微电阻四线量测法

除了在第3.2节介绍的所有低电压测量中要考虑的问题之外，在低电阻的测量中更容易引进附加的误差源，其中包括引线电阻、非欧姆接触以及器件的加热问题。这一节将要介绍这些误差源以及将其消除或者降至最小的各种方法。此外还要介绍其它一些测量中要考虑的因素，包括干电路测试和电感性器件的测试等。

3.3.1Lead Resistance and Four-Wire Method引线电阻和四线方法

Resistance measurements are often made using the two-wire method shown in Figure 3-14. The test current is forced through the test leads and the resistance (R) being measured. The meter then measures the voltage across the resistance through the same set of test leads and computes the resistance value accordingly.

电阻的测量常常使用图3-14所示的两线方法来进行。我们迫使测试电流流过测试引线和被测电阻（R）。然后仪表通过同一套测试引线来测量电阻两端的电压，并计算出相应的电阻数值。

The main problem with the two-wire method as applied to low resis tance measurements is that the total lead resistance (R LEAD) is added to the measurement. Since the test current (I) causes a small but significant volt age drop across the lead resistances, the voltage (V M) measured by the meter won’t be exactly the same as the voltage (VR) directly across the test

resistance (R), and considerable error can result. Typical lead resistances lie in the range of 1m. to 10mΩ, so it’s very difficult to obtain accurate two- wire resistance measurements when the resistance under test is lower than 10. to 100. (depending on lead resistance).

两线测量方法用于低阻测试时的主要问题是测量结果中增加了引线的总电阻（R LEAD）。由于测试电流（I）在引线电阻上产生了一个小的、但是很重要的电压降，所以仪表测量的电压（V M）就不会和被测电阻（R）上的电压完全相同，于是产生了相当的误差。典型的引线电阻在1mΩ 到10mΩ的范围内，所以当被测电阻小于10Ω到100Ω时，就很难用两线测量方法来获得准确的测量结果（取决于引线电阻的数值）。

Due to the limitations of the two-wire method, the four-wire (Kelvin) connection method shown in Figure 3-15 is generally preferred for low resistance measurements. These measurements can be made using a DMM, micro-ohmmeter, or a separate current source and voltmeter. With this

configuration, the test current (I) is forced through the test resistance (R) through one set of test leads, while the voltage (V M) across the DUT is measured through a second set of leads called sense leads. Although some small current may flow through the sense leads, it is usually negligible and can generally be ignored for all practical purposes. The voltage drop across the sense leads is negligible, so the voltage measured by the meter (VM) is essentially the same as the voltage (V R) across the resistance (R). Consequently, the resistance value can be determined much more accurately than with the two-wire method. Note that the voltage-sensing leads should be connected as close to the resistor under test as possible to avoid including the resistance of the test leads in the measurement.

由于两线方法的局限性，所以对低阻测量来说，人们一般都喜欢采用如图3-15所示的四线连接方法（开尔文法）。这种测量工作可以使用数字多用表、微欧姆计或者分离的电流源和电压表来进行。在这种配置下，迫使测试电流（I）经过一套测试引线流过被测电阻（R）；而被测电阻上的电压（V M）则是通过称为取样（Sense）引线的第二套引线来测量的。虽然在取样引线中有小的电流流过，但是这些电流在所有实际测量工作中都是可以忽略的。由于取样引线上的电压降是可以忽略的，所以仪表测量出的电压（V M）和电阻（R）上的电压实际上是相同的。这样，就能以比两线方法高得多的准确度来确定电阻的数值。注意，应当把电压取样引线连到尽可能接近被测电阻的地方，以避免在测量中计入测试引线的电阻。

3.3.2 Thermoelectric EMFs and Offset Compensation Methods热电动势和偏置补偿的方法

Thermoelectric voltages, as described in Section 3.2.1, can seriously affect low resistance measurement accuracy. The current-reversal method, the delta method, and the offset-compensated ohms method are three common ways to overcome these unwanted offsets.

