3 Coherent Calculations

Now is the time to do a bit of math. The ADC12DJ5200RF, which we used in the example FFT plots previously, has an ADC sampling frequency (Fs) of 5,200MSPS, 65,536FFT points and an analog input frequency of 1,011MHz. Going through the calculations, this equals an analog input of 1011.102295MHz. Enter this frequency into the signal generator and data-capture software.

One way to perform these calculations is to download TI’s high-speed data converter pro software, which is a GUI for evaluating TI high-speed data converter and analog front-end platforms.

This software can automatically calculate the exact coherent frequency when you select Auto Calculation of Coherent Frequencies under Test Parameters in the bottom-left corner.

Here is the math for calculating the coherent input frequency. There are three main parameters:

• Fs – the sampling frequency of the ADC.
• N – the number of points in the FFT. N must be a number that can be represented with a power of 2, such as 1,024, 2,048 or 4,096.
• Fin – the analog input frequency.

Plugging in the values for the ADC12DJ5200RF into these parameters, you have:

• Fs = 5,200MHz.
• N = 65,536.
• Fin = 1,011MHz.

The first thing you’ll need to calculate is the FFT bin size or frequency resolution, commonly known as the resolution bandwidth (RBW). RBW is the smallest difference between two frequency bins displayed on an FFT plot, expressed as Equation 1.

Next, calculate the FFT bin number corresponding to a Fin of 1,011MHz Equation 2.

As you can see, the bin number is not an integer value, which means that the energy of the 1,011MHz signal is not contained in a single FFT bin; this is also leaking into adjacent bins. To get coherent sampling, you need to bin-center the input signal – contain all energy to a single bin.

To obtain a bin-centered (coherent) signal, you must round the bin number to an integer number. In our example, rounding the bin number can give you a value of 12,742.

Next, recalculate the Fin based on the rounded bin number to obtain the coherent input frequency (Equation 3):

The Fin value calculated in Equation 3 is coherent, but you can further improve the FFT performance measurement by choosing a bin number that is a prime number. Doing so, can eliminate signal-quantization periodicity; in other words, you can prevent the ADC from hitting the same codes along the input signal over and over in a periodical manner. Choosing a prime number as a bin number also prevents the harmonics from landing on top of each other, an effect shown in Figure 3-1.

Next, you can need to modify Equation 3 and round the bin number integer value to the nearest prime number. Now, you can redo the calculation to find Fin Equation 4.

Again using the example, the nearest prime bin number obtained earlier, 12,742, become 12,743. Plugging in the example values into Equation 4, the recalculated Fin using the nearest prime bin number becomes:

Figure 3-2 shows an improved FFT measurement by choosing a prime bin number. Notice that none of the higher-order harmonics fold on top of each other as they did in Figure 3-1, thus enabling a more accurate evaluation of the ADC.