3 Solving for R

To conduct an RCL reactive match, first determine the R value of the front end. You could split the termination between the primary and secondary of the balun, but in this example we only terminate the secondary of the balun in order to minimize the number of components required. Depending on the application and signal-chain lineup, a split termination across the balun’s primary and secondary may make more sense.

As shown below, the calculations reveal how to solve the R value which completes the differential termination required by the secondary of the balun. A good starting point for setting up the secondary differential termination is to use the ideal case, 100Ω, since this balun has an 1:2 impedance ratio. The balun does have losses and parasitics that change over frequency. So, to start the calculation and obtain a more proper R value termination, use the balun’s RL number at the specified center frequency (940MHz in the example) to calculate the characteristic impedance (Zo) to which the balun needs to be properly matched for optimized signal power transfer to the load.

The example illustrates how to calculate the secondary termination of the balun chosen. The TCM2-33WX+ data sheet specifies –16.3dB at 940MHz. Using this value, solve for the characteristic impedance as reflected from the balun’s secondary (Equation 1):

Therefore, Zo = 36.72Ω (primary impedance).

In an ideal 1:2 impedance balun, 100Ω on the secondary should equal 50Ω on the primary; see Figure 3. This is not the case in actuality, however, as shown in the calculation. To determine the actual impedance reflected back to the primary, use the value of Zo found in the previous step, and back-calculate to get the proper termination on the secondary side (Equation 2):

Therefore, , where solving for X = 136.1Ω.

Because the balun has some unaccounted losses at this frequency, the 136Ω secondary termination helps compensate for these losses and provides a better termination value to start with on the secondary, reflecting back the correct impedance at this specific intermediate center frequency onto the primary of the balun. Proper impedance matching will achieve a closer 50Ω match on the primary to yield the maximum signal power transferred from the source.

The 136Ω secondary termination is an aggregate termination. Because the ADC itself already has a 100Ω differential termination inside, place one series 33Ω resistor on each side of the secondary. Review Figure 2 again. You have now solved for the R value required.

A –16dB RL at 940MHz may allow you to use smaller resistor values or possibly eliminate them altogether. I recommend keeping resistors in the design, however, as the ADC’s internal differential impedance has a ±10% tolerance range from process variations; the RL of the balun will have tolerances as well. Adding in a small amount of extra resistance helps keep the overall impedance more accurate, as you will notice when looking closely at the ADC’s S-parameter values at 940MHz.