CONTROLLED RECTIFIERS
1. Find the average dc voltage of the waveform shown below,
Peak voltage Vm = 40V, Frequency F = 1KHz.
AVERAGE DC Value of the output voltage
Vdc = Vm/2π ( cosα – cosβ)
Here,
Vi (rms) = Vm /√2 =40/√2 = 28.28V
t = 0.4ms = 400μs
T = 1/F = 1ms
α=0
β = 360 (t/T) = 360 (400μs/1ms) = 144˚
β = (π/180)144˚ = 2.513 rad
Vdc = Vm/2π ( cosα – cosβ) = 40/2π ( cos0˚– cos144˚)
Vdc = 40/2π ( cos0˚– cos144˚) = 40/2π ( 1 – cos144˚)
Vdc = 11.51V
R.M.S Value of the output voltage
2
Vm
1
1
(β − α − sin 2 β + sin 2 α )
4π
2
2
since α = 0 ,
V rms =
V rms =
√
√
V m2
1
(β − sin 2 β)
4π
2
1
1
(β − sin 2 β)
2π
2
1
P . F=
(2.513 + 0.475)
2π
P . F = 0.689 Leading
P . F=
√
√
2
40
1
V rms =
(2.513 − sin (2 × 144))
4π
2
V rms = √ 127.32 (2.513 + 0.475)
√
Vrms = 19.50V
Powerfactor (P.F) = Vrms/Vi (rms) = 19.50/28.28 = 0.689
Table 1
Sl.No. t(μs) α°
β° =360t/T
RMS
AVERAGE
VALUE (V)
VALUE (V)
(T=1/F=1ms.)
1.
2.
3.
4.
100
200
300
400
0
0
0
0
36°
72°
108°
144°
4.41
11.07
16.65
19.50
1.21
4.39
8.33
11.51
POWER
FACTOR
0.155
0.391
0.588
0.689
2. Find the average dc voltage of the waveform shown below,
Peak voltage Vm = 40V, Frequency F = 1KHz.
AVERAGE DC Value of the output voltage
Vdc = Vm/π ( cosα – cosβ)
Here,
Vi (rms) = Vm /√2 =40/√2 = 28.28V
t = 0.4ms = 400μs
T = 1/F = 1ms
α=0
β = 360 (t/T) = 360 (400μs/1ms) = 144˚
β = (π/180)144˚ = 2.513 rad
Vdc = Vm/π ( cosα – cosβ) = 40/π ( cos0˚– cos144˚)
Vdc = 40/π ( cos0˚– cos144˚) = 40/π ( 1 – cos144˚)
Vdc = 23.03V
R.M.S Value of the output voltage
2
Vm
1
1
V rms =
(β − α − sin 2 β + sin 2 α )
2π
2
2
since α = 0 ,
√
√
1
1
P . F = π (β − sin 2 β)
2
√
1
P . F = π (2.513 + 0.475)
P . F = 0.975 Leading
√
V m2
1
V rms =
(β − sin 2 β)
2π
2
2
40
1
V rms =
(2.513 − sin (2 × 144))
2π
2
V rms = √ 254.647 (2.513 + 0.475)
√
Vrms = 27.59V
Powerfactor (P.F) = Vrms/Vi (rms) = 27.59/28.28 = 0.975
Table 2
Sl.No.
1.
2.
3.
4.
t(μs)
α°
100
200
300
400
0
0
0
0
β° =360t/T
(T=1/F=1ms.)
36°
72°
108°
144°
RMS VALUE (V)
AVERAGE VALUE (V)
6.24
15.66
23.56
27.59
2.43
8.80
16.67
23.03
3. Find the average dc voltage of the waveform shown below,
Peak voltage Vm = 40V, Frequency F = 1KHz.