如第3.2.1节所述，热电动势电压能够严重地影响低电阻测量的准确度。电流反向法、Delta（德尔塔）法和偏置补偿欧姆法是消除这些不希望的偏置量的三种最常用的方法。

Current-Reversal Method 电流反向法

Thermoelectric EMFs can be canceled by making two measurements with currents of opposite polarity, as shown in Figure 3-16. In this diagram, a voltmeter with a separate bipolar current source is used. With the positive current applied as in Figure 3-16a, the measured voltage is:

使用极性相反的电流进行两次测量能够抵消热电动势，如图3-16 所示。在该图中，使用了一个电压表和一个分离的双极性电流源。如图3-16a 所示加入正极性电流时，测得的电压为：

V M+ = V EMF + I R

Reversing the current polarity as shown in Figure 3-16b yields the following voltage measurement:

如图3-16b所示，将电流的极性反向，则测量出的电压如下：

V M- = V EMF - I R

The two measurements can be combined to cancel thermoelectric EMFs:

将两次测量结合起来就能够抵消热电动势：

The measured resistance is computed in the usual manner: 用通常的方法计算出被测电阻：

Note that the thermoelectric voltage (V EMF) is completely canceled out by this method of resistance calculation.

注意，用这种方法计算电阻时，完全抵消了热电动势电压（V EMF）。

For the current-reversal method to be effective, it’s important to use a low noise voltmeter with a response speed that is fast compared with the thermal time constant of the circuit under test. If the response speed is too slow, any changes in the circuit temperature during the measurement cycle will caus e changes in the thermoelectric EMFs that won’t be completely canceled, and some error will result.

为了使这种电流反向法有效，很重要一点是要使用响应速度比被测电路的热时间常数更快的低噪声电压表。如果电压表的响应速度太慢的话，那么测量期间被测电路温度的变化将会引起热电动势发生变化。这样就不能完全抵消热电动势，从而产生某些误差。

Delta Method Delta法

When the thermoelectric voltages are constant with respect to the measurement cycle, the current-reversal method will successfully compensate for these offsets. However, if changing thermoelectric voltages are causing inaccurate results, then the delta method should be used. The delta method is similar to the current-reversal method in terms

of alternating the current source polarity, but it differs in that it uses three voltage measurements to make each resistance calculation. This method can best be explained through an illustration and mathematical computations.

当热电动势电压在测量期间为常数时，电流反向法能够成功地补偿这种热电动势引起的偏置。然而，当变化的热电动势电压引起不准确的测量结果时，就应当使用Delta法。在变换电流源的极性方面，Delta 法类似于电流反向法；而其区别是这种方法使用三次电压测量来完成每个电阻的计算。用一个图和数学计算可以很好地解释这种方法。

Figure 3-17 shows the voltage drop of a DUT as a function of time with an alternating polarity current applied. A voltage measurement (V M1、V M2、V M3 , etc.) is taken each time the polarity is changed. Each voltage measurement includes a constant thermal voltage offset (V EMF) and a

lin early changing voltage offset (δV). The thermal voltage drift may be approximated as a linear function over short periods, so the rate of change of voltage as a function of time (δV) can also be treated as a constant. The first three voltage measurements include the following voltages: 图3-17 表明在加入极性交替的电流时，被测元件（DUT）上的电压降与时间的函数关系。在每次电流的极性改变时，都进行一次电压测量（V M1、V M2、V M3等）。每次的电压测的结果都包括热电压偏置（V EMF）和线性变化的电压偏置（δV）。在短时间内，可以近似地将热电压漂移看作线性函数，所以，电压对时间的函数的变化率（δV）也可以作为常数来处理。前三次电压测量得到下列的电压：

