Highpass filters use modified equal-element design

By Richard Kurzrok, Queens Village, NY -- 5/24/2001

Using a modified equal-element design for a lumped-circuit lowpass filter has several advantages over the well-known equal-element design (Reference 1 and Reference 2). The modified design exhibits superior passband performance with only modest degradation of stopband selectivity. Moreover, the modified design is simple and easy to manufacture. You can extend the modified equal-element design to highpass LC filters. Both equal-element and modified equal-element filters use the normalized highpass prototype (Figure 1). For the equal-element filter, the normalized value of the outside capacitors C₁ and C₅ is 1; for the modified equal-element filter, it's 2. The design reference frequency, at normalized frequency x=1.0, is not the 3-dB cutoff frequency for the filters in Figure 1. The 3-dB cutoff frequency occurs close to x=1.9. In contrast, in Butterworth and Chebyshev filters, x can equal 1.0 at the 3-dB cutoff frequencies. You use this different normalization method to calculate the values of the circuit elements.

We designed, assembled, and tested two nine-pole, modified equal-element filters. The filters used vector boards in die-cast aluminum boxes with BNCs. All capacitors were ±5% polypropylene units. We selected the filter design frequencies based on available capacitor values. The first filter had a reference frequency of 6.773 MHz. Assuming a ratio of 1.902-to-1, this figure corresponds to a cutoff frequency of 3.561 MHz. After denormalizing the filter to actual circuit values (as in Reference 1), we determined all inductor values, L₁ through L₄, to be 1.175 µH. The interior filter capacitors, C₂, C₃, and C₄, are equal to 470 pF. The filter's input and output capacitors, C₁ and C₅, are then equal to 940 pF. To obtain this value, we connected standard 820- and 120-pF capacitors in parallel. All the inductors used 15 turns of number 26 magnet wire wound on Micro Metals T37-2 toroids. Table 1 shows the measured amplitude response.

The second filter had a reference frequency of 21.22 MHz. Assuming a ratio of 1.902-to-1, this figure corresponds to a cutoff frequency of 11.168 MHz. After denormalizing the filter to actual circuit values (as in Reference 1), we determined all inductor values, L₁ through L₄, to be 0.375 µH. The interior filter capacitors, C₂, C₃, and C₄, are equal to 150 pF. The filter's input and output capacitors, C₁ and C₅, are then equal to 300 pF. To obtain this value, we connected two standard 150-pF capacitors in parallel. All the inductors used 10 turns of number 26 magnet wire wound on Micro Metals T25-6 toroids. Table 2 shows the measured amplitude response. Assuming inductor unloaded Q of approximately 100, the measured data shows good correlation with calculated values. You can cascade the modified equal-element highpass filter with a similar lowpass filter to obtain a bandpass filter of high bandwidth. This technique provides an alternative to using image parameters (Reference 3).

REFERENCE

1.Kurzrok, Richard, 'Equal-element filter improves passband performance,' EDN, March 15, 2001, pg 123.

2. Taub, JJ, 'Design of Minimum Loss Bandpass Filters,' Microwave Journal, November 1963, pg 67.

3. Kurzrok, Richard, 'Wideband filter uses image parameters,' EDN, Oct 26, 2000, pg 174.

© 2009, Reed Business Information, a division of Reed Elsevier Inc. All Rights Reserved.