Interpreting the benefits of fully-differential amplifiers in the context of an electronic system is a key concern for the system designer. The frequently touted improvement in dynamic range will be explored here for the case wherein a fully-differential amplifier is used to drive a high-performance analog-to-digital converter.

Typically, the two-fold dynamic range increase afforded by a fully-differential amplifier is thought to come about due to the two-fold increase in maximum output voltage swing given by fully-differential amplifiers. In amplifiers, the output voltage can swing to within a certain range of the positive and negative voltage supplies. In fully-differential amplifiers, there are two outputs that are 180ý out-of-phase, so the differential output swing can be expressed as twice the output swing of a single output. This concept is illustrated and contrasted with a single-ended amplifier in the figure below.

Figure 1: Comparing Single-Ended and Differential Outputs

Certainly, twice the available output swing can be advantageous in many applications, particularly those where large signals are coupled with relatively small power supply voltages. However, the advantages of high-performance fully-differential amplifiers make them ideally suited for driving high-resolution, high-sampling rate analog-to-digital converters (ADCs). In this application, the advantage of having a two-fold increase in dynamic range due to the two-fold increase in output voltage swing seems to be without value, since the requirements on the amplifier's output voltage swing will be dictated by the full-scale input range of the ADC. The fully differential outputs do still provide dynamic range advantages in this type of system, though the advantage manifests itself differently than previously described. The distinction is subtle, but critical to understand when choosing a method for driving an ADC.

Defining Dynamic Range

The dynamic range of an amplifier is the relationship between the minimum detectable signal (MDS) at the output of the amplifier and the amplifier's full-scale output swing, as given in equation (1). Dynamic range is typically expressed in decibels.

Equation (1):

The minimum detectable signal is determined either by the noise floor or by the distortion products at the output of the amplifier. When the effect of distortion spurs are included, the dynamic range is often referred to as spurious-free dynamic range (SFDR).

The limiting factor for the minimum detectable signal typically depends on the frequency of operation. When the frequency band of interest is low, the noise floor of the amplifier generally dictates the minimum detectable signal. As the signal frequency increases, the distortion spurs become more pronounced and dictate the minimum detectable signal. In high-performance analog signal processing chains, distortion spurs inevitably determine the MDS. The annotated figure shows an example SFDR plot.

click for larger image
Figure 2: Example SFDR Plot Showing Third-Order Intermodulation Products Yielding 80 dB Dynamic Range

Distortion Fundamentals

Distortion is the result of the non-linearity that exists in a transfer function intended to be linear. Example polynomial representations of transfer functions for an ideal and a real amplifier are given in equations (2) and (3).

Equation (2): An ideal (linear) transfer function.

Equation (3): A non-linear transfer function.

A given transfer function can be expressed as a polynomial equation similar to the one presented in equation (3), with coefficients, a_X, representing the degree of non-linearity. For this discussion, it is only important to note that non-linearity becomes more pronounced as the output voltage, V_OUT, and hence the input voltage, V_IN, increases in magnitude. As the output voltage decreases, the magnitudes of the non-linear elements of the transfer function decrease rapidly due to their exponential dependence on the input voltage level.

A graphical illustration of this concept appears in the figure. A hyperbolic tangent is an example of a non-linear transfer function. It is shown with two polynomial expansions that use zero as the starting point for the approximation. As depicted in the figure, the linear approximation of the transfer function matches the hyperbolic tangent through the 0.0 to 0.35 region. After this point, the linear approximation begins to diverge from the actual function. As the deviation from the reference point (zero) becomes greater, the non-linear nature of the transfer function increases. A detailed explanation of amplifier distortion and modeling non-linearity with polynomial expansions is given by Karki [2].

Figure 3: An Example Non-Linear Transfer Function and Associated Polynomial Approximations

Dynamic Range Improvement with Fully-differential Amplifiers

As mentioned previously, the full-scale input range of the ADC generally dictates the maximum output voltage swing of the amplifier that drives it in a high-performance data acquisition system. With that in mind, the two-fold increase in output swing provided by a fully-differential amplifier does not appear to offer a performance advantage over a single-ended counterpart. A dynamic range improvement does occur with a differential output, but the improvement is due to a decrease in distortion spurs rather than the increase in full-scale output swing. In a data acquisition system, this distinction is of prime importance.

To fill the full-scale input range of a data converter, a single-ended amplifier would have to support output voltage levels equal to the entire data converter full-scale range on a single output. If the input to the ADC is driven with a fully-differential amplifier, each output only has to support half of the full-scale input range of the converter. This corresponds to a much smaller output voltage for each output of the fully-differential amplifier. As demonstrated in equations (2) and (3), the distortion produced will be smaller in the case of the fully-differential amplifier because each output of the amplifier deviates less from its operating point. Thus, fully-differential amplifiers do provide improvement in dynamic range, even when the maximum output swing is dictated by another portion of the system. This improvement manifests itself as a distortion reduction due to the smaller signal swing required on each amplifier output compared with a single-ended amplifier. The distinction is subtle, but nonetheless important when evaluating design options for a high-performance analog signal processing system.

Figure 4: Third Harmonic Distortion Comparison Between Single-Ended and Differential Amplifiers

To quantify the improvement in dynamic range, the THS4141 fully-differential amplifier from Texas Instruments is given as an example. Third harmonic distortion results are presented for the amplifier used as a fully-differential amplifier and as a single-ended amplifier. Using the same device allows for a legitimate comparison between distortion performance improvements directly related to output voltage swing. The intent is to illustrate a direct improvement given a specific amplifier topology. The fundamental point applies to comparisons between fully-differential amplifiers and single-ended amplifiers in general. Note that the third-harmonic distortion improves from 4 dB to 8 dB, depending on the output swing levels, when a fully-differential amplifier is used.

Since third-order non-linearity causes both harmonic distortion and intermodulation distortion, the third-order intermodulation demonstrates similar improvement from the single-ended case to the differential case. Often times, third-order intermodulation products are of greater concern to the system designer because they cannot be filtered as harmonic distortion products can be.

Fully-differential amplifiers exhibit numerous benefits over their single-ended counterparts, including common-mode noise rejection and even-order distortion suppression. However, the two-fold increase in dynamic range afforded by a fully-differential signal processing solution is often touted as a primary benefit. Unfortunately, the advantage of having twice the output voltage swing can be overlooked by a system designer working on an interface to an analog-to-digital converter with a fixed full-scale input range. Because the full-scale range of the data converter is fixed, it appears on the surface as if no advantage is gained from the dynamic range increase provided by the fully-differential amplifier output. Upon closer examination, this increase in dynamic range will indeed benefit the high-performance signal chain designer by improving the distortion performance of the ADC pre-amplifier. This improvement manifests itself as a distortion reduction due to the reduced signal swing required on each amplifier output compared with a single-ended amplifier. The distinction is subtle, but nonetheless important when evaluating design options for a high-performance analog signal processing system.

References

[1] Karki, Jim. "Fully-Differential Amplifiers." Texas Instruments Application Note, Literature Number SLOA054B. January 2001.

[2] Karki, Jim. "Designing for Low Distortion for High-Speed Amplifiers." Texas Instruments Analog Applications Journal, Literature Number SLYT027. July 2001.

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