Gleichspannungswert

Gleichspannungswert is a term used in electrical engineering and signal processing to denote the DC component or average value of a time-varying quantity, such as a voltage or current. It represents the portion of a signal that does not vary with time and is often referred to as the mean value or average level.

Mathematically, for a periodic signal u(t) with period T, the Gleichspannungswert is defined as U_DC = (1/T) ∫0^T u(t) dt. For non-periodic signals with a well-defined long-term average, it can be written as U_DC = lim_{T→∞} (1/T) ∫_{-T/2}^{T/2} u(t) dt, provided the limit exists. In the frequency domain, U_DC corresponds to the zeroth Fourier coefficient (the average over a period).

For discrete-time signals, the Gleichspannungswert is U_DC = (1/N) Σ_{n=0}^{N-1} u[n], given a finite sequence of samples. If the sequence is stationary or periodic, this average approximates the long-term DC level.

Examples illustrate the concept: a pure AC sine wave u(t) = Vm sin(ωt) has U_DC = 0, while a constant DC signal u(t) = U0 has U_DC = U0. For rectified sinusoidal waveforms, the DC values are known: full-wave rectified sin has U_DC = 2Vm/π, and half-wave rectified sin has U_DC = Vm/π.

Applications of the Gleichspannungswert include assessing the usable DC output of power supplies, separating AC and DC components in signals, and characterizing the steady-state level in circuit analysis. It is distinct from peak or instantaneous values and is central to understanding the average behavior of signals.