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# 用非补偿运放改进性能

设计者经常想使基于传感器的系统中的振幅误差最小。这个目的经常导致放大器闭环增益的特定增益误差超过传感器频率范围。工程师通常根据其–3dB频率指定放大器带宽，但就增益精度点来看，在这个频率几乎出现30%的增益误差。所谓“有效带宽”与放大器频率响应和应用所需的增益精度有关。定义有效带宽为增益误差小于或等于指定误差的带宽。

有效带宽

传感器具有相对低频响应，频率越低，由有限开环增益产生的增益误差越小。用少于单极、闭环、频率响应模式放大器的指定值，计算有效带宽维持误差。由特定的通常如在数据手册上的增益带宽指标，计算有效带宽是可行的。放大器闭环带宽等于增益带宽除以增益，对非反转放大器完全正确，对反转放大器近似正确。

为容易评估增益误差在频率函数中单极模式的效果，计算格式化单极函数。这个计算放置极点在1Hz，表示闭环增益降为–3dB，用理想闭环单增益或为0dB。使用这个单极模式，计算增益误差频率少于或等于给定误差。然后可以根据放大器闭环增益的–3dB带宽计算有效带宽。谨记–3dB点为几乎30%增益误差，且误差指标越小的带宽越窄。

(1)

(2)

(3)

表2显示数据表计算的一部分，将增益随频率下降的趋势形象化。计算公式1~3分别随列中频率值变化（图1）。

(4)

为计算增益误差等于½LSB误差的频率，用公式1重新整理替代公式4，得到公式5。使用公式4和公式5计算出表3的值。

(5)

以上为部分翻译，英文全文：

Decompensating amplifiers improve performance

Manufacturers offering unity-gain-stable amplifiers hope to address a wide market and minimize the effort of learning to use the devices. Yet these vendors sacrifice a significant portion of the potential ac performance. Learn when to consider decompensated amplifiers and what they can offer you.

By Walter Bacharowski, National Semiconductor -- EDN, 12/3/2007

Designers often want to minimize amplitude error in sensor-based systems. This goal often leads to specifying the gain error of an amplifier’s closed-loop gain over the frequency range of the sensor. Engineers commonly specify the bandwidth of an amplifier in terms of its –3-dB frequency, but, from a gain-accuracy point of view, almost a 30% gain error occurs at this frequency. The term “effective bandwidth” connects the frequency response of the amplifier and the gain accuracy that the application requires. You define the effective bandwidth as the bandwidth for which the gain error is less than or equal to a specified error.

Effective bandwidth

Sensors have a relatively low frequency response, and, at lower frequencies, the gain error due to finite open-loop gain is small. You can calculate the effective bandwidth to maintain an error at less than a specified value from the single-pole, closed-loop, frequency-response model of the amplifier. It would be useful to calculate the effective bandwidth from specifications such as gain bandwidth that are commonly available in a data sheet. The relationship of an amplifier’s closed-loop bandwidth being equal to the gain bandwidth divided by the gain is true for noninverting amplifiers and approximately true for inverting amplifiers.

The next consideration is what basis to use in defining the maximum amplitude error. In almost all systems, the analog portion of the signal path ends at the input of an ADC, and, by extension, the resolution of the ADC defines the error of interest. This article uses an error of ½ LSB of the ADC’s resolution as the maximum error. As the resolution of the ADC increases, the maximum error decreases. Table 1 shows the ½-LSB error for ADC resolutions of 8 to 18 bits.

To easily evaluate the effect of the single-pole model on the gain error as a function of frequency, you calculate a normalized single-pole function. This calculation places the pole at 1 Hz, which represents the –3-dB loss in closed-loop gain, with an ideal closed-loop gain of one, or 0 dB. Using this single-pole model, you calculate the frequency for a gain error less than or equal to the specified error. You can then calculate the effective bandwidth in terms of the –3-dB bandwidth of the closed-loop gain of the amplifier you are evaluating. Keep in mind that the –3-dB point is almost a 30% gain error and that the bandwidth is smaller with a lower error specification.