LIST OF EXPERIMENTS. Sl. No. NAME OF THE EXPERIMENT Page No.

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1 LIST OF EXPERIMENTS u Sl. No. NAME OF THE EXPERIMENT Page No Simulation of Transient response of RLC Circuit To an input (i) step (ii) pulse and(iii) Sinusoidal signals Analysis of Three Phase Circuit representing the generator transmission line and load. plot three phase currents and neutral current. Simulation of Single Phase full converter using RLE loads and single phase AC Voltage Controller using RL loads. Plotting of Bode plots, Root Locus and Nyquist plots for the transfer functions of systems up to 5 th order Power System load flow using Newton-Raphson Technique Modeling of Transformer and simulation of lossy transmission line 34 7 Integrator and Differentiator circuits using OP-AMP Simulation of D.C separately excited motor using Transfer function approach Simulation of Buck & Boost converters Simulation of single Phase Inverter with PWM control. 51

2 Expt. No: 1 Date: PSPICE SIMULATION OF SERIES RLC CIRCUITS FOR STEP, PULSE & SINUSOIDAL INPUTS AIM: To study the responses of series RLC circuits for a given step, pulse & sinusoidal inputs. SIMULATION TOOLS REQUIRED: PC with PSPICE Software CIRCUIT DIAGRAMS: Series RLC circuit for STEP input 1 R1 2 L1 3 4 R2 5 L2 6 7 R3 L3 8 9 V1 1 OHM 50uH C1 10UF V2 2 OHMS 50uH C2 10UF V3 8 OHMS 50uH C3 10UF 0 Series RLC circuit for SQUARE input 1 R1 2 L1 3 4 R2 5 L2 6 7 R3 8 L3 9 1 OHM 10uH 2 OHMS 10uH 3 OHMS 10uH V1 C1 10UF V2 C2 10UF V3 C3 10UF 0 Series RLC circuit for SINUSOIDAL input 1 R1 2 L1 3 4 R2 5 L2 6 7 R3 8 L OHM 10uH 2 OHMS 10uH 6 OHMS 10uH V1 C1 10UF V2 C2 10UF V3 C3 10UF SPECIFICATIONS: 0 Lendi Institute Of Engineering and Technology Page 2 of 55

3 THEORY: PROGRAMS: STEP INPUT Lendi Institute Of Engineering and Technology Page 3 of 55

4 PULSE INPUT SINUSOIDAL INPUT Lendi Institute Of Engineering and Technology Page 4 of 55

5 PROCEDURE: 1. Write the program in a new text file in PSpice AD. 2. Save the file using the notation filename.cir. 3. Activate the file by opening it. 4. Run the simulation process using blue button. 5. By clicking Add Trace icon, get the required waveform. MODEL CALCULATIONS: R 2* L 1 0 L * C A).OVER DAMPED ( 0 ) 0 B) UNDER DAMAPED ( 0 ) 0 C) CRITICALLY DAMPED ( 0 ) 0 RESULT: APPLICATIONS: Lendi Institute Of Engineering and Technology Page 5 of 55

6 MODEL GRAPH: 1.5V SERIES RLC CIRCUIT WITH STEP INPUT 1.0V 0.5V 0V 0s 100us 200us 300us 400us 500us 600us 700us 800us V(3) V(6) V(9) Time 15V SERIES RLC CIRCUIT WITH SQUARE INPUT 10V 5V 0V -5V -10V -15V 0s 40us 80us 120us 160us 200us 240us V(3) V(6) V(9) Time 200V SERIES RLC CIRCUIT WITH SINUSOIDAL INPUT 100V 0V -100V -200V 0s 10ms 20ms 30ms 40ms 50ms 60ms V(3) V(6) V(9) Time Lendi Institute Of Engineering and Technology Page 6 of 55

7 Expt. No: 2 PSPICE ANALYSIS OF THREE PHASE CIRCUIT Date: AIM: To study the analysis of simple three phase circuit for balanced and unbalanced loads. SIMULATION TOOLS REQUIRED: PC with PSPICE Software CIRCUIT DIAGRAMS: Three Phase circuit with Balanced load 7 L1 3MH L2 3MH L3 3MH R1 20 OHMS R2 20 OHMS R3 20 OHMS Vx 0V VS1 VS2 VS3 0 Three Phase circuit with Unbalanced load 7 L1 3MH L2 6MH L3 9MH R1 50 OHMS R2 10 OHMS R3 15 OHMS Vx 0V VS1 VS2 VS3 0 SPECIFICATIONS: Lendi Institute Of Engineering and Technology Page 7 of 55

