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Physics · 术语表

什么是 Transfer function？

Definition 9.1 University Physics — Year 1 · 第 9 章 — Filters and Transfer Functions

A linear circuit with an input voltage $\underline U_e$ and an output voltage $\underline U_s$ (taken with nothing connected at the output) has the transfer function

\underline H(j\omega) = \frac{\underline U_s}{\underline U_e}, \qquad G(\omega) = \abs{\underline H}, \qquad \varphi(\omega) = \arg\underline H,

the gain $G$ (ratio of amplitudes) and the phase shift $\varphi$ of the output relative to the input. A filter is such a circuit used for its frequency dependence: a sinusoid of amplitude $E$ at $\omega$ comes out as $G(\omega)E\cos(\omega t + \varphi(\omega))$ .

示例

Example 9.6 (AC coupling)

An oscilloscope’s AC input is a high-pass with $f_c \approx 10\,\mathrm{Hz}$ : a $1\,\mathrm{kHz}$ signal riding on a $5\,\mathrm{V}$ offset comes through at $-0.0002\,\mathrm{dB}$ with its offset removed. But a $50\,\mathrm{Hz}$ square wave is visibly distorted — its flat tops sag — because at $50\,\mathrm{Hz}$ the filter is only one decade above its cutoff and the signal’s low harmonics are shifted in phase (Exercise 9.12).

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