Third order non-linearity of differential op-amp

[Chinmaye]

Dear all,
I have designed a 2 stage op-amp with cmfb. I would like to measure the 3rd order non-linearity of the op-amp in open loop configuration. Also, I would like to measure the 3rd order non linearity when feedback is provided to it to obtain a gain of 2 (switched capacitor configuration). Please let me know how can one measure the 3rd order non linearity for these 2 configurations in cadence.

 

[deep_sea]

I am not aware of a particular method to measure 2rd order nonlinearity. How do you measure a first or a second order nonlinearity? You might plot the gain vs input and see what comes out.

 

[sutapanaki]

It is difficult to measure the the non-linearity of the opamp open loop because of the high gain and the difficulty of establishing an operating point. That's one of the reasons why people use feedback.. A possible way may be to simulate the input-output characteristic of the opamp and try to find the coefficients of the polynomial that approximates it - the first 3-4 Taylor coefficients. However, there is little sense of knowing the non-linearity of the opamp open loop.
For closed loop - just put a sine wave in and take the FFT of the output sine wave and look for the harmonics.

 

[Chinmaye]

It is difficult to measure the the non-linearity of the opamp open loop because of the high gain and the difficulty of establishing an operating point. That's one of the reasons why people use feedback.. A possible way may be to simulate the input-output characteristic of the opamp and try to find the coefficients of the polynomial that approximates it - the first 3-4 Taylor coefficients. However, there is little sense of knowing the non-linearity of the opamp open loop.
For closed loop - just put a sine wave in and take the FFT of the output sine wave and look for the harmonics.

Thank you for this reply. When i use the op-amp to in feedback configuration using switched capacitors i get the 3rd order non-linearity factor almost 25% of amplitude of fundamental harmonic which is not possible. I dont know where i am going wrong. When I use resistors for feedback and simulate it continuously, i get the 3rd order non-linearity 0.2% of amplitude of fundamental harmonic which is reasonable. Although I expected some difference, I didnt expect such a huge difference. Where am i going wrong?

 

[sutapanaki]

Well, how can I possibly know what you are doing wrong? Did you have a look at the input and output as functions of time? 25% non-linearity should be possible to spot visually.. Then the other thing to think about is how you measure the non-linearity in a switched-capacitor setting.

 

[Dominik Przyborowski]

In spectrerf documentation should be a tutorial how to use pss/qpss analysis to get IP3. There is also ac rapid-ip2/3 analysis available, but I can say nothing on it.

Basically, the simplest way is to provide two sinusoidal tones with small frequency offset, perform qpss and measure HD1 and HD3. The IP3 is then straightforward.

 

[KlausST]

Hi,

In my eyes there is no "third order nonlinearity".
Nonlinearities cause distortions. A pure sine gets overtones, these overtones usually are 3x, 5x, 7x ... of the fundamental frequency.
3x frequency is called 3rd overtone.

This 3rd overtone can be calculated with a DFT, or as mentioned before ,with an FFT.

Klaus

 

[Chinmaye]

Well, how can I possibly know what you are doing wrong? Did you have a look at the input and output as functions of time? 25% non-linearity should be possible to spot visually.. Then the other thing to think about is how you measure the non-linearity in a switched-capacitor setting.

Thank you. I realized that the my measurements are incorrect. I would request you to let me know how can one measure non linearity in switched capacitor setting. Also, generally What does the non linearity depend on other than the open loop gain? When a 2 stage op-amp with gain 400 is connected with feedback to obtain a gain of 2, What is the expected range HD3/HD1?

 

[sutapanaki]

It depends on many things. For example slewing, which is especially prominent in switched capacitors.
Maybe it is a good idea to send an input sine wave, get a sine wave out and plot the results. Then post here, so we can have a feel at least for the waveforms.

 

[Chinmaye]

Here I am attaching the waveforms of the input which is fed to a sample and hold amplifier (SHA), the output of the SHA is fed to switched capacitor amplifier of gain 2.

 

[sutapanaki]

It doesn't look like 25% distortion.
Here is what you can do. Decide on the number of sine wave cycles that you want to simulate for the fft to get the distortion. Set up an input frequency that is Fin=(cycles/N)*Fs, where N is the number of sample points and Fs is your sampling frequency. Make sure cycles and N are mutually prime numbers and they don't have common divisor. For example N=1024 cycles=57 would be such a pair. But you pick the concrete values based on the approximate Fin that you target.
You should set a strobeperiod in the transient simulation option equal to your sampling period. Before you start collecting the data for the fft wait for some time from the start of the simulation until whatever transient you have in the beginning of the simulation completely dies out. Make sure you take the sample at the end of the hold time, as I indicated in the picture. When setting up the FFT start from a sample time after your initial transient has died and end after N samples. This way you are sure that the FFT is calculated over an integer number of cycles and you avoid spectral leakage effects. It is good also to do one dry run, plot the signals and choose not to look at them in continuous plot but plot point only. Check that the sample points of the simulation fall where you want them to be.

 

[Chinmaye]

Thank you so much. I now get 3rd harmonic -65 db. This is pretty good. Thanks for the help.