# Tutorial: Combline resonator and Combline Filters

*[Quick contents for this page: A) Combline Resonator, B) Combline Filter (2nd order example)]*

*A) Combline Resonator*

## Introduction

In its simplest form a combline resonator consists of a conductive cavity (either rectangular or circular) with a cylindrical conductive resonator placed within it symmetrically. The latter is short circuited at one end with the bottom of the cavity, while the top is spaced some distance from the top cover of the cavity. Combline resonators can be used to design a higher order filters and they are cheaper to construct compared to dielectric resonators, however at the expense of higher losses (that is lower Qu=unloaded Q-factor).

In practice, people insert a conductive screw that penetrates the top wall of the cavity and it is terminated at some distance from the top face of the conductive cylinder. The tuning screw helps to change the resonant frequency in case of construction intolerances and when tuning a higher order filter, based on combline resonators. The longer the tuning screw the lower the resonator frequency of the resonator, so at the design stage it is useful to make the resonator operate at a slightly higher frequency (about 50-80 MHz) than required.

Below is shown a computer model of a resonator with a tuning screw placed symmetrically within a rectangular cavity. All walls (shown as transparent here) are metallic and the resonator lies on top of the bottom cavity wall.

## Calculation of combline resonator resonant frequency and Qu

I have prepared an excel file, which calculates automatically the following parameters

- Qu (Q unloaded, that is the Q of the structure when only cavity and resonator losses are taken into account, wihout the presence of any external port, etc.)
- The cylindrical resonator height
- The equivalent circular cavity radius, if you prefer to place the resonator within a circular cavity instead of a rectangular cavity (this does not affect fo of resonator)
- The recommended cavity height, to take into account the presence of a tuning screw (longer tuning screw results in the reduction of combline's resonator resonant frequency)
- Displays a graph, which shows the dependence of the Qu as the resonator radius is reduced
- Also, as a double check to the final calculations, intermediate values such as wavelength (free space) and diameter of resonator and circular cavity are shown .

For the input parameters you have to specify the desired resonant frequency, the conductivity of the metal (common for the resonator volume and cavity walls), the size of rectangular cavity and the resonator radius. Click on the image below to download the excel file.

The equation behind these calculations was extracted from this very nice paper: 'Narrowband Microwave Bandpass Filter Design by Coupling Matrix Synthesis' Morten Hagensen, Guided Wave Technology ApS, Denmark. Note: The equation assumes the presence of a factor 'n', which is the resonator length expressed in quarter wavelenghts with 0.5<n<0.8. This means that the actual resonator frequency will be well above the expected one. But, this is not of a problem, since a tuning screw can be used to correct this and this is a normal method to follow in practice. So, the equation assumes that you will be using a tuning screw to make fo come to the desired value.

On the excel file, the graph shows the depedence of losses with the resonator radius. For very small resonator radius the losses increase, since power is lost due to skin effect at the surface of the resonator, resulting in the reduction of Qu (Qu is inversly proportional to conductor losses). Similarly, when resonator radius is increasing and its distance from the cavity is reduced, more power is lost in the cavity wall, hence resulting again in more losses (lower Qu). In between those conditions, the Qu presents an optimum (peak) value.

## Example calculation for a 1.8 GHz combline resonator

Based on the excel program presented on the previous section, the following parameters were considered for the design of a 1.8 GHz combline cavity resonator:

- fo = 1.8 GHz (combline resonator resonant frequency)
- Metal conductivity = 5.8e7 (typical conductor loss for lossy copper)
- Resonator radius (r) = 10mm
- Rectangular cavity side (a)= 50 mm (normally 1.5 times or more the resonator radius, I picked up 2.5 times to improve Qu
- n = 0.55 (normally a fixed value)

The excel results are as follows:

## Qu = |
## 4418.59 |
## (unloaded Q-factor of cavity resonator) |

## cylindrical resonator height (h) = |
## 22.90 |
## mm |

## equiv. circular cavity radius = |
## 28.21 |
## mm |

## Recommended cavity height (b) = |
## 30.90 |
## mm (cyl.resonator height + 8 mm for tuning screw) |

For simplicity the results are approximated as: resonator height=23mm and cavity height=30mm, so we get 7 mm space for a tuning screw.

A parametric calculation was performed to show the dependence of the screw length 's' to the resonator frequency for the cavity with fo=1.8 GHz. The results are shown below:

Notice that when s=0 the fo corresponds to that when there is no screw present. To make resonator operate at 1.8GHz a screw length of approximately 4.5 mm long should be inserted in the cavity, as seen from the above graph. Note that the maximum allowable screw length is 7 mm (distance between resonator and cavity). As said before, the longer the screw length 's' the less the fo - this is because the presence of the screw introduces more capacitance, and hence reduces fo (hint: fo=1/(2*pi*sqrt(L*C)) ).

Also, keep in mind that fo depends on the cavity height 'b' (see next figure). Ideally, we want the top wall of the cavity to be near the resonator top face, but without touching it, it must stay as 'open circuit'.

Again, to compensate for this we use the tuning screw to adjust fo during a laboratory measurement. For the moment let's assume that b stays fixed at 30mm (we don't want a big and heavy cavity).

Obviously, resonator height 'h' affects fo too. This can be investigated from the next figure (cavity without screw and b=30mm):

For h= 0mm, we simply get a pure rectangular cavity mode (resonator dissappeared!). On the other hand, for h=30mm, the top cavity wall is short circuited with the resonator, that's the reason we see the sudden 'jump' from 27mm to 30mm. In between those values, we observe that as 'h' increases, fo drops, which is natural, since fo is inversly proportional to resonator length. For h=23mm, fo=1.9 GHz which is pretty close to the input value of fo=1.8 GHz, hence confirming the validity of our calculations based on the excel program (as said before, the discrepancy is due to factor 'n' which gives actual 'fo' above the input 'fo' value).

So, from the above graphs we have a good understanding of how fo is affected from main parameters, which are screw length, cavity height and resonator height.

These graphs can help us design visually a resonator by observing a point on a chart. Of course, in practice we are only interested in tuning fo by simply adjusting screw length, since changing the other parameters (cavity or resonator height) require to fabricate a new cavity, which is an expensive and time consuming process.

## EM field configuration

*B) Combline Filter (example of 2nd order design)*

(to be continued)