Rectifiers

PRECISION RECTIFIERS

1. SIGNAL PROCESSING CIRCUITS USING OP AMP
PrecisionRectifiers
Half Wave Rectifier(HWR)
•Saturation precision HWR
•Non Saturation Precision HWR
Full wave rectifier (FWR)
Limiting Circuits
Peak Clipper
Dead Zone Circuit
Precision Clipper
Sample and Hold Circuit
RAJESHG
Sr. Asst. Prof/ECE

2. Half-waverectifier
Consider adioderectifier:
Vo
Vi
D
R
i
VD
Vo
slope=1
V

3. Half-waverectifier
Consider adioderectifier:
Vo
Vi
D
R
i
VD
IfVi »VD,the diodedropcanbeignored.
However,ifVi issmall,e.g., Vi =0.2sinωt V,then the circuit doesnotrectify, and
Vo(t)=0V.
Vo
slope=1
V

4. Half-waverectifier
Consider adioderectifier:
Vo
Vi
D
R
i
VD
IfVi »VD,the diodedropcanbeignored.
However,ifVi issmall,e.g., Vi =0.2sinωt V,then the circuit doesnotrectify, and
Vo(t)=0V.
Precision rectifier circuits overcome thisdrawback.
Vo
slope=1
V

5. Half-waveprecision rectifier
Vo
DVi
R

6. Half-waveprecision rectifier
i−Vo Vo
DVi Vi VD
R iR
R
Consider twocases:
(i)Disconducting:The feedback loopisclosed,and the circuit lookslike(except
forthe diodedrop) the bufferwehaveseenearlier.
iD
Vo1

7. Half-waveprecision rectifier
i−Vo Vo
DVi Vi VD
R iR
R
Consider twocases:
(i)Disconducting:The feedback loopisclosed,and the circuit lookslike(except
forthe diodedrop) the bufferwehaveseenearlier.
Sincethe input currenti− ≈0,iR =iD.
Vo1Vo+0.7V
Further,V+ −V− = = ≈0V→Vo =Vi.
A AV V
iD
Vo1

8. Half-waveprecision rectifier
i−Vo Vo
DVi Vi VD
R iR
R
Consider twocases:
(i)Disconducting:The feedback loopisclosed,and the circuit lookslike(except
forthe diodedrop) the bufferwehaveseenearlier.
Sincethe input currenti− ≈0,iR =iD.
Vo1Vo+0.7V
Further,V+ −V− = = ≈0V→Vo =Vi.
A AV V
ThissituationarisesonlyifiD >0(since the diodecanonlyconductinthe
forward direction),i.e.,Vo >0→Vi =Vo >0V.
iD
Vo1

9. Half-waveprecision rectifier
Vo
i−Vo Vo
DVi Vi VD
R iR
R
Vi
Consider twocases:
(i)Disconducting:The feedback loopisclosed,and the circuit lookslike(except
forthe diodedrop) the bufferwehaveseenearlier.
Sincethe input currenti− ≈0,iR =iD.
Vo1Vo+0.7V
Further,V+ −V− = = ≈0V→Vo =Vi.
A AV V
ThissituationarisesonlyifiD >0(since the diodecanonlyconductinthe
forward direction),i.e.,Vo >0→Vi =Vo >0V.
slope=1
iD
Vo1

10. Half-waveprecision rectifier
Vo
DVi
R

11. Half-waveprecision rectifier
Vo Vo
DVi Vi
R
R
(ii)Disnot conducting→Vo =0V.
Vo1

12. Half-waveprecision rectifier
Vo Vo
DVi Vi
R
R
(ii)Disnot conducting→Vo =0V.
What about Vo1?
Sincethe OpAmpisnowinthe open-loop configuration,averysmallVi is
enough todriveittosaturation.
Vo1

13. Half-waveprecision rectifier
Vo Vo
DVi Vi
R
R
(ii)Disnot conducting→Vo =0V.
What about Vo1?
Sincethe OpAmpisnowinthe open-loop configuration,averysmallVi is
enough todriveittosaturation.
Note thatCase(ii)occurs whenVi <0V. SinceV+ −V− =Vi−0=Vi is
negative, Vo1 isdrivento−Vsat.
Vo1

