Lab21-1010 AC circuits.pdf - Class #24: Experiment 21...

J. Braunstein, M. Hameed, K. A. Connor - 1 - Revised: 22 November 2020
Rensselaer Polytechnic Institute Troy, New York, USA
Class #24: Experiment 21
Steady State AC Signals
Purpose: The objective of this experiment is to become familiar with and how to handle the phase shift between
signals in circuits and engineering in general.
Background: Before doing this experiment, students should be able to
• Analyze simple circuits consisting of combinations of resistors.
• Do a transient (time dependent) simulation of circuits using LTspice
• Build simple circuits consisting of combinations of resistors, inductors, capacitors, and op-amps on protoboards
and measure input and output voltages vs. time.
• Make differential voltage measurements using M1K board and Alice software.
• Review the background for the previous experiments.
Learning Outcomes: Students will be able to
• Determine and validate mathematical expressions for steady-state sine and cosine voltage and current waves
including offset, amplitude, frequency and phase.
• Use the mathematical expressions that describe voltage and current signals obtained both experimentally and
using simulation to validate and understand the relationships between voltage and current for inductors and
capacitors.
Equipment Required:
• M1K Board (with Alice tools) or Analog Discovery (with Waveforms Software)
• Part Kits
• LTspice
• Matlab
Helpful links for this experiment can be found on the course website under Class #24.

J. Braunstein, M. Hameed, K. A. Connor - 2 - Revised: 22 November 2020
Rensselaer Polytechnic Institute Troy, New York, USA
Part A – Sinusoidal Signals
Background
We have looked at sinusoidal signals in previous laboratories. Mathematically, we have written the expression as
( ) ( )
f t Asin t ω θ = +
There are three parameters of interest for any sinusoidal signal
1) A is the amplitude of the signal which corresponds to the maximum positive value (and minimum negative
value) of the signal as it oscillates with time. When implementing a source in LTspice or setting Alice AWG
configuration to a sinusoidal signal, the amplitude is one of the parameters that needs to be set.
2) ω is the radial frequency of the signal. Previously, we have related the radial frequency of the sinusoid to the
frequency using the expression
2 f ω π =
. Like amplitude, frequency, f in Hz, is one of the parameters set
in both LTspice and Alice AWG controls. It is important to recognize that the mathematical expression of
the sinusoid includes the radial frequency term while the frequency is the parameter that is specified. Also,
the frequency is related to the period of the signal, with the expression
1
f
T
=
. Substitution gives the
expression relating radial frequency to period,
2
T
π
ω =
.