AVERAGE DC Value of the output voltage
Vdc = Vm/π ( cosα – cosβ) or Vm/π ( 1 + cosα )
Here,
Vi (rms) = Vm /√2 =40/√2 = 28.28V
t = 0.1ms = 100μs
T = 1/F = 1ms
α = 360 (t/T) = 360 (400μs/1ms) = 36˚
β = 180˚
α = (π/180)36˚ = 0.628 rad
Vdc = Vm/π ( 1+ cosα ) = 40/π ( 1+cos36˚)
Vdc = 23.03V
R.M.S Value of the output voltage
2
Vm
1
V rms =
( π − α + sin 2 α )
2π
2
√
402
1
V rms =
( π − 0.628 + sin 2 × 36)
2π
2
√
1
1
P . F = π ( π − α + sin 2 α )
2
√
1
P . F = π (2.513 + 0.475)
P . F = 0.975 Lagging
√
V rms = √ 254.647 (2.513 + 0.475)
Vrms = 27.59V
Powerfactor (P.F) = Vrms/Vi (rms) = 27.59/28.28 = 0.975
Table 2
Sl.No. t(μs)
α°
β° =360t/T
RMS VALUE (V)
(T=1/F=1ms.)
1.
100
27.59
36°
180°
2.
200
23.56
72°
180°
3.
300
15.66
108°
180°
4.
400
6.24
144°
180°
AVERAGE VALUE (V)
23.03
16.67
8.80
2.43
1. Simulate the following using NGSPICE and find out following, 1. Peak input voltage, 2. Peak
output voltage, 3.RMS input voltage, 4. RMS output voltage, 5. Average output voltage, 6. Peak
output load power, 7. Average output load power.
NGSPICE NETLIST
*Spice netlist for Circuit: 00_2R.CKT
*SIN(dc-offset,Peak-Amplitude,Frequency,Start-Delay,Damping-Factor)
V1 VIN GND SIN(0 40 50 0 0) DC 0 AC 0 1
R1 VIN VOUT 13.5
R2 VOUT GND 10
.end
.SAVE VIN VOUT @v1[p] v1#branch @v1[z] @r2[p] @r2[i] @r1[p] @r1[i]
.control
TRAN 5u 20m 0 10u UIC
set color0=white
set color1=rgb:49/49/49
set color2=brown
set color3=red
meas tran vinmax MAX VIN from=0m to=20m
meas tran voutmax MAX VOUT from=0m to=20m
meas tran vinrms RMS VIN from=0m to=20m
meas tran voutrms RMS VOUT from=0m to=20m
meas tran voutavg AVG VOUT from=0m to=20m
meas tran poutmax MAX @r2[p]
meas tran poutavg AVG @r2[p] from=0 to=20m
plot VIN VOUT xlimit 1.00m 10.00m ylimit -20.00 20.00
plot VIN VOUT @r1[p] @r1[i]
.endc
RESULTS
1. Peak input voltage = 3.999995e+01 at= 5.004920e-03 =39.99V.
2. Peak output voltage = 1.702126e+01 at= 5.004920e-03=17.02V.
3.RMS input voltage = 2.82843e+01 from= 0.00000e+00 to= 2.00000e-02=28.28V.
4. RMS output voltage = 1.20359e+01 from= 0.00000e+00 to= 2.00000e-02=12.03V.
5. Average output voltage = 1.829457e-11 from= 0.000000e+00 to= 2.000000e-02≅0V.
6. Peak output load power = 2.897232e+01 at= 1.500492e-02=28.97W.
7. Average output load power = 1.448619e+01 from= 0.000000e+00 to= 2.000000e-02=14.48W.
RESULTS
SL.NO
1.
Peak input voltage
2.
Peak output voltage
3.
RMS input voltage
4.
RMS output voltage
5.
Average output voltage
6.
Peak output load power
7.
Average output load power
CALCULATED
40V
40(10/(10+13.5))=40(0.425)=17.02V
40/√2=40(0.707)=28.28V
(40/√2)(10/(10+13.5))=12.01V
Average value for full sine wave=0
(17.02)^2/10=28.96W
(12.01)^2/10=14.42W
SIMULATION
39.99V
17.02V
28.28V
12.03V
18.29pV
28.97W
14.48W
2. Simulate the following using NGSPICE and find out following, 1. Peak input voltage, 2. Peak
output voltage, 3.RMS input voltage, 4. RMS output voltage, 5. Average output voltage, 6. Average
output load power.