14. Half-waveprecision rectifier
Vo Vo
DVi Vi
R
R
Vi
(ii)Disnot conducting→Vo =0V.
What about Vo1?
Sincethe OpAmpisnowinthe open-loop configuration,averysmallVi is
enough todriveittosaturation.
Note thatCase(ii)occurs whenVi <0V. SinceV+ −V− =Vi−0=Vi is
negative, Vo1 isdrivento−Vsat.
Vo
Vo=0
Vo1

15. Half-waveprecision rectifier
2
0
−2
−4
−6
−8
o
Vi
superdiode
−10Vi
−12
0 1
t(ms)
2
*The circuit iscalleda“superdiode”(i.e., adiodewithzeroVon).
Doff
V
o=0
Vo
Don
V
o=V
i
D
Vo1 V
R
V
o
V
i

16. Half-waveprecision rectifier
2
0
−2
−4
−6
−8
o
Vi
superdiode
−10Vi
−12
0 1
t(ms)
2
*The circuit iscalleda“superdiode”(i.e., adiodewithzeroVon).
Doff
V
o=0
Vo
Don
V
o=V
i
D
Vo1 V
R
V
o
V
i
V
o1
−Vsat

17. Half-waveprecision rectifier
2
0
−2
−4
−6
−8
o
Vi
superdiode
−10Vi
−12
0 1
t(ms)
2
*The circuit iscalleda“superdiode”(i.e., adiodewithzeroVon).
*Note thatthe OpAmpneeds tocomeout ofsaturationwhenVi changes from
negative topositive values. Thisisarelatively slowprocess, and itlimitsthe
speed ofthiscircuit.
Doff
V
o=0
Vo
Don
V
o=V
i
D
Vo1 V
R
V
o
V
i
V
o1
−Vsat

18. Half-waveprecision rectifier
2
0
−2
−4
−6
−8
o
Vi
superdiode
−10Vi
−12
0 1
t(ms)
2
*The circuit iscalleda“superdiode”(i.e., adiodewithzeroVon).
*Note thatthe OpAmpneeds tocomeout ofsaturationwhenVi changes from
negative topositive values. Thisisarelatively slowprocess, and itlimitsthe
speed ofthiscircuit.
Doff
V
o=0
Vo
Don
V
o=V
i
D
Vo1 V
R
V
o
V
i
V
o1
−Vsat

19. Half-waveprecision rectifier

20. Improved/Non saturated half-waveprecisionrectifier
i
R2
i
R1
ViR1 Vo
i
R
R
R2
i
D2
Vo1
D2
i
D1
D1

21. i
R2
i
R1
ViR1 Vo
i
R
R
(i)D1 conducts:V− =V+ =0V,Vo1 =−VD1 ≈−0.7V.
R2
i
D2
Vo1
D2
i
D1
D1
Improved/Non saturated half-waveprecisionrectifier

22. i
R2
i
R1
ViR1 Vo
i
R
R
(i)D1 conducts:V− =V+ =0V,Vo1 =−VD1 ≈−0.7V.
D2 cannotconduct(show that,ifitdid,KCLisnot satisfied at Vo).
→iR2 =0,Vo =V− =0V.
R2
i
D2
Vo1
D2
i
D1
D1
Improved/Non saturated half-waveprecisionrectifier

23. Improvedhalf-waveprecisionrectifier
R2
i
R2
i
R1
Vi ViR1 R1Vo Vo
i
R RR
(i)D1 conducts:V− =V+ =0V,Vo1 =−VD1 ≈−0.7V.
D2 cannotconduct(show that,ifitdid,KCLisnot satisfied at Vo).
→iR2 =0,Vo =V− =0V.
Vi>0
Vo1
D2
D1
R2
i
D2
Vo1
D2
i
D1
D1

24. Improvedhalf-waveprecisionrectifier
R2
i
R2
i
R1
Vi ViR1 R1Vo Vo
i
R RR
(i)D1 conducts:V− =V+ =0V,Vo1 =−VD1 ≈−0.7V.
D2 cannotconduct(show that,ifitdid,KCLisnot satisfied at Vo).
→iR2 =0,Vo =V− =0V.
iR1 =iD1 whichcanonlybepositive ⇒ Vi >0V.
Vi>0
Vo1
D2
D1
R2
i
D2
Vo1
D2
i
D1
D1

