The low-frequency LC performance of a high-pass filter is strongly affected by the quality of the filter components. Typically, the inductor is the component that deviates most significantly from the ideal.
The first-order inductor paradigm consists of an inductor in series with a resistor that models the ohmic resistance of the inductor's wire. Low-frequency inductors can have a high value of loss resistance.
HPF1 in the circuit diagram shows an ideal third-order high-pass filter with an ideal inductor (Fig. 1). HPF2 depicts the same filter with a non-ideal inductor. The 15-Ω inductor loss-resistance is the equivalent of Q = 4 at the HPF cut-off frequency of 10 kHz.
Examining the frequency response in Fig. 2, the HPF2 output OUT2 deviates from the HPF1 ideal-filter curve (OUT1) as the frequency gets lower. The attenuation slope changes from 18 dB/octave (third-order) to 12 dB/octave (second-order).
This situation seems to be unavoidable due to the inductor's loss component. However, the use of a transformer instead of an inductor alters the situation dramatically. As in HPF3, the loss resistance is not in a branch that is common to the input and output. Therefore, it does not affect the ultimate attenuation at low frequencies.
Examination of the frequency re-sponse of the HPF3 filter's OUT3 shows that this value is identical to the ideal filter's output at low frequencies. The deviation from ideal of HPF3's frequency response is a small added loss at the passband for frequencies above the cut-off frequency. This loss is due to the resistor's voltage dividers at the input and output of the filter. In many cases, the source and load resistance values can be adjusted to compensate for this loss. In any case, the curve shape remains close to the ideal shape.
Reprints
