Measurement Technology › Offset in Signals

High-Pass Solution

If the sensor signal is an AC signal that changes with time, e.g. sinusoidally, the offset can be removed completely from the signal with a high-pass circuit. You can only understand this subchapter if you have worked through the chapter Filters completely. Thematically, this solution belongs here; you will understand it during exam preparation with the knowledge about filters in mind.

The high-pass solution exploits the fact that an offset that is constant over time has the frequency f = 0 Hz or ω = 2πf = 0 1/s. The transfer function of the high-pass filter is:

\[ \begin{gathered} H_{\mathrm{HP}}(\omega) = \frac{j\frac{\omega}{\omega_g}}{1 + j\frac{\omega}{\omega_g}} \\[6pt] H_{\mathrm{HP}}(\omega = 0) = \frac{j\frac{0}{\omega_g}}{1 + j\frac{0}{\omega_g}} = \frac{0}{1 + j0} = 0 \text{ for } \omega = 0\,\frac{1}{\mathrm{s}} \end{gathered} \]

If a DC signal that is constant over time is connected to the input of a high-pass filter, its amplitude is multiplied by 0. So this signal is no longer present at the output at all. This applies regardless of the choice of cut-off frequency. In this way, any offset signal disappears completely from your system.

However, if the sensor signal is also a DC signal, it is removed completely as well. So the method only works with AC sensor signals.