Click here to go to our main page on phase shifters
This page was contributed by Arne Lüker, a friend of Microwaves101! Arne also contributed a companion page on phased array antennas! Both were written in March 2006. Much of the content on ferroelectric phase shifters was originally reported by Professor Bob York of University of California Santa Barbara, here is a link to his Microwave Electronics Lab.
Did you know that Class 2 multi-layer ceramic capacitors (MLCCs) often exhibit ferro-electric properties? Check out our page on capacitor volltage effects, new for February 2019. Maybe one of these days we'll try to post a design on a phase shifter that employs MLCCs to control phase. It will be in the MHz frequencies, owing to the values of class 2 caps that are available.
Phase shifters are used to change the transmission phase angle (phase of S21) of a network. Ideally phase shifters provide low insertion loss, high power handling, instantaneous phase change response, and approximately equal loss in all phase states. While the loss of a phase shifter is often overcome using an amplifier stage, the less loss, the less power that is needed to overcome it. Most phase shifters are reciprocal networks, meaning that they work effectively on signals passing in either direction (which comes in handy when you are designing a transmit/receive system).
Phase shifters can be controlled electrically, magnetically or mechanically. Phase shifters can be analog or digital. Analog phase shifters provide a continuously variable phase, perhaps controlled by a voltage. Electrically controlled analog phase shifters can be realized with varactor diodes that change capacitance with voltage, or nonlinear dielectrics such as barium strontium titanate, or ferroelectric materials such as yttrium iron garnet. A mechanically-controlled analog phase shifter is really just a mechanically lengthened transmission line - as perfectly seen in Figure 3-(a).
Currently, most phased array antenna systems rely on ferrite - Figure 3-(b), MMIC, or MEMS phase shifters. Ferrite phase shifters are slow to respond to control signals and cannot be used in applications where rapid beam scanning is required. MEMS (micro-electro-mechanical systems) phase shifters have much faster response speeds (measure in milliseconds), however their major drawback is that they have high losses at microwave and millimeter-wave frequencies. Other disadvantages with MEMS phase shifters is that they have limited power-handling capability (perhaps 100 mW) and they may need expensive packaging to protect the movable MEMS bridges against the environment. MMIC phase shifters are blazing fast, they can easily change state in tens of nanoseconds, but power handling is limited to 10 milliwatts or so. They can also be quite expensive, as they are processed on gallium arsenide, not silicon. PIN diodes can also be used to make very low-loss phase shifters, but who wants to deal with thousands of devices that are controlled by current, not voltage?
Ferroelectric phase shifters using BST
Ferroelectric materials have the potential to overcome all the limitations of MEMS, ferrite and MMIC phase shifters. Several groups have investigated the possibility of implementing phase shifter circuits using barium strontium titanate (BST), which has an electric field tunable dielectric constant. In these circuits the ferroelectric material (BST) either forms the entire microwave substrate on which the conductors are deposited (thick film/bulk crystal) or a fraction of the substrate with thin BST film sandwiched between the substrate and the conductors, as seen in Figure 4. These circuits rely on the principle that because part or all of the microwave fields pass through the ferroelectric layer, the phase velocity of waves propagating on these structures can be altered by changing the permittivity of the ferroelectric layer. However, this approach has several limitations:
- The amount of capacitive loading due to the ferroelectric film cannot be easily varied to optimize phase performance;
- Conductor losses are high in this structure due to the high dielectric constant of the ferroelectric film on which the transmission lines are fabricated;
- The tunability of the film is not efficiently utilized; and
- The control voltages required for this approach tend to be very high (more than 100 Volts).
Quite recently (2002) Professor Robert A. York et al (University of California Santa Barbara) proposed a new device topology. Their approach is to periodically load a coplanar waveguide transmission line with tunable BST parallel plate capacitors. This new process provided 240° phase shift with an insertion loss of only 3 dB at 10 GHz at room temperature with only 17.5 Volts. The circuit has demonstrated a record figure of merit 93°/dB at 6.3 GHz and 87°/dB at 8.5 GHz at room temperature.
Actually this approach is a mixture of the ferroelectric phase shifter and MEMS phase shifter technology since it uses both the advantages of these technologies. It combines the low-loss properties of BST at microwave frequency with the distributed transmission line philosophy of the MEMS phase shifter which provides wide bandwidth and ease of design.
Distributed phase shifter - theory and design
A distributed phase shifter is created by adding tunable reactance to a transmission line. Adjusting the reactance alters the phase velocity of the signal propagating along the line, varying its electrical length, and therefore the phase shift. Changing the phase velocity also changes the characteristic impedance of the transmission line, so an impedance mismatch can occur as the circuit is tuned. In general, it should be possible to add both series and shunt tunable reactance to the transmission line to keep an impedance match with tuning; however, a technology for adding tunable series inductance has yet to be fully developed. The majority of distributed phase shifters focus on adding tunable shunt capacitances. Ferroelectric varactors, MEMS bridges and switches, and semiconductor diodes are all capable of performing this function. In the majority of cases, the shunt capacitance is added periodically as discrete elements to the transmission line. This capacitance loading makes the distributed phase shifter a periodic structure, with a pass-band and a stop-band. Careful design is necessary to ensure the frequencies of interest fall into the pass-band, while simultaneously maintaining a high performing, efficient structure.
