# Measure a video ADC’s differential gain and phase

A composite video signal consists of luminance and chrominance, both of which directly affect the quality of a video that you might see. Because most video today is digital, a video ADC is necessary to digitize the composite video signal. From the digital output, you can calculate the ADC’s differential phase and differential gain.

Luminance contains the information about brightness while chrominance contains the information about the color. Chrominance, in turn, has two components: saturation and hue. Saturation (intensity of the color) is determined by the amplitude of a video signal’s sub-carrier, while hue (shade of the color) is determined by the phase of the sub-carrier. The quality of video depends on how accurately a video ADC converts the analog video signal. The path from video source to the display is long and the system should make sure that any error in converting the video signal should not become large enough to be perceived by the viewer.

There are two important specifications of a video ADC: differential gain and differential phase, both of which affect luminance and chrominance. There are several methodologies to measure these parameters, but to measure them accurately on the bench is a challenging task.

We use a technique called staircase methodology to measure these parameters. We’ll describe how that works while explaining some practical limitations to the method.

**Differential Gain & Phase**

Differential Gain can be defined as the error in the amplitude of chrominance signal due to change in luminance level. Think of it as change in amplitude of sinusoidal

signal by changing DC offset of input signal. This error varies color saturation with brightness. For example, a red rose turns pink as evening approaches.

Differential phase can be defined as the error in the phase of chrominance signal due to change in luminance level. Here, the phase of the sinusoidal signal changes

with DC offset. This error varies the hue or the shade of the color with brightness. Figure 1 shows a representation of these errors.

**Figure 1. Illustration of Differential Gain and Differential Phase.**

**Measurement methodology
**There is no single predefined method for measuring differential phase and gain. Several methods can be used such as the Ramped-Sine method, Staircase method, or by overlapping slow sine on fast sinusoidal signal. The intent of each of these methodologies is to check how good a Video ADC can reproduce a fast varying sinusoid with slowly changing DC offset. We use the Staircase method because both differential gain and differential phase can be measured using the same setup in single test.

In the staircase method, the ADC’s input is a sinusoidal signal overlapped on each step of a staircase signal that covers the entire ADC range. This signal can be

created by simply varying the DC offset of a sinusoidal signal coming from a waveform generator. Figure 2 is a typical video ADC output when there is a sine-overlapped staircase waveform at its input.

**Figure 2. The test signal consists of a sine wave overlapped with staircase function.**

Measurement granularity and accuracy of the measurement improves as the number of steps increases. The number of steps should be decided in such a way so as to balance between the accuracy of the measurement and the test time. Amplitude of the sinusoid should be around 20% of full input range and staircase should cover entire ADC range. Peak-to-peak amplitude and phase are calculated for each step of the staircase.

There are quite a few methods for calculating the phase and amplitude of the ADC’s output signal. You can use frequency domain techniques, but accuracy decreases as the number of samples decreases per step. That’s why there is tradeoff between test time and accuracy. You can also use a time-domain approach like Quadrature Sampling.

**Quadrature Sampling Technique**

Any sinusoidal signal can be split up into two amplitude modulated sinusoids which are phase apart from each other by 90 degrees. These sinusoids are called In-phase and Quadrature components of the signal. By using these two signals, we can synthesize the actual signal. A mathematical representation of these components is shown in the equation below. It shows the in-phase and quadrature components of a sinusoidal waveform.

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 & 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 color 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 synchronization 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 analog video signal without losing quality. The staircase method we’ve described is an optimum way to measure these two parameters on bench.

**References:**

Brandon, David, AN-927, Determining if a Spur is Related to the DDS/DAC or to Some Other Source, Analog Devices, 2007.

Stephens, Randy Measuring Differential Gain and Phase, TI Application Report, SLOA040, November 1999.

D. Tayloe, N7VE, "Letter to the Editor, notes on "Ideal" Commutating Mixers (Nov / Dec 1991), "QEX, March/April 2001.