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Parallel Capacitor Network, Impedance, and Anti-Resonance

Combine 1–6 C-ESR-ESL branch types by complex admittance to calculate network impedance, branch self-resonance, and model anti-resonance peaks.

FORMULAv2.0.0
INPUT PARAMETERS

Enter parallel-capacitor network parameters

Supports 1–6 parallel branch types. C, ESR, ESL, and quantity are required for every branch; the data source is optional.

PARALLEL BRANCH 1Branch 1
Curve sweep rangeDisplay setting; does not change the current-frequency calculation
CALCULATION RESULT

Calculation result

Calculated locally
∿

Enter the parameters and run the calculation to see results and model assumptions here.

FORMULA & TRACEABILITY

Formulas and applicability

Formulas, variables, and model boundaries are published. References last reviewed on 2026-08-30.

4 formulas · 5 references
CORE EQUATIONS

Core equations

These equations directly produce the primary results and define the tool’s core model.

2
F01

Capacitor series-RLC equivalent impedance

Z(f) = ESR + j(2πf·ESL − 1/(2πfC))

Describe a capacitor’s first-order frequency response using series capacitance C, equivalent series resistance ESR, and equivalent series inductance ESL.

C
Equivalent series capacitanceF
ESR
Equivalent series resistanceΩ
ESL
Equivalent series inductanceH
f
FrequencyHz
Applicability
  • C, ESR, and ESL are treated as constant over the selected sweep
  • This equation applies to each independent branch; mounting inductance, DC bias, temperature, and frequency-dependent loss are excluded
F02

Parallel-capacitor network complex admittance

Y_total(f) = Σᵢ nᵢ/Zᵢ(f), Z_total(f) = 1/Y_total(f)

Retain the real and imaginary parts of each device type, then accumulate complex admittance by quantity; impedance magnitudes of unlike capacitors cannot be directly combined in parallel.

Zᵢ
Series-RLC complex impedance of one device of type iΩ
nᵢ
Parallel quantity of identical devices of type i1
Y_total
Total network complex admittanceS
Z_total
Total network complex impedanceΩ
Applicability
  • All branches connect to the same pair of ideal nodes
  • Shared trace, via and plane inductance, and mutual coupling between branches are excluded
  • Anti-resonance annotations are local impedance maxima of the lumped model and require verification with a vendor model or measurement
BOUNDARIES & RULES

Boundary and rule equations

Check model applicability, measurement conditions, and regulatory rules.

2
F03

Series self-resonant frequency

f_SRF = 1/(2π√(ESL·C))

In the first-order series-RLC model, capacitive and inductive reactance cancel; ESR sets the impedance floor at self-resonance.

f_SRF
Series self-resonant frequencyHz
C
Equivalent series capacitanceF
ESL
Equivalent series inductanceH
Applicability
  • First-order series-RLC model
  • ESR, ESL, and C are positive
F04

PDN target impedance

Z_target = ΔV_allowed / ΔI_max = V_DD·ripple% / ΔI_max

Define a PDN design target from the ratio of allowed voltage disturbance to maximum transient-current step; this is a design budget, not a standards limit.

Z_target
PDN target impedanceΩ
ΔV_allowed
Allowed voltage disturbanceV
ΔI_max
Maximum transient-current stepA
Applicability
  • Voltage and current use consistent peak or step conventions
  • For early design budgeting only
REFERENCES

References

01KEMET / YAGEO Group · Technical training material, equivalent circuit and SRFCapacitor Fundamentals2017 · Presents the series C-ESR-ESL model, impedance magnitude, and self-resonant-frequency relationship.
02Murata Manufacturing · Murata technical articleWhat are impedance/ESR frequency characteristics in capacitors?2012 · Explains how ESR and ESL affect high-frequency impedance and capacitive/inductive behavior around self-resonance.
03Keysight Technologies · Impedance measurement application guidanceHow to Measure Parasitic Capacitance in Test FixturesWeb edition accessed in 2026 · Explains how fixtures, connectors, calibration, and parasitics affect high-frequency impedance measurements.
04Analog Devices · Training and design handbook, Section 4Practical Power Solutions, Section 4: Power Supply System DesignOfficial technical material · Gives 1/Z_total=Σ(1/Z_i) for a parallel network and explains that unlike types or values require complex-impedance calculation.
05Analog Devices · Analog Devices Engineer-to-Engineer Note EE-253EE-253: Design Considerations for High Frequency Decoupling Networks2004 · Explains that unlike capacitor values in parallel can form anti-resonant peaks above individual branch impedances and cause ringing.
Engineering use notice

Results use the models and assumptions shown on this page for design estimates and pre-compliance risk review. Complex structures, dispersion, near-field coupling, and test setup can cause significant deviation.

FAQ

Frequently asked questions

What is the capacitor self-resonant frequency formula?

f_SRF = 1 / (2π·√(L·C)), where L is the equivalent series inductance (ESL). Above the SRF the capacitor behaves inductively and decoupling fails.

What is an anti-resonance peak?

When capacitors of different values are paralleled, the ESL of the larger capacitor resonates with the C of the smaller one, creating an impedance peak (anti-resonance)—a classic decoupling pitfall.

How should decoupling capacitors be combined?

Overlap impedance curves to cover the target band while keeping anti-resonance peaks below the target impedance. Use decade spacing (e.g., 10 μF / 100 nF / 1 nF) and low-ESL packages.

PRE-COMPLIANCE SUPPORT

Need accredited testing or pre-compliance support?

These tools support design-stage estimates. For accredited EMC testing, compliance decisions, and troubleshooting, contact us.

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