Nuts and Volts - July/August 2018

18 July/August 2018

attenuation in the filter’s pass-band. A perfect filter would have no insertion loss at all, but all practical filters have some insertion loss. The filter in Figure 3 has an IL of about 1 dB.

• Stop-band Attenuation and Notch Depth: In the stop-band, a minimum amount of attenuation is required of the filter. If the filter rejects a narrow range of frequencies with a stop-band in between two pass-bands, notch depth is the maximum attenuation between those two pass-bands. Both of these parameters are specified in dB.

• Input and Output Impedance: Filters have a characteristic impedance that affects how a signal source or load will perform when connected to the filter. For the filter to have only the desired effect, it’s impedance should match the impedance of whatever it is connected to: a signal generator, a microphone, a transmission line, or an amplifier. If the impedances don’t match, filter performance may not be as expected.

Filter Families and Orders

Looking through websites and books of filter designs, you’ll notice that along with the type of frequency response, there are other categories: Butterworth, Chebyshev, Bessel, Elliptical, and more. These are known as filter families. Many of the families are named for the designer who worked out the equations describing them. (Elliptical filters are so-named because the solutions to functions describing them form an ellipse in Cartesian coordinates.) Each set of equations has different solutions that translate into different component values.

Each family of filters has a different frequency response shape. They might all be designed to have the same cutoff frequency but the amount of ripple in the pass- and stop-bands and the steepness of the rolloff vary quite a bit. (The filter’s phase responses are also quite different.)

For example, compare the Chebyshev and Butterworth low-pass filter response curves in Figure 4. Both are low-pass filters with a cutoff frequency of 1,000 Hz. The curves have very different shapes, though. The Butterworth has a very smooth response with no ripple at all — Butterworth filters are often referred to as maximally-flat for that reason — but the rolloff is smooth and gradual, as well. The Chebyshev filter trades a smooth response for steeper rolloff by allowing various amounts of ripple. The filter response in Figure 4 is known as a “1 dB ripple Chebyshev.” Depending on what you’re using the filter for, ripple or gradual rolloff might be okay. The different filter families offer choices about how the filter will perform and what effects they have on the signals. For example, hams trying to design an audio filter for receiving the single tones of Morse code (CW) find that a lot of ripple means distortion and smearing of the carefully shaped dits and dahs. At high speeds, that can make the code “tough copy.” In that case, it’s worth allowing a more gradual rolloff so you hear some of the adjacent signals in order for the Morse elements to be reproduced clearly. Each application is a little bit

PRACTICAL TECHNOLOGY FROM THE HAM WORLD

Brick-wall or Ideal Filters

The filter responses in Figure 2 vary smoothly between the pass-band and the stop-band. This is the way a real filter behaves. Nevertheless, you will encounter references to “ideal” or “brick-wall” filters for which the pass-band and stop-band responses are completely uniform or “flat.” The transition region for such a filter is a vertical line on the response graph with an infinite rolloff. Needless to say, these filters can’t actually be built, although some sophisticated digital filters get close. n FIGURE 4. Filter responses for a Butterworth and a Chebyshev low-pass filter. Both have the same cutoff frequency of 1,000 Hz but have significant differences in rolloff and ripple in the passband. (Figure courtesy of the American Radio Relay League.) Attenuation - Is it Positive or Negative?

If an output signal is smaller than the input signal, the ratio in dB will be negative. For example, if the output is five times less powerful than the input to a filter, that is a power ratio of - 7 dB with the minus sign indicating a ratio less than 1. That represents an attenuation or loss of 7 dB, with no minus sign.

The rule is that power ratios in dB have a positive or negative value, while loss or attenuation are given without the minus sign.

The - 7 dB power ratio is a loss or attenuation of 7 dB. Similarly, if the output was five times greater than the input, that would be a gain of 7 dB.