4 Solving for L

The next step is to “resonate out” the ADC’s internal C to determine an equivalent shunt inductor or L value for the match. To choose this value, first find the internal C value of the ADC using one of two methods:

• Use the ADC model given in the data sheet (Figure 1) to determine the aggregate parasitic internal front-end capacitance or C value, estimated as approximately 1.85pF.
• Use the S-parameters from the ADC3669 webpage. See reference [4].

The second approach offers a more precise capacitive number at the frequency of interest, as the capacitive value found at 940MHz will be more absolute versus the first approach, where the C value in the model covers the full range of the ADC’s input BW. Let’s review both approaches in order to understand the trade-offs.

In both methods, the idea is to simply set the two reactive elements to be equal (Equation 3):

Next, set f to the resonate center frequency of your NB application. For the example, I will use 940MHz.

In the first method, if f = 940MHz,

Then, solving for L = 15.5nH.

In the second method, you need to use the S-parameters and plot them in a simulator in order to determine the C value at 940MHz; see Figure 4.

The second method is a bit more involved; the Smith chart plots the S-parameters in a series R + jXc configuration. The R + jXc needs to be parallel-transformed so that the R and Xc are in parallel, or R||Xc. See Figure 5 and Equation 4:

Use Equation 5 to obtain the parallel transformation:

Recalling the two inflated 33Ω resistors used to set the R value in the previous section brings the aggregate resistive termination seen by the balun to 130.2Ω, which is closer to 100Ω differential that the balun would see ideally with a smaller or no R value at all.

Next, solve for the parallel capacitor at 940MHz, see Equation 6:

Now use the same equation as above in order to find the appropriate shunt L value. If f = 940MHz, C = 1.62pF, then . Solving for L = 18.1nH.

These two C values found in the two methods above (eg: 1.85pF and 1.62pF) are on the order of the same magnitude; therefore, you need to consider the internal inductive L parasitics, as well as the external L parasitics that get added in, based on your layout.

It is also possible to simulate the entire frontend in ADS simulator package, as shown in Figure 6, which uses the S-parameters of the TCM2-33WX+ balun and the ADC3669. The simulation results shown in Figure 7 show very good RL (<–15dB), indicating that 18nH is a good match at 940MHz.

Next, let’s compare our simulated results against some measured data in the lab. Figure 8 illustrates the use of the ADC3669 EVM to implement the front-end match to measure a passband flatness response. The resonant point is centered, but the match is a bit more wideband than expected. This is where simulation can be inadequate. A 3D electromagnetic simulation solver might be able to capture all of the board parasitics in order to get a closer 1:1 match between the simulation and lab measurements. There are a few second- and third-order nuances to uncover, however. Next, we will add in a shunt C to complete the RCL reactive match to make the lab measurement narrower, as expected.