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Understanding Oscilloscope Phase-Angle Measurement for Engineers

Learn how to measure phase angle using an oscilloscope in electrical engineering. Discover the steps to determine phase shift, magnitude, and sign. Obtain valuable insights on analyzing AC signals.

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Understanding Oscilloscope Phase-Angle Measurement for Engineers

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  1. Engineering 43 OscilloscopePhase-Angle Measurement Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

  2. Oscope Summarized • An Oscope does ONE thing: Draws a PLOT of VOLTAGE vs TIME • And That’s IT!

  3. These are Easy Check the VOLTS/DIV setting on the Scope FILL screen vertically Count VERTICAL Deflection Divisions i.e; Count Squares Multiply DIVs times VOLTS/DIV Amplitude Measurements 5.1 DivHigh

  4. Vertical (V) Scale for Digital Scope

  5. Phase Angle,  • The Equation for a Phase-SHIFTED Sinusoidal Electrical-Potential Signal • Where • VXM The AMPLITUDE (Max, or Peak Value) of the Sinusoid in Volts •   The PHASE Angle in DEGREES • MAGNITUDE <180° • SIGN can be POSITIVE or NEGATIVE

  6. Scope Phase-Angle • The Scope Trace Tells usNOTHING 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  • Define (pick) a BASELINE Signal • Get ±  from shifted-Signal LEAD or LAG • Get -Magnitude from TIME-SHIFT, td

  7. 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

  8. 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

  9. 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-

  10. This is the BASELINE Signal The X-Signal LAGS the BASELINE; its PEAK occurs LATER in Time vX(ωt±||) vS(ωt)

  11. 2. Lead or Lab = +/− by MATLAB • LEADING → POSITIVE • LAGGING → NEGATIVE

  12. 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, td • Now Realize that td will be some FRACTION of a Period; Thus • Find tdby SEC/DIV, Multiply by 360°/T

  13. td= 1.6DIV vX Lagging VXpp = 4.6DIV T = 4.1DIV T = 360°

  14. Horizontal (t) Scale for digital scope

  15. 3. -Magnitude • From The Scope Time-Measurements on the on the Last Slide Find • T = 4.1 DIV = 360° • td= 1.6 DIV, Lagging • SEC/DIV = 0.5 millisec/Div • Calc T & 

  16. 3. -Magnitude • Now since td/T is a Fraction of a Period Multiply td/T by 360° to Find  • In this Case • Use the LAGGING observation to apply the sign of  as NEGATIVE

  17. Complete The Example • From The Scope Voltage-Measurements on the on the “” Slide Find • VXpp = 4.6 DIV • VOLTS/DIV = 0.5 V/Div • Calc VXM

  18. Now Can Fully Characterize the Unknown Sinusoid Relative to the BaseLine Complete the Example • Using The Results of the Phase and Amplitude Calcs vX • Note that ω = 2πf • Alternatively in Std Phasor Form

  19. Example: Find H(f) = VC/VS • Find Vc in the Scope-Measured Series RC Circuit SCOPE BaseLine

  20. Vc LAGS T = 0.77 mS td= 0.11 mS Vcm =6.15V

  21. The RC Series Ckt Phasor • Calc The Frequency Parameters • Calc  noting that Vc LAGS • Then Vcby 6.15VAmplitude

  22. The RC Transfer Function • The Transfer Function for the R→C Circuit at 1.3 kHz

  23. Example: Swap C↔R for H(f) • Find Vr in the Scope-Measured Series CR Circuit SCOPE BaseLine

  24. Vr LEADS td= 0.084 mS T = 0.77 mS Vrm = 7.5V

  25. The CR Series Ckt Phasor • Calc The Frequency Parameters • Calc  noting that Vr LEADS • Then Vrby 7.5VAmplitude

  26. The CR Transfer Function • The Transfer Function for the C→R Circuit at 1.3 kHz

  27. All Done with the Tutorial PhasErsonStun... • A phaser RIFLE (often referred to as a type-3 phaser)

  28. 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 = -0.925; % 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°')

  29. More Scope Traces

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