# Understanding Harmonic Distortion Versus Amplitude in Operational Amplifiers, Part 1

Depending on the low-distortion needs of an application, the system engineer can choose from plenty of signal amplifiers. The first step in making the right choice is to understand the typical datasheet curves that characterize total harmonic distortion plus noise, THD+N, in amplifiers.

Harmonic distortion versus amplitude is one of the typical datasheet curves that describe THD+N, and it is the topic of this series of articles. Another important typical curve is THD+N versus frequency.1

In the THD+N versus amplitude curve, the first region is noise dominated and is explained in terms of the amplifier's signal-to-noise ratio (SNR). Next is a moderate-distortion region, which is explained in terms of the internal amplifier topology, as well as loading. And last is the clipping-dominated region. Figures 1a and 1b show examples.

Figure 1a THD+N (%) versus amplitude.

Figure 1b THD+N (V-rms) versus amplitude.

In Part 1, we will examine how THD+N is affected by the amplifier's noise and why it seems to improve with amplitude level. First, let's take a brief look at the measurement setup.

THD+N versus amplitude measurement
A distortion analyzer tool is usually used to make THD+N measurements.1 For simplicity, the amplifier is configured in a closed-loop gain of one. I say “simplicity,” because this is not always the case, especially when the distortion components are below the instrument's noise level. We'll have more on this in a subsequent article. For now, we can assume a buffer configuration is good enough for our measurements.

In the setup shown below, the positive input is connected to the instrument's pure sine wave generator, and the amplifier's output is connected back to the instrument for distortion analysis. The frequency of the sine wave is fixed to a single, constant frequency while the amplitude is swept across the dynamic range of the amplifier.

Figure 2 DUT and tool measurement setup.

Datasheets usually present the THD+N versus amplitude curve with a fixed frequency of 1kHz and amplitude swept from 100mV-rms up to the amplifier's dynamic range limit. The distortion analyzer's bandwidth setting limits the noise and the number of harmonics the instrument takes into account. Typical settings for the bandwidth are 80kHz and 500kHz. The measurements in this article use a bandwidth of 80kHz.

The tool generates a frequency spectrum for each amplitude in the sweep and uses the following equation to calculate THD+N.

Equation 1 In this equation, V1 is the fundamental of the input signal. This is the variable that is swept. VN is the harmonics, and VNOISE is the amplifier's noise. When the tool completes the amplitude sweep, it has a family of frequency spectra to generate THD+N as a function of amplitude.

Noise-dominated region
The THD+N in the noise-dominated region in Figure 1a decreases (or improves) with increasing amplitude, because the THD+N is reported as a ratio to the increasing amplitude signal. The noise floor of an amplifier for a given bandwidth and frequency is a fixed quantity, so for smaller signal amplitudes, the SNR is the limiting factor for an amplifier's linearity. As the signal amplitude increases, SNR improves, and so does THD+N.

Figure 1b presents THD+N by showing results in absolute values, rather than as a percentage ratio of the amplitude signal. In this case, the units used are V-rms, but they can also be shown in dBV (voltage relative to 1V). Figure 1b uses the following equation to show the results in absolute units.

Equation 2 When THD+N is presented in absolute units, the measurement in the noise dominated region is independent of the fundamental signal's amplitude. This makes it clear that the noise component is constant and unrelated to the signal amplitude. However, at a particular signal amplitude level, the amplifier stages begin to depart from their linear regions, and the THD contribution begins to dominate. At this point, the curve enters the moderate-distortion region. This happens between 3V-rms and 4V-rms in Figure 1b.

Figure 3a shows frequency spectra for three different input signals to further illustrate that the noise component in THD+N is constant and unrelated to signal amplitude. The noise is dominant at signal amplitudes of 100mV-rms and 1V-rms, but at 4V-rms, the amplifier's nonlinear behavior begins to produce harmonics. THD (and not noise) becomes dominant at this point.

Figure 3 Frequency spectra that show noise is constant in the noise-dominated region.

The noise-dominated region in Figure 1a can also be understood in terms of the equation shown below. In this equation, the numerator is constant and representative of the dominant noise. THD is insignificant, and x is the increasing signal amplitude. The function f(x) is representative of THD+N in the noise-dominated region.

