Name: Due Date: Grade

Name: Due date: Grade:

ECE 2006 LABORATORY 8

RLC TRANSIENT RESPONSE

Objectives

The learning objectives for this laboratory are to give the student the ability to:

use the function generator to generate a step input with an appropriate repetition rate.
use the oscilloscope to measure RLC overdamped and underdamped transient response values.
use the PSPICE transient response tool.

References

D. E. Johnson, J. R. Johnson, J. L. Hilburn, and P. D. Scott, Electrical Circuit Analysis. 3rd Edition, Prentice-Hall, 1997.

Background

See above reference, Chapter 7 for RLC equations.

Equipment

Oscilloscope

Function generator

Resistor, 100 

Resistor, 1.0 k

Capacitor, 1.0 F

Inductor, 220 mH

Procedure

1.Overdamped RLC circuit capacitor voltage transient response to a step input.

1.1For the circuit in Figure 1, determine the output response, V2(t), 0 < t, to an input step, V1(t),

V1(t) = 5 volts t < 0

= +5 volts 0 < t

Add your equation calculated for V2(t) to the Data section. Also add your values for V2 (t=), V2(t=0+), and dV2(t=0+)/dt to the Data section. From your equation for V2(t), calculate V2(t=0.5 msec), V2(t=1.0 msec), and V2(t=2.0 msec). Add these values to the Data section.

1.2With the RLC circuit disconnected, adjust the function generator to produce a repetitive pulse that is 5 volts for about 10 msec, then +5 volts for about 10 msec.

1.3Connect the circuit in Figure 1. Measure the final value, V2(t=), and the initial value, V2(t=0+), from the oscilloscope and record in the Data section. Also measure the voltages V2(t=0.5 msec), V2(t=1.0 msec), and V2(t=2.0 msec)from the oscilloscope and record in the Data section.

1.4Write and run a PSPICE program for the circuit in Figure 1. Have the program plot the voltage across the capacitor from 0 to 5 msec in 0.1 msec increments. Print the output file and attach.

2.Underdamped RLC circuit capacitor voltage transient response to a step input.

2.1For the circuit in Figure 2, determine the output response, V2(t), 0<t, to an input step, V1(t),

V1(t) = 5 volts t < 0

= +5 volts 0 < t

Add your equation calculated for V2(t) to the Data section. Also add your values for V2(t=), V2(t=0+), and dV2(t=0+)/dt to the Data section. From your equation for V2(t), calculate V2(t=0.5 msec), V2(t=1.0 msec), V2(t=2.0 msec), and T/2 where T is the period, T = 1/f = 2 π/ Add these values to the Data section.

2.2With the RLC circuit disconnected, adjust the function generator to produce a repetitive pulse that is 5 volts for about 10 msec, then +5 volts for about 10 msec.

2.3Connect the circuit in Figure 2. Measure the final value, V2(t=), the initial value, V2(t=0+), and T/2 from the oscilloscope and record in the Data section. Also measure the voltages V2(t=0.5msec), V2(t=1.0msec), and V2 (t=2.0msec) from the oscilloscope and record in the Data section.

2.4Write and run a PSPICE program for the circuit in Figure 2. Have the program plot the voltage across the capacitor from 0 to 5 msec in 0.1 msec increments. Print the output file and attach.

3.Underdamped RLC circuit resistor voltage transient response to a step input.

3.1For the circuit in Figure 3, determine the output response, V2(t), 0<t, to an input step,

V1(t),

V1(t) = 5 volts t < 0

= +5 volts 0 < t

Add your equation calculated for V2(t) to the Data section. Also add your values for V2(t=), V2(t=0+), and dV2(t=0+)/dt to the Data section. From your equation for V2(t), calculate V2(t=0.5msec), V2(t=1.0msec), V2(t=2.0msec) and T/2 where T is the period, T = 1/f = 2/. Add these values to the Data section.

3.2With the RLC circuit disconnected, adjust the function generator to produce a repetitive pulse that is 5 volts for about 10 msec, then +5 volts for about 10 msec.

4.1Connect the circuit in Figure 3. Measure the final value, V2(t=), the initial value, V2(t=0+), the initial derivative, dV2(t=0+)/dt and T/2 from the oscilloscope and record in the Data section. Also measure the voltages V2(t=0.5msec), V2(t=1.0msec), and V2(t=2.0msec) from the oscilloscope and record in the Data section.

3.4Write and run a PSPICE program for the circuit in Figure 3. Have the program plot the voltage across the resistor from 0 to 5 msec in 0.1 msec increments. Print the output file and attach.

Conclusions:

None

Sample calculations

None.

Figure 1. Overdamped RLC circuit with output across the capacitor.

Figure 2. Underdamped RLC circuit with output across the capacitor.

Figure 3. Underdamped RLC circuit with output across the resistor.

Data

1. Overdamped RLC circuit with output across the capacitor.

Calculated

V2(t=) =

V2(t=0+) =

dV2(t=0+) =

V2(t=0.5 msec) =

V2(t=1.0 msec) =

V2(t=2.0 msec) =

Equation

V2(t) =

Measured

V2(t=) =

V2(t=0+) =

dV2(t=0+) = 0.00 volts/sec

V2(t=0.5 msec) =

V2(t=1.0 msec) =

V2(t=2.0 msec) =

volts 0<t

Data continued

2. Underdamped RLC circuit with output across the capacitor.

Calculated

V2(t=) =

V2(t=0+) =

dV2(t=0+) =

V2(t=0.5 msec) =

V2(t=1.0 msec) =

V2(t=2.0 msec) =

Equation

V2(t) =

Measured

V2(t=) =

V2(t=0+) =

dV2(t=0+) = 0.00 volts/sec

V2(t=0.5 msec) =

V2(t=1.0 msec) =

V2(t=2.0 msec) =

volts 0<t

Data continued

3. Underdamped RLC circuit with output across the resistor.

Calculated

V2(t=) =

V2(t=0+) =

dV2(t=0+) =

V2(t=0.5 msec) =

V2(t=1.0 msec) =

V2(t=2.0 msec) =

Equation

V2(t) =

Measured

V2(t=) =

V2(t=0+) =

dV2(t=0+) =

V2(t=0.5 msec) =

V2(t=1.0 msec) =

V2(t=2.0 msec) =

volts 0<t