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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 1 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engineering 43 Oscilloscope Phase-Angle Measurement

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 2 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Oscope Summarized An Oscope does ONE thing: Draws a PLOT of VOLTAGE vs TIME AAnd That’s IT!

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 3 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Amplitude Measurements These are Easy 1.Check the VOLTS/DIV setting on the Scope FILL screen vertically 2.Count VERTICAL Deflection Divisions i.e; Count Squares 3.Multiply DIVs times VOLTS/DIV 5.1 Div High

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 4 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Vertical (V) Scale for TDS-340

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 5 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Phase Angle, The Equation for a Phase-SHIFTED Sinusoidal Electrical-Potential Signal Where V XM The AMPLITUDE (Max Value) of the Sinusoid in Volts The PHASE Angle in DEGREES – MAGNITUDE <180° –SIGN can be POSITIVE or NEGATIVE

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 6 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Scope Phase-Angle The Scope Trace Tells us NOTHING about the MAGNITUDE and SIGN of the Phase Angle It Doesn’t Even give a Starting Point All we get is TWO v(t) Traces The Steps to Get to 1.Define (pick) a BASELINE Signal 2.Get ± from shifted-Signal LEAD or LAG 3.Get -Magnitude from TIME-SHIFT,

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 7 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis 1. Define the BaseLine Signal For ANY Steady-State AC Signal (SS-AC) We, as Ckt Analysts, get to PICK ONE Node-Voltage exOR Branch- Current as having a ZERO Phase Angle i.e., We can SET the point where = 0° Analogous to Selecting a GND Since the Scope ONLY measures Potential we can Pick any Node VOLTAGE as the BaseLine Signal which has ZERO Phase

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 8 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis 1. Define the BaseLine Signal The BaseLine Signal is USUALLY (not Always) the +Side of the Supply On the Scope The BaseLine Signal is typically The “A” or CH1 Trace The Trigger Source

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 9 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis 2. Determine the Sign of Looking at the Traces we can OBSERVE whether the Unknown, or “X” Signal LEADS or LAGS the BaseLine See Next Slide The Question Then becomes: Does LEAD Imply POSITIVE- ? –Then Lag implies NEGATIVE- LAG Imply POSITIVE- ? –Then Lead implies NEGATIVE-

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 10 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis This is the BASELINE Signal The X-Signal LAGS the BASELINE; its PEAK occurs LATER in Time v S (ωt) v X (ωt±| |)

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 11 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis 2. Lead or Lab = +/ − by MATLAB LEADING → POSITIVE LAGGING → NEGATIVE

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 12 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis 3. -Magnitude Notice from the Scope Trace that ONE Sinusoidal CYCLE-TIME-PERIOD, T, corresponds to 360°: T↔ 360° Further Notice from the Dual-Trace Display that the X-Signal will Lead or Lag the BaseLine by the TIME-Shift, Now Realize that will be some FRACTION of a Period; Thus Find by SEC/DIV, Multiply by 360°/T

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 13 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis T = 4DIV v X Lagging T = 360° = 1.6DIV V Xpp = 4.6DIV

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 14 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Horizontal (t) Scale for TDS-340

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 15 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis 3. -Magnitude From The Scope Time-Measurements on the on the Last Slide Find T = 4 DIV = 360° = 1.6 DIV, Lagging SEC/DIV = 0.5 millisec/Div Calc T &

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 16 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis 3. -Magnitude Now since /T is a Fraction of a Period Multiply / T by 360° to Find In this Case Use the LAGGING observation to apply the sign of as NEGATIVE

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 17 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Complete The Example From The Scope Voltage- Measurements on the on the “ ” Slide Find V Xpp = 4.6 DIV VOLTS/DIV = 0.5 V/Div Calc V XM

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 18 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Complete the Example Now Can Fully Characterize the Unknown Sinusoid Relative to the BaseLine vXvX Using The Results of the Phase and Amplitude Calcs Note that ω = 2πf Alternatively in Std Phasor Form

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 19 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Another Example Find Vc in the Scope-Measured Series RC Circuit SCOPE BaseLine

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 20 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis T = 0.77 mS Vc LAGS = 0.11 mS Vcm =6.15V

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 21 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis The RC Series Ckt Phasor Calc The Frequency Parameters Calc noting that Vc LAGS Then Vc by 6.15V Amplitude

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 22 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Series CR Example Find Vr in the Scope-Measured Series CR Circuit SCOPE BaseLine

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 23 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis T = 0.77 mS Vr LEADS = mS Vrm = 7.5V

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 24 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis The CR Series Ckt Phasor Calc The Frequency Parameters Calc noting that Vr LEADS Then Vr by 7.5V Amplitude

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 25 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis All Done with the Tutorial PhasErs on Stun... A phaser RIFLE (often referred to as a type-3 phaser)

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 26 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis MATLAB Script-Code % B. Mayer % ENGR43 * 19Jan06 % Phase-Shift Lag Plot % % Parameters w = 1500; % Angular Freqency in rad/sec Vsa = 9.7; % Voltage Source Amplitude in Volts AR =.73; % Attenuation Ratio phi = ; % phase Angle in Rads phi_deg = 180*phi/pi % degrees % % % Calc period T = 2*pi/w % seconds % % Define t vector over 1.2 periods t = linspace(0, 2.2*T, 200); % % Calc Vs & Vc over 1.2 periods Vs = Vsa*cos(w*t); Vx = AR*Vsa*cos(w*t + phi); % % Plot both plot(1000*t, Vs, 1000*t, Vx, '--'), xlabel('time (mS)'),... ylabel('Electrical Potenial (V)'),... legend('Vs(t)', 'Vx(t)'), title('Vx LAGS by 53°')

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ENGR-43_Scope_Phase-Angle_Tutorial.ppt 27 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis More Scope Traces

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