Quadrature reflection phase shifters

Updated December 29, 2009

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Click here to go to our main page on reflection phase shifters

Click here to learn about hybrid couplers

Click here to go to our page on quadrature couplers

Click here to go to a companion page on reflection attenuators

Hybrid (3dB) quadrature couplers are used in most reflection-style phase shifters. Quad couplers can be realized as branchline couplers (distributed or with lumped elements), Lange couplers, or other coupled line couplers of many varieties. The bandwidth of the quadrature reflection phase shifter is mostly limited by the choice of coupler, you can achieve an octave with many coupled-line coupler structures. In terms of bandwidth, the best quadrature coupler (but hardest to make) is a broadside coupler in stripline, the worst is a branchline on microstrip (the easiest to make).

Quadrature phase shifter with open/short terminations

Quadrature bybrids are often used to create reflection phase bits. The simplest bit to consider is shown in the ADS schematic below. The resistors R1 and R2 are used to create a two-state device from the upper and lower ideal couplers in the simulation (when ON=1, the upper coupler is selected, when ON=0, the lower one is selected). The even mode and odd mode impedances have been selected to provide perfect 3.01 dB coupling at the center frequency (10 GHz) for 50 ohm system. The upper coupler has open circuits on the power split ports, the lower coupler has short circuits. Note that in each state, it is important to present the same impedance to each power split port to get the power to transfer out the normally isolated port.

The phases of S21 and S43 are the phases of the two states in this simulation, and they are exactly parallel over frequency as shown below. Thus 180 phase shift is provided exactly at all frequencies in this (ideal) situation. The bandwidth of the ideal coupler restricts the approach to perhaps one octave.

Reflection phase shifter with line stretcher terminations

Another simple way to create a reflection phase bit using a quadrature hybrid is to add terminations that merely stretch the paths made to short circuits on the split ports. This behaves very similar to a switched line phase shifter; it provides phase shift that varies with frequency by definition. This is not something you'd want to use in a phase array, if you want to have any bandwidth. You'll find an explanation here...

US Patent 5379007 uses this scheme. so does 4764740.

Here's the response. It has the same S-parameter magnitudes of the previous example, but the phase shift is now linear with frequency. This is going to give you a very narrow-band response ini terms of phase errors, and should be avoided.

Many MEMS phase shifters have taken this topology in recent years. You can place multiple MEMS shunt switches across the termination lines, and provide multiple phase states with one bit. But consider the error of the response below from 8 to 12 GHz. You'd get 36 degrees of error at the upper and lower frequencies! Why do MEMS guys offer this kind of crap circuitry as a phase shifter? They seem to be narrowly focused on low loss as the one characteristic they can beat MMIC phase shifters at; they seem to have ignored the rest of the requirements...

Reflection phase shifter with lumped element terminations

One well-known phase shifter that has flat phase shift versus frequency is the high-pass/low-pass phase shifter. Maybe a similar technique could be used in the quadrature reflection phase bit? Of course it can!

Shunt capacitors and shunt inductors can both provide either a short circuit or an open circuit, and one is a high-pass, while one is a low-pass element. They can provide all of the in-between reactance values as well, and with opposite signs. Hrrrmmm...

Below is an ADS schematic where we have chosen a capacitor and an inductor to provide j50 ohms reactance:

Here's the response of these two elements at 10 GHz, plotted on a Smith chart. They are 180 degrees apart, the capacitor is at -90 degrees and the inductor is at +90 degrees. What if we used these as switchable terminations in a quadrature reflection phase shifter?

OK, let's try it.

Flat phase shift is provided. The mojo is back!

Usiong lumped elements are the the best way to create a reflection phase shifter from a quad coupler. If you don't use a capacitor in the circuit, you'll be like a MEMS guy, and no one will want your circuit.

You can create any value phase shift with lumped elements, and the phase shift will stay relatively flat over frequency (but not as perfect as the 180 degree case). Below are two tables for element values to achieve phase shift at 10 GHz, you can scale them to any frequency you want. The values are approximate, we didn't spend the time to derive the closed-form expression, if anyone wants to help us out we'd be happy to give you credit and a pocketknife for the correct formula!

It turns out there are two solutions for each bit value. For a 90 degree bit, you can either choose the -45 and +45 values, or the -135 and +135 values. For a 45 bit, you can choose the -22.5 and +22.5 values, opr the -157.5 and 157.5 values, and you can do the math yoursenf for 22 and 11 degree bits. Be aware, you should keep the phase shifts of the inductor and capacitor equal for best results.

Now let's look at the two solutions for 45 degree bit:

More to come...

This stuff is left over from before...

The quadrature phase shifter is shown below. Here an equal-split quadrature coupler divides the input signal into two signals 90 degrees out of phase (the definition of "quadrature" is two signals 90 degrees apart, click here for more info on quad couplers). These signals reflect from a pair of switched loads, and combine in phase at the phase shifter output, as long as the loads are identical in reflection coefficient (both magnitude and phase). Unlike the loaded line structure discussed previously, the quadrature phase shifter can be used to provide any desired phase shift. Ideally, the loads should present purely reactive impedances, which can range from a short circuit to an open circuit or anything in between. This structure provides a bandwidth of up to an octave, depending on the bandwidth of the quadrature coupler itself. The coupler can be a Lange or a box hybrid on microstrip, or an overlay coupler in a stripline circuit. The size of a quadrature phase shifter is directly related to the frequency band of operation, as the coupler typically uses one or more quarter-wave sections. Only one control signal is required for a quadrature phase shifter, since the loads can be biased simultaneously.

Quadrature phase shifter

Below are the two states that the diode provides to effect a reflection phase shifter (the same two states that are used in PIN diode switches). Note that both states have high reflection coefficients (poor return loss). Ideally they would be perfect open or short circuits, and reflect 100% of the incident power, at phase angle 180 degrees apart (left and right side of the Smith chart).