Practical Filters and Couplers: A Collection from Applied Microwave & Wireless

Low-pass to High-pass Transform

Any of the low-pass filters presented above can be transformed into an equivalent high-pass by using a simple transform. In active filters, low-pass pole-forming components are simply replaced with high-pass components. With the exception of gain controlling elements (for example, R 4 and R 5 in Figure 2), all capacitors become resistors, and all resistors become capacitors. The new normalized elements have a value equal to the inverse of the corresponding low-pass elements. This transform has the advantage (in the case of Figure 1) of producing a high-pass filter with equal-valued capacitors (The original low-pass filter did not possess this luxury).

Figure 4 shows a transformed schematic of the lowpass filter in Figure 1. The new high-pass element values are indicated in terms of their untransformed lowpass equivalents. Figures 5 and 6 are transformed versions of Figures 2 and 3, respectively.


Figure 4: High-pass unity-gain filter.

Figure 5: High-pass filter with 6 dB gain.

Figure 6: High-pass filter with selectable gain.

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