# 增益带宽积

## 概述

### 示例

$A_1(\omega)$ 为一阶传递函数，由下式给出：

$A_1(\omega)= \frac{{{H_0}}}{{\sqrt {1 + {{\left( {\frac{\omega }{{{\omega_c}}}} \right)}^2}} }}$

$GBWP_{\omega > > {\omega_c}} = {A_1}(\omega )\cdot\omega \approx const.$

$GBWP = {A_1}(\omega )\cdot\omega = \frac{{{H_0}}}{{\sqrt {1 + {{\left( {\frac{\omega }{{{\omega_c}}}} \right)}^2}} }}\cdot\omega \simeq \frac{{{H_0}}}{{\sqrt {{{\left( {\frac{\omega }{{{\omega_c}}}} \right)}^2}} }}\cdot\omega = {H_0}\cdot{\omega_c} = const.$

$GBWP = \frac{{{H_0}}}{{\sqrt {\frac{{\omega_c^2 + 25{\omega _c}^2}}{{\omega_c^2}}} }}\cdot5{\omega_c} = \frac{5}{{\sqrt {26} }}{H_0}\cdot{\omega_c} = 0.98\cdot{H_0}\cdot{\omega_c}$

## 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>, 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