Astonishingly, 200 years ago in France in 1826, Felix Savary observed the oscillatory nature of Leyden jar discharges. This oscillatory behavior is an essential requirement for resonance.1 The theory of resonance would take another 50 years to mature. In 1887, Heinrich Hertz in Germany devoted one section of his papers to describing his experimental observations of what he called “Resonance Phenomena”.1 That is nearly 150 years ago, which is still amazing.
Cavity filters are ubiquitous today, and they are not new to the world of RF and microwave engineering. Cavity filters have been around for almost 80 years, since Fano and Lawson completed their initial work in 1948.2,3 They are widely used in RF and microwave systems where high selectivity, low insertion loss, and excellent power handling are required. They are commonly found in SATCOM, radar, EW, ECM, and even test and measurement systems. One critical aspect of cavity filter design is how energy is coupled into and out of the resonant structure. Among the various techniques available, coupling loops and coupling probes (henceforth, more commonly “loops” and probes”) are the two most common methods. Each method relies on a different electromagnetic coupling mechanism and offers distinct advantages depending on frequency, power level, bandwidth, and mechanical constraints.
This article furnishes the reader with a basic understanding of the operating principles, design considerations, and practical tradeoffs of loop and probe coupling methods for cavity filters.
Fundamentals of Cavity Coupling
In a cavity resonator, standing magnetic fields (H-fields) and electric fields (E-fields) exist at discrete resonant frequencies determined by the physical dimensions of the cavity as well as boundary conditions. To construct a cavity filter, energy transfer into, between, and out of the resonant cavities must take place. The energy transfer into and out of the filter most often takes place between an external transmission line (such as coaxial cable or waveguide) and the internal resonant H-field or E-field in the cavities.
Input and output coupling is generally achieved by placing a conductive element into the cavity in such a way that it interacts with either the H-field (inductive coupling) or the E-field (capacitive coupling) of the resonant mode. Loops generally couple to magnetic fields, while probes couple to electric fields. A loop that couples magnetic field energy can be viewed as roughly a single turn of the center conductor of a length of coax or a single turn of the center conductor of a coaxial connector. Not only is the outer conductor shorted to the cavity wall, but the end of the loop of the center conductor terminates there as well. A quick look ahead to Figure 1 shows loops protruding from the ends of the coaxial connectors and terminating on the connector body. A probe couples electric field energy and is much simpler than a loop. It can be viewed as a straight section of the center conductor of a coaxial cable or connector with the dielectric stripped away. In this case, the center conductor is left open. Two simple probes are shown in Figure 2.
The TE011 Mode RF Preselector Application
To describe the operation of loop coupling, we have chosen TE011 as the mode in which cavity resonance occurs for its simplicity. In the TE011 mode, the magnetic field lines must form closed loops. These lines run up the center, bend radially outward at the top end of the cavity, and return along the outer wall and bottom end of the cavity, as shown in Figure 1 for the peak of the magnetic field. Naturally this field will weaken over time, cross zero, and begin to manifest itself as a field in the opposite direction, as the input signal causes the cavity to resonate. As per the laws of electromagnetism, a corresponding electric field, oriented relative to the magnetic field by the right-hand rule is established in the cavity as well and is also shown in Figure 1. For the TE011 mode, the E-field only has a component in the θ direction, hence the mode nomenclature Transverse Electric.
It can be assumed that the structure shown in Figure 1 is a notional X-band, 3-cavity preselector for a radar application. Granted it is oversimplified, as there is a distinct lack of tuning rods or any other mechanism for filter alignment, but it provides excellent views of how the fields interface with our loops, and even a glimpse of how the H-field couples through the irises.
