EC-22.5 Passive Microwave Structures: Filters, Couplers and Circulators

What this is and why it exists

At these frequencies passive components are shapes rather than parts.

A filter is a pattern of coupled lines etched into copper. A divider is a junction with one resistor across it. A coupler is two lines running close enough together to share energy. Nothing here is bought in a bag of components.

This topic connects the response you want to the geometry that produces it. It is where the waveguide theory of the electromagnetics module turns into something you can order from a board house.

The vocabulary

• Passband — the frequency range a filter is meant to pass.
• Stopband — the range it is meant to reject.
• Ripple — the variation in loss across the passband.
• Order — the number of resonators in a filter, setting how steeply it falls.
• Coupled lines — two conductors close enough to exchange energy.
• Power divider — a component splitting power between two ports.
• Directional coupler — a component sampling a fixed fraction of one direction only.
• Circulator — a three-port device passing energy one way around a junction.
• Quality factor — a resonator's stored energy compared with its loss per cycle.

The mental model

A filter specification has four parts. Where the passband is, how flat it must be there, how steeply it must fall, and how much loss is acceptable. Those four decide the number of resonators before any geometry is chosen. Asking for all four to be excellent produces a filter that cannot be built.

The classical responses are different compromises. One is flat in the passband and falls gently. One falls steeply and ripples. One preserves the shape of a pulse and rejects poorly. Knowing which property the application actually needs prevents a great deal of over-specification.

Turning a response into copper uses coupled lines. Each resonator becomes a section of line about a quarter wavelength long, and the spacings between sections come from the prototype element values. Seeing that translation once explains why microwave boards look like rows of parallel fingers.

Power dividers and directional couplers are both defined by their matrices. A divider splits incoming power between two output ports while keeping those two isolated from each other. That isolation stops one output disturbing the other. A coupler samples a known fraction of a wave travelling in one direction and ignores the other. That is how forward and reflected power are measured separately.

Circulators are the interesting exception. A magnetised ferrite makes energy pass one way around a three-port junction and not the other. This breaks reciprocity, which no ordinary passive component does. It is how a single antenna serves a transmitter and a receiver at once.

The unglamorous parts set the accuracy of everything else. A termination that is not quite the right impedance corrupts every measurement made through it. And the loaded quality factor connects a resonator's loss to the bandwidth it produces. That is why a lossy substrate makes a narrow filter impossible.

What you should now be able to explain or do

• Specify a filter from an application's requirements, in four parts.
• Say which classical response suits a given requirement, and what it gives up.
• Explain how a filter response becomes a pattern of coupled lines.
• Read a divider and a coupler from their scattering matrices.
• Say what a circulator does and why it is not reciprocal.
• Explain how quality factor limits the narrowest achievable filter.

Check yourself