# THD calculation with two outputs

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#### talking

##### Member level 2
I have a flash ADC with +/-2v input range.
In general, the total harmonic distortion (THD) is measured as:
input x(t)=2*sin(wt) is applied to the ADC, and output y(t) is measured. Then THD is calculated from y(t) as

THD(V/V) = (v_s)^2 / {(v_xh1)^2 + (v_xh2)^2 + ...} (eq.1)
where v_s: signal magnitude in voltage, v_xh1: harmonic magnitude in voltage, ...

Due to some reason, I need to measure the THD differently. Here is my procedure:
One at a time, 2 different sine inputs are applied to a flash ADC with +/-2v input range.
That is,
input x1(t) = sin(wt)+1 : this input swings from 0v to 2v, and output y1(t) was measured.
input x2(t) = sin(wt)-1 : this input swings from -2v to 0v, and output y2(t) was measured.

So, each input stimulates upper input range (0~2v) and lower input range(-2~0v) of the ADC.
Only using y1(t) and y2(t) outputs, the same overall THD, which was calculated in (eq.1), should be calculated.

For y1(t),
THD1(V/V) = (v_s1)^2 / {(v_x1h1)^2 + (v_x1h2)^2 + ...} (eq.2)
where v_s1: signal magnitude in voltage, v_x1h1: harmonic magnitude in voltage, ...

For y2(t),
THD2(V/V) = (v_s2)^2 / {(v_x2h1)^2 + (v_x2h2)^2 + ...} (eq.3)
where v_s2: signal magnitude in voltage, v_x2h1: harmonic magnitude in voltage, ...

I'm stuck at this status now.
Could you help to calculate the same THD shown in (eq.1), using (eq.2) and (eq.3)?

There will also be intermodulation products so you cant merely take ratios of each harmonic.

just add total signals (v_s1)^2 + (v_s2) and divide by all harmonics^2 and intermod products^2 or better yet measure results with a good DAC on a Spectrum Analyzer/

Then check linearity and montonicity errors with a sawtooth +/-2V and output on a better DAC to compare Out-In or compare on scope, CH1+Ch2Invert.

Often monotonicity errors occur at 000111xxx to 001000xxx due to Vref ground shift from logic current coupled to analog ground. This results in THD including IHD in addition to linearity errors.

Thank you, SunnySkyguy.
From my understanding, your suggestion might be as

THD(V/V)= {(v_s1)^2 + (v_s2)^2 } / [ {(v_x1h1)^2 + (v_x1h2)^2 + ...} + {(v_x2h1)^2 + (v_x2h2)^2 + ...} + intermodulation_terms^2]

Correct?

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