With L1 = 25 nH, C1 = 1 µF, L2 = 30 nH, C2 = 0.033 µF, and LX = 1 µH, the item #6 decoupler shifts the 4-MHz resonance of the item #4 circuit into the 800- to 900-kHz range. The responses at 3 MHz and at 5 MHz are almost quenched. But, the response at 1 MHz undergoes a substantial increase, compared to the item #4 results, because it then resides in the neighborhood of the resonance. All of these outcomes can be predicted, at least directionally, from the ac model.
The heavier filtering of the item #7 decoupler virtually quenches the responses at all three odd frequencies. It moves the resonances to still lower regions of the kilohertz range.
The decoupler of item #8 exchanges the parallel branches of the item #6 decoupler about LX. This results in the 1-MHz and 5-MHz responses being quenched while the 3-MHz response increases slightly from its item #6 value. Consider the resonance that appears for the circuit of item #8. This frequency was found by figuring out the roots of the denominator in Equation 7. We obtain a resonance at around 3.7575 MHz.
This range-of-concern resonance is quite narrow. Its influence appears in the slight increase in the response at 3 MHz for item #8 compared to that of item #6 at 3 MHz. Given the suppression advantage that the lightly filtered item #8 configuration enjoys over the lightly filtered item #6 configuration, it may be worth the risk of accepting a weak resonance in the frequency range of concern by choosing the item #8 decoupler not only over the item #6 circuit, but also over the heavily filtered item #7 decoupler. This would achieve a lower component count/cost. Keep in mind, though, that when the higher-frequency branch is placed first to the voltage source, a resonance, however weak, remains in the frequency range of concern.
As a final consideration for the pi decoupler, we investigated the question of a minimum value for LX, which would be the smallest inductance capable of moving the resonance out of the frequency range of concern. Using the decoupler from Figure 4 (with L1 = 25 nH, C1 = 1 µF, L2 = 30 nH, and C2 = 0.033 µF), the ac model found the minimum LX value, 368 nH, which is the LX value that zeroes the denominator of Equation 7 at f = 1 MHz. The Spice method found 340 nH for minimum LX. Furthermore, inserting LX = 333 nH into our hardware model yielded the result of Figure 14.
LC Filter: The generic LC filter is shown in Figure 5. Both the lightly filtered (item #9) and the heavily filtered (item #10) versions provide good suppression. Also, both produce resonances well below the frequency range of concern. In fact, the lightly filtered item #9 decoupler results in suppression matched only by the higher-parts-counts configurations of items #7, #8, and #10. On a cost-effective basis, the configuration of item #9 is the decoupler of choice for multifrequency suppression.
The results obtained with the decoupler of item #11 illustrate the importance of careful tuning (in this case, tuning the parallel branch to a frequency equal to or less than the lowest frequency value of concern). The resonance at 864 kHz is sufficiently strong and wide to cause a spike, rather than a suppression, in the response for the 1-MHz component of iS.
One may legitimately ask why we spent so much time studying the pi configuration if the simple LC filter is so effective and cost-effective as a multifrequency decouple. Well, several reasons come immediately to mind. First, the pi filter is sometimes touted as the configuration of choice. So, it's essential to know its strengths and its weaknesses.
Consider the case of a single-branch tuned decoupler too, as in Figure 3a. If a parasitic reactive branch occurs in parallel with that decoupler, and that parasitic branch is antiresonant at a frequency other than where the decoupler produces a zero, a situation like the one in Figure 3b would result. A pole would develop at an intermediate frequency. Plus, increased emissions could occur if the new resonance multiplies one of the harmonics of iO.
A similar situation would result if the second parallel branch, rather than being parasitic, was the tuned decoupler of a nearby circuit that was switching at a rate other than that of the first circuit. In such instances, one might want to consider introducing a series inductance (LX), observing all of the points required to make the introduction effective.
Another potential cause of those "unintended consequences" so familiar to EMC workers is an LC decoupler on a nearby circuit. This could combine with the first decoupler to form a network like that shown in Figure 4, with the possibility of the various undesirable outcomes described in the Pi Filter section.
Whether it's with or without discrete inductors, tuned decoupling can be a useful way to suppress electromagnetic emissions from switched circuits. It's important, though, to carefully choose and design decouplers in order to obtain the optimum effect in a given situation.