8 THEORY: PROGRAMS: BALANCED LOAD CONDITION Lendi Institute Of Engineering and Technology Page 8 of 55

9 UNBALANCED LOAD CONDITION PROCEDURE: 1. Write the program in a new text file in PSpice AD. 2. Save the file using the notation filename.cir. 3. Activate the file by opening it. 4. Run the simulation process using blue button. 5. By clicking Add Trace icon, get the required waveform. RESULT: Lendi Institute Of Engineering and Technology Page 9 of 55

10 MODEL CALCULATIONS: A) FOR BALANCED LOAD Ir Iy Ib In Ir Iy Ib B) FOR UNBALANCED LOAD Ir Iy Ib 0 0 In Ir 0 Iy 120 Ib s Lendi Institute Of Engineering and Technology Page 10 of 55

11 MODEL WAVEFORMS: INPUT WAVEFORM 200V 100V 0V -100V -200V 0s 5ms 10ms 15ms 20ms 25ms 30ms 35ms 40ms V(1) V(2) V(3) Time 10A BALANCED LOAD CONDITION 5A 0A -5A -10A 0s 5ms 10ms 15ms 20ms 25ms 30ms 35ms 40ms I(L1) I(L2) I(L3) Time 20A UNBALANCED LOAD CONDITION 10A 0A -10A -20A 0s 5ms 10ms 15ms 20ms 25ms 30ms 35ms 40ms I(L1) I(L2) I(L3) Time Lendi Institute Of Engineering and Technology Page 11 of 55

12 Date: Expt. No: 3(a) PSPICE ANALYSIS OF SINGLE PHASE FULL CONVERTER WITH RL & RLE LOADS AIM: To analyze the single phase full converter with RL and RLE Loads. SIMULATION TOOLS REQUIRED: PC with PSPICE Software CIRCUIT DIAGRAMS: Single Phase full converter with RL load 7 Vs 3 4 XT1 XT3 1 2 R 10 OHMS 8 E 100V 9 XT4 6 XT2 5 L 100MH Single Phase full converter with RLE load 7 0 XT1 3 4 XT3 R 10 OHMS Vs XT4 6 XT2 5 L 100MH 0 Lendi Institute Of Engineering and Technology Page 12 of 55

13 SPECIFICATIONS: THEORY: PROGRAMS: WITH RL LOAD Lendi Institute Of Engineering and Technology Page 13 of 55

14 WITH RLE LOAD SIGLE-PHASE FULL CONVERTER CIRCUIT WITH RLE LOAD Lendi Institute Of Engineering and Technology Page 14 of 55

15 CIRCUIT DIAGRAMS FOR ANALYSIS USING CIRCUIT: Single Phase full converter with RL load X1 2N1595 X3 2N1595 R1 10 OHMS VS VOFF = 0V FREQ = 50HZ VAMPL = 169.7V V1 = 0V V2 = 100V TD = US TR = 1NS TF = 1NS PW = 100US PER = 20000US VG1 V1 = 0V V2 = 100V TD = US TR = 1NS TF = 1NS PW = 100US PER = 20000US VG3 X4 2N1595 X2 2N1595 L1 100 MH V1 = 0V V2 = 100V TD = US TR = 1NS TF = 1NS PW = 100US PER = 20000US VG4 V1 = 0V V2 = 100V TD = US TR = 1NS TF = 1NS PW = 100US PER = 20000US VG2 Single Phase full converter with RLE load 0 X1 2N1595 X3 2N1595 R1 10 OHMS VS VOFF = 0V FREQ = 50HZ VAMPL = 169.7V V1 = 0V V2 = 100V TD = US TR = 1NS TF = 1NS PW = 100US PER = 20000US VG1 V1 = 0V V2 = 100V TD = US TR = 1NS TF = 1NS PW = 100US PER = 20000US VG3 E 100 V X4 2N1595 X2 2N1595 L1 100 MH V1 = 0V V2 = 100V TD = US TR = 1NS TF = 1NS PW = 100US PER = 20000US VG4 V1 = 0V V2 = 100V TD = US TR = 1NS TF = 1NS PW = 100US PER = 20000US VG2 0 Lendi Institute Of Engineering and Technology Page 15 of 55

