运算放大器基础：分贝测量与频域分析

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"了解分贝测量方案和频域分析是研究运算放大器的前提" 运算放大器（Op Amp）是线性集成电路（Linear Integrated Circuits）中的一个重要组成部分，它们在电子工程中扮演着至关重要的角色。在深入研究运算放大器之前，我们需要掌握一些基本的理论和分析工具，例如分贝测量方案和频域分析。这些概念不仅对于理解运算放大器的工作原理，而且对于提升电路设计和分析的效率都至关重要。分贝测量方案是一种在通信工程中广泛应用的表示信号强度的方法。相对于传统的测量单位，分贝具有对数尺度的特点，能够更有效地处理广泛的动态范围。通过学习如何将不同形式的值（如功率、电压或电流）转换为分贝，我们可以更直观地比较和分析电路性能。在本章节中，我们会探讨分贝测量的优势，并学习如何进行这种转换。频域分析则是电路分析的重要组成部分，特别是当涉及到频率响应时。电路的频率响应描述了其对不同频率输入信号的增益和相位行为。我们将会学习如何手动和使用计算机软件进行频域分析，绘制出增益和相位的波特图。这些技能不仅对运算放大器的应用有帮助，而且对设计和分析离散电路也同样适用。差分放大器是运算放大器的核心结构之一，它使用两个有源器件（通常是晶体管）并接受双输入。这种设计提供了一些独特的特性，如高共模抑制比（CMRR），使得差分放大器成为许多运放电路的首选起点。我们将详细讨论差分放大器的直流和交流操作，理解其在不同工作条件下的行为。本书《Operational Amplifiers & Linear Integrated Circuits: Theory and Application》由James M. Fiore撰写，版本3.1.0，旨在提供关于运算放大器及其应用的全面理论和实践知识。作者鼓励读者投资时间学习这些基础，因为它们对于成为一个熟练的电路设计师至关重要。此外，书中的内容也强调了实际应用，使用了简单离散电路作为示例，以便于理解和学习。掌握分贝测量和频域分析对于理解和设计包含运算放大器的电路至关重要。这些基础知识将为您的电路设计职业生涯打下坚实的基础，并使您能够更高效地解决复杂的电子问题。

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Variable Naming Convention

One item that often confuses students of almost any subject is nomenclature. It is

important, then, that we decide upon a consistent naming convention at the outset.

Throughout this text, we will be examining numerous circuits containing several

passive and active components. We will be interested in a variety of parameters and

signals. Although we will utilize the standard conventions, such as f

for critical

frequency and X

for capacitive reactance, a great number of other possibilities exist.

In order to keep confusion to a minimum, we will use the following conventions in

our equations for naming devices and signals that haven’t been standardized.

R Resistor (DC, or actual circuit component)

r Resistor (AC equivalent, where phase is 0 or ignored)

C Capacitor

L Inductor

Q Transistor (Bipolar or FET)

D Diode

V Voltage (DC)

v Voltage (AC)

I Current (DC)

i Current (AC)

Resistors, capacitors and inductors are differentiated via a subscript that usually

refers to the active device it is connected to. For example, R

is a DC bias resistor

connected to the emitter of a transistor, while r

refers to the AC equivalent

resistance seen at a transistor’s collector. C

refers to a capacitor connected to a

transistor’s emitter lead (most likely a bypass or coupling capacitor). Note that the

device related subscripts are always shown in upper case, with one exception: If the

resistance or capacitance is part of the device model, the subscript will be shown in

lower case to distinguish it from the external circuit components. For example, the

AC dynamic resistance of a diode would be called r

. If no active devices are

present, or if several items exist in the circuit, a simple numbering scheme is used,

such as R

. In very complex circuits, a specific name will be given to particularly

important components, as in R

source

Voltages are normally given a two-letter subscript indicating the nodes at which it is

measured. V

is the DC potential from the collector to the emitter of a transistor,

while v

indicates the AC signal appearing across a transistor’s base-emitter

junction. A single-letter subscript, as in V

, indicates a potential relative to ground

(in this case, base to ground potential). The exceptions to this rule are power

supplies, that are given a double letter subscript indicating the connection point (V

is the collector power supply), and particularly important potentials that are directly

named, as in v

(AC input voltage) and V

(DC voltage appearing across R

). If an

equation for a specific potential is valid for both the AC and DC equivalent circuits,

the uppercase form is preferred (this makes things much more consistent with the

vast majority of op amp circuits that are directly coupled, and thus can amplify both

AC and DC signals). Currents are named in a similar way, but generally use a single

subscript referring to the measurement node (I

is the DC collector current). All

other items are directly named. By using this scheme, you will always be able to

determine whether the item expressed in an equation is a DC or AC equivalent, its

approximate circuit location, and other factors about it.

1.2 The Decibel

Most people are familiar with the term “decibel” in reference to sound pressure. It’s

not uncommon to hear someone say something such as “It was 110 decibels at the

concert last night, and my ears are still ringing.” This popular use is somewhat

inaccurate, but does show that decibels indicate some sort of quantity - in this case,

sound pressure level.

Decibel Representation of Power and Voltage Gains

In its simplest form, the decibel is used to measure some sort of gain, such as power

or voltage gain. Unlike the ordinary gain measurements that you may be familiar

with, the decibel form is logarithmic. Because of this, it can be very useful for

showing ratios of change, as well as absolute change. The base unit is the Bel. To

convert an ordinary gain to its Bel counterpart, just take the common log (base 10)

of the gain. In equation form:

Bel gain=log

(ordinary gain)

Note that on most hand calculators common log is denoted as “log” while the natural

log is given as “ln”. Unfortunately, some programming languages use “log” to

indicate natural log and “log10” for common log. More than one student has been

bitten by this bug, so be forewarned! As an example, if a circuit produces an output

power of 200 milliwatts for an input of 10 milliwatts, we would normally say that it

has a power gain of:

out

i n

200mW

10 mW

G=20

For the Bel version, just take the log of this result.

G '=log

G '=1.301

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