how to simulate the lineartiy of amplifier in cadence?

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chichi

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as asked in the topic, i have no idea how to define the linearity of amplifier and how to simulate it ?i am doing a Gm-C filter in my master thesis, the linearity of which is very important for me to know...I have summit thesis soon, i hope someone could help me with that, thanks a lot.
 

checkmate said:
Total Harmonic Distiortion (THD) is often used as the measure of linearity.
Click to expand...
And additionally you could simulate / measure
  • gain vs. input voltage (its large signal dependency)
  • gain vs. input common voltage range
  • gain vs. frequency
 


When linearity is "very important" for your filter, I suppose you have something like a specification (or upper limit) for it, don't you ? Because "as linear as possible" is not a sufficient requirement.
Therefore, in what terms is linearity specified for the filter?
 

it´s just the professor has been telling me that gm c filter has a really bad linearity, which degrade the whole system a lot, so i need to find out this parameter, therewith i determine whether it fits my design or not..e.g the input signal ranges from 50uv to 5mv, so he told me that ,my filter master has a linearity of 40DB=5mv/50uV=100. so i am asking how can i know that my filter linearity is better than 40DB or not?

Added after 2 minutes:

checkmate said:
Total Harmonic Distiortion (THD) is often used as the measure of linearity.[/quote
hi , do u know how to find out Total harmonic Distortion by simulation?
Click to expand...
 

Sounds a bit confusing. Linearity is not specified in dB. The mentioned value of 40 dB is just the required dynamic range. How can you decide whether it "fits your design"?
For example: Is a THD of 0.1% OK or not ?

THD can be found by most simulation programs as a a result of a Tran analysis.
 

chichi said:
... a linearity of 40DB=5mv/50uV=100. so i am asking how can i know that my filter linearity is better than 40DB or not?
Click to expand...
I guess it was meant that the filter should have a satisfying linearity for an input range of 40 dB. So I'd suggest you ac simulate its gain linearity over this range, i.e. sweep your input voltage (at your operating frequency/ies) over this range and plot the gain (or better: the gain deviation) vs. input voltage.
 

erikl said:
...........
I guess it was meant that the filter should have a satisfying linearity for an input range of 40 dB.
..........
Click to expand...

Yes, this was also my understanding. However, there remains the question:
What means "satisfying"? THD=0.1 or 0.01%? Or even less?
 

LvW said:
What means "satisfying"? THD=0.1 or 0.01%? Or even less?
Click to expand...
Right: The measure of the tolerable deviation is not yet clear. For a filter design, I'd think the THD isn't that important, as the 3rd harmonic should be far outside of the operating bandwidth - but of course this depends on the filter bandwidth. That's why I suggested to investigate the gain linearity within the required dynamic input voltage range.
Let me know if you think I'm wrong with my THD speculation!
 


1.) I am afraid, if the output signal of the active device (opamp , OTA,..) is large enough (limit region of the dynamic range), the filter circuit itself cannot improve the situation.
2.) The THD examples as given in my former post are, of course, a joke (0.01%). I just wanted to know if CHICHI has a feeling for realistic THD values.
 

hi guys, i am somehow confused, i don't have a feeling for THD, i asked a tutor of me, who told me that the linearity, he said that the linearity of large signal is the dVout/dvin vs vin, when no distortion, the y axis will equals to gain..
 
chichi said:
... the linearity of large signal is the dVout/dvin vs vin, when no distortion, the y axis will equals to gain..
Click to expand...
Perfect, chichi,
that's what I suggested on Tue, 09 Feb 2010 13:26 (above) ;-) .
 


No, I don' think it is "perfect".
Of course, you can see the effect of a non-linearity by drawing dVout/dVin vs. Vin.
However, you have to quantify the non-linearity! That means, you have to derive a measure for the non-linearity from this drawing! Chichi, do you have such requirements?
 

yes , i have this requirements. i need to do a perfect thesis on linearity..

Added after 2 minutes:

i think may be the difference between the worst gain due to distortion should not too large, but how to define it...

Added after 2 minutes:

i think peple may often use dynamic range when THD=1% e,g, to define a linearity, right? but how to calculate the THD?
 
you could also use signal to THD ratio, that can be expressed in dB.

you can export the waveform and import it in Matlab, do FFT, and do signal / THD, where THD is defined as 2nd harmonic + 3rd + .... all the way until you feel like stopping.
 

As mentioned, there are many ways to define linearity. Large-signal linearity degrades as the input signal gets larger, so worst-case linearity for your case occurs at 50mV input.

THD works on the premise that a pure sinusoidal input (of a specified frequency and magnitude) should ideally give a pure sinusoidal output. If it does not, regardless whether it's due to non-linearity, limited slew rate or clipping, it will result to distortion. Looking at the FFT, the higher-order spectral components (ie harmonics greater than the first) will be non-zero!

This said, THD is simply the power ratio of the higher order harmonics to all the harmonics. This power ratio can be expressed as dB form or percentage form.

With that said, another measure of linearity may be the input range whereby a certain THD threshold can be achieved.
 

THD is simply the power ratio of the higher order harmonics to all the harmonics?harmonics over harmonivs?

Added after 1 minutes:

THD is simply the power ratio of the higher order harmonics to all the harmonics?harmonics over harmonivs?
 
Yes, it is the ratio of the sum of the power of all harmonics except the fundamental of course, to the fundamental, expressed in dB or in %. Put a pure sine wave to your filter - you can sweep the amplitude of this sine wave. Look at the output, which preferably will resemble a sine wave. Leave some time in the beginning for the output to settle to avoid any transients. Take one or few of the last output periods in your output and do an FFT on them. Measure the harmonics - it helps if you normalize the fundamental to 0dB. Usually, if the circuit is differential your biggest worry is the 3rd harmonic but have a look at the others too. Make sure you do FFT on integer number of periods.
 

i did the THD simulation using cacence, i find that with a from 1mv to 10mV input , i find the THD result to be 1.3e-02, with a 100uV input, i get the THD result 3.7e-1. so my dynamic range is only(1m to 10m) 20 DB when THD=1%??
 
Hi Chichi!
I designed a few amplifiers in my Undergrad Thesis, where the measure of the linearity was very important for me. I measured it by two methods:
1. 1dB compression point- input power for which the gain of the amplifier degrades by 1dB as the input power increases from a very small value. It let me know up to which input power limit my amplifier would remain linear.
2. IIP3 (Input Referred 3rd Order Intercept point): Gain of the amplifier for the 3rd Harmonic (A3) is much small comparing to the Gain of the Fundamental (A1). But A3 increases 3 times faster than A1 as the input power increases. IIP3 determine the input power after which gain for the 3rd harmonic is greater than that of the Fundamental, giving rise to a 3rd harmonic dominating distortion at the output.
I think, any of the above methods can be used to quantify the degree of linearity of an analog circuit, specially when operating in high frequencies ...
 

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