NGSPICE NETLIST
*Spice netlist for Circuit: Firing-angle-control(alpha).CKT
*SIN(dc-offset,Peak-Amplitude,Frequency,Start-Delay,Damping-Factor)
V1 VIN1 VIN2 DC 0 SIN(0 42 50 0 0) AC 1 0
*PULSE(Initial-Amplitude,Pulse-Amplitude,Start-Delay,Rise-Time,Fall-Time,Pulse-width,Time-period)
V2 VG1 0 DC 0 PULSE(5 0 0 1n 1n 1m 10m)
RL 0 VOUT 10
RDUMMY 0 VFWR 1k
XXD1 0 VIN1 VFWR VIN2 XKBPC610
SVcSW1 VFWR VOUT VG1 0 SSW05-PE
.SAVE VIN2 VIN1 VOUT VG1 VFWR @v1[p] v1#branch @v1[z] @v2[p] v2#branch @v2[z]
.SAVE @rdummy[p] @rdummy[i] @rl[p] @rl[i]
*KBPC610 1000V 6A Si pkg:D-72
.SUBCKT XKBPC610 1 2 3 4
D1 1 2 KBPC610
D2 1 4 KBPC610
D3 2 3 KBPC610
D4 4 3 KBPC610
.MODEL KBPC610 D (IS=24.2N RS=42M N=1.75 BV=1K IBV=936U
+ CJO=248P VJ=.75 M=.333 TT=4.32U)
.ENDS XKBPC610
*SW05-PE Threshold voltage= 0.5V
.MODEL SSW05-PE SW(VT=0.5 RON=1E-9 )
.END
.control
TRAN 5u 20m 0 10u UIC
set nfreqs=10
set color0=white
set color1=rgb:49/49/49
set color2=brown
plot VOUT, 0-@rl[i], @rl[p]
plot (VIN1-VIN2) VG1 VOUT
meas tran vinmax MAX VFWR from=0m to=20m
meas tran voutmax MAX VOUT from=0m to=20m
meas tran vinrms RMS VFWR from=0m to=20m
meas tran voutrms RMS VOUT from=0m to=20m
meas tran voutavg AVG VOUT from=0m to=20m
meas tran poutmax MAX @rl[p]
meas tran poutavg AVG @rl[p] from=0 to=20m
fourier 100 VOUT
plot fourier11[1] vs fourier11[0]
.endc
3. Simulate FIRING ANGLE CONTROL using NGSPICE and find out following, 1. Peak input
voltage, 2.RMS input voltage, 3. Peak output voltage, 4. RMS output voltage, 5. Average output
voltage, 6. powerfactor.
NGSPICE NETLIST
*Spice netlist for Circuit: FIRING ANGLE CONTROL.CKT
V3 VG 0 DC 0 PULSE(5 0 0 1n 1n 5m 10m)
V1 VIN1 0 DC 0 SIN(0 40 50 0 0) AC 1 0
V2 VIN2 0 DC 0 SIN(0 40 50 -10m 0) AC 1 0
SVcSW1 VIN1 VFWR VIN1 0 SSW-AE306
SVcSW2 VIN2 VFWR VIN2 0 SSW-AE306
SVcSW3 VFWR VOUT VG 0 SSW-AE306
RL VOUT 0 10
RDUMMY 0 VFWR 1k
.SAVE VG VIN2 VIN1 VFWR VOUT @v3[p] v3#branch @v3[z] @v2[p] v2#branch @v2[z]
.SAVE @v1[p] v1#branch @v1[z] @rl[p] @rl[i] @rdummy[p] @rdummy[i]
*SW-AE306
.MODEL SSW-AE306 SW(VT=0.001 RON=0.001 )
.END
.control
set freq=100
set transtm=40m
set nfreqs=10
set color0=white
set color1=black
set color2=brown
set color3=grey
set color4=red
set color5=grey
TRAN 1u $transtm 0 2u UIC
fourier $freq VOUT
plot fourier11[1] vs fourier11[0]
plot VOUT VIN1 @rl[i] VFWR
meas tran vinmax MAX VIN1
meas tran vinrms RMS VIN1
meas tran voutmax MAX VOUT
meas tran voutrms RMS VOUT
meas tran voutavg AVG VOUT
let powerfactor= voutrms/vinrms
print powerfactor
.endc
4. Simulate FIRING ANGLE CONTROL using NGSPICE and find out following, 1. Peak input
voltage, 2.RMS input voltage, 3. Peak output voltage, 4. RMS output voltage, 5. Average output
voltage, 6. powerfactor.