The Coupling Loop Method – Principles of Operation
The coupling loops in Figure 1 are formed from loops bent in the center conductors of the RF connectors (generally around a mandrel) and electrically terminated on the connector bodies. The reason they solder to the connector bodies themselves is so they can be removed from the cavity and bent again, or “tuned” without having to perturb the cavity itself. In Figure 1, these loops are oriented at a 45⁰ angle, such that their planes intersect the illustrated magnetic field lines. These H-field lines pass through the loops like thread through the eye of a needle, as shown in the figure. Naturally, many fringing fields occur in the vicinity of the loop that are nearly impossible to illustrate, and the H-field is three-dimensional as well. Designating the left-hand side loop the input and the right-hand side the output, an RF input current flowing in the left-hand loop will induce the magnetic field shown in the cavity. This magnetic field couples from one cavity to the next through two irises, which are the small holes that perturb the magnetic field at the walls between the cavities in Figure 1. On the output (right-hand) side the magnetic field induces a current in the loop according to Faraday’s law of induction. This induced current completes the process of transferring energy from the external circuit driving the input and through the 3-cavity preselector to the output connector. Loop coupling is most often referred to as inductive coupling.
Loop Coupling Strength – Geometry and Orientation
The coupling strength of a loop primarily depends on the loop open area, since a larger loop will naturally intercept more magnetic flux lines and increase coupling. Similarly, the angular orientation of the loop determines coupling strength, such that maximum coupling occurs when the loop plane is perpendicular to the magnetic field lines. For instance, rotating our loops from 45⁰ to 90⁰ relative to the H-field will increase coupling strength greatly, and can also be viewed as increasing the open area (open relative to the direction of the magnetic flux lines). Additionally, the greater the insertion depth, the stronger the magnetic field. Loop shape (circular, rectangular, semicircular) is far less critical than loop open area and/or orientation.
Advantages and Disadvantages of Loop Coupling
Loop coupling is common in high-power and high-Q cavity filters for several reasons. First and most importantly, loop coupling exhibits high power handling because E-fields are not concentrated at sharp conductors, making loops less prone to RF corona and arcing. Secondly, magnetic coupling yields lower current densities, improving intermodulation distortion (IMD), and thirdly, loop coupling is relatively immune to small dimensional changes and temperature variations. Because of these advantages, loop coupling can often be found in system front ends where it is necessary to filter transmissions as well as received signals.
Despite its advantages, loop coupling has a few disadvantages. Size can often become a concern, particularly at lower frequencies, where loops can become physically large. Additionally, wideband filters can often require inordinately large loops, so there are bandwidth limitations. Loop location in the cavity for each resonant mode can be critical, and selecting the correct location for the desired mode is often tricky.
The TM010 Mode RF Preselector Application
To provide a worthy description of probe coupling we have chosen TM010 as the mode in which cavity resonance occurs for its simplicity and its favorable orientation of the E- and H-fields. In the TM010 mode, the magnetic field lines must still form closed loops, and these loops are horizontal (often called “azimuthal”) in the θ direction as shown in Figure 2. This is why the mode is named Transverse Magnetic. Our interest in the magnetic field lines is mostly because of the magnetic coupling through the irises from one cavity to the next, even though the subtle effect of this coupling on the magnetic field is not shown directly Figure 2. The electric field lines in the cavity on the left run upwards from the bottom, in the positive Z direction. The E-field is at its maximum intensity in the center of the cavity and decreases with distance r from the center of the cavity as denoted by both the thickness and length of the E-field lines. Figure 2 shows an instant in time at which the E-field peaks. As the cavity resonates with input excitation, the field strength experiences a reduction over time, crosses zero, and re- emerges as a field in the opposite direction, as shown by the opposing direction of the E-field peak in the middle cavity. Once again, the laws of electromagnetism govern that the electric and magnetic fields are always related by the right-hand rule. In short, for the TM010 mode, the H-field only has a component in the θ direction, whereas the E-field is parallel to the axis of the cylinder, with maximum intensity in the center and declining radially to minimum intensity at the walls.
Consider the component in Figure 2 to be a greatly simplified X-band, 3-cavity preselector for a radar application. There is, of course, a distinct lack of tuning rods or any other mechanism for filter alignment (which, for TM010 mode is heavily dependent on cavity radius r anyway), but it provides an excellent perspective for how the E-fields interface with our probes, and even a framework for imagining how H-field couples/leaks through the irises.
Coupling Probe Method – Principles of Operation
The coupling probe shown in Figure 2 consists of the conductive pin or center conductor of the coaxial connector. This pin extends into the TM010 cavity. The outer conductor is in intimate electrical contact with the cavity end wall. Unlike a loop, the probe couples primarily to the electric field, and the E-field lines in proximity to the probe are shown in Figure 2.
