Gainwert

Gainwert is a term used in electronics and signal processing to denote the amount by which a system increases the amplitude of a signal. In German-language contexts, gainwert is often used interchangeably with Verstärkungswert or Verstärkung to describe the gain of an amplifier, filter, or other transfer element. The gain can be specified for different signal properties: voltage gain, current gain, and power gain.

Mathematically, the voltage gain is Av = Vout / Vin, the current gain is Ai = Iout / Iin, and the power gain is Ap = Pout / Pin. For linear time-invariant systems, the transfer function H(s) describes gain as a function of frequency; at a given frequency the gain is the magnitude |H(jω)|. In practice, gain may depend on frequency, leading to concepts such as bandwidth and gain–bandwidth product (GBW). In many applications, the closed-loop gain is set by a feedback network.

Expressed in decibels, the voltage gain is Gv(dB) = 20 log10(|Av|) and the power gain is Gp(dB) = 10 log10(|Ap|). A negative gain indicates signal inversion (a 180-degree phase shift), while the magnitude reflects attenuation or amplification.

In electronics, gains are often frequency dependent and practical devices have limits due to noise, distortion, and saturation. Common examples include operational amplifiers with gains set by resistor ratios (for example, non-inverting Av = 1 + R2/R1 and inverting Av = −R2/R1). Programmable gain amplifiers (PGA) allow adjustable gain settings for dynamic signal conditioning.