Charlie Hughes查理-休斯
May 11, 20072007 年 5 月 11 日

To determine the input impedance of a device both the voltage across the device and the current flowing into the device must be known. The impedance is simply the voltage across the device, E, divided by the current flowing into it, I. This is given by the following equation
要确定设备的输入阻抗，必须知道设备两端电压和流入设备的电流。阻抗就是器件两端电压 E 除以流入器件的电流 I。

It should be understood that since the voltage, E, and the current, I, are complex quantities the impedance, Z , is also complex. That is to say impedance has a magnitude and an angle associated with it.
要知道，由于电压 E 和电流 I 都是复数，阻抗 Z 也是复数。也就是说，阻抗有一个幅度和一个角度。

When measuring loudspeaker input impedance it is common today for many measurements to be made a relatively low drive levels. This is necessitated because of the method employed in the schematic of Figure 1.
如今，在测量扬声器输入阻抗时，许多测量通常都是在相对较低的驱动电平下进行的。这是因为图 1 原理图中采用了这种方法。
In this setup a relatively high value resistor, say 1 kohm, is used for Rs. As seen from the input of the DUT, it is being driven by a high impedance constant current source.
从 DUT 的输入端可以看到，它正由一个高阻抗恒流源驱动。
Had it been connected directly to the amplifier/measurement system output it would in all likelihood, be driven by a low impedance constant voltage source.
如果它直接连接到放大器/测量系统的输出端，很可能会由一个低阻抗恒压源驱动。
In both of these cases constant refers to there being no change in the driving quantity (either voltage or current) as a function of frequency or load.
在这两种情况下，恒定指的是驱动量（电压或电流）随频率或负载的变化而不变。

When Rs is much larger than the impedance of the DUT, the current in the circuit is determined only by Rs. If the voltage at the output of the amplifier, Vo, is known this current is easily calculated with the following equation and is constant.
如果放大器输出端电压 Vo 已知，则电流很容易通过下式计算出来，并且是恒定的。

(Equation 2)(等式 2）
Now that we know the current flowing in the circuit all we need to do is measure the voltage across the DUT and we can calculate its input impedance.
现在我们知道了电路中的电流，只需测量 DUT 两端的电压，就能计算出其输入阻抗。

There is nothing wrong with this method. It is limited, as previously mentioned however, in that the drive level exciting the DUT will not be very large due to the large value of Rs. For some applications this may be problematic.
这种方法没有任何问题。不过，如前所述，这种方法也有局限性，那就是由于 Rs 值较大，激励 DUT 的驱动电平不会很大。
Loudspeakers are seldom used at the low drive levels to which we are limited using the above method. It may be advantageous to be able to measure the input impedance at drive levels closer to those used in actual operation.
扬声器很少在低驱动电平下使用，而使用上述方法时，我们只能在低驱动电平下使用扬声器。如果能在更接近实际使用的驱动电平下测量输入阻抗，可能会更有优势。

Figure 1 - Schematic of a common method of measuring loudspeaker impedance
图 1 - 测量扬声器阻抗的常用方法示意图

Figure 2 - Schematic of an alternate method of measuring loudspeaker impedance
图 2 - 测量扬声器阻抗的另一种方法示意图

If the current in the circuit can be measured rather than having to be assumed constant this limitation can be avoided. Using a measurement system with at least two inputs, as shown in Figure 2, can do just that. In this case Rs is made relatively small, say 1 ohm or less.
如果电路中的电流可以测量，而不是假定为恒定，就可以避免这种限制。如图 2 所示，使用至少有两个输入端的测量系统就可以做到这一点。在这种情况下，Rs 相对较小，例如 1 欧姆或更小。
This is called a current sensing resistor. It may also be referred to as a current shunt. Technically this is incorrect for this application as a current shunt is always in parallel with a component from which current is diverted.
这就是所谓的电流检测电阻器。也可称为电流分流器。从技术上讲，在此应用中这是不正确的，因为电流分流器总是与电流分流的元件并联。
The voltage drop across Rs is measured by input #2 of the measurement system. The current in the circuit is then calculated using the equation
Rs 上的压降由测量系统的 2 号输入端测量。然后利用公式计算出电路中的电流

Is = Vs / Rs
(Equation 3)(等式 3）
The voltage across the DUT is measured by input #1 of the measurement system. We now know both the voltage across and the current flowing into the DUT so its input impedance can be calculated.
DUT 两端电压由测量系统的 1 号输入端测量。现在我们知道了 DUT 两端的电压和流入 DUT 的电流，因此可以计算出其输入阻抗。

