zoukankan      html  css  js  c++  java
  • The Non-Inverting Amplifier Output Resistance by Adrian S. Nastase [转载]

    Source Address: http://masteringelectronicsdesign.com/the-non-inverting-amplifier-output-resistance/

    It is customary to consider the output resistance of the non-inverting amplifier as being zero, but why is that? An Op Amp’s own output resistance is in the range of tens of ohms. Still, when we connect the Op Amp in a feedback configuration, the output resistance decreases dramatically. Why?

    To answer these questions, let’s calculate the output resistance of the non-inverting amplifier.

    It is widely accepted that the output resistance of a device can be calculated using a theoretical test voltage source connected at the device output. The input, or inputs, are connected to ground. Nevertheless, instead of using this method, let’s try a different one: The small signal variation method.

    Figure 1 shows the non-inverting amplifier, which drives a load, RL. This circuit has an equivalent Thevenin source as in Figure 2.

    non_inverting_amplifier

    Figure 1

    The Non-Inverting Amplifier Output Resistance

    by Adrian S. Nastase 

    thevenin_source

    Figure 2

    From Figure 2, one can see that the output voltage, Vout, can be written as

    image003 (1)

    If we keep VTH constant and apply small variations to Vout, by varying RL for example, the Vout variation, noted ΔVout can be written as follows:

    image004 (2)

    Equation (2) shows that, when the load current increases, the load voltage decreases due to the output resistance. They vary in opposite direction and that is why the negative sign that appears in the Rout calculations is canceled out.

    Equation (2) also tells us that we can use a small signal variation method to determine Rout. If, instead of ΔVout and ΔIout we write the small signal notation vout and iout, the output resistance becomes

    image005 (3)

    Let’s apply this method to the non-inverting amplifier.

    non_inverting_amplifier

    Figure 3

    An ideal Op Amp can be represented as a dependent source as in Figure 3. The output of the source has a resistor in series, Ro, which is the Op Amp’s own output resistance. The dependent source is Ao vd, where Ao is the Op Amp open-loop gain and vd is the differential input voltage. The input differential resistance, between the Op Amp inputs, is considered high, so I removed it for simplicity. The same with the common mode input resistances, between the non-inverting input and ground and the inverting input and ground. The non-inverting input is connected to ground, because a fixed value voltage source does not bring any change from a small-signal variation point of view. Thus, we are in line with the general rule that the output resistance of a circuit is calculated with the circuit inputs connected to ground.

    Inspecting the loop made by Ao vd, Ro, and RL, vout can be expressed as in the following equation.

    image002 (4)

    where iout is the small variation load current and if is the small variation feedback current.

    The differential voltage vd appears across R1, but with negative sign, so if is

    image008 (5)

    And vout becomes

    image009 (6)

    At the same time vd depends on vout.

    image010 (7)

    After replacing vd in equation (6), the resulting mathematical expression depends on vout and iout as in equation (8).

    image011 (8)

    Based on (3) and (8) Rout is

    iinverting_amplifier_output_resistance1 (9)

    Ao is large, about 100000 or 100 dB. Therefore, the second term of the denominator is predominant.

    inverting_amplifier_output_resistance2 (10)

    This proves that the output resistance of the non-inverting amplifier is

    inverting_amplifier_output_resistance3 (11)

    where ACL=1+R2/R1 and it is the closed-loop gain of the non-inverting amplifier. For a proof of the closed loop gain read this article,MasteringElectronicsDesign.com:How to Derive the Non-Inverting Amplifier Transfer Function.

    As equation (11) shows, the output resistance of the non-inverting amplifier is several orders of magnitude smaller than that of the Op Amp, because Ro is divided by the operational amplifier open loop gain. Therefore, the non-inverting amplifier output resistance can be considered zero.

  • 相关阅读:
    .NET对象克隆的深究(转)
    25条哈佛成功金言 (转)
    __doPostBack()方法研究
    一个好的人事博客
    (转)IIS的inetinfo.exe进程占用CPU达100%解决办法
    .net开发随笔
    visual studio.net已检测到web服务器运行的不是asp.net1.1版"故障的排除
    Infragistics NetAdvantage控件的使用:该关系不是此 DataView 指向的表的父关系
    新的一年开始了
    六种方法,做一名更好的开发者
  • 原文地址:https://www.cnblogs.com/blue-box/p/5713386.html
Copyright © 2011-2022 走看看