Matthaei (et al) writes that a common choice is Y_{ai} = 1/70; I've seen ranges from 1/60 to 1/100.
Please could someone provide some intuition on the choice for Y_{ai} in Matthaei's design procedure?
Thank you in advance.
Sincerely,
Hugo
The optimal resonator admittance, Yai, for a microstrip combline filter depends on the specific design of the filter. However, there are some general principles that can be used to choose Yai for optimal Q.
One important principle is to choose Yai such that the resonator is critically coupled to the input and output transmission lines. This means that the resonator should absorb all of the power from the input transmission line, and none of the power should be reflected back to the input.
Another important principle is to choose Yai such that the resonator has a high unloaded Q factor. The unloaded Q factor is a measure of the resonator's ability to store energy, and it is inversely proportional to the resonator's bandwidth.
In general, the following guidelines can be used to choose Yai for optimal Q:
- Choose Yai such that the resonator is critically coupled to the input and output transmission lines. This can be done by using a coupling factor of 0.707.
- Choose Yai such that the resonator has a high unloaded Q factor. This can be done by using a resonator with a high aspect ratio and a low loss tangent.
Once Yai has been chosen, the other parameters of the filter, such as the resonator lengths and widths, can be calculated using a filter design software program.
Here is a more detailed explanation of how to choose Yai for optimal Q in a microstrip combline filter:
The coupling factor between the resonator and the input and output transmission lines is given by the following equation:
k = (Z_0 - Z_r)/(Z_0 + Z_r)
where:
- k is the coupling factor
- Z_0 is the characteristic impedance of the transmission line
- Z_r is the input impedance of the resonator
For critical coupling, k = 0.707. This means that the resonator impedance must be equal to the characteristic impedance of the transmission line at the center frequency of the filter.
The unloaded Q factor of the resonator is given by the following equation:
Q = 1/(2πf * R * C)
where:
- Q is the unloaded Q factor
- f is the center frequency of the filter
- R is the resistance of the resonator
- C is the capacitance of the resonator
To increase the unloaded Q factor of the resonator, it is necessary to reduce the resistance and capacitance of the resonator. This can be done by using a resonator with a high aspect ratio and a low loss tangent.
Once the coupling factor and unloaded Q factor of the resonator have been chosen, the other parameters of the filter, such as the resonator lengths and widths, can be calculated using a filter design software program.
Here is an example of how to choose Yai for optimal Q in a microstrip combline filter:
Suppose that we want to design a microstrip combline filter with a center frequency of 1 GHz and a bandwidth of 10 MHz. We want the filter to have a critical coupling factor and an unloaded Q factor of 100.
The characteristic impedance of the transmission line is 50 ohms. Therefore, the resonator impedance must be equal to 50 ohms at the center frequency of the filter.
To increase the unloaded Q factor of the resonator, we will use a resonator with a high aspect ratio and a low loss tangent. For example, we can use a substrate with a dielectric constant of 2.2 and a loss tangent of 0.001.
Using a filter design software program, we can calculate the resonator lengths and widths to achieve a critical coupling factor and an unloaded Q factor of 100.
Once the resonator lengths and widths have been calculated, we can fabricate the filter using a printed circuit board (PCB) fabrication process.