I used EASERA for the measurements in this article. It has facilities for performing all of these calculations as should most dual channel FFT measurement systems.
我在本文中使用 EASERA 进行测量。与大多数双通道 FFT 测量系统一样，它也具有执行所有这些计算的功能。
Referencing Figure 2, channel #1 across the DUT should be set as the measurement channel while channel #2 should be set as the reference channel. Dual channel FFT systems divide the measurement channel by the reference channel so we have
参照图 2，DUT 的 1 号通道应设置为测量通道，而 2 号通道应设置为参考通道。双通道 FFT 系统将测量通道除以参考通道，因此我们可以得出

By substitution from Equation 3
代入公式 3

Since $Z=V_{\text{DUT}}/$$Z=V_{\text{DUT }}/$Z=V_("DUT ")//Z=V_{\text {DUT }} / Is it follows that
因为 $Z=V_{\text{DUT}}/$$Z=V_{\text{DUT }}/$Z=V_("DUT ")//Z=V_{\text {DUT }} / 所以

All we have to do it multiply our dual channel FFT measurement by the value of Rs used and we get the correct value for impedance. If Rs is chosen to be 1.0 ohm this becomes really easy.
我们只需将双通道 FFT 测量值乘以所使用的 Rs 值，就能得到正确的阻抗值。如果将 Rs 选为 1.0 欧姆，这就变得非常容易。

In EASERA there is not an Ohm display selection. Selecting a Volt display will yield the correct values for the displayed curve.
EASERA 中没有欧姆显示选择。选择伏特显示将为所显示的曲线提供正确的数值。
For other measurement systems this may work as well, but it is recommended to check the display by measuring a known resistor value for proper calibration.
对于其他测量系统，这可能也有效，但建议通过测量已知电阻值来检查显示，以进行正确校准。

A very useful device for performing impedance measurements using this current sensing resistor method is the VI Box from LinearX (Photo 1). The signal from the amplifier is routed through the VI Box, which contains the current sensing resistor, and then onto the DUT.
LinearX 的 VI Box（照片 1）是使用这种电流感应电阻器方法进行阻抗测量的一个非常有用的设备。来自放大器的信号通过包含电流检测电阻器的 VI Box，然后到达 DUT。
It actually contains two selectable sensing resistors, 1 ohm and 10 mohm (milliohm), which allow for measurements using a greater range of current supplied to the load (DUT). The voltage across the selected resistor is present across pins 2 and 3 of one of the XL connectors.
实际上，它包含两个可选的传感电阻，分别为 1 欧姆和 10 欧姆（毫欧），可在更大的电流范围内对负载（DUT）进行测量。所选电阻上的电压跨接在其中一个 XL 连接器的针脚 2 和 3 上。
The voltage across the DUT is present across pins 2 and 3 of the other XL connector. These connectors allow for quick and easy interface with balanced inputs of a computer/audio interface (sound card).
DUT 上的电压跨接在另一个 XL 连接器的针脚 2 和 3 上。使用这些连接器可以快速、方便地连接计算机/音频接口（声卡）的平衡输入。
There is also a selectable voltage divider so the input of the audio interface won’t be overloaded when testing with very high voltage.
此外，还有一个可选的分压器，这样在测试非常高的电压时，音频接口的输入就不会过载。

Photo 1 - VI Box from LinearX
照片 1 - LinearX 的 VI 盒

I mentioned earlier that measuring input impedance at low drive levels may present a problem for some applications. A couple of these that come to mind are vented loudspeaker enclosures and constant voltage distributed system transformers.
我在前面提到过，在低驱动电平下测量输入阻抗可能会给某些应用带来问题。我想到的其中几种应用是通风扬声器外壳和恒压分布式系统变压器。
I’m sure the interested reader will find others.
我相信感兴趣的读者还会找到其他的。

The impedance response of a vented loudspeaker enclosure is shown in Figure 3. The angle of the impedance for this device is shown in Figure 4. The vent tuning resonance of this loudspeaker is found when the impedance angle is zero indicating the voltage and current are in phase.
通风扬声器箱体的阻抗响应如图 3 所示。该装置的阻抗角如图 4 所示。当阻抗角为零时，表示电压和电流同相，这就是扬声器的通气孔调谐共振。
This is denoted by the marker at approximate 98 Hz . These graphs show measurements using both the constant current method with a 1 kohm resistor and using a current sensing resistor. The current sensing resistor measurement used a 0 dBV $(1.0\mathrm{V})$$(1.0\mathrm{V})$(1.0V)(1.0 \mathrm{~V}) drive level to excite the loudspeaker. There is some difference between these two measurements. The impedance measurements in Figure 5 tell us much more. In this graph we have additional measurements at $+18,+24$$+18,+24$+18,+24+18,+24 and +27 dBV . We can see that at these higher drive levels the impedance curve changes rather dramatically.
这由大约 98 Hz 的标记表示。这些图表显示了使用 1 kohm 电阻器的恒流方法和使用电流感应电阻器的测量结果。电流感应电阻器测量使用 0 dBV $(1.0\mathrm{V})$$(1.0\mathrm{V})$(1.0V)(1.0 \mathrm{~V}) 驱动电平来激励扬声器。这两种测量方法之间存在一些差异。图 5 中的阻抗测量结果告诉我们更多信息。在该图中，我们还对 $+18,+24$$+18,+24$+18,+24+18,+24 和 +27 dBV 进行了测量。我们可以看到，在这些较高的驱动电平下，阻抗曲线发生了相当大的变化。

