Designing Balanced L/C Filters
At RF frequencies, circuits connected in a differential or balanced configuration are relatively common, whether it be the input to a feedline or the inputs/outputs of an integrated circuit (think the output of an SA602). However, when I went looking for tutorials on designing L/C filters for these connnections I was surprised at the lack of information. While balanced filters are mentioned in passing, I couldn’t find anything describing how to design them for a desired response in the same way that filter tables are available for single-ended low-pass or high-pass filters.
This seemed strange but after thinking about it I realized using the filter design tables for a balanced design is relatively straightforward since it’s really the same problem. To understand why, consider the low-pass filter design shown below.
This is a typical configuration where the filter is fed differentially from a source with resistance RS and terminated in a load resistance RL. Since each branch of the filter is identical there is a virtual ground going down the center and the circuit can be redrawn as shown below.
Recognizing the existence of this virtual ground is the key because when the circuit is redrawn in this fashion, it becomes obvious that what we are dealing with is two single-ended filters whose shunt impedances, source resistance, and load resistance are 1/2 that of the balanced design. So to design a balanced filter for a particular response, start with a single-ended filter designed for that same response but with source and load resistances of 1/2 the desired values. Then convert it to a balanced design by mirroring it around ground and combining the shunt elements.
As an example, consider the design for a 10 MHz low-pass Butterworth filter. The single-ended design along with its response is shown below.
For the corresponding balanced design, first we’ll design a filter for the same response but source and load resistances of 1/2 the desired values:
then mirror it, combining the shunt elements, source, and load resistance into single elements.
You can see from the plots that the frequency response for all three filters is the same, as expected.
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