just depends on whether you are building a demonstration system in your lab, designing a communications chip for a cell phone, or trying to make a radar scanner. An ideal phase shifter in our mind would have perfect phase and amplitude balance from DC to daylight.

7: Power Split with Delay Line

Pro: Easy to Implement, Can be tuned

Con: Only works at a single frequency

This is the trivial case, where you just put the signal through a power divider and then time delay one side. If you have a tunable time delay, and you want a fixed frequency LO, this can be used to get very accurate 90˚ phase differential. If you have a low loss time delay, the amplitudes will also be matched. It only works at a single frequency, though, in the graph below only at 5 GHz, for example.

6: Branchline Coupler

Pro: Easy to Implement, Very Low Loss, Isolated, Planar

Con: Narrowband, Physically Large

This is the easiest way to make a 90 degree phase shift in a microstrip microwave circuit. It consists of a ring illustrated below. The insertion and return losses can be made perfect, though only over a small bandwidth:

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This single stage offers 33% bandwidth with 5 degree phase difference. As with the polyphase splitter below, this can be improved a little bit with a two stage design:

Here the bandwith is 38% without increasing the insertion or return loss, but the impedance range gets higher, so it is harder to interface the lines in a single circuit. It becomes increasingly difficult to expand the bandwidth this way. So if you only need 30% bandwidth or so, and can sacrifice the space, this is a fine choice for communication applications.

5: Schiffman Phase Shifter

Pro: Broadband, suitable for data, high power handling, works with differential signals

Con: Requires a pre-existing power split

Schiffman comes in at number five primarily because it is not used often enough, probably. It is similar to the stripline coupler later in the article, but it provides a broadband phase shift (not a time shift) to an existing signal. This is difficult to visualize, and you need to have a pre-existing power split so that you can run one signal through the Schiffman, and one signal through a matched delay line. If used properly it can take a differential signal and turn it into a set of quadrature signals.

Pro: Very cheap, small, can be implemented in CMOS

Con: High Loss, relatively narrowband, complicated, requires differential input, low isolation, low power handling

This quadrature phase splitter makes the list for one significant reason: it is probably the most ubiquitous quadrature splitter on the planet. CMOS chip makers frequently tie a polyphase splitter with Gilbert cell mixers to create billions of cheap IQ modulators for cell and wifi applications. It is perfect for CMOS applications because it uses lumped elements, differential inputs, and small areas, all of which are suitable for CMOS but not higher frequency analog applications. Here is the basic circuit:

As you can see it is fairly complicated. As the most ubiquitous quadrature circuit in the world, there is a tremendous amount of information available about polyphase filters, both in analog and digital implementations, so I won’t go into the details other than to show the benefits and tradeoffs. First off there is the loss. Discounting the 3 dB for the differential split, and another 3 dB to go to quadrature, the filter still has 4 dB or so of insertion loss. As you can see from the phase plot, it doesn’t create a very broadband quadrature signal. This can be improved by adding a second stage:

And a third stage:

Now this is a very broadband phase shift. The cost is that each stage adds another 3-4 dB of insertion loss, meaning that the broadband three stage phase shifter has over 10 dB of insertion loss, in addition to the splitting loss. Further, since it is implemented with lump elements it cannot be made at high frequencies where the capacitors and resistors resonate. However, at low frequencies it works quite well, can be made cheaply, and is suitable both for LO splitting and data combining for image reject/single sideband use.

3: Lange Coupler

Pro: Wideband, quasi-planar, compatible with MMIC

Con: More complicated to design, requires wire bonds or air bridge, low power handling

The Lange coupler is the most common device used in MMIC balanced amplifiers and other balanced technologies. The fundamental problem of planar couplers is that two edge-coupled microstrip lines are very weakly coupled unless the gap between them is very small. This is limited by the fabrication tolerances of the process, and so 3 dB couplers are difficult to realize. Lange couplers solve this problem by using wire bonds or air bridges to connect different fingers of an interdigitated coupling structure, as shown below.

The four finger Lange Coupler shown can have a pretty good bandwidth, around an octave or more in insertion loss/amp balance, and very good phase. The amp balance can be expanded by going to more fingers, but this comes at the expense of phase balance. Overall the Lange coupler is an excellent choice, and really the only one if you have a quasi-two dimensional structure.

2: Digital Phase Splitter

Pro: Ultra-broadband, excellent phase and amplitude balance

Con: Limiting (no analog mode), requires 2xLO frequency, low power

For a perfect quadrature phase shift, it is difficult to beat a digital phase splitter. The circuit is very simple – it just takes a double rate clock and switches one output on the rising edge, and one of the falling edge. The result is two outputs that are in quadrature with each other. It is implemented with two D flip-flops with the inverted signal connected to the input (also called a T flip flop). Here is the basic circuit:

When implemented in CMOS or SiGe this circuit is usually differential, meaning that it will provide all four phases of the output signal. These can be made very fast, up to 30 GHz outputs, and work down to arbitrarily low frequencies.

