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# Example39Charge and Discharge of Capacitor

### General

• The process of charging and discharging capacitor is analyzed. The capacitor is set as a lumped constant boundary.

• The current discharged from the capacitor can be used as a current waveform for the ESD test.

• Unless specified in the list below, the default conditions will be applied.

• Electromagnetic-transient analysis is available in an optional package.

### Analysis Condition

 Item Setting Solver Electromagnetic Analysis [Hertz] Analysis Space 3D Analysis Type Transient Analysis Unit mm

 Tab Setting Item Setting Mesh Frequency-Dependent Meshing Select “The conductor bodies thicker than the skin depth constitute the boundary condition.” Select Determine the reference frequency automatically from the input waveform Transient Analysis Finish Time of Calculation 2.0×10-6 [s] (HBM) 0.5×10-6 [s] (MM)   Deselect End automatically if the ratio residual fields falls below the threshold

### Model

The process of charging and discharging capacitor depends on the circuit configuration where the capacitor is used. The discharged current of capacitor used for the ESD testing

has a transitional waveform. The circuit is configured so as to reproduce the environment where the ESD testing is conducted.

In this example, two types of circuits are prepared for the ESD testing at the component level.

• HBM (Human Body Model) Fig. 1 left: Simulates the discharged current from a human body. Capacitor and resistor are placed in series in the RC circuit.

• MM (Machine Model) Fig. 1 right: Simulates the discharged current from a metal device. Capacitance, inductor, and resistor are placed in series in the RLC circuit.

Fig. 1: Capacitor and Circuit (left: HBM, right: MM)

### Body Attributes and Materials

 Body Number/Type Body Attribute Name Material Name Body0/Solid SUBSTRATE 006_Glass_epoxy * Body1/Solid AIR 000_Air * Body2, Body4, Body6/Sheet (HBM) Body2, Body4, Body6, Body8/Sheet (MM) ELECTRODE 003_Ag

(*) Available from the material DB

### Boundary Condition

Boundary Condition Name/Topology

Tab

Boundary Condition Type

Setting

V/Face

Electric

Port

Integral Path:

• Set Path1

Voltage Port

Input Waveform (HBM)

 Waveform Type Pulse Rise Time 50×10-9 [s] Duration 1.0×10-6 [s] Pulse Interval 1.0×10-6 [s] Amplitude of Waveform 2.0×103 [V]

Input Waveform (MM)

 Waveform Type Pulse Rise Time 10×10-9 [s] Duration 250×10-9 [s] Pulse Interval 250×10-9 [s] Amplitude of Waveform 2.0×102 [V]

C/Face

Electric

Lumped constant

Capacitance

• 1.0×10-10 [F] (HBM)
• 3.0×10-10 [F] (MM)

Set the integral path*

R/Face

Electric

Lumped constant

Resistance

• 1.5×103 [Ω] (HBM)
• 1.0×101 [Ω] (MM)

Set the integral path*

L/Face

Electric

Lumped constant

Inductance

• 32.5×10-7 [H] (MM)

Set the integral path*

Ground/Face

Electric

Electric wall

Outer Boundary Condition

Electric

Open boundary

* The integral path on the lumped constant boundary is set so as to connect the conductors that are in contact with the lumped constant boundary.

### Results

The result table of the electromagnetic analysis (time domain) will display the voltage and current on the lumped constant boundary, and the current in the ports.

#### HBM

The voltage on the capacitor is as shown in Fig. 2. While the voltage is applied to the port, the capacitor is charged for up to 1.0 [ns].

At 1.0 [ns], when the port is short-circuited, the discharge begins.

The voltage Vc [V] at the time t [s] in the RC circuit is obtained theoretically as follows.

Vc = V0 × (1- exp(-t/RC))

where V0 is direct voltage connected to the circuit, R is resistance, and C is capacitance.

From this equation, the time taken to charge 99% of the capacitor (Vc=0.99V0) is about 690 [ns]. As shown in the analysis result (Fig. 2), the time taken to charge 99% of the capacitor

is 720 [ns]. This is close to the theoretical value of 690 [ns] and confirms that the analysis is correctly performed.

The difference between the theoretical value and the analysis result is due to the rise time of the voltage waveform applied to the port. If the rise time is shorter, the difference will become smaller.

However, if the rise time is shorter, the timestep for analysis will become smaller and the analysis time will become longer.

Fig. 2: Charge and Discharge of Capacitor (HBM)

The current discharge in the HBM can be confirmed by the current flowing through the port. The result is shown below.

The current flowing into the model from the port is treated as positive. Therefore the current in the discharge process (after 1.0[ns]) is negative.

As shown in Fig. 3, the pulse rises up steeply and then the current is slowly damped.

Fig. 3: Charge and Discharge Current (HBM)

#### MM

The voltage on the capacitor is as shown in Fig. 4. The discharge current from the capacitor is shown in Fig. 5.

The behaviors of voltage and current in the RLC circuit largely depend on the values of R, L, and C. In a circuit like MM having small resistance value,

the discharge current which is oscillated by C and L shows damped oscillation where the amplitude of oscillation gradually reduces due to R.

Actually, as shown in Fig. 5, the discharge current from the port shows damped oscillation.

Fig. 4: Charge and Discharge of Capacitor (Voltage)

Fig. 5: Discharge Current from Capacitor

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