I have a few questions about harmonic distortion as follows:

1. In a specific circuit, we assume that there is no phase delay to the circuit, what about the relative phase between the fundamental wave and its 2nd harmonic distortion for a single-tone input of an opa? Is the relative phase difference is fixed? If it is fixed, we assume that the value is a and there is additive phase delay of the circuit b, then what about the relative phase between the fundamental wave and its 2nd harmonic distortion?

2. How about the relative phase between the fundamental wave and its 2nd harmonic distortion for cascade circuit of two op amplifiers(of the same type)? For instance, if the input fundamental wave is 1Vpp of amplitude and frequency of 1MHz, and 2nd harmonic distortion is -60dBc for the specific input frequency and amplitude of an opa, when it goes through the opa(the gain is 1), then the fundamental signal will produce a 2MHz signal (2nd harmonic distortion) of 1mVpp(Vh1). If the fundamental signal and Vh1 go through another opa (of the same case with above), then then the fundamental will produce another 2MHz signal of 1mVpp(Vh2), then how to calculate the total 2nd harmonic distortion of the 1MHz fundamental signal?

3. Is there a universal mathematical mode for an opa? How to calculate the harmonic distortion accurately?

4. I find a figure(as shown in figure below) about harmonic distortion about AD829. For a general application, I abtain a 2nd harmonic distortion of -65 dBc( f=156.25kHz, 2Vpp,RL=100 ohm), but from the figure, I can only abtain about -55 dBc. I don't know why. Does the figure show the harmonic distortion of worst case to most extend?

Thank you very much!

Hello Zhang,

I've addressed your questions below:

1) The relationship between the fundamental and HD2 is fixed, and they are in essence "locked" by virtue of the fact that the HD2 is derived from the fundamental. HD is characterized in general by modeling the Vo vs. Vi transfer characteristic (which is ideally a perfectly straight line that passes through the origin) as a power series expansion about 0. The transfer characteristic is therefore:

Vo = a0 + a1*(Vi) + a2*(Vi)^2 + a3*(Vi)^3 + ...

In a low distortion amplifier the dominant series terms are a0 (DC offset) and a1*(Vi) (desired output), and the coefficients of the higher-order terms are very small. When Vi is A*sin(wt), the output contains terms that include even and odd powers of sin(wt). The second harmonic distortion product comes from the a2*(Asin(wt))^2 term, which can be expanded using a trigonometric identity to be a2*(A^2)*(1 - cos(2wt)). You can see that the second harmonic is a cosine, while the fundamental is a sine, and that the term produces a shift in DC level. The phase difference between the fundamental and HD2 grows linearly with time since they are different frequencies. (I apologize for the math symbols -- had to go back and remove the "symbol" fonts since they didn't get presented right when posted.)

Phase shift through the amplifier consists of a shift that varies linearly with frequency with a very small negative slope that is due to the very small propagation delay through the amplifier, along with a contribution from the open-loop phase shift that is included in the closed-loop gain expression (this contribution only becomes appreciable at high frequencies and high gains where the loop gain magnitude is small).

2) You can model the HD2 for the second amplifier in the same manner you did for the first amplifier.

3) The major causes of HD are well understood, but there is no universal model. The power series expansion provides the best approach. Distortion performance in negative feedback amplifiers depends directly on available loop gain, and also depends on other factors such as load current, output swing, gain configuration, supply voltage, supply decoupling, board layout, etc...

4) As in 3), many factors affect HD performance, and the curves presented in the data sheets are "typical" for the stated conditions. Under identical conditions, there could be a few dB difference either way simply due to unit-to-unit variations. It is also difficult to perfectly duplicate the conditions under which the TPC curves were measured. Characterizing extremely low levels of HD, such as -120 dBc, is very difficult since seemingly minor changes in measurement conditions can have a large effect on the circuit.

If you're interested in more details, I cover distortion along with many other topics in the following two ADC-driving webinars:

http://www.analog.com/en/content/WC_DRIVING_ADCS1/webcast.html

http://www.analog.com/en/content/WC_DRIVEADCS_2/webcast.html

Best regards.

--Jonathan Pearson