ID 683073
Date 1/28/2022
Public

## 5.1.5.5.2. Determine the Bandwidth

Figure 44 shows that the voltage at any instant t is:

Figure 44. Characteristic Voltage Plot for Charging of an AC Circuit

At 10 percent of the curve, you have:

At 90 percent of the curve, you have:

The 10 percent equation divided by the 90 percent equation gives:

Where:

The time constant variable is related to the 3-dB frequency by the equation:

From the previous equation, we can determine the equation for the time constant, r.

Plug the time constant into the voltage equation to get:

Use the following equation to determine the bandwidth for sinusoidal signal

The highest frequency component for a signal with a rise time of Tr have a frequency given by this equation.

The signal previously discussed had a rise time of 300 ps, which means that the highest frequency component present in the signal be:

Using the equation with the bandwidth and speed numbers, you can determine that:

If the transmission line is longer than wavelength/10, then termination is required. In this design example, the transmission line is two inches long, so termination is required.

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