弱信号测量技术：精密直流电流、电压和电阻测量手册

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“弱信号测量手册”是一本详细探讨低级别直流电流、电压和电阻测量的英文原版PDF书籍，由Keithley出版。该手册旨在提高测量的精度和可靠性，为弱信号测量提供更大的信心。在手册的第一部分，作者介绍了低级别直流测量仪器的基本概念和类型。1.1章节引入了弱信号测量的主题，强调了在微小信号环境下进行精确测量的挑战。1.2章节讨论了理论测量限制，解释了在测量极低电平信号时可能遇到的技术边界。接着，1.3章节详细定义了不同类型的测量仪器： 1.3.1 电表（Electrometer）：一种极其灵敏的仪器，用于测量极低电流和电压。 1.3.2 数字多用表（DMM）：多功能工具，能够测量电压、电流、电阻等多种参数，但其精度和灵敏度可能不适用于弱信号。 1.3.3 纳伏表（Nanovoltmeter）：专为测量纳伏级电压而设计。 1.3.4 皮安表（Picoammeter）：用于测量皮安级别的电流。 1.3.5 源测量单元（Source-Measure Unit）：可以同时源出和测量电压和电流，适合复杂的测试场景。 1.3.6 源表（SourceMeter® Instrument）：结合了电源和多用表功能，特别适合半导体器件的特性测试。 1.3.7 低电流前置放大器（Low Current Preamp）：增加微弱电流信号的放大，以提高测量精度。 1.3.8 微欧表（Micro-ohmmeter）：专门用于测量极低电阻。 1.4章节深入解析了仪器规格的重要性和理解方法，包括精度术语的定义、精度、降额（Deratings）、噪声与噪声抑制以及速度等关键性能指标。1.4.1至1.4.5分别详细阐述了这些概念，强调了它们在实际测量中的影响。 1.5章节涵盖了电路设计的基础知识，包括1.5.1的伏特计电路，1.5.2的安培计电路，1.5.3的库仑计电路（用于测量电荷），以及1.5.4的高阻抗欧姆表电路。这部分内容旨在帮助读者了解如何构建和优化测量电路，以减小误差并提高测量结果的准确性。这本书是工程师、科学家和技术人员的宝贵参考资料，他们需要在实验室或现场进行微弱信号的测量工作。通过深入理解这些基本概念和技术，读者可以更好地选择和使用适当的测量工具，确保数据的可靠性和精确性。

1.4 Understanding Instrument Specifications

Knowing how to interpret instrument specifications properly is an impor-

tant aspect of making good low level measurements. Although instrument

accuracy is probably the most important of these specifications, there are

several other factors to consider when reviewing specifications, including

noise, deratings, and speed.

1.4.1 Definition of Accuracy Terms

This section defines a number of terms related to instrument accuracy.

Some of these terms are further discussed in subsequent paragraphs. Table

1-1 summarizes conversion factors for various specifications associated with

instruments.

SENSITIVITY - the smallest change in the signal that can be detected.

RESOLUTION - the smallest portion of the signal that can be observed.

REPEATABILITY - the closeness of agreement between successive measure-

ments carried out under the same conditions.

REPRODUCIBILITY - the closeness of agreement between measurements of

the same quantity carried out with a stated change in conditions.

ABSOLUTE ACCURACY - the closeness of agreement between the result of a

measurement and its true value or accepted standard value. Accuracy

is often separated into gain and offset terms.

RELATIVE ACCURACY - the extent to which a measurement accurately

reflects the relationship between an unknown and a reference value.

ERROR - the deviation (difference or ratio) of a measurement from its true

value. Note that true values are by their nature indeterminate.

RANDOM ERROR - the mean of a large number of measurements influenced

by random error matches the true value.

SYSTEMATIC ERROR - the mean of a large number of measurements influ-

enced by systematic error deviates from the true value.

UNCERTAINTY - an estimate of the possible error in a measurement, i.e., the

estimated possible deviation from its actual value. This is the opposite

of accuracy.

“Precision” is a more qualitative term than many of those defined here.

It refers to the freedom from uncertainty in the measurement. It’s often

applied in the context of repeatability or reproducibility, but it shouldn’t be

used in place of “accuracy.”

1.4.2 Accuracy

One of the most important considerations in any measurement situation is

reading accuracy. For any given test setup, a number of factors can affect

accuracy. The most important factor is the accuracy of the instrument itself,

which may be specified in several ways, including a percentage of full scale,

1-10

SECTION 1

Section 1 8/6/04 4:31 PM Page 1-10

a percentage of reading, or a combination of both. Instrument accuracy

aspects are covered in the following paragraphs.

