Engineering Guide
Capacitor Networks, Reactance, Impedance, and AC Behavior
Equivalent capacitance is only the start of a network design. Frequency, phase, voltage sharing, ripple current, ESR, ESL, leakage, derating, and layout determine whether the real bank behaves like the ideal result.
Network Analysis Workflow
| Step | Action | Engineering Check |
|---|---|---|
| Define the waveform | Set DC bias, RMS and peak AC voltage, frequency range, harmonics, transient energy, and duty cycle. | |
| Choose topology | Use parallel parts for more capacitance and current sharing; use series parts only with voltage-sharing analysis. | |
| Calculate ideal equivalent | Apply the correct reciprocal or additive relationship using base units. | |
| Calculate frequency behavior | Find reactance and complex impedance at every relevant frequency, not only a nominal point. | |
| Calculate current and energy | Use RMS current for heating and peak voltage for dielectric stress and stored energy. | |
| Add nonideal elements | Include ESR, ESL, leakage, tolerance, bias derating, temperature, and self-resonance. | |
| Check ratings | Verify voltage distribution, ripple current, dissipation, temperature rise, and surge or pulse limits. | |
| Validate | Measure capacitance, impedance, current, voltage sharing, and temperature under the real assembly conditions. |
Ideal and Real Quantities
| Quantity | Formula or Meaning | Boundary |
|---|---|---|
| Parallel capacitance | Ceq = sum(Ci) | Voltage is common; ideal current divides by branch impedance |
| Series capacitance | 1/Ceq = sum(1/Ci) | Charge is common; voltage division depends on capacitance and leakage |
| Reactance XC | 1/(2 pi f C) | Magnitude of ideal capacitor impedance |
| Ideal impedance | ZC = 1/(j omega C) = -jXC | Includes the -90 degree phase relation |
| Real impedance | ESR + j(omega ESL - 1/(omega C)) | Changes near self-resonance |
| Stored energy | 0.5 C V squared | Uses capacitor terminal voltage |
| Ripple loss | Approximately Irms squared x ESR | ESR varies with frequency and temperature |
Series and Parallel Networks
Formula reference
Equivalent capacitance
Parallel: Ceq = sum(Ci)Series: 1/Ceq = sum(1/Ci)Two in series: Ceq = C1 C2/(C1 + C2)Series ideal voltage: Vi = Q/CiVariable definitions
- Parallel branches share voltage
- Ideal series parts share charge
- Real DC voltage sharing depends on leakage
- Recalculate tolerance corners
Use the Series & Parallel Capacitor Calculator for ideal equivalents, then check voltage and ripple-current sharing.
Reactance, Impedance, Current, and Loss
Formula reference
AC capacitor model
XC = 1/(2 pi f C)Zideal = -jXCIrms = Vrms/XCZreal approximately ESR + j(omega ESL - 1/(omega C))Ploss approximately Irms squared x ESRE = 0.5 C V squaredVariable definitions
- Reactance is not real resistance
- Use RMS current for heating
- ESR and ESL depend on frequency and construction
- Check self-resonance and bias derating
Use the Capacitive Reactance Calculator for the ideal frequency relationship. Use the existing RC design Guide when a resistor and transfer function define the circuit.
Worked Examples
Parallel pair
10 uF and 22 uF in parallel give 32 uF ideal equivalent capacitance.
Series pair
10 uF and 22 uF in series give about 6.875 uF ideal equivalent capacitance.
Equal series parts
Two equal 100 uF capacitors in series give 50 uF and ideally split applied voltage equally.
Tolerance corner
Parallel minimum and maximum values are found by summing the individual tolerance corners, not by assuming nominal.
Reactance
A 1 uF ideal capacitor at 1 kHz has XC about 159.15 ohms.
AC current
With 10 V RMS across that ideal capacitor, current magnitude is about 62.83 mA.
Frequency scaling
Doubling frequency halves ideal capacitive reactance.
Stored energy
A 100 uF capacitor at 12 V stores 7.2 mJ.
ESR heating
A 2 A RMS ripple current through 40 milliohms ESR produces about 0.16 W loss.
Self-resonance
Above self-resonant frequency, ESL dominates and the part behaves increasingly inductively rather than as an ideal capacitor.
Common Mistakes
Related Calculators
Support reference
FAQ
How do capacitors add in parallel?
Ideal parallel capacitances add directly because every branch has the same voltage and branch charge adds.
How do capacitors add in series?
The reciprocal equivalent is the sum of reciprocal capacitances. For two parts, Ceq equals C1 times C2 divided by C1 plus C2.
Why is series capacitance smaller than either capacitor?
The same charge must develop voltage across each part, so total voltage per unit charge is larger and equivalent capacitance is smaller.
Do series capacitors share voltage equally?
Only identical ideal capacitors do. Real DC sharing depends strongly on leakage, tolerance, temperature, and balancing networks.
What is capacitive reactance?
Capacitive reactance magnitude is 1 divided by 2 pi frequency and capacitance. It decreases as frequency or capacitance increases.
Is capacitive reactance the same as resistance?
No. Ideal capacitor impedance is imaginary and produces phase shift; resistance dissipates real power.
How do I calculate capacitor AC current?
For a sinusoid in the ideal model, RMS current magnitude equals RMS voltage divided by reactance, or 2 pi f C times RMS voltage.
How is capacitor energy calculated?
Stored energy is one half capacitance times terminal voltage squared.
Why does a capacitor heat under AC ripple?
RMS ripple current dissipates power in ESR and other dielectric and conductor losses.
What is capacitor self-resonance?
Capacitance resonates with package and connection inductance. Near resonance impedance reaches a minimum; above it the part becomes increasingly inductive.
Can I parallel capacitors to increase ripple-current capability?
Often yes, but current sharing depends on ESR, ESL, value, temperature, and layout. Verify individual and bank ratings.
How should I validate a capacitor network?
Use the exact parts' impedance and derating data, inspect layout parasitics, and measure voltage sharing, ripple current, impedance, and temperature over operating corners.
Summary
Apply the correct network equation, calculate complex behavior across frequency, and close the design with voltage sharing, ripple-current, ESR, ESL, self-resonance, derating, tolerance, and thermal checks using the exact component data.