Filter Design Part 18. How to Use Connecting Line & Shunt Shorted Stubs to Design a BandPass Filter.
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A bandpass filter can be created using shunt λg/4 (quarter-wavelength) short-circuited stubs and connecting lines by exploiting the impedance transformation properties of transmission lines and the resonant behavior of the stubs.
1. Quarter-Wavelength (λg/4) Short-Circuited Stubs:
A λg/4 short-circuited stub behaves as an open circuit at its resonant frequency. This is because the short circuit at the end of the stub is transformed into an open circuit at the input due to the quarter-wavelength impedance inversion.
At frequencies away from resonance, the stub presents a reactive impedance (either inductive or capacitive), which affects the transmission characteristics of the filter.
2. Connecting Lines:
The connecting lines between the stubs provide the necessary phase delay and impedance matching to ensure proper signal transmission at the desired passband frequencies.
These lines also help in creating the desired frequency response by interacting with the stubs' impedance characteristics.
3. Bandpass Filter Design:
By placing multiple λg/4 short-circuited stubs at regular intervals along a transmission line, you create a structure that selectively allows signals within a specific frequency range (the passband) to pass through while attenuating signals outside this range (the stopband).
The stubs act as resonators, and their spacing and dimensions determine the center frequency and bandwidth of the filter.
The connecting lines ensure proper coupling between the stubs and maintain the desired impedance matching across the passband.
4. Working Principle:
At the resonant frequency (center frequency of the passband), λg/4 stubs present a high impedance (open circuit) to the transmission line, allowing signals to pass through with minimal reflection.
At frequencies below or above the resonant frequency, the stubs introduce mismatches and reflections, attenuating the signal and creating the stopband regions.
5. Design Steps:
Determine the center frequency (f0): This is the frequency at which the stubs are λg/4 long.
Calculate the stub lengths: The physical length of each stub is λg/4 at f0, where λg is the guided wavelength.
Choose the number of stubs: More stubs result in a sharper transition between the passband and stopband (higher selectivity).
Optimize the connecting lines: The length and impedance of the connecting lines are adjusted to achieve the desired bandwidth and impedance matching.
6. Advantages:
Simple design using distributed elements (transmission lines).
Suitable for high-frequency applications (microwave and RF).
Can be implemented in planar technologies like microstrip or stripline.
7. Limitations:
The filter's performance is sensitive to manufacturing tolerances.
The physical size of the filter can be large at lower frequencies due to the λg/4 requirement.
By carefully designing the stubs and connecting lines, you can create a bandpass filter with the desired center frequency, bandwidth, and rejection characteristics.
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