Delta法

V M1 = V1 + V EMF

V M2 = V2 + V EMF+ δV V M3 = V3 + V EMF+ 2δV

where: V M1、V M2、V M3 are voltage measurements

其中：V M1、V M2、V M3为电压测量结果。

V M1 is presumed to be taken at time = 0

假定V M1为在时间= 0 时测量的电压。

V1、V2、and V3are the voltage drop of the DUT due to the applied current V1、V2、V3为所加电流在被测元件上的电压降。

V EMF is the constant thermoelectric voltage offset at the time the

V M1 measurement is taken

V EMF为在进行V M1 测量时的恒定的热电动势电压偏置量。

V is the thermoelectric voltage change

V为热电动势的变化量。

Cancellation of both the thermoelectric voltage offset (V EMF) term and the ther moelectric voltage change (δV) term is possible through mathematical computation using three voltage measurements. First, take one-half the difference of the first two voltage measurements and call this term V A:

使用三次测量，通过数学计算就可能消去热电动势电压偏置项（V EMF ）和热电动势电压变化项（δV）。首先，求出前两次电压测量值之差的一半，并将其称为V A：

Then, take one-half the difference of the second (V M2) and third (V M3) voltage measurements and call this term V B:

然后，求出第二次（V M2）和第三次（V M3）电压测量值之差的一半，并将此项称为V B ：

Both V A and V B are affected by the drift in the thermoelectric EMF, but the effect on V A and V B is equal and opposite. The final voltage reading is the average of V A and V B and is calculated as:

V A 和V B都受到热电动势漂移的影响，但是其对于V A和V B的影响是相等、相反的。最后的电压读数是V A和V B的平均值，并计算如下：

Notice that both the VEMF and δV terms are canceled out of the final voltage calculation.

注意，在最后的电压计算结果中，VEMF 和δV这两项都被抵消了。

In the delta method, each data point is the moving average of three voltage readings. This additional averaging of the voltage measurements means that the data resulting from the delta method has lower noise than the data derived when the current-reversal method is used to calculate it, even when both sets of data are taken over the same time period.

在Delta法中，每个数据点都是三个电压读数的移动平均值。这种对电压测量值求平均的算法意味着采用Delta法所得到的测量结果比使用电流反向法测量出的结果具有更低的噪声，即使两种方法的数据是在相同的时间内进行的也是这样。

The success of the delta method depends on the linear approximation of the thermal drift, which must be viewed over a short period. Compensating successfully for changing thermoelectric voltages dictates that the measurement cycle time must be faster than the thermal time constant of the DUT. Therefore, an appropriately fast current source and voltmeter must be used for the delta method to be successful. Refer to Section 4.7.2 for information on specific test equipment.

Delta法的成功与否决定于热漂移的线性近似情况，所以必须在较短的时间期间内进行。要想成功地补偿变化的热电动势电压，测量的周期必须比被测设备的热时间常数要小。所以要使Delta法成功，必须使用比较快的电流源和电压表。有关特定测试设备的信息请参见第4.7.2节。

Offset-Compensated Ohms Method 偏置补偿欧姆法

Another offset-canceling method used by micro-ohmmeters and many DMMs is the offset-compensated ohms method. This method is similar to the current-reversal method except that the measurements are alternated between a fixed source current and zero current.

微欧姆计和很多数字多用表使用的另一种消除偏置的方法是偏置补偿欧姆法。这种方法和电流反向法类似，只是这种方法在固定的源电流和零电流之间交替进行测量。

As shown in Figure 3-18a, the source current is applied to the resistance being measured during only part of the cycle. When the source current is on, the total voltage measured by the instrument (Figure 3-18b) includes the voltage drop across the resistor as well as any thermoelectric EMFs, and it is defined as:

如图3-18a所示，只在测量周期的一部分时间里将源电流加到被测电阻上。当源电流接通时，仪器测量出的总电压包括电阻器上的电压降和热电动势（图3-18b），并可以表示为：

