1.4 Getting Started with Current Sense Amplifiers, Session 4: How to Choose an Appropriate Shunt Resistor

Hello, my name is Rabab Itarsiwala, and I'm an Applications Engineer for Texas Instruments Sensing Products. In today's training I will go over the basics of choosing an appropriate shunt resistor for a current sensing application. Here, we will look into the primary factors that impact the choice of the resistor and how to arrive at a maximum shunt resistor value for an application.
We will also briefly touch upon the shunt resistor tolerance error. Now, let's define a shunt resistor. Shunt resistor is a resistor through which a current flows and the voltage drop developed across it is measured using a differential amplifier like a current shunt monitor.
It just sometimes also referred to as a current sensing resistor. The load shown in this diagram can be an entire system. Selecting the value of current sensing resistor is based primarily on two factors-- required accuracy at minimum load current, and power dissipation at maximum load current, and the associated size and cost.
Now, let's look into how to determine current accuracy for a current-sensing application. For simplicity, we will only consider amplifier offset error for accuracy estimation and ignore other sources of amplifier error, which is the topic of other videos in this series. Amplifier internal offset voltage, also known as VOS, is the dominant source of error at low sense voltages. Sense voltage, or Vsense, is the differential voltage input to the amplifier, which is the product of shunt resistor and the load current flowing through the resistor.
The plot here shows that offset error decreases with increasing Vsense. The larger the voltage developed across the shunt resistor, the more accurate of a measurement can be made due to this fixed error. This fixed internal amplifier error results in a larger uncertainty as the input signal gets smaller.
Let's look at this in some more detail using a current shunt monitor with 1 millivolt offset voltage. When the drop across the shunt resistor is equal to the offset voltage-- 1 millivolt-- the uncertainty of measurement is 100%. When the Vsense is increased to 10 millivolts, the measurement error drops significantly to 10%.
Here is a plot of power dissipation versus shunt resistor for a fixed load current. Power dissipation in the shunt resistor is the product of voltage across it and current flowing through it. Or it can also be calculated as the product of the shunt resistor value and square of the current flowing through it.
Increasing the value of the current shunt resistor increases the differential voltage developed across that resistor. However, the power that is dissipated across the shunt resistor also increases. Now, let's look at minimum current accuracy versus power dissipation at maximum current trade off.
Consider an application with minimum current of 1 amp and maximum current off 10 amps. The red plot shows the variation in offset error at minimum current versus shunt resistor for an amplifier with an offset of 1 millivolt. And the blue plot shows the variation in power dissipation at maximum current versus shunt resistor.
What we can see here is increasing the shunt resistor value improves current accuracy, but also increases power dissipation. Decreasing the value of the current shunt resistor reduces the power dissipation requirements, but increases the measurement errors resulting from decreasing input signal and thus, reduces accuracy. Finding the optimal value for the shunt resistor requires factoring both the accuracy requirement of the application and allowable power dissipation into the selection of the resistor.
Let's look at this in some detail. If a 5 milliohm resistor is chosen for this application the power dissipation at full scale current of 10 amps will be about 0.5 watt. And accuracy at minimum load current will be 20%.
If we wanted to improve the minimum current accuracy to 15%, then a shunt resistor of about 6.6 milliohms can be chosen. But this choice will cost us about 0.66 Watt of power dissipation at full scale. Higher power dissipation requirement will drive up the size and the cost of the shunt resistor.
So there is a trade off to be made. In this case, 5% less error in exchange for 32% more power dissipation, and possible increase of the resistor, size and cost. We saw on previous slides that increasing the resistor gives us better accuracy.
But there is an upper bound for the resistor value. Maximum resistor value in an application depends on full scale current to be measured, full scale output range of the sensing device, or full scale input range of the circuitry following the sensing device and the gain of the sensing device. Maximum shunt resistor value is calculated as the ratio of full scale output of the amplifier divided by its gain to maximum load current.
It should be noted that full scale output range depends on the device supply and its output swing limitation. So far we talked about the sensing amplifier offset error and how it contributes to the overall accuracy of the system. Shunt resistors are not ideal. And their non-idealities have significant impact on system accuracy.
Among the shunt resistor non-idealities, shunt resistor tolerance error is a significant source of error. It is expressed as a percentage, and is defined as maximum deviation from the ideal resistance value. The resistance value could vary by the tolerance amount in the positive or negative direction.
For example, a 10 milliohm 1% shunt resistor can vary in value from 10 millohm plus or minus 0.1 milliohm. That is, it can vary from 9.9 milliohm to 10.1 milliohm. Unlike the amplifier offset error, shunt resistor tolerance error contribution is constant over the entire load current range.
