# How to Calculate Passband

Written by peter syslo
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In audio electronics, the Passband is the broad range of frequencies that is maintained or "boosted" (raised in volume), by a filter. A filter is an electronic circuit that shapes the sound, affecting a very broad range of either low or high frequencies. For example, a low-pass filter would maintain or boost the bass frequencies (the Passband) in the sound and the higher frequencies would be lowered in volume, or attenuated. A high-pass filter would boost the treble frequencies (the Passband) and the lower frequencies would be attenuated. Mathematically, the Passband can be identified by knowing the Critical Frequency (point where the Passband ends) or it can be calculated by knowing the individual component values of the filter.

Skill level:
Moderate

### Things you need

• Scientific calculator
• Filter schematic or data sheet

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## Instructions

1. 1

Obtain the Critical Frequency, or Fc, value of the low-pass or high-pass filter. This number will be a frequency listed in Hertz, or Hz, which means sine-wave cycles (periods) per second. The Fc value may be included in the name of the filter, such as "500 Hz low-pass filter."

2. 2

Obtain the value of Fc from a filter setting. An adjustable filter may not have a frequency designation and may just be labelled "low-pass filter" or "high-pass filter." If you can manually set the frequency of the filter with a knob, slider or digital interface, that frequency is the number you will use for Fc.

3. 3

Identify the Passband for a low-pass filter, using Fc. If Fc is 500 Hz, the Passband is any frequency below and including Fc (one Hz to 500 Hz).

4. 4

Identify the Passband for a high-pass filter, using Fc. If Fc is 500 Hz, the Passband is any frequency above and including Fc (500 Hz to 20,000 HZ and beyond).

1. 1

Identify the type of low-pass or high-pass filter. Both filters can either be Resistor-Capacitor (RC) or Resistor-Inductor (RL). A circuit schematic or data sheet will tell you the type of filter.

2. 2

Obtain component values from the circuit schematic or data sheet. For RC you will need the values of the resistor and the capacitor and for RL you will need the values of the resistor and the inductor.

3. 3

Using the RC equation for Critical Frequency (Fc = 1 / 2piRC), insert the values of the resistor and the capacitor. For this example, insert a resistor value of 10,000 ohms and a capacitor value of .033 microfarads into the equation (Fc = 1 / 2 * 3.14 * 10000 * .000000033).

4. 4

Solve the equation for Fc (Fc = 1 / .0020724, Fc = 482.5 Hz). For an RC low-pass filter, the Passband is anything below and including 482.5 Hz and for an RC high-pass filter, the Passband is anything above and including 482.5 Hz.

5. 5

Using the RL equation for critical frequency (Fc = R / 2piL), insert the values of the resistor and the inductor. For this example, insert a resistor value of 10,000 ohms and an inductor value of 100 millihenries into the equation (Fc = 10000 / 2 * 3.14 * .100).

6. 6

Solve for Fc (Fc = 10000 / .628, Fc = 15,924 Hz). For an RL low-pass filter, the Passband is anything below and including 15,924 Hz and for an RL high-pass, the Passband is anything above and including 15,924 Hz.

#### Tips and warnings

• 1. The resistor will have its value listed in ohms (Ω) or kilohms (K, kΩ), the capacitor will have its value listed in farads (F), millifarads (mf) or microfarads (uF) and the inductor's value will be listed in henries (H), millihenries (mH) or microhenries (uh).
• 2. Actual Passband and Stopband (range of attenuated frequencies) values will be decimals of frequencies. For example, a Passband of one Hz to 500 Hz will actually begin at a value such as .00001 Hz. In the same example, the Stopband will begin at a value such as 500.00001 Hz.
• 3. There is some attenuation at the Critical Frequency (Fc) point. It is the point where attenuation reaches -3dB (decibels, a logarithmic measure of audio volume). It is also called the "70.7%" or ".707" point. After that, the true attenuation of undesired frequencies begins.
• Pay close attention to the component values and where the decimal point lies. Refer to an explanation of metric abbreviations for accuracy, such as the U.S. Metric Association's "Commonly Used Metric system Units, Symbols, and Prefixes."

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