During the second half of the measurement cycle, the source current is turned off and the only voltage measured by the meter (Figure 3-18c) is any thermoelectric EMF present in the circuit:

在测量周期的后一半时间内，将源电流关闭。这时仪表测量出的总电压就只是电路中出现的热电动势（图3-18c）：

Given that VEMF is accurately measured during the second half of the cycle, it can be subtracted from the voltage measurement made during the first half of the cycle, so the offset-compensated voltage measurement becomes:

若在测量周期的后一半时间内，我们将V EMF准确地测出。就可以从测量周期前一半所测量出的电压中将其减去。这样偏置补偿电压测量结果就成为：

V M = V M1 - V M2

V M = (V EMF+I R) - V EMF

V M = I R

and,

于是，

Again, note that the measurement process cancels the thermoelectric EMF term (V EMF).

同样，我们注意到，该测量过程消除了热电动势项（V EMF）。

3.3.3 Non-Ohmic Contacts 非欧姆接触

Non-ohmic contacts are evident when the potential difference across the contact isn’t linearly proportional to the current flowing through it. Nonohmic contacts may occur in a low voltage circuit as a result of oxide films or other non-linear connections. A non-ohmic connection is likely to rectify any radio frequency energy (RFI) present, causing an offset voltage to appear in the circuit. (A further discussion on RFI can be found in Section 3.2.1.) There are several ways to check for non-ohmic contacts and methods to reduce them.

非欧姆接触出现在接点两端的电位差与流过接点的电流不是线性的比例关系的情况下。非欧姆接触可能发生在由氧化膜形成的低压电路或其它非线性连接中。非欧姆连接能够对出现的任何射频能量（RFI）进行整流，从而使电路中出现偏置电压。（关于射频干扰的更进一步的讨论请见第3.2.1节。）有若干方法可以检查非欧姆接触的存在，还有一些方法可以将其降低。

If using a micro-ohmmeter or DMM to make low resistance measurements, change the range to check for non-ohmic contacts. Changing the measurement range usually changes the test current as well.

A normal condition would indicate the same reading but with higher or lower resolution, depending on whether the instrument was up or down ranged. If the reading is significantly different, this may indicate a

non-ohmic condition.

如果使用微欧姆计或数字多用表来进行低电阻的测量，可以改变测量量程来检查非欧姆接触。改变测量量程通常也就改变了测试电流。在一般情况下，测量的读数是相同的。只是依据仪器量程的升降，读数的分辨率变低或变高。如果测量的读数有很大的差别，那么就表示可能存在着非欧姆接触。

If using a separate current source and voltmeter to make low resistance measurements, each instrument must be checked for non-ohmic contacts. If the current source contacts are non-ohmic, there may be a significant difference in the compliance voltage when the source polarity is reversed. If the voltmeter contacts are non-ohmic, they may rectify any AC pickup present and cause a DC offset error. If this is the case, the offset compensated ohms method is preferred to the current-reversal method for canceling offsets.

如果使用分离的电流源和电压表来进行低电阻测量，则必须检查每台仪器的非欧姆接触情况。如果电流源接点有非欧姆接触特性，那么当源的极性反向时，其输入端压降就可能会有很大的不同。如果电压表接点有非欧姆接触特性，那么它就可能对出现的任何交流干扰进行整流并引起直流偏置误差。在这种情况下，最好使用偏置补偿欧姆法而不使用电流反向法来消除偏置。

To prevent non-ohmic contacts, choose an appropriate contact material, such as indium or gold. Make sure the compliance voltage is high enough to avoid problems due to source contact non-linearity. To reduce error due to voltmeter non-ohmic contacts, use shielding and appropriate

grounding to reduce AC pickup.