Now, let's work through an example to better understand what we discussed so far. Let's consider an application with minimum current of 100 milliamps and maximum current off 10 amps. We chose INA 199 A1 to be the current sense amplifier for this application.
INA 199 A1 has an offset voltage maximum specification of 150 microvolt. For this example, we are ignoring other sources of amplifier error. The gain of this device is 50 volt per volt. Required full scale output voltage is 5 volts.
Using the equations we introduced earlier, our shunt maximum is calculated to be 10 milliohm. 10 milliohm shunt resistor will dissipate 1 watt of power at 10 amps and error due to offset at minimum current off 100 milliamp will be 15%. Offset voltage contribution to error at maximum current is 0.15%. But at the full scale input, there are other error sources, like amplifier gain error and shunt resistor tolerance error, that dominate.
Therefore, choosing a resistor with 1% tolerance, and given the 1.5% maximum gain error of INA199 A1, the total error at full scale is around 1.8%. Total error is calculated by adding errors in the square root of the sum of the squares fashion, which is discussed in detail in other videos of this series. If the chosen shunt resistor has a tolerance greater than 1.5%, then the tolerance will dominate full scale error in this example.
Here is a table listing unit price of 10 milliohm resistors with different power and tolerance ratings. It can be noted that in general, with higher power-rated resistor, the price goes up. And so does the size. And choosing a higher precision resistor also demand higher price and larger bore space.
In this video, we defined a shunt resistor, discussed the trade off between minimum current accuracy versus power dissipation at full scale current. We also discussed how to calculate the maximum value of the shunt resistor for an application. We briefly touched upon the shunt resistor tolerance error and its effect on system accuracy.
For more information on TI's Current Sense Amplifiers, please watch the remainder of the Current Sense Video Series, as well as go to www.ti.com/currentsense. Thank you for your time today. 大家好，我叫 Rabab Itarsiwala， 是德州仪器 (TI) 的 传感器产品的应用 工程师。 在今天的培训中， 我将介绍 有关如何为 电流感应应用 选择合适的分流电阻 的基本知识。 在此我们将 探讨 电阻选择的主要影响因素 以及如何 在应用中 实现 最大的分流电阻值。 我们还简单涉及 分流电阻的容许 误差。 现在，我们给分流电阻 下个定义。 分流电阻是 这样一个电阻， 在其上有电流流过， 在其两端产生的电压降通过 诸如电流分流 监控器等差分放大器 来测量。 有时它 也称为 电流感应电阻。 该图中显示的负载 可以是一个完整的系统。 电流感应电阻的 选择 主要基于 两个因素 -- 最小负载电流下 所需的精度 和最大负载电流下的 功耗， 以及相关的 尺寸和成本。 现在，让我们看看如何 确定电流感应 应用的电流 精度。 为简单起见，在精度估算中 我们将只考虑 放大器的偏移误差， 而忽略 放大器误差的 其他来源， 这些来源是本系列 其他视频的主题。 