25. R2
i
R2
i
R1
Vi ViR1 R1Vo Vo
i
R RR
(i)D1 conducts:V− =V+ =0V,Vo1 =−VD1 ≈−0.7V.
D2 cannotconduct(show that,ifitdid,KCLisnot satisfied at Vo).
→iR2 =0,Vo =V− =0V.
iR1 =iD1 whichcanonlybepositive ⇒ Vi >0V.
(ii)D1 isoff;thiswillhappen whenVi <0V.
Vi>0
Vo1
D2
D1
R2
i
D2
Vo1
D2
i
D1
D1
Improved/Non saturated half-waveprecisionrectifier

26. R2 R2
i
R2
i
R1
Vi Vi ViR1 R1 R1Vo Vo Vo
i
R R RR
(i)D1 conducts:V− =V+ =0V,Vo1 =−VD1 ≈−0.7V.
D2 cannotconduct(show that,ifitdid,KCLisnot satisfied at Vo).
→iR2 =0,Vo =V− =0V.
iR1 =iD1 whichcanonlybepositive ⇒ Vi >0V.
(ii)D1 isoff;thiswillhappen whenVi <0V.
Inthiscase, D2 conductsand closesthe feedback loopthroughR2.
Vi<0Vi>0
Vo1
D2
D1
Vo1
D2
D1
R2
i
D2
Vo1
D2
i
D1
D1
Improved/Non saturated half-waveprecisionrectifier

27. R2 R2
i
R2
i
R1
Vi Vi ViR1 R1 R1Vo Vo Vo
i
R R RR
(i)D1 conducts:V− =V+ =0V,Vo1 =−VD1 ≈−0.7V.
D2 cannotconduct(show that,ifitdid,KCLisnot satisfied at Vo).
→iR2 =0,Vo =V− =0V.
iR1 =iD1 whichcanonlybepositive ⇒ Vi >0V.
(ii)D1 isoff;thiswillhappen whenVi <0V.
Inthiscase, D2 conductsand closesthe feedback loopthroughR2.
„
0−Vi
«
R2
Vo =V− +iR2R2 =0+ R2 =−
R
Vi.
R1 1
Vi<0Vi>0
Vo1
D2
D1
Vo1
D2
D1
R2
i
D2
Vo1
D2
i
D1
D1
Improved/Non saturated half-waveprecisionrectifier

28. R2
1k
−
R1
i
1k
ViR1
Vo
o
R
Vo
R
2
V
V =0
V
i
Vo1
D2
D
1
Improved/Non saturated half-waveprecisionrectifier

29. 2
R2
1k
1
−
R1
i
1k
ViR1
Vo
0
o
R
−1
0 1
t (ms)
2
Vo
R
2
V
V =0
V
i
Vo1
D2
D
1
V
i V
o
Improved/Non saturated half-waveprecisionrectifier

30. 2
R2
1k
1
−
R1
i
1k
ViR1
Vo
0
o
R
−1
0 1
t (ms)
2
Vo
R
2
V
V =0
V
i
Vo1
D2
D
1
V
o1
V
i V
o
Improved/Non saturated half-waveprecisionrectifier

31. 2
R2
1k
1
−
R1
i
1k
ViR1
Vo
0
o
R
−1
0 1
t (ms)
2
*Note thatthe OpAmpdoesnot enter saturationsinceafeedback path is
available forVi >0Vand Vi <0V.
Vo
R
2
V
V =0
V
i
Vo1
D2
D
1
V
o1
V
i V
o
Improved/Non saturated half-waveprecisionrectifier

32. 2
R2
1k
1
−
R1
i
1k
ViR1
Vo
0
o
R
−1
0 1
t (ms)
2
*Note thatthe OpAmpdoesnot enter saturationsinceafeedback path is
available forVi >0Vand Vi <0V.
SEQUELfile:precisionhalfwave.sqproj
Vo
R
2
V
V =0
V
i
Vo1
D2
D
1
V
o1
V
i V
o
Improved/Non saturated half-waveprecisionrectifier

33. R2
D1
ViR1
i
Vo
2
V
i
R
The diodesarenowreversed.
Vo
Vo=0
V
R
−
R1
Vo1
D2
Improved/Non saturated half-waveprecisionrectifier

34. R2
D1
ViR1
i
Vo
2
V
i
R
The diodesarenowreversed.
Byconsidering twocases: (i)D1 on,(ii)D1 off,the Vo versusVi relationshipshownin
the figureisobtained(show this).
Vo
Vo=0
V
R
−
R1
Vo1
D2
Improved/Non saturated half-waveprecisionrectifier

35. R2
D1
ViR1
i
Vo
2
V
i
R
The diodesarenowreversed.
Byconsidering twocases: (i)D1 on,(ii)D1 off,the Vo versusVi relationshipshownin
the figureisobtained(show this).
Vo
Vo=0
V
R
−
R1
Vo1
D2
Improved/Non saturated half-waveprecisionrectifier

36. Two Output half-waveprecisionrectifier
The diodesD2is connected in series with the opampo/p terminal and R
2exactly is connected
as in improved precision HWR.

