# Tuned Decoupling Tames Noise In Switching Circuits

As printed-circuit boards become more densely populated, the opportunities for* *"intra-module" interference grows. Similarly, the probability of "inter-module" interference increases. The move to higher switching rates, higher spectral content, and higher power exacerbates these trends. At the same time, engineers struggle with more stringent emissions regulations. Together, these considerations elevate the need to effectively decouple switching circuits.

To achieve effective decoupling, the decoupling source—invariably a good-quality capacitor located close to the switching circuit—must provide the ac content of the switched current. Meanwhile, the main power source—usually located away from the target—must provide the average current and, hence, all of the energy. This confines the high-frequency currents to a small loop in the vicinity of the target, thus minimizing board emissions. In addition, high-frequency currents are kept off the power and ground buses, which minimizes inductively coupled interference. Furthermore, because the ripple voltage across the decoupler (i_{1}Z_{1}) appears on the power bus, minimizing this voltage will reduce capacitively coupled interference *(Fig. 1)*.

A number of recent papers have considered the effect of both the pc board's bus structure^{1, 2} and the characteristics of the decoupling capacitors themselves^{3 }on suppressing emissions. Here, we mainly investigate the benefits and caveats of using decoupling networks, which suppress specific frequencies. Engineers are often challenged to suppress one or more clock frequencies and, perhaps, related harmonics or sub-harmonics. In most cases, general decoupler choices do not efficiently address the highly defined suppression targets.

Consider the lumped-parameter model shown in Figure 1. Here, the target (switching) circuit is modeled as an ac current source. V_{y }(f, t) is the ac voltage developed at point y on the power bus, due to the interaction of switching currents and system impedances; i_{0} (f, t) is the ac current drawn by the target circuit; i_{1} (f, t) is that part of i_{0} supplied by the decoupler, and i_{S} (f, t) is the part of i_{0} that flows on the power bus. Z is the total impedance of the power bus; Z(y) is the power bus impedance between the decoupler and point y; Z_{1} is the impedance of the decoupler; and Z_{0} is the impedance between the decoupler and the target. For convenience, we have incorporated the internal impedance of the main power source into Z. The equations are:

Notice that both i_{S} and V_{y} have zeroes at Z_{1} = 0 and have poles at Z_{1}+ Z = 0.

Now, let's consider some familiar decoupler configurations: 1) single-branch, pure (ideal) capacitance; 2) single-branch, capacitance plus inductance; and 3) dual-branch, capacitance plus inductance.

Pure Capacitance In the good old days, before the advent of modern switching frequencies, it was reasonable to assume pure capacitance for a decoupler. Switching rates were low enough that trace, lead, and connection inductances could usually be ignored. In this case, the model of Figure 2 guides the analysis. From now on, we shall ignore the effect of Z_{0}, since doing so does not affect the generality of our analyses. The equations for this configuration are:

where

The frequency response of the relative amplitude, i_{S}/i_{0}, has a pole at f = f_{}.

The main consideration in such a situation is the selection of C^{1}. This value should be such that the amplitude, |i_{S}/i_{0}|, is well rolled-off in the frequency range of interest, and f_{} is far from this region.

where

is a zero of the response, and

is a pole.

The existence of a zero at f = f_{1} immediately suggests a method of optimally decoupling a specific frequency. That is, choose a decoupling capacitor that just happens to have its impedance anti-resonant at the target frequency. Then, connect this component into a negligible-inductance decoupler branch. At the target frequency, all of the current is provided by the decoupler. None of this current flows in the power bus (or ground bus).

Between the target frequency and the anti-resonant frequencies of the available decoupling capacitors, a sufficiently close match cannot always be found. In this situation, a tuned decoupling can still be achieved by choosing a capacitor with an anti-resonant frequency, f_{ar}, such that f_{ar} > f_{1}, where f_{1} now designates the target frequency. Let C_{1} be, once again, the capacitance of the decoupling component. Then

where l_{1} is the intrinsic inductance of the component. Consequently, if external inductance is added to the decoupling circuit, as in

a branch is constructed that maximally decouples the target frequency.

The additional inductance may be inserted in the form of a discrete component. Or, it may be obtained in the form of a pc-board trace of appropriate geometry. For an example of the calculation of trace inductances, see the Rostek article.^{4}

In some situations, it may be worth considering multiple decoupling branches. For example, tuned circuits have residual, if minor, resistance at the anti-resonant frequency. In order to achieve an even lower response at this frequency, identically tuned decoupling branches are sometimes placed in parallel in the circuit.

A second example of an application for multiple decoupling branches is provided by the need to suppress several frequencies simultaneously. In this case, several decoupling branches, each one tuned to a different target frequency, might be used. Though the following analysis is for dual decoupling branches *(Fig. 4)*, the extension to more than two branches can be made relatively easily.

