Electrical Engineering homework help. ENGR 2105 Lab 4a: Simulation of RLC circuit transient response

1. Introduction and Goal: This is an individual simulation demo but still group report assignment as a warm up for lab 4.  Use NI MultiSim 14.0 (available on the lab computers) or other simulation tool to simulate and observe the transient behavior of RLC circuits under DC power.  The instructions in the experimental procedure are for MultiSim.  Download it to your computer.  It is installed on the lab computers, also.

The password for the bonus quiz is 1010

1. Equipment List:

YouTube video tutorial posted on eCampus.

A circuit simulation program such as Multisim.  Multisim is available on computers in WH 127, 151, 163, 165 and the four computers in WH 159.

You may also try Multisim Live at https://www.multisim.com/ or download it per the instructions in the announcement posted on eCampus.

1. Experimental Theory:

The three common passive circuit elements are resistor, capacitor and inductor. Capacitors and inductors cause very brief non-linear effects when a DC voltage is applied or changed.  Shortly after a DC voltage change, capacitor and inductor circuits reach “steady state.” These extremely brief effects are called transient behavior.

• Resistor: A resistor limits the amount of current in a circuit and help modulate transient behavior in RLC circuits.  The voltage across it V is related to current through it i by Ohm’s law

V = Ri, where R is the resistance of the resistor.  Equation 3.1
The impedance Z of a resistor is its resistance.

• Capacitor: A capacitor collects electrical It is made of two or more conductors separated by insulators. Under DC power, it does not allow any current flow through it once it is charged.  The voltage across a capacitor cannot change instantaneously.  It is related to current through the capacitor by

i = C dVC /dt where C is the capacitance.    Equation 3.2

The impedance of a capacitor is Zc = -jXc where j is the unit imaginary number and Xc is the reactance expressed in Ohms.  The reactance is related to the capacitance by Xc = 1/(2 p f C) where f is the frequency of the AC power source.

• Inductor: An inductor is a coil of wire with the property of electrical Inductors resist increase or decrease in current. The current through an inductor cannot change instantaneously.  It is related to the voltage across the inductor by

VL =L di/dt where L is the inductance.     Equation 3.3

The impedance of an inductor is ZL = jXL where j is the unit imaginary number and XL is the reactance expressed in Ohms.  The reactance is related to the inductance by XL = 2 p f L where f is the frequency of the AC power source.

• Series RLC Circuit:

Using Kirchhoff’s voltage law (KVL), we have

V= VR + VL + VC

Using equations 3.1, 3.2 and 3.3 and calculus, we can solve for the voltage across the capacitor.

Figure 1.  Circuit diagram

The voltage across the capacitor C in a series RLC circuit powered by a DC voltage V is given by:

VC (t ) =V (1 –  [cos w t ]   ea t )

a = R/2L is called the damping coefficient

w = SQRT((1/LC) – (R/2L)2) = 2 π f , f is the oscillation frequency.

The time constant is given by:  τ = RC

To see the transient effect at power up and power down, we use a square wave signal.  The voltage across the capacitor will vary as show in figure 2 for a 500 Hz, 8V square wave input signal.  There will be oscillations if w is a real number (argument of the square root function is a positive number).

Figure 2.  Source Voltage in red and capacitor Voltage in blue

1. Pre-work:

Make sure you understand the concepts of transient behavior and how to calculate the damping coefficient, duration of transition, time constant and oscillation frequency.

# 5.  Experimental Procedure – Simulate a series RLC circuit

Use Multisim or other circuit simulator and build the circuit shown in figure 1.  Use a clock voltage under signal voltage sources, as the source to emulate multiple cycles of a DC voltage, a resistor R, an inductor L and a capacitor C.  Place all components including ground and connect them.  Set the values of the components then set up your analysis parameters.

To set up our transient analysis. Go to: Simulate -> Analyses and simulation -> Transient

Under output, set your variables for analysis to V1 and V3 to show the input signal and the voltage across the capacitor respectively.  You may rename the variables by double clicking on the corresponding wire connection.

Set “TSTART” to 0, and set “TSTOP” to 0.0035. This will show about 1.5 periods of our square wave input waveform.

Click Run or hit F5 to simulate. This will show us the 400 Hz square wave input voltage V(1), and the output voltage across the capacitor V(3). To measure the frequency of oscillation, you need to show the grid and the cursors for x axis (time axis).  Use the graphic cursors to measure the frequency of the oscillation of V(3) and the duration of transient.  Figure 3 shows the measurement for a 500Hz, 8V square wave input signal after changing the time axis to display about half the period of the input signal.

Figure 3.  Expanded plot.

dx indicates the oscillation period is 148.7 ms.      1/dx is the frequency, or 6.726kHz

Build the circuit shown in figure 1 and change the value of the resistance R for the cases below.  Analyze the output (voltage across the capacitor), capture graphs and measure the parameters as instructed.

Case 1:  R = 100 Ohms.
You should see a graph similar to Figure 2.  Include your graph in your report and/or simulation file.

Capture two plots as in figure 2 (for 3.5 ms) and figure 3 (for 1ms) and measure the transient oscillation frequency and duration of transient.  Also, calculate the damping coefficient and the time constant.  Record the data in the datasheet.

Case 2:  Change R to 200 Ohms.

Capture two plots as above and measure the transient oscillation frequency and duration of transient.  Also, calculate the damping coefficient and the time constant.  Record the data in the datasheet.

What did you notice about the oscillations?

Case 3:  Change R to 0 Ohms.

Capture one plot as in figure 3 above and measure the transient oscillation frequency.  Also, calculate the damping coefficient and the time constant.   Record the data in the datasheet.

What did you notice about the oscillations?

Case 4:  Change R to the value R1 that satisfies the equation

(R1/2L)2 = 1/LC with L and C same as in original circuit.

This is the critical damping case (transition between oscillations and no oscillations).  Capture one plot as in figure 3 above and measure the duration of transient.  Record the value of R1 , the duration of transient and the calculated time constant in the datasheet.

Are there any oscillations?

Case 5:  Change R to 2 KOhms.

Capture a plot as in figure 3 above and measure the duration of transient.  Record the duration of transient and the calculated time constant in the datasheet.

Are there any oscillations?

1. Laboratory Cleanup: Turn off the computers

1. Laboratory report: You need one report per student. Follow the standard lab format and make sure to include all the plots captured for each case. Make sure to discuss the results of each case separately.  In your conclusion, state what you learned and what still confuses you.

1. How does the duration of transient compare in cases 1 and 2?

1. How many time constants is the duration of transient in cases 4 and 5?

1. How does the measured value of the frequency for case 3 of the circuit in figure 1 compare to 1/(2p)/sqrt(LC)? Explain any differences.

1. What is the advantage of using a circuit simulator over building the circuit and testing it?

1. What is the disadvantage of using a circuit simulator?

Lab 4a Data Sheet

# R=100 Ohms

Oscillation frequency in KHz =

Duration of transient in us =

Calculate RC time constant (τ) in us =

Calculate damping coefficient in KHz =

# R=200 Ohms

Oscillation frequency in KHz =

Duration of transient in us =

Calculate RC time constant (τ) in us =

Calculate damping coefficient in KHz =

# For R=0 Ohms

Oscillation frequency in KHz =

Calculate RC time constant (τ) in us =

Calculate damping coefficient in KHz =

# For R=R1 =

Duration of transient in us =

Calculate RC time constant (τ) in us =

# For R=2 KOhms

Duration of transient in us =

Calculate RC time constant (τ) in us =

Electrical Engineering homework help