放大器内部偏移 电压，也称为 VOS， 是低感应电压下 主要的误差来源。 感应电压，或 Vsense，是 放大器的 差分电压输入， 它是分流电阻 与流过电阻的负载电流 的乘积。 该图显示 偏移误差会 随着 Vsense 的增大而减小。 由于该误差是固定的， 在分流电阻上 产生的 电压越大， 测量可能 越精确。 随着输入信号的降低，这一固定的内部 放大器误差 会导致 更大的不确定性。 让我们通过 具有 1 毫伏偏移电压的 电流分流监控器 来更详细地了解这一点。 当分流电阻 上的电压降 等于偏移 电压（即 1 毫伏）时， 测量的不确定度 为 100%。 当 Vsense 增加 到 10 毫伏时， 测量误差大幅 下降到 10%。 下面是一个 在固定负载电流下 的功耗与分流电阻 的关系图。 分流电阻中的 功耗 是其两端的 电压与流过它的 电流的乘积。 也可以通过 将分流电阻值 与流过它的 电流的平方相乘 而得到。 增大电流 分流电阻的值 会增加 该电阻上 产生的差分电压。 但是，在分流 电阻上 的功耗 也会增加。 现在，让我们来看看 在最大电流下 最低电流精度与 功耗之间的折衷关系。 假设一个应用 采用 1 安的 最小电流和 10 安的 最大电流。 红线显示对于 具有 1 毫伏偏移的 放大器， 在最小电流下 偏移误差的变化 与分流电阻的关系。 蓝线显示 在最大电流下 功率耗散的变化 与分流电阻的关系。 在此我们可以看到的是， 增大分流电阻的值 可以提高电流精度， 但也会增加 功耗. 减小电流 分流电阻的值 会降低 功耗要求， 但会因降低 输入信号 而增加测量误差， 导致精度下降。 要找出最佳的 分流电阻值， 需要在选择 电阻时兼顾 应用对 精度的要求 和允许的 功率耗散量。 让我们详细 来看这一点。 如果在该应用中选择 一个 5 毫欧的电阻， 则在 10 安的 满载电流下， 功耗大约为 0.5 瓦。 而最小负载电流下 的精度为 20%。 如果要将最大 电流精度提高 到 15%，可以选择 大约 6.6 毫欧的 分流电阻。 但该选择在满载情况下将带来 大约 0.66 瓦的 功耗。 功耗 的增加 会提高分流电阻的 尺寸和成本。 因此需要 进行折衷。 在本例中，是通过 增加 32% 的功耗 并可能增加电阻、 尺寸和成本，来换取误差 5%的降低。 在上一个幻灯片中 我们看到，增大电阻 可以提高精度。 但电阻的值 有上限。 应用中所使用的 最大电阻值 取决于所测量的 满刻度电流、 感应器件的 满刻度输出范围 或跟踪感应器件的 电路的满刻度 输入范围 和感应器件的增益。 最大分流电阻值的 计算公式为， 放大器的满刻度输出 除以其增益所得的结果 与最大负载电流 的比。 需要注意的是， 满刻度输出 范围取决于器件 的供电电压及其输出摆幅 限制。 迄今为止，我们讲述了 感应放大器偏移误差 以及它对系统 总体精度的影响。 分流电阻并不是理想的。 其不理想的因素 对系统精度 有重要影响。 在分流电阻的 各种不理想因素中， 分流电阻的容差 是重要的 误差来源。 它以百分比的 形式表示， 定义为相对于 理想电阻值的 最大偏差。 电阻的值可能 会因正向或负向的 容差量的 不同而不同。 例如，10 毫欧 1% 分流 电阻的值 可能会在 10 毫欧 加减0.1 毫欧之间变化。 也就是说，它可以在 9.9 毫欧至 10.1 毫欧之间变化。 与放大器 偏移误差不同， 分流电阻容差 的误差部分 在整个负载电流范围内 都是恒定的。 现在，我们完成一个 示例以更好地了解 目前已经讨论的问题。 我们假设一个应用 具有 100 毫安的 最小电流和 10 安的最大电流。 我们选择 INA 199 A1 作为 该应用的 电流感应放大器。 INA 199 A1 的偏移 电压最大规格为 150 毫伏。 对于本示例， 我们将忽略 放大器其他误差来源。 该器件的增益为 50倍。 所需的 满刻度输出 电压为 5 伏。 使用我们之前 介绍过的方程式， 我们计算的最大分流电阻值 为 10 毫欧。 10 毫欧分流电阻 在 10 安时的耗散功率将为 1 瓦， 并且 100 毫安 最小电流下的 偏移导致的误差将为 15%。 在最大电流下 偏移电压导致的误差 为 0.15%。 但在满刻度 输入时， 会有其他的误差来源 起决定性作用， 例如放大器增益误差 和分流电阻容差。 因此，如果选择 具有 1% 容差的 电阻，并且 INA199 A1 的最大增益误差 为 1.5%，则 满刻度下的总误差 约为 1.8%。 总误差的计算方法是 以平方和 的平方根的形式 将误差相加， 这在本系列的其他视频中 有详细介绍。 如果所选的分流电阻的 容差大于 1.5%， 则该容差将 决定本示例中的 满刻度容差。 下表列出了 具有不同功率 和容差等级的 10 毫欧电阻的单价。 可以注意到， 一般而言， 额定功率较高的电阻 价格也更高， 并且尺寸也更大。 选择精度更高的 电阻也需要 更高的价格和 更大的电路板空间。 在本视频中，我们 定义了分流电阻， 讨论了在 满刻度电流下 最小电流精度与 功耗之间的折衷。 我们还讨论了 如何计算 应用中的分流电阻的 最大值。 我们简要地涉及了 分流电阻容差 及其对 系统精度的影响。 有关 TI 的电流感应 放大器的更多信息， 请观看电流感应 视频系列的其余部分， 并访问 www.ti.com/currentsense。

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Date:
May 12, 2015

The Getting Started with Current Sense Amplifiers series helps engineers learn how to to maximize the performance achieved when measuring current with a current sense amplifier (also called a current shunt monitor). Session four discusses how to choose an appropriate shunt resistor.