37. Two Output half-waveprecisionrectifier
The diodesD2is connected in series with the opampo/p terminal and R
2exactly is connected
as in improved precision HWR.
The diodesR
4 is added in series D
1where D
1exactly is connected as in improved precision
HWR.

38. Two Output half-waveprecisionrectifier
When V
i> 0V , Op-amp output terminal goes ‘-ve’, resulting
D
1in Forward Bias and D
2in reverse bias [ No Current flows in R
2]
op amp together with R
1and R
4function as inverting amplifier.
So, at node ‘B’
V
B= -[+V
i] (R
4/R
1)

39. Two Output half-waveprecisionrectifier
When V
i< 0V , Op-amp output terminal goes ‘+ve’, resulting
D
2in Forward Bias and D
1in reverse bias [ No Current flows in R
4]
op amp together with R
1and R
2function as inverting amplifier.
So, at node ‘A’
V
A= -[-V
i] (R
2/R
1)

40. AM demodulationusingapeakdetector
0.15
Super
diode
AM
signal
Vo2
0
−0.15
0 1
t(ms)
2
*charging throughsuperdiode,discharging throughresistor
*The time constant(RC)needs tobecarefullyselected.
Vo1 filter
Vi
Vo1

41. Full-waveprecision rectifier
V
B
V
i
o
V
i
V
o1 V
A
V
i
V
i
V
i
x(−1)
V
B V
VoHalf−wave
rectifier
(inverting)
x(−2)
V
o1 V
A

42. Full-waveprecision rectifier
V
B
V
i
o
V
i
V
o1 V
A
V
i
V
i
V
i
oV
i
inverting half−waverectifier inverting summer
(SEQUELfile:precision_full_wave.sqproj)
D
1
R
1
R
R
R/2
R
1
D
2
V
V
o1
x(−1)
V
B V
VoHalf−wave
rectifier
(inverting)
x(−2)
V
o1 V
A

43. Full-waveprecision rectifier
V
B
2
V
i
1
o
0
V
i
V
o1 V
A
V
i
−1
i
V
i
V
i
−2
0 1
t(ms)
2
oV
i
inverting half−waverectifier inverting summer
(SEQUELfile:precision_full_wave.sqproj)
D
1
R
1
R
R
R/2
R
1
D
2
V
V
o1
x(−1)
V
B V
VoHalf−wave
rectifier
(inverting)
x(−2)
V
o1 V
A
V
Vo

44. Full-waveprecision rectifier
2
1
0
−1
i
−2
0 1
t(ms)
2
V
Vo
oV
i
inverting half−waverectifier inverting summer
D
1
R
1
A
R
3
R
4
R
5
R
2
= 2R
1
D
2
V
B
When V
i> 0V [‘+ve’ Cycle] ,
at ‘A’ , V
A= + V
i
And at ‘B’ , V
B= -2V
i
therefore , V
B =-[R
4
/R
3] (V
A + V
B )
= [R
4
/R
3] V
i
When V
i< 0V [‘-ve’ Cycle] ,
at ‘A’ , V
A= -V
i
And at ‘B’ , V
B= 0
therefore , V
B =-[R
4
/R
5] (V
A + V
B )
= [R
4
/R
5] V
i

45. Full-waveprecision rectifier
2
1
0
−1
i
−2
0 1
t(ms)
2
V
Vo
oV
i
inverting half−waverectifier inverting summer
D
1
R
1
A
R
3
R
4
R
5
R
2
= 2R
1
D
2
V
B
When V
i> 0V [‘+ve’ Cycle] ,
at ‘A’ , V
A= + V
i
And at ‘B’ , V
B= -2V
i
therefore , V
B =-[R
4
/R
3] (V
A + V
B )
= [R
4
/R
3] V
i
When V
i< 0V [‘-ve’ Cycle] ,
at ‘A’ , V
A= -V
i
And at ‘B’ , V
B= 0
therefore , V
B =-[R
4
/R
5] (V
A + V
B )
= [R
4
/R
5] V
i
A precision FWR circuit is also known as an “absolute value circuit”.