为了避免非欧姆接触现象，应当选用适当的接点材料，例如铟或者金。要确保输入端钳位电压足够的高，以避免由于源接点的非线性而产生的问题。为了降低电压表的非欧姆接触所产生的误差，采用屏蔽和适当的接地措施来降低交流干扰。

3.3.4 Device Heating 器件的加热

Device heating can be a consideration when making resistance measurements on temperature-sensitive devices such as thermistors. The test currents used for low resistance measurements are often much higher than the currents used for high resistance measurements, so power dissipation in the device can be a consideration if it is high enough to cause the device’s resistance value to change.

在对温度敏感的器件，如热敏电阻，进行温度测量时，要考虑器件的加热问题。进行低电阻测量时所使用的电流常常要比进行高电阻测量时所使用的电流大的多。如果测试电流足够高，而使器件的电阻值发生变化时，就要考虑器件的功率耗散问题。

Recall that the power dissipation in a resistor is given by this formula:

我们知道，电阻器的功率耗散由下式决定：

P = I2 R

From this relationship, we see that the power dissipated in the device increases by a factor of four each time the current doubles. Thus, one way to minimize the effects of device heating is to use the lowest current possible while still maintaining the desired voltage across the device being tested. If the current cannot be reduced, use a narrow current pulse and a fast responding voltmeter.

由此关系式可以看出，当电流增加一倍时，器件的功率耗散会增加到4倍。所以将器件的加热效应降到最低的一种方法是使用尽可能低的电流，而在被测器件上仍然保持希望的电压。如果不能降低电流的话，使用窄的电流脉冲和快速响应的电压表。

Most micro-ohmmeters and DMMs don’t have provisions for setting the test current. It is generally determined by the range. In those cases,

alternate means must be found to minimize device heating. One simple but effective way to do so is to use the instrument’s one-shot trigger mode during measurements. While in this mode, the instrument will apply only a single, brief current pulse to the DUT during the measurement cycle, thereby minimizing errors caused by device heating.

大多数的微欧姆计和数字多用表都不能设置测试电流。测试电流通常由量程决定。在这种情况下，必须找到另一种替代的方法将器件加热效应降到最低。一个简单但是有效的方法是在测量时使用仪器的单脉冲触发功能。在这种模式下，在测量周期中，仪器只向被测器件施加单个的、简短的电流脉冲，这样就将器件加热引起的误差降低到最小。

3.3.5 Dry Circuit Testing 干电路测试

Many low resistance measurements are made on devices such as switches, connectors, and relay contacts. If these devices are to be used under “drycircuit” conditions, that is, with an open-circuit voltage less than 20mV and a short-circuit current less than 100mA, the devices should be tested in a manner that won’t puncture any oxi de film that may have built up on the contacts. If the film is punctured, the measured contact resistance will be lower than if the film remains intact, compromising the validity of the test results.

很多低电阻测量是在诸如开关、连接器和继电器接点等器件上进行的。如果这些器件在“干电路”的条件下使用，也就是说其开路电压小于20mV、短路电流小于100mA时，则应当采用一种不会击穿触点上可能形成的氧化膜的方法来测试这种器件。如果该氧化膜被击穿，则测量出的触点电阻就会比氧化膜保持原状时的电阻要低，从而破坏了测试结果的有效性。

To avoid oxidation puncture, such measurements are usually made using dry circuit testing, which typically limits the voltage across the DUT to 20mV or less. Some micro-ohmmeters and DMMs have this capability built in, as shown in Figure 3-19. In this micro-ohmmeter, a precision shunt resistor (R SH) is connected across the source terminals to clamp or limit the voltage across the DUT to <20mV. The remaining aspects of the circuit are very similar to the conventional four-wire measurement method: V and RREF make up the current source, which forces current through the unknown resistance (R). This current should be no more than 100mA. The value of the unknown resistance is computed from the sense voltage (V M), the voltage across clamping resistor (V SH), the known value of R SH, and the

source current. Refer to Section 1.4.4 for more detailed circuit information.

