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

2. BMayer@ChabotCollege.edu 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 AAnd That’s IT!

3. BMayer@ChabotCollege.edu 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

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

5. BMayer@ChabotCollege.edu 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

6. BMayer@ChabotCollege.edu 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, 

7. BMayer@ChabotCollege.edu 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

8. BMayer@ChabotCollege.edu 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

9. BMayer@ChabotCollege.edu 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- 

10. BMayer@ChabotCollege.edu 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±|  |)

11. BMayer@ChabotCollege.edu 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 

12. BMayer@ChabotCollege.edu 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

13. BMayer@ChabotCollege.edu 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

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

15. BMayer@ChabotCollege.edu 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 & 

16. BMayer@ChabotCollege.edu 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

17. BMayer@ChabotCollege.edu 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

18. BMayer@ChabotCollege.edu 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

19. BMayer@ChabotCollege.edu 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

20. BMayer@ChabotCollege.edu 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

21. BMayer@ChabotCollege.edu 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

22. BMayer@ChabotCollege.edu 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

23. BMayer@ChabotCollege.edu ENGR-43_Scope_Phase-Angle_Tutorial.ppt 23 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis T = 0.77 mS Vr LEADS  = 0.084 mS Vrm = 7.5V

24. BMayer@ChabotCollege.edu 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

25. BMayer@ChabotCollege.edu 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)

26. BMayer@ChabotCollege.edu 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 = -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°')

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