EMC Resonance Part II: Decoupling Capacitors

EMC Concepts Explained

EMC Resonance
Part II: Decoupling Capacitors

n Part I [1] the concept of resonance was introduced and applied to the circuit models of the non-ideal passive components. In Part II the resonance phenomenon is explained using several common decoupling capacitor configurations. Simulation results are compared to the measurement results for different decoupling approaches.

1. Decoupling Capacitor and an RLC Resonant Structure

In [1] it was shown that a capacitor itself is an RLC resonant structure, with the input impedance curve similar to the one shown in Figure 1.

The plot shown in Figure 1 corresponds to a 120 pF capacitor with an internal parasitic capacitance of 0.214 nH. When a decoupling capacitor is placed on a PCB, an additional parasitic inductance coming from the PCB trace itself needs to be added to the circuit model.

Figure 1: Input impedance curve of a 120 pF capacitor with a parasitic inductance of 0.214 nH

To account for the inductance of a short PCB trace let’s increase the parasitic inductance in the circuit of Figure 1 to 2.4 nH and study the resonance for different combinations of capacitor values, each with the parasitic inductance of 2.4 nH, and parasitic resistance of 0.1 Ω.

We begin by comparing the input impedance of a single 1 nF capacitor vs. the impedance of multiple capacitors of the same value.

Figure 2: Single 1 nF capacitor vs. multiple 1 nF capacitors

2. Resonance – Single Capacitor vs. Multiple Capacitors of the Same Value

Consider a network consisting of a 1 nF capacitor with a circuit parasitic inductance of 2.4 nH, and a parasitic resistance of 0.1 Ω. Let’s look at the impedance curves of three different networks: single 1 nF capacitor, two 1 nF capacitors, and four 1 nF capacitors, shown in Figure 2.

The impedance curves for these networks are shown in Figure 3.

Figure 3: Impedance simulation results – capacitors of the same value

The resonant frequency of the series RLC circuit is given by [1]:

and is consistent with the value shown in Figure 3. L and C in Eq. (1) are the total inductances and capacitances, respectively. These values do not change for different configurations of Figure 2 since, at resonance, the capacitor networks are connected in parallel. The total parallel capacitance, C_par, and the total parallel inductance, L_par, (assuming that the mutual inductances are negligible [2]) are given by

where n is the number of capacitors. And thus

The impedance value at resonance does not stay constant and is equal to

In [3] we measured the impedance of four-layer PCBs populated with one 1 nF, two 1 nF and four 1 nF capacitors.

Figure 4 shows the impedance curves for the case of a single 1 nF capacitor vs. two 1 nF capacitors, while Figure 5. Compares two 1 nF capacitors vs. four 1 nF capacitors.

Figure 4: Impedance measurement – single 1 nF vs. two 1 nF capacitors

Figure 5: Impedance measurement – two 1 nF vs. four 1 nF capacitors

Note that, in Region 1, the measurement results, shown in Figures 4 and 5, are consistent with the simulation results of Figure 3.

3. Resonance – Two Capacitors with Values Decades Apart

Next, consider a network with two capacitors, with their values either one or two decades apart, as shown in Figure 6.

The impedance curves for these networks are shown in Figure 7.

Figure 6: Two capacitors decades apart

Figure 7: Impedance curves – two capacitors decades apart

Let C₁ = 100 nF, C₂ = 10 nF, C₃ = 1 nF. Under the condition C₁ << C₃, the first resonant frequency is approximately [4],

while under the condition C₂ << C₃, the second resonant frequency is approximately

The anti-resonant frequency can be approximated from

Note that these calculated resonant frequencies are consistent with the simulation results in Figure 7. Next, let’s compare these results with the measured values, shown in Figure 8.

Figure 8: Impedance measurement – capacitors decade apart

Again, the measured resonant frequencies are consistent with the analytical and simulation results.

4. Resonance – Three Capacitors with Values Decades Apart

Finally, let’s consider a network with three capacitors decades apart and compare their impact against four capacitors of the same value, as shown in Figure 9.

The impedance curves for these networks are shown in Figure 10.

Note that now we have three resonant frequencies and two anti-resonant frequencies. Next, let’s compare these results with the measured values, shown in Figure 11.

Note that the measured resonant frequencies are consistent with the calculated and simulated values. Also, the measured anti-resonant frequencies agree with the predicted simulated values.

Figure 9: Three capacitors decades apart vs. four capacitors of the same values

Figure 10: Impedance curves – three capacitors decades apart

Figure 11: Impedance measurement – three capacitors decade apart

References

Bogdan Adamczyk, “EMC Resonance – Part I: Non-Ideal Passive Components,” In Compliance Magazine, February 2021.
Henry W. Ott, Electromagnetic Compatibility Engineering, Wiley, 2009.
Bogdan Adamczyk and Jim Teune, “Impact of Decoupling Capacitors and Embedded Capacitance on Impedance of Power and Ground Planes – Part II,” In Compliance Magazine, April 2020.
Clayton R. Paul, Introduction to Electromagnetic Compatibility, Wiley, 2006.

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Dr. Bogdan Adamczyk is professor and director of the EMC Center at Grand Valley State University (http://www.gvsu.edu/emccenter) where he regularly teaches EMC certificate courses for industry. He is an iNARTE certified EMC Master Design Engineer. Prof. Adamczyk is the author of the textbook “Foundations of Electromagnetic Compatibility with Practical Applications” (Wiley, 2017) and the upcoming textbook “Principles of Electromagnetic Compatibility with Laboratory Exercises” (Wiley 2022). He can be reached at adamczyb@gvsu.edu.

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