为了避免击穿氧化层，这种测量通常使用干电路测试法，一般要把被测器件上的电压限制在20mV或者更低。某些微欧姆计和数字多用表具备这种能力，如图3-19所示。在这种微欧姆计中，把一个精密的分流器电阻（R SH）跨接到源的两端，以便将被测器件上的电压钳位或者限制到小于20mV。电路的其它方面和普通的四线测量方法非常类似：V和R REF构成电流源，并强制电流流过未知电阻（R）。该电流应当不大于100mA。未知电阻的数值可以由取样电压（V M）、钳位电阻器上的电压（R SH）、已知电阻值（R SH）和源电流计算出来。有关电路的更详细的信息请参见1.5.4节。

If dry circuit testing is to be done with a separate current source and voltmeter, the compliance voltage on the current source must be limited to 20mV or less. If it isn’t possible to limit the compliance voltage to this level, a compliance limiting resistor must be used, as shown in Figure 3-20. In this circuit, R C is the resistor used to limit the voltage to 20mV and R is the unknown resistance.

如果使用分离的电流源和电压表来进行干电路测试，则必须将电流源上的输入端压降限制在20mV或者更小。如果不能将输入端压降限制到这个电平，则必须使用一个限制负荷电阻器，如图3-20 所示。在这个电路中，R C是用来把电压限制到20mV的电阻器，R是未知电阻。

The value of R C must be chosen to limit the voltage at a given test current. For example, if the voltage limit is 20mV and the test current is 200μA, R C can be calculated as:

必须选择R C的数值，以便在给定的测试电流之下来限制电压。例如，如果电压限制值为20mV，测试电流为200μA ，则可以计算出R C为：

R C= 20mV /200μA = 100Ω

If the unknown resistance (R) is 250mΩ, then RC will cause a 0.25% error in the measured resistance.

如果未知电阻（R）为250mΩ,那么R C将会引起0.25%的被测电阻误差。

The exact value of the unknown resistance (R) can then be calculated by the following equation:

被测电阻的准确值可以由下列公式来计算：

where RMEASURED is the calculated resistance measurement from the measured voltage (V M) and the source current (I).

其中，R MEASURED是从测量的电压（V M）和源电流（I）计算出的电阻测量值。

3.3.6 Testing Inductive Devices 电感性器件的测试

Inductive devices usually have a small resistance in addition to the

inductance. This small resistance is normally measured with a DMM or a micro- ohmmeter. However, the measurements are often difficult because of the interaction between the inductance and the measuring instrument. This is particularly true with high L/R ratios.

电感性器件通常除了其电感之外还有一个很小的电阻。这个小的电阻值通常用数字多用表或者微欧姆计来测量。然而，由于电感和测量仪器的相互作用，这种测量通常比较困难。在L/R的比值比较高的时候，这种情况尤为明显。

Some of the problems that may result include oscillations, negative readings and generally unstable readings. An oscilloscope picture of an unstable measurement of a 200H inductor is shown in Figure 3-21.

这时可能产生的问题包括：振荡、负读数以及通常不稳定读数。测量200H的电感器时不稳定情况的示波器图形如图3-21所示。

When problems occur, try to take measurements on more than one range and check if the values correspond.

当发生上述问题时，尝试在多个量程上进行测量，并检查其读数是否互相对应。

If possible, do not use offset compensation (pulsed current) because inductive reaction to the current pulse may cause unstable measurements or make autoranging difficult. Try using a higher resistance range when possible.

如果可能的话，不要使用偏置补偿（脉冲电流）。因为对脉冲电流的感抗可能会使测量不稳定，或者使自动量程功能难于工作。在可能的时候，尝试使用较高的电阻量程。

Check for oscillations by connecting an oscilloscope in parallel with the device and the meter. Sometimes, a diode across the inductor may settle down the oscillations by reducing the inductive kick.

将示波器并联到器件和电压表上，检查振荡情况。有的时候，在电感器上跨接一个二极管，能够降低感性冲击，从而消除可能的振荡。