16 PROCEDURE: 1. Write the program in a new text file in PSpice AD. 2. Save the file using the notation filename.cir. 3. Activate the file by opening it. 4. Run the simulation process using blue button. 5. By clicking Add Trace icon, get the required waveform. THERITICAL CALCULATIONS: A)FOR RL LOAD 2V M V 0 COS( ) 2V M V 0 COS( ) V B)FOR RLE LOAD t At We know i.e. at t. i o = 0 t V m sin( ) E 1 E 1 Min value of firing angle sin ( ) sin ( ) 3 V m Max value of firing angle RESULT: APPLICATIONS: The single-phase full-wave controlled rectifier is used to control power flow in many applications (e.g., power supplies, variable-speed dc motor drives, and input stages of other converters) Lendi Institute Of Engineering and Technology Page 16 of 55

17 MODEL WAVEFORMS FOR FULL CONVERTER: 200V INPUT WAVEFORM 100V 0V -100V -200V 0s 10ms 20ms 30ms 40ms 50ms 60ms V(1,2) Time 200V OUTPUT WAVEFORM WITH RL LOAD 100V 0V -100V -200V 0s 10ms 20ms 30ms 40ms 50ms 60ms V(7) Time 300V OUTPUT WAVEFORM WITH RLE LOAD 200V 100V 0V -100V 0s 10ms 20ms 30ms 40ms 50ms 60ms V(7) Time Lendi Institute Of Engineering and Technology Page 17 of 55

18 Date: Expt. No: 3(b) PSPICE ANALYSIS OF SINGLE PHASE AC VOLTAGE CONTROLLER WITH RL LOAD AIM: To analyze the single phase full converter with RL and RLE Loads. SIMULATION TOOLS REQUIRED: PC with PSPICE Software CIRCUIT DIAGRAM: Single Phase AC VOLTAGE CONTROLLER with RL load XT1 1 2 Vs XT2 R 10 OHMS 3 L 10MH SPECIFICATIONS: 0 THEORY: Lendi Institute Of Engineering and Technology Page 18 of 55

19 PROGRAM: SIGLE-PHASE AC VOLTAGE CONTROLLER CIRCUIT WITH RL LOAD Lendi Institute Of Engineering and Technology Page 19 of 55

20 CIRCUIT DIAGRAM FOR ANALYSIS USING CIRCUIT: X1 2N1595 V1 = 0V V2 = 100V TD = US TR = 1NS TF = 1NS PW = 100US PER = 20000US VG1 VS1 VOFF = 0V VAMPL = 169.7V FREQ = 50HZ VG2 X2 2N1595 V1 = 0V V2 = 100V TD = US TR = 1NS TF = 1NS PW = 100US PER = 20000US R1 10 OHMS L1 10 MH 0 PROCEDURE: 1. Write the program in a new text file in PSpice AD. 2. Save the file using the notation filename.cir. 3. Activate the file by opening it. 4. Run the simulation process using blue button. 5. By clicking Add Trace icon, get the required waveform. THERITICAL CALCULATIONS(FOR RL LOAD): Wt= = ms VM V 0 [ COS( ) 1] VM V 0 [ COS( ) 1] V RESULT: Lendi Institute Of Engineering and Technology Page 20 of 55

21 APPLICATIONS: Lendi Institute Of Engineering and Technology Page 21 of 55

22 MODEL WAVEFORMS: 200V INPUT WAVEFORM 100V 0V -100V -200V 0s 10ms 20ms 30ms 40ms 50ms 60ms V(1) 200V Time OUTPUT WAVEFORM 100V 0V -100V -200V 0s 10ms 20ms 30ms 40ms 50ms 60ms V(2) Time Lendi Institute Of Engineering and Technology Page 22 of 55

23 Expt. No: 4 STABILITY ANALYSIS OF LINEAR TIME INVARIANT SYSTEMS (Bode, Root Locus, Nyquist plots using MATLAB) Date: AIM: To analyze the stability of given linear time invariant systems using MATLAB. SIMULATION TOOLS REQUIRED: PC with MATLAB Software THEORY: Lendi Institute Of Engineering and Technology Page 23 of 55

