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Calculate video ADC's differential gain, phase

01 Feb 2016  | Sambhav Jain, Abhijan Chakravarty

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When the signal's phase is zero, only in-phase components will remain, which corresponds to the signal's amplitude. This can also be described in polar form, where in-phase component (It) shows the amplitude and quadrature component (qt) is at right angle to in-phase component. As shown below, both in-phase and quadrature component can be plotted in a complex plane. Figures 3 and 4 depict the in-phase and quadrature components in polar form.


Figure 3: In-phase component in the real plane.


Figure 4: It and Qt components in complex plane.


The above principle can be used to find amplitude and phase of any sinusoidal signal, i.e. by mixing the signal separately with two copies of signals with same frequency, but delayed by 90 degree from each other. The resultant signals are called I (in-phase component) and Q (quadrature component) of the signal.

To compute the amplitude and phase of the signal, we use concepts of trigonometry.

We can simply use The Pythagoras' theorem. to calculate amplitude and phase of each sinusoidal step waveform by using the equations above.


Calculate differential gain and phase
By using quadrature modulation technique, we can calculate amplitude and phase of each sinusoidal step waveform from less number of samples with more accuracy. Since we do not use any video source, we don't have any reference signal (like colour burst in video signal) to compare amplitude and phase with. This is why we use relative mechanisms to calculate differential gain and differential phase.



After calculating magnitude and phase of each step, we use equations above for calculating differential gain and differential phase.


Limitations and workarounds
To calculate the phase at each step of the sinusoid, coherency is necessary. This means that each step of sinusoid should start from same instant and cover a complete number of cycles per step. It is difficult to achieve coherency on the bench because that requires a high-resolution function generator with accuracy up to about ten decimal places. We recommend using a DDS (Direct Digital Synthesis) based function generator because they can generate signals with lowest residual phase noise.

The video ADC under test must start each conversion from same point for each step sinusoid. This requires some type of synchronisation between the video ADC's start conversion signal and channel trigger of the function generator, such that, for each step, sinusoid starts from pre-defined value (say, from zero).

Differential gain and differential phase results are more accurate if you use higher number of stairs to cover the ADC's whole range because that provides the most granularity of the DC offset value. As we increase the number of stairs, test time also increases proportionally. That's why there is always a trade-off between test time and accuracy. We've observed that around 256 steps in the staircase are enough to check the actual performance of the video ADC.


Conclusion
Differential gain and differential phase are the two important parameters of a video ADC that need to be accurately measured to convert an analogue video signal without losing quality. The staircase method we've described is an optimum way to measure these two parameters on bench.


References
1. Brandon, David, AN-927, Determining if a Spur is Related to the DDS/DAC or to Some Other Source, Analog Devices, 2007.
2. Stephens, Randy Measuring Differential Gain and Phase, TI Application Report, SLOA040, November 1999.
3. D. Tayloe, N7VE, "Letter to the Editor, notes on "Ideal" Commutating Mixers (Nov / Dec 1991), "QEX, March/April 2001.


About the author
Sambhav Jain and Abhijan Chakravarty contributed this article.


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