In addition to the need for a double rate clock there are a few other drawbacks, however. Since the circuit uses limiting circuits, it is not suitable for analog inputs (meaning that it obviously can’t be used for data). It also cannot be used for combining two signals, even at a single frequency. If there is any duty cycle distortion or level distortion on the input, it will show up as a phase distortion on the output. Also any amplitude noise on the input will show up as phase noise on the output.

So in general this is not a very good device as a quadrature splitter, but it is excellent for the narrow purpose of creating an LO drive for an IQ mixer. This is what is frequently used in low frequency silicon RFICs for LO clock generation, which means that it is abundant.

1: 3 dB Quadrature Hybrid Coupler

Pro: Multi-octave bandwidth, amplitude and phase balance, suitable for data, high power handling

Con: Large, difficult to integrate, difficult to design and fabricate

This is the gold standard for quadrature signal generation. It can operate across a broad bandwidth (2 to 26 GHz for example), it has excellent balance in both amplitude and phase, and it can be used on the data side of an image reject or single sideband mixer to get better than 20 dB rejection. These are generally built in a tri-plate stripline construction, which has the physical advantage of matching the dielectric constant around the circuit. This construction is also capable of handling 20 watts of CW power or more.

All stripline directional couplers will create a 90 degree phase shift, so in theory any of them could be used to create the LO drive for a mixer. The trick is to find a way to make the coupling strong enough to create a 3 dB coupling. There is nothing magical about this, it just has to be carefully engineered to be critically coupled across a broad bandwidth. Below we show the basic coupler circuit, along with the amplitude and phase deviation that can be achieved, in this case by the QH-0R714 quadrature hybrid.

Trying to integrate these is difficult, however, because they require a multilayer construction for broadside coupling. Additionally, they need to be in a material that has good dielectric properties. Fortunately for us, the Microlithic platform has both of these things. That is how we are able to make the only 2-18 GHz integrated IQ mixer in the world, the MLIQ-0218. This device is amazing because the LO hybrid is so difficult to make. The fact that it can achieve 30 dB of image rejection, despite being in such a small package, is amazing. This is also the key to our other Microlithic IQ mixers, the MLIQ-0416 and the MLIQ-1845.

So, what is the future of quadrature phase generation? Certainly IC processes will improve, making higher frequency digital phase splitters more available at higher frequencies. Simultaneously, more systems are designed where both I and Q signals are being directly converted to digital signals, and then a quadrature phase shift is applied digitally. As IC processes and design improvements push ADCs to higher and higher frequencies, IQ and single sideband functionality will be available directly from software defined radios and the like. However, for zero power consumption and high power handling, we believe there will always be a place for analog hybrid couplers.

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• Mark Beck

One thing to note on the digital phase splitter, the two flops must be resettable or you can’t guarantee what phase relationship will be between the two outputs. Either it’s 90 degrees or it’s 270 degrees. This is due to the fact that you can’t know what state the flops will be in when powered up unless there is a reset circuit.

A better solution is to tap out the master latch output’s directly from the first flop to generate the first 90 degree phase shift.

• Doug Jorgesen

Wow that is a really good point that I had not considered. If the phase of the digital splitter is set inconsistently, then you would randomly get one sideband or the other from a single sideband conversion. This is pretty important.

• Joseph Maroun

Another idea is to use a Johnson counter. That is simply a series of FF’s all clocked by the input clock. All FF’s must be initialized by way of resets except 1 FF being set. This 1 is rotated around. With two N FF’s you get divide by N with 1/N duty-cycle. Useful if you want divide by 4 and 25% duty-cycle. In this case, the quadrature generation is tapped out from any two adjacent FF’s. It’s quite easy to get back the 50% duty-cycle from even number N division greater than 2. A cool feature is that you can divide by any integer (even or odd) since it’s just a counter. Cheers.

• Doug Jorgesen

This is an interesting technique, I am curious what kind of frequency response you can get out of a chain of flip flops like this.

• Hani

Can you name a discrete module/IC for a digital phase splitter?
I need one that is capable of working inthe frequency range of 1MHz to 50MHz.

Thanks

• Doug Jorgesen

I don’t actually know of anyone that sells low frequency modules, since that is not our area. Below 100 MHz you could easily build a surface mount or through hold board with some D flip flops and build your own T-flip flop to make a quadrature splitter. I don’t know of anyone that actually does this in a module format.

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