24 TRANSFER FUNCTION: The given system is represented by a transfer function as follows THEORITICAL CALCULATIONS: Draw Bode, Nyquist and Root locus plots for the given transfer function. Lendi Institute Of Engineering and Technology Page 24 of 55

25 PROGRAMS: BODE PLOT: NYQUIST PLOT: ROOT LOCUS PLOT: PROCEDURE: 1. Open the MATLAB command window clicking on the MATLAB icon. 2. Click on file menu and open new M file. 3. Enter the MATLAB code. 4. Click on the debug menu and run the code. 5. Then copy the obtained plot. RESULT: APPLICATIONS: Lendi Institute Of Engineering and Technology Page 25 of 55

26 MODEL GRAPHS: BODE PLOT NYQUIST PLOT Lendi Institute Of Engineering and Technology Page 26 of 55

27 ROOT LOCUS PLOT Lendi Institute Of Engineering and Technology Page 27 of 55

28 Expt. No: 5 POWER SYSTEM LOAD FLOW USING GAUSS-SEIDEL AND NEWTON-RAPHSON TECHNIQUE Date: AIM: To find the power flow solution of a given power system using Gauss-Seidel and Newton Raphson methods. SIMULATION TOOLS REQUIRED: PC with MATLAB Software SINGLE LINE DIAGRAM: Lendi Institute Of Engineering and Technology Page 28 of 55

29 THEORY: Lendi Institute Of Engineering and Technology Page 29 of 55

30 PROGRAM: PROCEDURE: NEWTON RAPHSON METHOD: 1. Open the MA TLAB Command window by clicking on the MA TLAB.exe icon. 2. Enter the programs LF-Bus, LF-Newton busout and lineflow in the MATLAB Text Editor. 3. Prepare the line, transformer parameters and transformer tap settings data in a matrix named line data. 4. Run the programs LF-Y-Bus, LF-Newton, busout and line flow in MATLAB Command Window to get the power flow solution using Newton-Raphson. RESULT: APPLICATIONS: Lendi Institute Of Engineering and Technology Page 30 of 55

31 Expt. No: 6(a) MODELING OF TRANSFORMER Date: AIM: To simulate an Op-amp based Integrator & Differentiator circuits using Pspice. SIMULATION TOOLS REQUIRED: PC with PSPICE Software CIRCUIT DIAGRAMS: THEORY: Lendi Institute Of Engineering and Technology Page 31 of 55

32 SPECIFICATIONS: PROGRAMS: PROCEDURE: 1. Write the program in a new text file in PSpice AD. 2. Save the file using the notation filename.cir. 3. Activate the file by opening it. 4. Run the simulation process using blue button. 5. By clicking Add Trace icon, get the required waveform. RESULT: APPLICATIONS: MODEL GRAPTH Lendi Institute Of Engineering and Technology Page 32 of 55

33 Lendi Institute Of Engineering and Technology Page 33 of 55

34 Expt. No: 6(b) PSPICE Simulation of a Lossy Transmission Line Date: Aim: Calculation of lossy transmission line parameters by applying PSPICE simulation. Software tools required: PSPICE THEORY: Procedure: 1. Open PSPICE and create 5 sections of a lossless transmission line by placing 5 inductors (use values of L=10H) in series, then connect each node between the inductors (and the node after the last inductor) to ground through a capacitor (use C=1nF) as shown in Figure 1. This is the lumped element model for a lossless transmission line. Figure 1 2. Calculate the characteristic impedance for this lossless transmission line model. 3. Place a resistor having a value of the characteristic impedance of your line at the end of your line in parallel with the final capacitor. This is the load. 4. Place a VSIN source on the left side of your circuit and connect it to the line by means of the first inductor. Adjust VSIN such that it has amplitude of 10 V, phase of 0 degrees, and a frequency of 1 khz. Note that VSIN also requires that you set a Voff value. Set this to zero. 5. Determine the phase velocity of the transmission line model. A. The lumped element model is in terms of segments rather than position, so the phase velocity will be in units of segments/seconds. B. Place a marker at the node between L2 and L3, between L3 and L4, and between L4 and L5. C. Go to the Analysis menu and open the setup window. Find the transient analysis section and then open it. Set the following parameters: Print Step (.01m), final Time (5m), No- Print Delay (0), and Step Ceiling (.01m). Run the simulation and examine the trace plots associated with each marker. Lendi Institute Of Engineering and Technology Page 34 of 55

