# 增益带宽积

## 概述

### 示例

${\displaystyle A_{1}(\omega )}$为一阶传递函数，由下式给出：

${\displaystyle A_{1}(\omega )={\frac {H_{0}}{\sqrt {1+{{\left({\frac {\omega }{\omega _{c}}}\right)}^{2}}}}}}$

${\displaystyle GBWP_{\omega >>{\omega _{c}}}={A_{1}}(\omega )\cdot \omega \approx const.}$

${\displaystyle GBWP={A_{1}}(\omega )\cdot \omega ={\frac {H_{0}}{\sqrt {1+{{\left({\frac {\omega }{\omega _{c}}}\right)}^{2}}}}}\cdot \omega \simeq {\frac {H_{0}}{\sqrt {{\left({\frac {\omega }{\omega _{c}}}\right)}^{2}}}}\cdot \omega ={H_{0}}\cdot {\omega _{c}}=const.}$

${\displaystyle GBWP={\frac {H_{0}}{\sqrt {\frac {\omega _{c}^{2}+25{\omega _{c}}^{2}}{\omega _{c}^{2}}}}}\cdot 5{\omega _{c}}={\frac {5}{\sqrt {26}}}{H_{0}}\cdot {\omega _{c}}=0.98\cdot {H_{0}}\cdot {\omega _{c}}}$

## 参考文献

1. ^ U. A. Bakshi and A. P. Godse. Analog And Digital Electronics. Technical Publications. 2009: 2–5. ISBN 978-81-8431-708-4.
2. ^ Srinivasan, S. "A universal compensation scheme for active filters." International Journal of Electronics 42.2（Feb. 1977）: 141. Science & Technology Collection. EBSCO. Dallas Public Library <http://www.dplibrary.org 互联网档案馆存檔，存档日期2011-06-30.>, Dallas, TX, USA. retrieved 31 July 2009 from <http://search.ebscohost.com/login.aspx?direct=true&db=syh&AN=5259750&site=ehost-live>.
3. ^ Stanley William Amos and Mike James. Principles of transistor circuits: introduction to the design of amplifiers, receivers, and digital 9th. Newnes. 2000: 169. ISBN 978-0-7506-4427-3.
4. ^ M K Achuthan and K N Bhat. Fundamentals of semiconductor devices. Tata McGraw-Hill Education. 2007: 408. ISBN 978-0-07-061220-4.
5. ^ Martin Hartley Jones A practical introduction to electronic circuits, Cambridge University Press, 1995 ISBN 0-521-47879-0 page 148