NGSPICE NETLIST
*Spice netlist for Circuit: FIRING ANGLE CONTROL.CKT
.param AMP=40 FREQ=50 VD=1m RD=1m CNTRL=1 ANGLE=90
*********************************************************
.param TRIG={(ANGLE/(360*FREQ))}
.param TSIG={(1/(2*FREQ))}
.param ALPHA={(CNTRL*5)} BETA={(1-CNTRL)*5}
.csparam TRANST={1.5*(1/(FREQ))}
.csparam FREQ={(2*FREQ)}
*********************************************************
V3 VG 0 DC 0 PULSE({ALPHA} {BETA} 0 1n 1n {TRIG} {TSIG})
V1 VIN1 0 DC 0 SIN(0 {AMP} {FREQ} 0 0) AC 1 0
V2 VIN2 0 DC 0 SIN(0 {AMP} {FREQ} {-TSIG} 0) AC 1 0
SVcSW1 VIN1 VFWR VIN1 0 SSW-AE306
SVcSW2 VIN2 VFWR VIN2 0 SSW-AE306
SVcSW3 VFWR VOUT VG 0 SSW-AE306
RL VOUT 0 10
RDUMMY 0 VFWR 1k
.SAVE VG VIN2 VIN1 VFWR VOUT @v3[p] v3#branch @v3[z] @v2[p] v2#branch @v2[z]
.SAVE @v1[p] v1#branch @v1[z] @rl[p] @rl[i] @rdummy[p] @rdummy[i]
*SW-AE306
.MODEL SSW-AE306 SW(VT={VD} RON={RD})
.END
.control
set freq=$&FREQ
set transtm=$&TRANST
set nfreqs=10
set color0=white
set color1=black
set color2=brown
set color3=grey
set color4=red
set color5=grey
TRAN 1u $transtm 0 2u UIC
fourier $freq VOUT
plot fourier11[1] vs fourier11[0]
plot VOUT VIN1 @rl[i] VFWR
meas tran vinmax MAX VIN1
meas tran vinrms RMS VIN1
meas tran voutmax MAX VOUT
meas tran voutrms RMS VOUT
meas tran voutavg AVG VOUT
let powerfactor= voutrms/vinrms
print powerfactor
.endc
5. Simulate EXTINCTION ANGLE CONTROL using NGSPICE and find out following, 1. Peak
input voltage, 2.RMS input voltage, 3. Peak output voltage, 4. RMS output voltage, 5. Average output
voltage, 6. powerfactor.