35 D. Divide the number of segment by the time difference between the peak for each marker. E. Determine the phase velocity for following three cases (1) between L2-L3 and L3-L4, (2) between L3-L4 and L4-L5, and (3) between L2-L3 and L4-L5. The phase velocity for these cases should be approximately the same. (See Figure 2) Figure 2. The phase velocity between segments 3 and 4 is 1/ t. 1. Determine the propagation constant,, for this lumped element model. a. The propagation constant is the position variable quantity. b. It is easier to determine the wavelength,, and then calculate the propagation constant as given by 2. c. To find the wavelength you need to place a voltage monitor between each segment and then measure the voltage on each marker at the same time. (see Figure 3) wave. d. Add more segments until you can map out more than one entire period of the sinusoidal e. Plot the voltage as a function of segment number. f. Measure the period in terms of segments. Lendi Institute Of Engineering and Technology Page 35 of 55

36 Figure 3 2. Compare the relationship of your calculated phase velocity and wavelength to that derived in the book (Eq. 2.53). 3. Add resistors in series with each inductor that causes the sinusoid to be visibly damped while still showing oscillation. This lumped element models the finite resistance of the metal lines of the transmission line. Describe your new circuit and its values for decay constant. Include a printout with your description. 4. Add resistors in parallel with each capacitor that causes the sinusoid to be visibly damped while still showing oscillation. This lumped element models the small conductivity of the insulator (between the two metal lines of the transmission line. Describe your new circuit and its values for decay constant. Include a printout with your description. Lendi Institute Of Engineering and Technology Page 36 of 55

37 THEROTICAL CALCULATIONS: CHARACTERISTIC IMPEDENCE RESULT: Z 0 C L APPLICATION: Lendi Institute Of Engineering and Technology Page 37 of 55

38 Expt. No: 7 PSPICE SIMULATION OF INTEGRATOR & DIFFERENTIATOR Date: AIM: To simulate an Op-amp based Integrator & Differentiator circuits using Pspice. SIMULATION TOOLS REQUIRED: PC with PSPICE Software CIRCUIT DIAGRAMS: INTEGRATOR CIRCUIT DIFFERENTIATOR CIRCUIT Lendi Institute Of Engineering and Technology Page 38 of 55

39 THEORY: PROGRAMS: INTEGRATOR: Lendi Institute Of Engineering and Technology Page 39 of 55

40 DIFFERENTIATOR: RESPENSE OF DIFFERENTIATOR Lendi Institute Of Engineering and Technology Page 40 of 55

41 PROCEDURE: 1. Write the program in a new text file in PSpice AD. 2. Save the file using the notation filename.cir. 3. Activate the file by opening it. 4. Run the simulation process using blue button. 5. By clicking Add Trace icon, get the required waveform. MODEL CALCULATION: A).FOR DIFFERENTATIOR dv V 0 RF * C * dt B).FOR INTEGRATOR 1 V 0 R1* C T F 0 Vdt RESULT: APPLICATIONS: Lendi Institute Of Engineering and Technology Page 41 of 55

42 MODEL WAVEFORMS: 1.0V INTEGRATOR INPUT & OUTPUT WAVEFORMS 0V -1.0V -2.0V 5.0V V(1) 0V SEL>> -5.0V 0s 0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms V(4) Time DIFFERENTIATOR INPUT & OUTPUT WAVEFORMS 1.0V 0.5V SEL>> 0V 5.0V V(1) 0V -5.0V 0s 0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms V(4) Time Lendi Institute Of Engineering and Technology Page 42 of 55

43 Expt. No: 8 SIMULATION OF D.C SEPARATELY EXCITED MOTOR USING TRANSFER FUNCTION APPROACH. Date: AIM: To Simulation of D.C separately excited motor using Transfer function approach using MATLAB. SIMULATION TOOLS REQUIRED: PC with MATLAB Software SPECIFICATIONS: CIRCUIT DIAGRAMS: THEORY: Lendi Institute Of Engineering and Technology Page 43 of 55