Equation 3 For this function, a small input value for x yields a large output value, and vice versa . In a log-log scale, the slope of this function is -20dB per decade. Figures 4a and 4b show the results for f(x) = 1/x and f(x) = 0.1/x to illustrate the effects of high and low noise on THD+N.

Figure 4a Linear-linear plot of the function of a constant with respect to x.

Figure 4b Log-log plot of the function of a constant with respect to x.

As soon as the signal becomes large enough and the nonlinearities of the amplifier begin to produce harmonics, the amplifier enters the moderate-distortion region. In my next article, I will take a look at the input and output stages of the amplifier in this region and how they play a role in setting the THD+N.

We initiated this series of articles by discussing the noise-dominated region of the THD+N versus amplitude curve. As you become familiar with this curve, keep in mind that the noise floor of an amplifier for a given bandwidth and frequency is a fixed quantity. For smaller signal amplitudes, the SNR is the limiting factor for an amplifier's linearity.

References and additional information:

1. Jorge Vega and Raj Ramanathan, “Harmonic Distortion: Part I – Understanding Harmonic Distortion vs. Frequency Measurements in Op Amps,” En-genius, January 30, 2012.
2. David Johns and Kenneth Martin, Analog Integrated Circuit Design , John Wiley & Sons, Inc., 1997.
3. OPA1652/54 op-amp datasheet, Texas Instruments.

Related posts:

## 7 comments on “Understanding Harmonic Distortion Versus Amplitude in Operational Amplifiers, Part 1”

1. Davidled
June 7, 2013

Noise was described in the Figure 3. I am wondering where is signal in the Figure 3. I think that red line is noise and Figure 3 come from DUT diagram. To get clarification, Time domain is also a good presentation for SNR.

2. amrutah
June 9, 2013

Jorge,

Thanks for the discussion on THD+N topic and looking forward to learn more here.

In the Figure 4 you meant:

“The function f(x) is representative of THD+N in the noise-dominated region”.

At low amplitudes of “x”, the f(x) is a inverse function of x and fits into the curve as shown in Fig.1.  There is no information about the frequency.  Do you think it makes sense to add the frequency as another dimension

3. amrutah
June 9, 2013

DaeJ,

I agree. I also think a THD+N Vs. Freq should also accompany a figure of Noise Vs. Freq. so that the contribution of Noise for particular freqency with THD is high at 4V.

4. Jorge Vega
June 10, 2013

Thanks for your question on Figure 3. The measurement for this figure was obtained using an Audio Precision instrument for THD+N measurements. The settings on the instrument were such that it collected only the harmonics with the fundamental of the signal notched out. You can see the notch right 1Khz (counting the hairlines). Thus, there is no signal only noise on the first two upper graphs in figure 3.  The third graph however does begins to show discernible harmonics and thus THD components.  So we shouldn't be seeing any signal because the nature of the measurement notches it out leaving only the distortion components in addition to noise.

5. Jorge Vega
June 10, 2013

Hi Amrutah,

You are correct, one over x is representative of THD+N only in the noise dominated region.

Sure thing, the other dimension to this graph is one where the amplitude is fixed and a frequency sweel is performed.  So, you can actually cross-verify that both of the graphs match each other.

For example, if you look at the datasheet of OPA1604 (http://www.ti.com/lit/ds/symlink/opa1604.pdf), figures 7 and 11, you can cross check them.  Figure 7 shows the over-frequency graph with a fixed amplitude of 3VRms.  At 1Khz, THD+N for the 2KΩ load is btw 0.00002% and 0.00003%, now go to Figure 11 (THD+N versus Amplitude).  Here you will see that THD+N at 3Vrms is also btw 0.00002% and 0.00003%.  They match and now you know that the data presented is consistent.  This link shows more on THD+N versus Frequency: http://www.en-genius.net/includes/files/acqt_013012.pdf and also http://www.en-genius.net/includes/files/acqt_042312.pdf

6. Jorge Vega
June 10, 2013

Hello Amrutah, THD+N versus frequency is a graph that usually always accompanies THD+N versus Amplitude.  I didn't include it here just because of topic constraints but you can check out this reference to: http://www.en-genius.net/includes/files/acqt_013012.pdf.  It goes in depth on the topic.  Let me know however if it is still unclear.

7. 