The vent surface area of this loudspeaker is relatively small compared to the surface area of the driver. When the woofer is driven harder it moves a lot more air. The vents are too small to allow this same volume of air to be moved through them. The vents saturate.
与驱动器的表面积相比，这款扬声器的通气孔表面积相对较小。当低音扬声器被大力驱动时，会产生更多的空气。通气孔太小，无法容纳相同体积的空气通过。通气孔会饱和。
As more air attempts to move through the vents they saturate more and have less of an effect on the loudspeaker response. The impedance response begins to look less like a vented box and more like that of a sealed box.
当更多的空气试图通过通风口时，通风口的饱和度就会增加，对扬声器响应的影响就会减小。阻抗响应开始变得不像通风孔，而更像密封箱。

Figure 3 - Impedance of vented loudspeaker measured with a 1 kohm resistor (red) & a current sensing resistor at 0 dBV (blue)
图 3 - 用 1 kohm 电阻器（红色）和 0 dBV 电流感应电阻器（蓝色）测量的通风扬声器阻抗

Figure 4 - Impedance angle for vented loudspeaker measured with a 1 kohm resistor (red) & a current sensing resistor at 0 dBV (blue)
图 4 - 使用 1 kohm 电阻器（红色）和 0 dBV 电流感应电阻器（蓝色）测量的通风扬声器阻抗角

Figure 5 - Impedance of vented loudspeaker measured with a 1 kohm resistor & a current sensing resistor at $0,+18,+24\mathrm{\&}+27\mathrm{dBV}$$0,+18,+24\mathrm{\&}+27\mathrm{dBV}$0,+18,+24&+27dBV0,+18,+24 \&+27 \mathrm{dBV}
图 5 - 在 $0,+18,+24\mathrm{\&}+27\mathrm{dBV}$$0,+18,+24\mathrm{\&}+27\mathrm{dBV}$0,+18,+24&+27dBV0,+18,+24 \&+27 \mathrm{dBV} 处使用 1 kohm 电阻器和电流感应电阻器测量的通风扬声器阻抗

A constant voltage distributed loudspeaker system typically requires transformers to be placed immediately in front of the loudspeakers to step down the voltage and step up the current.
恒压分布式扬声器系统通常需要在扬声器前方安装变压器，以降低电压和增加电流。
Testing these types of transformers at low voltage levels typically will not reveal some of the problems that may occur in actual usage.
在低电压水平下测试这些类型的变压器，通常不会发现实际使用中可能出现的一些问题。
Figure 6 shows the input impedance for each primary tap of a 70.7 V step down transformer with its secondary loaded by an 8 ohm power dissipation test resistor. For each of these measurements the drive voltage was 6.5 V .
图 6 显示了 70.7 V 降压变压器每个初级抽头的输入阻抗，其次级负载为 8 欧姆功率耗散测试电阻。每次测量的驱动电压均为 6.5 V。
This is approximately -21 dB from the full rated voltage of 70.7 V. As expected the impedance curves are fairly well behaved.
这与 70.7 V 的全额定电压相差约 -21 dB。不出所料，阻抗曲线表现相当不错。

