Transcript Phasors and Kirchoff`s Current Law

Phasors and
Kirchhoff’s Current Law
Week 3: Experiment 23
Measurement Issues
• Thevenin Equivalent Circuit
• Amplitude vs. Voltage Peak-to-Peak
• True RMS
Thevenin Equivalent Circuit
• The arbitrary function generator can be
modeled as a 50mV-5V source with an
internal resistance of 40 W.
– Consider this when trying to deliver power to your
circuit (Rload)
Function
Generator
Thevenin Equivalent Circuit
• The oscilloscope can be modeled as a 1MW
load resistor in parallel with your circuit.
Your Circuit
Amplitude and Peak-to-Peak Voltage
VM
Vpp
RMS – Root Mean Square
VRMS
1

T
I RMS
1

T

T
0

T
0
2
v (t )dt
2
i (t )dt
RMS vs. True RMS
• RMS of a sinusoid is 0.707 VM
– Some instruments assume that the voltage
measured is always a sinusoid
• Output RMS values are wrong for all other waveshapes
– This is what your digital multimeter does.
– True RMS, which is what the Velleman outputs, is
calculated using the equation on the previous
slide.
Changes to Experiment
• Frequency of operation: 40 kHz
– You will have to use the arbitrary function generator on the Velleman
scope
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Amplitude of voltage supply: 5 V
Inductor: 10 mH
Capacitor: 2.2 nF
R1: 4 kW
R3: 2 kW
Pick R2 and R4 (shunt resistors) appropriately.
– Be aware that the stored energy in the inductor could send amount of
current out of phase with the voltage back into the scope if incorrect
components are used (XC appraches -j ∞ W).
• Reference all phase measurements to the phase of the voltage
supply.
New Circuit
Transient Analysis
• Source: Vsin
– Instructions state that you need to wait a few
cycles before making any measurements from the
plot.
• This is because the capacitor has an initial condition of
0V (no charge stored on the electrodes).
– This can be changed as IC (initial condition) is an attribute in
the capacitor model.
» In certain circuits, the capacitor and inductor in a circuit
can store energy extremely efficiently (i.e., the time
constant of the circuit is much shorter than 1/f).
Transient Plot
Automatically generated when current markers are placed in the schematic.
To Obtain Smooth Curve
Set the Step Ceiling to a small
fraction of T, the period of one cycle.
Bode Plots
• Phase angles can be determined from PSpice
by:
– Measuring the difference in the zero crossing of
the voltage from the arbitrary function generator
and the DUT using the transient analysis
– Displaying the phase angle on a plot generated
during an AC Sweep.
• Note that the voltage source must be changed from
Vsin to Vac.
• P() marco will display the phase angle of the parameter
inserted [e.g., V(R2:2)]
Schematics
• PSpice Schematics uses superposition
when performing the AC Sweep. So,
both voltage sources may be put into the
same circuit.
– You select which plot is generated during
the simulation run.
To Plot Phasor Information
Add a Trace to the New Plot
Select P() in the List of
Functions or Macros
Select Voltage or Current from the List
of Simulation Output Variables
• It will appear
within the
paraphrases as the
argument of the
phase function.
You can add
multiple traces at
once by putting a
comma between
each on the list at
the bottom of the
pop-up window.
Then, click OK.
To Change the x axis to Log(f)
Phase Angle in Degrees Vs. Frequency
The angle in phasor notation should be between -180o to +180o.
Phase Angle Measurement
• Two techniques using the Velleman scope
– Waveform Parameters
• Measurement of relative phase to internal reference at
the operating frequency of the arbitrary function
generator.
– Bode Plot
• Measurement of the phase of the signal on Channel 1
with respect to the signal on Channel 2 over a
frequency range specified by the user.
Waveform Parameters
Bode Plot
Select Phase Plot
from View menu
after having set the
Frequency Range,
Frequency Start,
and other
measurement
parameters and
then click Start to
obtain the phase
measurement.
Natural Frequency of Circuit
• The specified frequency of operation of the
voltage source is close to the natural
frequency of the RLC network.
– If a sharp square wave was obtained from the
arbitrary voltage source, you would be able to see
the ringing associated with the energy transfer
between the inductor and capacitor before the
system reached steady-state.
Transient Response
If you wanted to, you could
look at the transient
response to a square wave
input (i.e., see the ringing
associated with the natural
and forced response of this
RLC circuit), by adding
Vpulse to the circuit.
Set the amplitude of Vsin
to 0V. Then set the
amplitude of Vpulse to 5V
and the PW to 100us and
PER to 200us. The plot of
the response for a similar
circuit is shown on the
following slide.
Transient Response:
Square Wave Input
Voltage at the node
after the inductor.
Currents (in mA)
through the inductor,
capacitor, and R1.