Consider a dual branch decoupler in which the each of the branches is tuned to different frequencies, f_{1} and f_{2}. The equation is:

where

and

for f_{2} > f_{1}.

For the real-life application of these techniques, consider the reduction of radiated emissions from the I/O harness of a pre-production electronic module. Shielding the harness was not an option. Furthermore, since the design was all but "frozen," extensive rework of the pc board was out of the question. Appreciable reduction of radiated emissions, with minimal intervention, was required.

Regulator Noise The offending frequencies were the 750-kHz fundamental and 1.5-MHz second harmonic, produced by a commercially available switching regulator. The power-input pin of the regulator was connected to the filtered output of a pre-regulator by 1.5 in. of a 100-mil wide, 2-mil thick isolated trace. Using Rostek's formula^{4}, the inductance of this trace calculates to be 29.4 nH. The regulator was returned directly to a very low-impedance ground plane.

In an initial attempt at decoupling, the board already had a high-quality dielectric, 1-µF ceramic surface-mount capacitor "downstream" of the regulator at a site designated C236 *(Fig. 5)*. The capacitor at this site was connected to the power-input pin of the regulator by a two-section, series-connected trace. One section of the trace measured 0.94 in. long, 100 mils wide, and 2 mils thick. The other section measured 0.150 in. by 100 mils by 2 mils. The capacitor was returned to the ground plane by a 0.32-in. by 50-mil by 2-mil trace. All of these traces were located at a height of 20 mils over the ground plane. The inductance of the complete trace calculates to be 17.6 nH.

A 1-µF capacitor of this type has a minimum impedance, which is a zero, at about 5 MHz. This yields an intrinsic inductance (equation 6) of about 1 nH. Thus, the zero of the decoupling loop, for a 1-µF capacitor at C236, calculates to 1.17 MHz, with a pole (equation 7) at 728 kHz.

Preliminary benchtop tests were conducted using an H-field "wand" and a spectrum analyzer. The tests measured the relative strengths of the frequencies radiating from the harness. Baseline measurements were made with no decoupling *(Fig. 6)*. For the second case, measurements were made with the 1-µF surface-mount capacitor at the C236 site. The decoupling significantly reduced the second harmonic, as expected, but had little effect on the fundamental. This latter result is due in part to the pole at 728 kHz being located so close to the fundamental.

The surface- mount capacitor was replaced by a 1- µF radial capacitor for the third case. This was tuned to have a zero at 700 kHz, obtained by providing about 52 nH of lead inductance. With this capacitor, the decoupling loop has a zero at 600 kHz and a pole at 500 kHz, yielding significant reduction at the fundamental frequency, and some reduction at the second harmonic.

Capacitor Returned For the fourth case*(Fig. 7)*, the surface mount capacitor was returned to the C236 site, and the radial capacitor was connected directly on the power input and ground pins of the regulator. This resulted in zeros at 698 kHz and 1.17 MHz, unity at 847 kHz (equation 11), and poles at 531 kHz and 916 kHz. The reduction at the fundamental is not as great as in the third case, probably because of the proximity of the unity to the higher-frequency pole. However, the reduction at the second harmonic is as substantial as that obtained in the third case, in spite of the 916-kHz pole.

Subsequent radiated emissions measurements—in an anechoic chamber—supported the "wand" results. A variation of the fourth case was used for the production module.

The use of tuned decouplers can be very helpful, particularly in those situations in which the main contributors to interference are sharply defined, well-separated frequencies. As shown, however, the technique introduces poles as well as zeros, and should be applied with these considerations in mind. For maximum effectiveness, the poles should be located in the frequency-range regions in which there is no interference structure. They should also be located at a sufficient distance from the zeros, so that the presence of the poles does not degrade the decoupling effect.

References:

- Shi, H., Yuan, F., Drewniak, J. L., Hubing, T.H. and VanDoren, T.P., "Simulation and Measurement for Decoupling on Multilayer PCB DC Power Buses,"
*IEEE Electromagnetic Compatibility Symposium Digest*, Santa Clara, CA, 1996. pp. 430-435. - Hubing, T., Van Doren, T., Sha, F., Drewniak, J., and Wilhelm, M., "An Experimental Investigation of 4-layer Printed Circuit Board Decoupling,"
*IEEE Electromagnetic Compatibility Symposium Digest*, Atlanta, GA, 1995, pp. 308-312. - Daijavad, S. and Heeb, H., "On the Effectiveness of Decoupling Capacitors in Reducing EM Radiation from PCBs,"
*IEEE Electromagnetic Symposium Digest*, Dallas, TX, 1993, pp. 330-333. - Rostek, P. M., "Avoid Wiring-Inductance Problems,"
*Electronic Design*, Dec. 6, 1974, pp. 62-65.