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A primer on signal bandwidth

Posted: 25 Feb 2016 ?? ?Print Version ?Bookmark and Share

Keywords:signal bandwidth? signal-processing? amplifier? A/D converter? resistor?

You have certainly read about signal bandwidth in various technical literature, but exactly what is it and why does it matter in signal processing projects? All circuits and transmission paths limit the frequency response of any signal. If you don't properly address this limitation, you'll jeopardise the performance of electronic circuits.

The performance of any signal-processing component such as an amplifier, A/D converter, PCB trace, connector, etc. is dependent on the applied signal's frequency. That is to say, its transfer functionthe relationship between its output and its inputvaries with frequency. The equation below formulates the transfer function of a simple RC network in figure 1.

Figure 1: This simple RC low-pass filter circuit lets you see the concept of frequency response.

Clearly, the RC network's transfer function is frequency dependent. Figure 2 shows the frequency-response plot for a 1 k resistor and 10?F capacitor.

Figure 2: The frequency response of a simple low-pass filter, with amplitude dropping as frequency increases.

Notice that as the input frequency increases, the output amplitude decreases. By definition, the frequency at which the output amplitude is about 70% of its nominal level is called the 3-dB bandwidth frequency. Therefore, a signal processor bandwidth represents the frequency range that it can process a signal without a considerable amount of loss. For the RC circuit in figure 1, the 3 dB frequency point about 15.9kHz, marked by the blue circle on the plot.

To test for bandwidth in real life, we need to use a swept signal or white noise as the input signal and look at the output response of the circuit on a spectrum analyser. The reason to use a swept signal or white noise is that they ideally contain infinite frequencies. Therefore, these signals stimulate the circuit for a wide range of frequencies. Figure 3 shows the output response of the RC circuit on a spectrum analyser when a white noise source is connected to its output.

Figure 3: As frequency increases, output amplitude decreases.

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