NGSPICE NETLIST
*Spice netlist for Circuit: EXTINCTION ANGLE CONTROL.CKT
V3 VG 0 DC 0 PULSE(0 5 0 1n 1n 5m 10m)
V1 VIN1 0 DC 0 SIN(0 40 50 0 0) AC 1 0
V2 VIN2 0 DC 0 SIN(0 40 50 -10m 0) AC 1 0
SVcSW1 VIN1 VFWR VIN1 0 SSW-AE306
SVcSW2 VIN2 VFWR VIN2 0 SSW-AE306
SVcSW3 VFWR VOUT VG 0 SSW-AE306
RL VOUT 0 10
RDUMMY 0 VFWR 1k
.SAVE VG VIN2 VIN1 VFWR VOUT @v3[p] v3#branch @v3[z] @v2[p] v2#branch @v2[z]
.SAVE @v1[p] v1#branch @v1[z] @rl[p] @rl[i] @rdummy[p] @rdummy[i]
*SW-AE306
.MODEL SSW-AE306 SW(VT=0.001 RON=0.001 )
.END
.control
set freq=100
set transtm=40m
set nfreqs=10
set color0=white
set color1=black
set color2=brown
set color3=grey
set color4=red
set color5=grey
TRAN 1u $transtm 0 2u UIC
fourier $freq VOUT
plot fourier11[1] vs fourier11[0]
plot VOUT VIN1 @rl[i] VFWR
meas tran vinmax MAX VIN1
meas tran vinrms RMS VIN1
meas tran voutmax MAX VOUT
meas tran voutrms RMS VOUT
meas tran voutavg AVG VOUT
let powerfactor= voutrms/vinrms
print powerfactor
.endc
6. Simulate EXTINCTION ANGLE CONTROL using NGSPICE and find out following, 1. Peak
input voltage, 2.RMS input voltage, 3. Peak output voltage, 4. RMS output voltage, 5. Average output
voltage, 6. powerfactor.
NGSPICE NETLIST
*Spice netlist for Circuit: EXTINCTION ANGLE CONTROL.CKT
.param AMP=40 FREQ=50 VD=1m RD=1m CNTRL=1 ANGLE=90
*********************************************************
.param TRIG={(ANGLE/(360*FREQ))}
.param TSIG={(1/(2*FREQ))}
.param ALPHA={(CNTRL*5)} BETA={(1-CNTRL)*5}
.csparam TRANST={1.5*(1/(FREQ))}
.csparam FREQ={(2*FREQ)}
*********************************************************
V3 VG 0 DC 0 PULSE({ALPHA} {BETA} 0 1n 1n {TRIG} {TSIG})
V1 VIN1 0 DC 0 SIN(0 {AMP} {FREQ} 0 0) AC 1 0
V2 VIN2 0 DC 0 SIN(0 {AMP} {FREQ} {-TSIG} 0) AC 1 0
SVcSW1 VIN1 VFWR VIN1 0 SSW-AE306
SVcSW2 VIN2 VFWR VIN2 0 SSW-AE306
SVcSW3 VFWR VOUT VG 0 SSW-AE306
RL VOUT 0 10
RDUMMY 0 VFWR 1k
.SAVE VG VIN2 VIN1 VFWR VOUT @v3[p] v3#branch @v3[z] @v2[p] v2#branch @v2[z]
.SAVE @v1[p] v1#branch @v1[z] @rl[p] @rl[i] @rdummy[p] @rdummy[i]
*SW-AE306
.MODEL SSW-AE306 SW(VT={VD} RON={RD})
.END
.control
set freq=$&FREQ
set transtm=$&TRANST
set nfreqs=10
set color0=white
set color1=black
set color2=brown
set color3=grey
set color4=red
set color5=grey
TRAN 1u $transtm 0 2u UIC
fourier $freq VOUT
plot fourier11[1] vs fourier11[0]
plot VOUT VIN1 @rl[i] VFWR
meas tran vinmax MAX VIN1
meas tran vinrms RMS VIN1
meas tran voutmax MAX VOUT
meas tran voutrms RMS VOUT
meas tran voutavg AVG VOUT
let powerfactor= voutrms/vinrms
print powerfactor
.endc
7. Simulate SYMMETRICAL ANGLE CONTROL using NGSPICE and find out following, 1. Peak
input voltage, 2.RMS input voltage, 3. Peak output voltage, 4. RMS output voltage, 5. Average output
voltage, 6. powerfactor.
