In this tutorial we will learn how to synthesize and implement a chebyshev response with a combline cavity topology using Couplings Designer. Couplings are extracted and linked to physical dimensions and then combined to realize the final filter layout. It will be shown that unintended couplings may distort the passband and stopband performance. These coupling are analyzed by Couplings Designer with a new coupling matrix that takes them into account and the final physical dimensions are tuned to reflect the change, finally retreiving the chebyshev response.
- Center frequency at 2000 MHz.
- 5% bandwidth.
- Minimum insertion loss.
- 20 dB return loss.
- 20 dB rejection at +/- 300 MHz.
Couplings Designer synthesizes a general coupling matrix that can be realized with any type of resonating structure. What’s available to the designer is limited by physical parameters such as size, quality factor, tolerances, power handling, machining etc. In this tutorial we will design a combline filter inside a cavity.
Resonators used in a combline topology are a quarter wavelength long at the center frequency and connected to ground at one end. The resonating frequency can be tuned by loading the resonator with a tuning screw (shunt capacitance) hence reducing the frequency and the resonator should therefore be designed by incorporating the tuningscrew in its nominal position. To make it resonate close to 2000 MHz the resonator should be around 0.3/2/4 = 37.5 mm long.
An eigenmode simulation of a 2000 MHz resonator rod with diameter 5 mm reveals that the exact length is 34.5 mm. The simulation also predicts an unloaded Q of around 2000 if all metal parts are made of aluminum. It is important that the cavity has the dimensions, width and height, of the filter cavity as it will interact with the resonator. The filter cavity itself should not be resonant or support waveguide modes close to passband frequencies.
Insert the requirements on center frequency, bandwidth, return loss and the predicted unloaded quality factor from the eigenmode simulation into Couplings Designer. Playing with the order reveals that the filter order, number of resonators, should be 3 to meet the requirements on rejection.
The synthesized coupling matrix gives us the required external coupling from input/output to first/last resonator and the resonator-resonator couplings. One can notice that the filter is symmetrical, it is also seen that the resonators are all tuned to 2000 MHz with a quality of 2000, that is, the filter is synchronous. We have already designed a resonator to be used with this coupling matrix and later on we will extract the physical dimensions needed to realize the required external quality and coupling factors.
A perfect chebyshev response is now synthesized, however in reality this is only accurate close to the passband. We will later see that a fullwave simulation will reveal a more complicated nature of this otherwise so simple filter. Note that the relatively high resonator quality of 2000 will yield low loss of around 0.1-0.2 dB and a non-distorted passband linearity.
Extraction of external quality
The external quality factor 17.1 is read from the couping matrix and is common to both input and output due to symmetry. One can implement this coupling in several ways but a common method with the combline topology is to tap the resonator directly from the coaxial port. This allows high coupling (low Qe) required by broad filters by tapping close to the open end. Low coupling (high Qe) is obtained by tapping close to the shorted end but for very low bandwidths it is more practical with probe-coupling.
The extraction is made by adjusting the tap position and calculate external quality from s-parameters. If the shape of the resonator is symmetrical one can use two taps and obtain S21 transmission and use the formula below. Note that it includes the factor 2 because the resonator is doubly loaded. If the shape is not symmetrical one can somehow weakly couple the second port or use one tap to calculate the quality from phase characteristics of S11. Remember that this is external quality and the simulation should therefore be completely lossless, remove conductor and dielectric losses!
A tapping position of 5.2 mm (15% of resonator length) gives 2*2000/(2200-1975) = 17.7 which is very close to what we desire.
Extraction of coupling factor
The physical coupling factor, 0.515, is read from the coupling matrix and is identical for first to second and second to third resonator due to symmetry. Since there are no non-adjacent couplings the sign of each coupling may be either positive or negative, inductive or capacitive. Physical couplings are always a hybrid of these two, that is magnetic and electric, however one of them is dominating and depends on the coupling structure. In our combline case it is more likely that the magnetic coupling is stronger and hence the couplings will be inductive, or positive.
The hybrid coupling factor, k or M, is extracted by coupling two resonators to each other by placing them in close proximity and adjust the separation. The input and output probes are weakly coupled to the first and second resonator respectively. The coupling factor is calculated from the split resonance, that is even and odd mode resonances. Theoretically this can be imagined by placing an electric (odd) and magnetic (even) wall between the resonators and record the resonance frequency of each case, f1 and f2. It is also possible to obtain the split resonance from an eigenmode simulation. The resonances are easy to distinguish when materials are made lossless.
A resonator separation of 2 mm gives (2040^2-1940^2)/(2040^2+1940^2) = 0.502, which is close enough to what’s required.
The combline filter has been designed in an aluminum cavity of dimensions 15x40x29 mm. The first waveguide mode (TE01) cutoff is therefore 3.7 GHz and first cavity mode (TE011) at 6.4 GHz, which is far from the passband. A quarterwave resonator introduces its first spurious passband at 3X the center frequency ideally but depending on how the input and output is coupled to the waveguide mode (TE01) one could expect spurious behaviour starting from 3.7 GHz.
All three aluminum resonators are identical, 5 mm in diameter and 34.5 mm long, resonating synchronously at 2000 MHz. Tuning screws has also been added. The first and last resonator are coupled to the input and output with taps at a location 5.2 mm from the shorted end. These taps are extensions of the coaxial connector center conductor. Each resonator is separated by 2 mm. All dimensions in accordance and put together from the extracted and synthesized external quality and coupling factors.
The realized filter, simulated below, is severely distorted and has two zeros at the high side. This happens due to non-adjacent coupling which is typical for this filter topology, especially between resonator 1 and 3. This can be demonstrated by tuning the 1-3 coupling in Couplings Designer which gives us a response quite similar to the fullwave response.
Final tuned design
This type of non-adjacent coupling requires asynchronous resonators to realize a chebyshev response. This can be done by detuning the first and last resonator to 1975 MHz or equally the middle resonator to 2025 MHz with tuning screws according to Couplings Designer. We choose the first option and introduce tuning screws of length 3.1 mm above the open end (capacitive loading) of these resonators to reduce the resonance down to 1975 MHz.
The final and tuned combline filter shows great agreement with the synthesized and tuned coupling matrix response, even tho this is just the first iteration with dimensions taken directly from the extraction process. It is slightly shifted in frequency and the non-adjacent coupling is stronger in the fullwave simulation, reducing lower stopband rejection. However, the specifications are met with an isertion loss around 0.1 dB. Final layout is shown below. In a practical implementation one would adjust the length of each individulal resonator and leave the tuning screws at a nominal position to allow +/- tuning.