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

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J. Braunstein, M. Hameed, K. A. Connor- 1 -Revised: 22 November 2020Rensselaer Polytechnic InstituteTroy, New York, USAClass #24:Experiment 21Steady State AC SignalsPurpose:The objective of this experiment is to become familiar with and how to handle the phase shift betweensignals in circuits and engineering in general.Background:Before doing this experiment, students should be able toAnalyze simple circuits consisting of combinations of resistors.Do a transient (time dependent) simulation of circuits using LTspiceBuild simple circuits consisting of combinations of resistors, inductors, capacitors, and op-amps on protoboardsand 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 toDetermine and validate mathematical expressions for steady-state sine and cosine voltage and current wavesincluding offset, amplitude, frequency and phase.Use the mathematical expressions that describe voltage and current signals obtained both experimentally andusing simulation to validate and understand the relationships between voltage and current for inductors andcapacitors.Equipment Required:M1K Board (with Alice tools) or Analog Discovery (with Waveforms Software)Part KitsLTspiceMatlabHelpful 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 2020Rensselaer Polytechnic InstituteTroy, New York, USAPart A – Sinusoidal SignalsBackgroundWe have looked at sinusoidal signals in previous laboratories. Mathematically, we have written the expression as( )()ftAsintωθ=+There are three parameters of interest for any sinusoidal signal1)Ais the amplitude of the signal which corresponds to the maximum positive value (and minimum negativevalue) of the signal as it oscillates with time. When implementing a source in LTspice or setting Alice AWGconfiguration to a sinusoidal signal, the amplitude is one of the parameters that needs to be set.2)ωis the radial frequency of the signal. Previously, we have related the radial frequency of the sinusoid to thefrequency using the expression2fωπ=. Like amplitude, frequency,fin Hz, is one of the parameters setin both LTspice and Alice AWG controls. It is important to recognize that the mathematical expression ofthe 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 expression1fT=. Substitution gives theexpression relating radial frequency to period,2Tπω=.

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Rensselaer Polytechnic Institute, RC circuit, J Braunstein, LTSpice