Figure 5. BST distributed phase shifter, a close-up of a single varactor and its equivalent circuit model.
A simple circuit model for the distributed phase shifter is shown on Figure 5. The distributed inductance and capacitance per unit length of the transmission line are presented as L0 and C0 respectively. These values are derived from the intrinsic characteristic impedance Z0 and phase velocity ph of the unloaded transmission line. The tunable shunt capacitance per unit length is represented by Cvar.
The relationship between the distributed transmission line parameters and the lumped circuit model elements are given by Equations (1a) and (2a). These values are functions of the geometry and material properties of the transmission line and cannot be changed. The addition of the tunable capacitance alters the effective characteristic impedance Z0 and phase velocity ph as indicated in (1b) and (2b). It can be seen from Equation (1b) that the addition of a Cvar lowers the effective characteristic impedance. Therefore it is necessary that the intrinsic Z0 of the transmission line is larger than the characteristic impedance of the external circuit in order to attempt an impedance match. A perfect match is not possible under all tuning conditions, as seen from (1b). The variation in ph is responsible for the phase shifting behavior of the distributed phase shifter.
One crucial design aspect not covered by the previous equations is the periodic nature of the circuit. The discontinuities created by the addition of tunable capacitors result in small reflections from each capacitor as the signal propagates along the length of the circuit. As the frequency of the signal approaches a certain value, the phase of the incident and reflected signal interfere destructively, preventing forward propagation. When the signal cannot propagate the transmission loss increases, and the signal is reflected back towards its source. This frequency is called the Bragg frequency and is defined by Equation (3).
The l parameter represents the spacing between the tuning capacitors, and can be adjusted to change the Bragg frequency independent of the other transmission line parameters. The highest operating frequency of the phase shifter must be significantly below fBragg to avoid large transmission losses.
The phase shift of each section of the distributed phase shifter varies as ph is tuned. The length l divided by the maximum change in ph determines the differential phase shift of the circuit. This is expressed in Equation (4) with the phase velocity expanded into its constituent terms.
The terms Cmin and Cmax denote the extremes of the values Cvar can assume with tuning. A sufficient number of sections should be cascaded to obtain the desired differential phase shift.
A loss optimized distributed phase shifter design depends on proper selection of l and Z0. Increasing l brings the Bragg frequency closer to the operating frequency and reduces the number of sections required to achieve a given phase shifter. Increasing Z0 lowers C0 and allows a greater variation in ph, also reducing the number of sections. This is beneficial if the tunable capacitor is lossy, since fewer are needed in a given design. However, operating closer to the Bragg frequency increases the transmission loss through reflection of the input signal. Also high impedance transmission lines generally has more ohmic loss than lower impedance ones. These conflicting requirements lead to an optimized design that balances the losses, resulting in the lowest loss design. As a result, the best design from a loss perspective doesn't necessary have the shortest length or fewest sections.
Micromachined silicon substrates
Low-loss millimeter wave circuits require substrates with low losses and low dielectric constants. One approach is to use glass/quartz ( R~3.8) substrates which intrinsically have low dielectric constants and to develop new BST deposition parameters for these substrates. Another possible technique is the micro-machining of high resistivity (HR) silicon which is attractive because of compatibility with standard BST deposition procedures. Ordinarily silicon is a bad substrate due to its low resistivity but advances in float zone silicon technology have made it possible to get high resistivity silicon substrates. However the problem of the high dielectric constant of the substrate still exists and Robert York's team has addressed this by micro-machining the silicon substrate.
Figure 6 shows the structures that they explored in this study. The control sample consisted of coplanar waveguide (CPW) metal placed directly on HR silicon. The second sample had a layer of silicon nitride as a dielectric barrier between the CPW metal and the HR silicon substrate. In the case of the third sample, V-shaped grooves were etched away in the gap region of the CPW using an anisotropic etching procedure. The etchant used was potassium hydroxide and the CPW metal itself was used as the mask layer. The CPW lines were characterized by measuring the 2-port S-parameters on a vector network analyzer. From Figure 7 it can be readily seen that the micro-machined substrate has a lower effective dielectric constant than the control sample. Also, the losses on the CPW line on the micromachined substrate are lower than the control sample (see Figure 8). Another point worth noting is that the use of a dielectric barrier between the substrate and the CPW metal, while attractive for reducing DC-leakage, is extremely detrimental to the loss characteristics of the CPW. This is because the MIS (metal-insulator-semiconductor) structure is associated with free charges at the semiconductor-insulator interface due to accumulation/inversion.
Outlook
A distributed phase shifter with BST tunable capacitors combines the advantages of both BST low-loss properties in the microwave or millimeter-wave region and the easy design and wide bandwidth of MEMS distributed phase shifter and is the state of the art today. Ferroelectric distributed phase shifters for the Ka and X-band with promising quality and performance were introduced by Robert York's group in recent years. However, further improvement in BST capacitor quality factors due to advances in BST film processing and growth should lead to phase shifters with even better insertion loss performance.