Topology and power handling

 
How much power a filter can handle before break-down occurs is dependent on factors like pressure, temperature, resonator geometry, unloaded Q, return loss, topology, frequency, signal dynamics (modulation, duty-cycle, prf) etc.
 
The stored energy of a resonator is proportional to the square of the peak electric field strength of the resonator.
 
Therefore - a low stored energy level in a resonator means that a low peak electric field is present, which implies that a good margin to break-down probably exists.
 
In CMS the stored energy (or equivalent - the loaded Q) for each resonator can be plotted versus frequency. The calculated stored energy levels in CMS are normalized to 1 W applied at the input.
 
This feature allows the filter designer to optimize designs with respect to power handling.
 
For Tx filters, where break-down may be a problem, an important task is therefore to find a topology, which has a low stored-energy level. 
Because: If the maximum stored-energy level of a filter 'A' is half of that of a filter 'B', filter 'A' will have twice the power handling capability of filter 'B' (the two filters are assumed identical - except for the topology).
 
In the following is shown some examples of how the choice of topology may influence on the power handling capability of a filter. The same filter is considered in all the examples.
 
Example 1:
A 6-pole Tx filter with center frequency at 400 MHz and 5.5 MHz bandwidth is investigated.
There is a 95 dB rejection requirement up to 392 MHz on the low side of the passband.
 
In the example below this filter has been implemented with two transmission zeroes at the low side in order to meet the rejection demand. Two triplets in series have been used to make the transmission zeroes. This is a topology which is very common and widely used both in Tx and Rx filters.
 

 
A plot of the stored energy levels for all the resonators is shown below:
 

 
This plot shows that the most critical resonator in this design is resonator 2, which has by far the highest stored energy level (216 nJ/W). If the input power was increased until break-down occured - resonator 2 would be the place where arching would first take place (if the frequency was at the lower band-edge. If the frequency instead was at the high band-edge, resonator 3 would be most critical).
Example 2:
 
The exact same filter characteristics as above can be obtained by a folded design:
 

 
The corresponding energy levels are shown below:
 

 

It is seen that the folded topology has a max stored energy level that is 22% lower than the two-triplets topology.
For the folded topology the critical resonator is now resonator 4, closely followed by resonator 2.

Example 3:
The rejection requirement can be fulfilled with other transmission zero configurations than was used in the two previous examples.
If an extra notch is placed above the passband we have the following situation:
 

 
The two most distant notches relative to the passband are the result of the single x-coupling between resonator 1 & 4. It is seen that the rejection requirement is still fulfilled - but with reduced margin.
The only reason to include the notch above the passband is because the related topology has improved power handling capability as can be seen below.
In order to use only two x-couplings for implementation of the shown characteristic, the two most distant notches have been placed symmetrically relative to the center frequency. These two notches are as mentioned the result of the single x-coupling between resonator 1 & 4. The leftmost notch (at 389.8 MHz) has been slightly tuned (+ 0.3 MHz) in order to minimize the synthesis error (shown in the bar to the right in the plot-window).
 

 
The shown series combination of quadruplet and triplet is seen to have more than 30% lower stored-energy levels than the two triplets in series (example 1). The break-down power threshold will therefore also be 30% higher for the topology in example 3. The critical resonator is now resonator 2, closely followed by resonator 3.
If input and output were exchanged so that power instead was applied at the "L" port,  the above results would not be valid. Instead new simulations would have to be carried out where the triplet and quadruplet changed place.
 
Example 4:
The exact same characteristic as used in example 3 can be implemented with the folded topology shown below.

This topology has approx. the same maximum stored-energy level as the topology in example 3, but an extra x-coupling is required. This extra x-coupling makes the filter more complicated and will probably result in a design, which is more sensitive to coupling variations than the previous one (can be verified by making a MonteCarlo analysis).
Conclusion:
The above has shown that topology may have an impact on a the power handling capability of a filter.
The most critical frequency is at the band edge with the steepest slope.
CMS pinpoints the resonator(s) where break-down will occur first and also the corresponding stored energy.
This energy can easily be scaled to power levels other than 1W.
 
In order to calculate the power level, which will result in break-down, conversion from stored energy to peak electrical field is necessary. This is a more complicated task - which often requires a 3D EM model (like HFSS or CST) of the resonator type in question. An exception is 'straight' rectangular waveguide filters operating in the TE10 mode where analytical expressions exist [1].
 
An article describing how to combine the stored energy found from CMS simulations with 3D EM models of single resonators to find the break-down power of a filter can be found here.
This and other subjects related to power break-down are also treated in a paper by Ming-Yu [2]
 
 
 
[1]  Chi Wang, Kawthar A. Zaki
Analysis of Power Handling Capacity of Band Pass Filters
2001 IEEE MTT-S Digest, pp. 1611-1614
 
[2]   Ming Yu
Power-handling Capability for RF Filters
IEEE Microwave Magazine, October 2007, pp.88-97