NESS ENGINEERING
TECHNICAL DATA
RLC CIRCUIT FORMULAS

Underdamped Overdamped Critically Damped

 

The formulas on this page are associated with a series RLC circuit discharge since this is the primary model for most high voltage and pulsed power discharge circuits.

Each of the following waveform plots can be clicked on to open up the full size graph in a separate window.

Underdamped

Underdamped RLC circuit condition equation

The circuit schematic for the underdamped case is shown below. In this specific model, the resistance is an order of magnitude (10X) less than the value required for a critically damped circuit.

 

 Underdamped RLC circuit schematic diagram

The results of the circuit model are shown below. V(1) is the voltage on the 1 mF capacitor as it discharges in an oscillatory mode. V(3) is the voltage on the load resistor, in this case a 0.2 ohm value. The circuit current is graphed in the second, lower plot and reaches its peak value very nearly at t=p/2w0.

 

Underdamped RLC circuit voltage and current waveforms

 

Underdamped RLC circuit equation for omega

Omega

L is the circuit inductance (H) 

C is the circuit capacitance (F) 

R is the circuit resistance (W)

Underdamped RLC circuit equation for current as a function of time

Current

V0 is the initial voltage on the capacitance (V)

Underdamped RLC circuit equation for peak current

Peak Current

Same as above

 

Overdamped

Overdamped RLC circuit condition equation

The circuit schematic for the overdamped case is shown below. In this specific model, the resistance is an order of magnitude (10X) more than the value required for a critically damped circuit.

 

 Overdamped RLC circuit schematic diagram

The results of the circuit model are shown below. V(1) is the voltage on the 1 mF capacitor as it discharges in a simple RC decay mode. V(3) is the voltage on the load resistor, in this case a 20 ohm value. In this case, once the switch closes and the voltage on the load resistor rises to match the capacitor voltage, both waveforms then essentially overlap and decay at the same rate since the voltage across the inductor is minimal. The circuit current is graphed in the second, lower plot.

 

Overdamped RLC circuit voltage and current waveforms

 

 Overdamped RLC circuit equation for omega

Omega

L is the circuit inductance (H) 

C is the circuit capacitance (F) 

R is the circuit resistance (W)

Overdamped RLC circuit equation for current as a function of time

Current

V0 is the initial voltage on the capacitor (V)

 

Critically Damped

Critically damped RLC circuit condition equation

The circuit schematic for the critically damped case is shown below. In this specific model, the resistance is exactly equal to the value required for a critically damped circuit.

 

 Critically damped RLC circuit schematic diagram

The results of the circuit model are shown below. V(1) is the voltage on the 1 mF capacitor as it discharges towards zero with no overshoot. V(3) is the voltage on the load resistor, in this case a 20 ohm value. One can see that the resistor voltage also does not overshoot. The circuit current is graphed in the second, lower plot and reaches its peak value at t=2L/R.This circuit is often desirable (if possible) with high voltage, energy storage capacitors since voltage reversals can frequently decrease the lifetime of the capacitor.

 

Critically damped RLC circuit voltage and current waveforms


Critically damped RLC circuit equation for current as a function of time

Current

V0 is the initial voltage on the capacitor (V) 

L is the circuit inductance (H) 

R is the circuit resistance (W)

Critically damped RLC circuit equation for peak current

Peak Current

Same as above

 


Send consulting inquiries, comments, and suggestions to nessengr@san.rr.com

[BACK] [HOME] [RESUME] [PUBLICATIONS] [NEWS] [LINKS] [CAPABILITIES] [TECHDATA]

Ness Engineering, Inc.
P.O. Box 261501
San Diego, CA 92196
(858) 566-2372
(858) 240-2299 FAX

Richard M. Ness and Ness Engineering, Inc.
Last Updated:

Website File Auto-Update Javascript courtesy of www.javafile.com   Download the Script