When driven at $35\mathrm{V},-6\mathrm{dB}$$35\mathrm{V},-6\mathrm{dB}$35V,-6dB35 \mathrm{~V},-6 \mathrm{~dB} from full rated voltage, there is a problem with the 32 W tap seen in Figure 7. At very low frequencies this transformer does not like being driven at this voltage. The result is that the core saturates.
在全额定电压 $35\mathrm{V},-6\mathrm{dB}$$35\mathrm{V},-6\mathrm{dB}$35V,-6dB35 \mathrm{~V},-6 \mathrm{~dB} 下驱动时，图 7 中的 32 W 分接存在问题。在非常低的频率下，该变压器不喜欢在此电压下驱动。其结果是铁芯饱和。
The reflected impedance of the load (on the secondary) as seen by the primary is no longer linear. This violates one of the requirements of the measurement method used (FFT); that the DUT be linear, time invariant (LTI).
初级看到的负载（次级）反射阻抗不再是线性的。这违反了所使用测量方法（FFT）的要求之一，即 DUT 必须是线性的、时间不变的（LTI）。
By placing a second order Butterworth high pass filter in front of the amplifier driving the transformer this core saturation condition can be corrected. A doubling of voltage to 70 V would require the corner frequency of the high pass filter to also be doubled.
通过在驱动变压器的放大器前放置一个二阶巴特沃斯高通滤波器，可以纠正这种磁芯饱和状态。如果将电压提高一倍至 70 V，高通滤波器的角频率也需要提高一倍。
In this case, the corner frequency should be increased from 30 Hz to 60 Hz.
在这种情况下，角频率应从 30 赫兹提高到 60 赫兹。

Figure 6 - Impedance of different taps of a 70 V transformer driven at 6.5 V terminated into $8\mathrm{\Omega }$$8\mathrm{\Omega }$8Omega8 \Omega
图 6 - 以 6.5 V 电压驱动的 70 V 变压器不同抽头的阻抗，终端为 $8\mathrm{\Omega }$$8\mathrm{\Omega }$8Omega8 \Omega

Figure 7 - Impedance of 32 W tap of a 70 V transformer driven at $35\mathrm{V};20\mathrm{Hz}\mathbf{H}\mathbf{P}$$35\mathrm{V};20\mathrm{Hz}\mathbf{H}\mathbf{P}$35V;20HzHP35 \mathrm{~V} ; 20 \mathrm{~Hz} \mathbf{~ H P} filter (red), $\mathbf{3}\mathbf{0}\mathbf{H}\mathbf{z}$$\mathbf{3}\mathbf{0}\mathbf{H}\mathbf{z}$30Hz\mathbf{3 0} \mathbf{~ H z} HP filter (blue)
图 7 - 在 $35\mathrm{V};20\mathrm{Hz}\mathbf{H}\mathbf{P}$$35\mathrm{V};20\mathrm{Hz}\mathbf{H}\mathbf{P}$35V;20HzHP35 \mathrm{~V} ; 20 \mathrm{~Hz} \mathbf{~ H P} 滤波器（红色）和 $\mathbf{3}\mathbf{0}\mathbf{H}\mathbf{z}$$\mathbf{3}\mathbf{0}\mathbf{H}\mathbf{z}$30Hz\mathbf{3 0} \mathbf{~ H z} HP 滤波器（蓝色）上驱动的 70 V 变压器 32 W 分接的阻抗

Figure 8 - Impedance response of vented loudspeaker
图 8 - 通风扬声器的阻抗响应

Another use for these types of measurements is to investigate resonance behavior. This can be particularly interesting when viewed as a 3D waterfall. The impedance response of a vented enclosure is shown in Figure 8. There are two features in this graph that should be noted.
这类测量的另一个用途是研究共振行为。如果以 3D 瀑布图的形式来观察，则会特别有趣。通风外壳的阻抗响应如图 8 所示。图中有两个特征值得注意。
This is the dip/peak at 80 and 120 Hz . Notice these same frequency regions in Figure 9 & Figure 10. These features don’t occur initially. It is only after approximately 60 ms that they become evident.
这就是 80 赫兹和 120 赫兹的骤降/峰值。请注意图 9 和图 10 中相同的频率区域。这些特征最初并没有出现。只有在大约 60 毫秒后，它们才会变得明显。
Knowing how long it requires for this resonance to develop may help in determining its cause and implementing a solution.
了解这种共振需要多长时间才能形成，可能有助于确定其原因并实施解决方案。

Figure 9 - 3D view of measurement in Figure 8
图 9 - 图 8 中测量的 3D 视图

Figure 10 - 3D view of measurement in Figure 8 (note the “wiggling” of the 75 Hz resonance peak)
图 10 - 图 8 中测量结果的三维视图（注意 75 赫兹谐振峰的 "摆动"）。

I hope that the method discussed here to measure impedance at typical application drive level and illustrating some possible uses will be of benefit.
我希望本文所讨论的在典型应用驱动器级别测量阻抗的方法以及一些可能的用途说明能对您有所帮助。
Thanks to Jay Mitchell (Frazier Loudspeakers) and Dr. Eugene Patronis (Professor Emeritus, Physics - Georgia Institute of Technology) for their insights on some of these applications.
感谢 Jay Mitchell（弗雷泽扬声器公司）和 Eugene Patronis 博士（佐治亚理工学院物理学名誉教授）对其中一些应用的见解。