44 PROCEDURE: 1. Open the MATLAB software by clicking on the MATLAB icon. 2. Click on file menu and open new Model file. 3. Add the required blocks from simulink library browser to model file. 4. Click on the start button to simulate. 5. Draw the plot. RESULT: APPLICATIONS: MODEL WAVEFORMS: Lendi Institute Of Engineering and Technology Page 44 of 55

45 Expt. No: 9(A) SIMULATION OF BOOST CONVERTERS Date: AIM: To simulate boost converters using Pspice. SIMULATION TOOLS REQUIRED: PC with PSPICE Software CIRCUIT DIAGRAMS: SPECIFICATIONS: THEORY: Lendi Institute Of Engineering and Technology Page 45 of 55

46 BOOST CHOPPER PROCEDURE: 1. Write the program in a new text file in PSpice AD. 2. Save the file using the notation filename.cir. 3. Activate the file by opening it. 4. Run the simulation process using blue button. 5. By clicking Add Trace icon, get the required waveform. Lendi Institute Of Engineering and Technology Page 46 of 55

47 MODEL CALCULATIONS: VS Ton V 0 where 1 T RESULT: APPLICATIONS: MODEL WAVEFORMS: Expt. No: 9(B) Lendi Institute Of Engineering and Technology Page 47 of 55

48 Date: SIMULATION OF BUCK CONVERTERS AIM: To analyze Buck chopper using Pspice. SIMULATION TOOLS REQUIRED: PC with PSPICE Software CIRCUIT DIAGRAM: Buck chopper Vy T1 Le L 0V UH 40.91UH Vs 110V RB 250 OHMS Vg Dm Ce 8.33UF Vx R 3 OHMS 0V10 V 0 SPECIFICATIONS: THEORY: Lendi Institute Of Engineering and Technology Page 48 of 55

49 PROGRAM: Lendi Institute Of Engineering and Technology Page 49 of 55

50 PROCEDURE: 1. Write the program in a new text file in PSpice AD. 2. Save the file using the notation filename.cir. 3. Activate the file by opening it. 4. Run the simulation process using blue button. 5. By clicking Add Trace icon, get the required waveform. MODEL CALCULATIONS : V 0 *VS Ton VS T RESULT: APPLICATIONS: MODEL WAVEFORMS: Lendi Institute Of Engineering and Technology Page 50 of 55

51 Expt. No: 10 SINGLE PHASE INVERTER WITH PWM CONTROL Date: AIM: PSpice analysis of single phase inverter with PWM control. SIMULATION TOOLS REQUIRED: PC with PSPICE Software CIRCUIT DIAGRAM: 1 Single phase inverter with PWM control 2 8 Vy 0V Rg1 T1 7 3 D1 Vx 4 R 5 L 12 Rg3 T3 11 D3 Vs 100V 0V 2.5 OHMS 10MH 6 Rg4 T4 13 D Rg2 T2 9 D2 0 PWM Generator R4 1 R1 1k KOHMS 3 Vr 2 R2 1k Rin 2MEG Ro 75 OHMS Co 10pf Vc 4 0 Lendi Institute Of Engineering and Technology Page 51 of 55

52 15 Carrier and Reference signals Vc1 Rc1 2MEG Vc3 Rc3 2MEG Vr Rr 2MEG SPECIFICATIONS: 0 THEORY: Lendi Institute Of Engineering and Technology Page 52 of 55

53 PROGRAM: PROCEDURE: Lendi Institute Of Engineering and Technology Page 53 of 55

54 1. Write the program in a new text file in PSpice AD. 2. Save the file using the notation filename.cir. 3. Activate the file by opening it. 4. Run the simulation process using blue button. 5. By clicking Add Trace icon, get the required waveform. MODEL WAVEFORM: AMPLITUDE OF VC1&VC2 >AMPLITUE OF VR AMPLITUDE OF VC1&VC2 =AMPLITUE OF VR Lendi Institute Of Engineering and Technology Page 54 of 55

55 MODEL CALCULATIONS: CASDE A :OVER MADULATION (Ar >Ac) ==5>1 >Mr>1 =>Ar/Ac = N=number of pulses per half cycle N=1 CASDE A :UNDER MADULATION (Ar <Ac) =>Mr<1 =>Ar/Ac = = N-1=number of pulses per half cycle N fc /(2 fr) N 1 RESULT: APPLICATIONS: Lendi Institute Of Engineering and Technology Page 55 of 55