Other factors such as input loading, leakage resistance and current,

shielding, and guarding may also have a serious impact on overall accuracy.

These important measurement considerations are discussed in detail in

Sections 2 and 3.

Measurement Instrument Specifications

Instrument accuracy is usually specified as a percent of reading, plus a per-

centage of range (or a number of counts of the least significant digit). For

example, a typical DMM accuracy specification may be stated as: ±(0.005%

of reading + 0.002% of range). Note that the percent of reading is most sig-

nificant when the reading is close to full scale, while the percent of range is

most significant when the reading is a small fraction of full scale.

Accuracy may also be specified in ppm (parts per million). Typically, this

accuracy specification is given as ±(ppm of reading + ppm of range). For

example, the DCV accuracy of a higher resolution DMM might be specified

as ±(25ppm of reading + 5ppm of range).

Resolution

The resolution of a digital instrument is determined by the number of

counts that can be displayed, which depends on the number of digits. A typ-

ical digital electrometer might have 5

⁄2 digits, meaning five whole digits

(each with possible values between 0 and 9) plus a leading half digit that

can take on the values 0 or ±1. Thus, a 5

⁄2-digit display can show 0 to

199,999, a total of 200,000 counts. The resolution of the display is the ratio

of the smallest count to the maximum count (1/200,000 or 0.0005% for a

⁄2-digit display).

Low Level DC Measuring Instruments 1-11

Percent PPM Digits Bits dB

Portion

of 10V

Number of time

constants to settle

to rated accuracy

10% 100000 1 3.3 –20 1V 2.3

1% 10000 2 6.6 –40 100mV 4.6

0.1% 1000 3 10 –60 10mV 6.9

0.01% 100 4 13.3 –80 1mV 9.2

0.001% 10 5 16.6 –100 100 µV 11.5

0.0001% 1 6 19.9 –120 10 µV 13.8

0.00001% 0.1 7 23.3 –140 1µV 16.1

0.000001% 0.01 8 26.6 –160 100 nV 18.4

0.000001% 0.001 9 29.9 –180 10 nV 20.7

TABLE 1-1: Specification Conversion Factors

Section 1 8/6/04 4:31 PM Page 1-11

Transfer Stability

A special case of relative accuracy is the transfer stability, which defines

instrument accuracy relative to a secondary reference standard over a very

short time span and narrow ambient temperature range (typically within

five minutes and ±1°C). The transfer stability specification is useful in situ-

ations where highly accurate measurements must be made in reference to a

known secondary standard.

Calculating Error Terms from Accuracy Specifications

To illustrate how to calculate measurement errors from instrument specifi-

cations, assume the following measurement parameters:

Accuracy: ±(25ppm of reading + 5ppm of range)

Range: 2V

Input signal: 1.5V

The error is calculated as:

Error = 1.5(25 × 10

–6

) + 2(5 × 10

–6

)

= (37.5 × 10

–6

) + (10 × 10

–6

)

= 47.5 × 10

–6

Thus, the reading could fall anywhere within the range of 1.5V ±

47.5µV, an error of ±0.003%.

1.4.3 Deratings

Accuracy specifications are subject to deratings for temperature and time

drift, as discussed in the following paragraphs.

Temperature Coefficient

The temperature of the operating environment can affect accuracy. For this

reason, instrument specifications are usually given over a defined tempera-

ture range. Keithley accuracy specifications on newer electrometers, nano-

voltmeters, DMMs, and SMUs are usually given over the range of 18°C to

28°C. For temperatures outside of this range, a temperature coefficient such

as ±(0.005 % + 0.1 count)/°C or ±(5ppm of reading + 1ppm of range)/°C

is specified. As with the accuracy specification, this value is given as a per-

centage of reading plus a number of counts of the least significant digit (or

as a ppm of reading plus ppm of range) for digital instruments. If the instru-

ment is operated outside the 18°C to 28°C temperature range, this figure

must be taken into account, and errors can be calculated in the manner

described previously for every degree less than 18°C or greater than 28°C.

Time Drift

Most electronic instruments, including electrometers, picoammeters, nano-

voltmeters, DMMs, SMUs, and SourceMeter instruments, are subject to

changes in accuracy and other parameters over a long period of time,

whether or not the equipment is operating. Because of these changes,

instrument specifications usually include a time period beyond which the

Low Level DC Measuring Instruments 1-13

Section 1 8/6/04 4:31 PM Page 1-13

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