The probe behaves like a small monopole antenna. When placed in a region of strong electric field, it experiences a voltage proportional to the local E-field intensity, allowing energy to be capacitively transferred from the external source into the cavity and from the cavity to the external circuit. Therefore, probe coupling is fundamentally best understood as capacitive coupling.
Probe Coupling Strength – Geometry and Placement
The coupling strength of a probe is largely controlled by the length of the probe, since longer probes capture a greater amount of the electric field. Similarly, the insertion depth increases the amount of coupling as it too can couple more E-field intensity. The probe diameter can affect coupling to a lesser degree by providing a slight increase in capacitance and coupling for an increase in diameter. Position in the cavity is critical for probe coupling, and it is often necessary to place a probe at or near the region of maximum E-field intensity for effective coupling.
Advantages and Disadvantages of Probe Coupling
Probe coupling is particularly valuable in low-power and compact cavity filter designs for several reasons. Probes are quite simple, easy to construct and very easy to fine-tune (tweak). Probe length can be varied to achieve a whole range of coupling from weak to strong and they consume less space than their loop counterparts at a given frequency. Probes are perfect for low-power, tunable filter applications.
Despite being favored for their simplicity and ease of use, there are some significant drawbacks to probe coupling. High E-field intensity at the probe tip, while necessary for good coupling, can lead to RF corona at higher power levels. Even without arcing, the high current densities associated with intense E-fields can generate nonlinear behavior, worsening IMD. Coupling strength is largely dependent on probe dimensions, and probes are sensitive to even small mechanical changes. Consequently, probe coupling is generally relegated to lower power applications, and where performance over temperature is less critical.
Practical Design Considerations
When designing cavity filters, at times the coupling mechanism is not simulated by the engineers because the surrounding, fringing fields can be so complex, and empirical tuning is so easy to perform. If a filter is outfitted with adjustable coupling loops and probes (e.g. shimmed, rotatable loops or thread-in probes), it is often only necessary to incorporate fine adjustments during test and alignment, provided proper placement has been chosen. It is not uncommon to see a blend of coupling methods within a single filter, for example using probe coupling on the low power receive side of a multiplexer and loop coupling on the transmit side. We chose to show irises between internal cavities, but that coupling could just as well be performed utilizing loops for our TE011 and TM010 modes. Choices of materials and their associated coefficients of thermal expansion (CTEs) are critical to filter stability and even apply to the probes and loops. For example, a probe or loop fabricated from a connector with a TeflonTM dielectric is probably not going to provide particularly temperature-stable coupling strength, as Teflon expands at elevated temperatures. CTE of various materials is so important, that even cavity filter tuning rods have fabricated from silver-plated Invar®, which has an extremely low CTE.
Couple More Points
Loops and probes are two fundamental techniques with which to interface external circuits and subsystems to cavity filters. Loop coupling takes advantage of magnetic fields that exist within the cavities, encircling them to couple energy in and out. Loops are a low-loss, high-power and temperature-stable prospect in terms of their performance attributes. By contrast, probes use electric fields, and coupling is achieved when an RF center conductor is immersed in an E-field. For probes, it is quite easy to achieve compact and easily adjustable designs. We reviewed the basic principles behind each coupling method and discussed their advantages and disadvantages using TE011 and TM010 cavities. Each method allows engineers to optimize cavity filter performance in different ways, and across a wide range of RF and microwave applications.
References
- https://commons.princeton.edu/josephhenry/wp-content/uploads/sites/71/2020/02/blanchard-bell-technical-journal.pdf
- Ralph Levy and Seymour B. Cohn, (0.5) A History of Microwave Filter Research, Design, and Development | PDF | Electronic Filter | Low Pass Filter
- Microwave Transmission Circuits, M.I.T. Rad. Lab. Series, vol. 9, G. L. Ragan, Ed. New York: McGraw Hill, 1948. See chs. 9 and 10 by R. M. Fano and A. W. Lawson.
- (PDF) Microwave leakage from field modulation slots in TE011 electron paramagnetic resonance cavities
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