NGSPICE NETLIST
*Spice netlist for Circuit: SYMMETRICAL ANGLE CONTROL
V3 VG 0 DC 0 PULSE(0 5 2m 1n 1n 6m 10m)
V1 VIN1 0 DC 0 SIN(0 40 50 0 0) AC 1 0
V2 VIN2 0 DC 0 SIN(0 40 50 -10m 0) AC 1 0
SVcSW1 VIN1 VFWR VIN1 0 SSW-AE306
SVcSW2 VIN2 VFWR VIN2 0 SSW-AE306
SVcSW3 VFWR VOUT VG 0 SSW-AE306
RL VOUT 0 10
RDUMMY 0 VFWR 1k
.SAVE VG VIN2 VIN1 VFWR VOUT @v3[p] v3#branch @v3[z] @v2[p] v2#branch @v2[z]
.SAVE @v1[p] v1#branch @v1[z] @rl[p] @rl[i] @rdummy[p] @rdummy[i]
*SW-AE306
.MODEL SSW-AE306 SW(VT=0.001 RON=0.001 )
.END
.control
set freq=100
set transtm=40m
set nfreqs=10
set color0=white
set color1=black
set color2=brown
set color3=grey
set color4=red
set color5=grey
TRAN 1u $transtm 0 2u UIC
fourier $freq VOUT
plot fourier11[1] vs fourier11[0]
plot VOUT VIN1 @rl[i] VFWR
meas tran vinmax MAX VIN1
meas tran vinrms RMS VIN1
meas tran voutmax MAX VOUT
meas tran voutrms RMS VOUT
meas tran voutavg AVG VOUT
let powerfactor= voutrms/vinrms
print powerfactor
.endc
8. Simulate SYMMETRICAL ANGLE CONTROL using NGSPICE and find out following, 1. Peak
input voltage, 2.RMS input voltage, 3. Peak output voltage, 4. RMS output voltage, 5. Average output
voltage, 6. powerfactor.
NGSPICE NETLIST
*Spice netlist for Circuit: SYMMETRICAL ANGLE CONTROL
.param AMP=40 FREQ=50 VD=1n RD=1n ANGLE=54
*********************************************************
.param TP={(1/(2*FREQ))} ALPHA={(ANGLE/(360*FREQ))} BETA={(TP-(2*ALPHA))}
.csparam TRANST={1.5*(1/(FREQ))}
.csparam FREQ={(2*FREQ)}
*********************************************************
V3 VG 0 DC 0 PULSE(0 5 ALPHA 1n 1n BETA TP)
V1 VIN1 0 DC 0 SIN(0 AMP FREQ 0 0) AC 1 0
V2 VIN2 0 DC 0 SIN(0 AMP FREQ tp 0) AC 1 0
SVcSW1 VIN1 VFWR VIN1 0 SSW-AE306
SVcSW2 VIN2 VFWR VIN2 0 SSW-AE306
SVcSW3 VFWR VOUT VG 0 SSW-AE306
RL VOUT 0 10
RDUMMY 0 VFWR 1k
.SAVE VG VIN2 VIN1 VFWR VOUT @v3[p] v3#branch @v3[z] @v2[p] v2#branch @v2[z]
.SAVE @v1[p] v1#branch @v1[z] @rl[p] @rl[i] @rdummy[p] @rdummy[i]
*SW-AE306
.MODEL SSW-AE306 SW(VT={VD} RON={RD})
.END
.control
set freq=$&FREQ
set transtm=$&TRANST
set nfreqs=10
set color0=white
set color1=black
set color2=brown
set color3=grey
set color4=red
set color5=grey
TRAN 1u $transtm 0 2u UIC
fourier $freq VOUT
plot fourier11[1] vs fourier11[0]
plot VOUT VIN1 @rl[i] VFWR
meas tran vinmax MAX VIN1
meas tran vinrms RMS VIN1
meas tran voutmax MAX VOUT
meas tran voutrms RMS VOUT
meas tran voutavg AVG VOUT
let powerfactor= voutrms/vinrms
print powerfactor
.endc