ENGR 338 2021 Fall

Lab 1 :
Review of Superposition, Thevenin's Equivalent Circuit, and LTSpice

By: Roxie Sandoval
  rlsandoval@fortlewis.edu


I. Introduction

In circuit analysis there are several way to calculate voltages and currents, however this lab focused on superposition and Thevenin's equivalent circuit. Thevenin's equivalent circuit is a theorem used to simplify a circuit, unlike Thevenin's theorem, superposition is not a theorem, it is a method. The purpose of this lab was to review how to calculate voltages and currents using both the theorem and method. The lab also reviewed how to use the software LTSpice as a check for the calculations.
 
II. Materials and Methods
i. Materials
1. LTSpice Software
2. Paper
3. Pencil
ii. Method(s)
For the first given circuit schematic, the method of superposition was used to calculate three voltages and currents then LTSpice was used to check. For the second schematic, Thevenin's equivalent was used to simplify a circuit to a RC or resistor capacitor circuit. Once simplfied, the time delay was calculated, and LTSpice was used to verify calculation.
   

III. Results

i. Example 1 -
Using superposition, voltages and currents were calculated by hand shown in Figure 1. The original circuit schematic can be seen in the upper left of Figure 1. Following the superposition procedure, and applying the voltage divider theory all three voltages and currents were calculated. The voltage across resistor 1 or R1 was found to be 2.1 V, the voltage across R2 was 0.9V and across R3 was 2.4V. Each of the currents were calculated to be 1.4mA, 0.6mA and 0.8mA, respectively. All calculations can be seen in the lower right.


                                                                 (a)                                                                                                                                                       (b)
Figure 1: (a): First schematic's hand calculations using superposition. (b) : Hand calculations showing final voltage and current calculations.

As per the lab instructions, only spice code was used which can be seen in Figure 2 below. The figure also shows each of the voltages and currents, however V(1) below clearly shows a volatge of 3V, this is because the code is taking the voltage at node 1 just above the 3V voltage supply. But the current across R1 is equal to 1.4mV, from which the volatge can be calculated using Ohm's Law. As a result, all calculations have been verified using LTSpice.


Figure 2: Calculations from LTSpice, to verify calculations.

ii. Example 2-
Using Thevenin's equivalent circuit to simplify the schematic to an RC circuit shown in Figure 3, below. Once simplifed the time delay was found to be 5.6 micro-seconds.

Figure 3: The hand calculations for the second schematic, which the time delay was found to equal 5.6 micro-seconds.
Figure 4 shows the LTSpice simulation using only the spice code, and the difference or time delay of the circuit shown in the lower right. The simulation showed a difference of 5.67 micro-seconds, which is relatively close to the hand calculations result.   




IV. Discussion
As a result, the lab did help with circuit analysis. Thevenin's equivalent circuit was a bit easier than the method of superposition, probably because example 1 had two voltage supplies. However, there is a better understanding how to approach each analysis.