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Diodes Waveform shaping Circuits
Lecture notes: page 2-20 to 2-31
Sedra & Smith (6th Ed): Sec. 4.5 & 4.6 Sedra & Smith (5th Ed): Sec. 3.5 & 3.6
F. Najmabadi, ECE65, Winter 2012
Two-port networks as building blocks
F. Najmabadi, ECE65, Winter 2012
Recall: Transfer function of a two-port network can be found by solving this circuit once.
Concept of input resistance can be used to find vi/vsig (will be discussed in transistor amplifier section)!
We focus on finding transfer function, vo vs vi (circuit below) o “Open-loop” Transfer function (RL → ∞ or io = 0)
Rectifier Circuit
F. Najmabadi, ECE65, Winter 2012
LoD
DiooDi
Do
Rvivvvvvv
ii
/ :Law :KVL
:KCL
=Ω−=→+=
=
00
0
0
and 0 :OFF Diode
DioiDD
DLo
DDD
VvvvVviRv
Vvi
<=−→<==
<=
0
0
0
0 0/
0 and :ON Diode
DiDioLoD
DiDio
DDD
VvvvvRviVvvvv
iVv
≥→≥−=→≥=−=−=
≥=
0 and OFF Diode ,For and ON Diode ,For
0
00
=<−=≥
oDi
DioDi
vVvVvvVv
Rectifier Circuit: vo is the positive portion vi
F. Najmabadi, ECE65, Winter 2012
0 and OFF Diode ,For and ON Diode ,For
0
00
=<−=≥
oDi
DioDi
vVvVvvVv
Application of Rectifier Circuit: AC to DC convertor for power supply
F. Najmabadi, ECE65, Winter 2012
Full-wave rectifier (converts all of AC input to DC value)
Half-wave rectifier (only converts half of AC input to DC value)
Each pair of diodes conduct only for half of the cycle
F. Najmabadi, ECE65, Winter 2012
Clipper or Limiter Circuit (open-loop transfer function)
F. Najmabadi, ECE65, Winter 2012
00 0R
DiDD
iooi
VvVvvvvv
<→<=→+×=
00
0
0/)( DiDiD
Do
VvRVviVv
≥→≥−==
0 and 0 :OFF Diode DDD Vvi <= 0 and :ON Diode 0 ≥= DDD iVv
ioDi
DoDi
vvVvVvVv
=<=≥
and OFF Diode ,For and ON Diode ,For
0
00
Clipper Circuit does not allow vo > VD0 to go through
F. Najmabadi, ECE65, Winter 2012
ioDi
DoDi
vvVvVvVv
=<=≥
and OFF Diode ,For and ON Diode ,For
0
00
Impact of RL is discussed as an exercise problem
Rectifier & clipper circuits are the same but vo is taken at different locations
F. Najmabadi, ECE65, Winter 2012
Half-wave Rectifier
Clipper
Clipper circuit limits vo when the diode is ON
F. Najmabadi, ECE65, Winter 2012
By adjusting “VD0 ” we can adjust limiting voltage!
Limiting voltage can be adjusted
F. Najmabadi, ECE65, Winter 2012
vo limited to ≤ VD0 + VZ vo limited to ≤ VD0 + VDC
Bottom portion of signal can also be clipped
F. Najmabadi, ECE65, Winter 2012
vo limited to ≥ − VD0 − VDC
vo limited ≥ − VD0 −VZ
vo limited to ≤ VD0 + VDC1 and ≥ − VD0 − VDC2
Both top & bottom portions of the signal can be clipped simultaneously
F. Najmabadi, ECE65, Winter 2012
vo limited to ≤ VD0 + VZ1 and ≥ − VD0 − VZ2
“Ideal” Peak Detector Circuit
Because vc cannot change suddenly, the state of diode will depend not only on vi but also on the “history” of the circuit (e.g., dvi/dt , vc at certain times,)
F. Najmabadi, ECE65, Winter 2012
000
0
const.
DciDciD
co
VvvVvvvvv
+<→<−===
0 and 0 :OFF Diode DDD Vvi <=
Capacitor does not charge or discharge! vc (t) = vc0 where vc0 is the capacitor voltage at
the moment diode turned OFF!
“Ideal” Peak Detector Circuit (open-loop transfer function)
F. Najmabadi, ECE65, Winter 2012
0 and :ON Diode 0 ≥= DDD iVv
constvvVvvVvvvVvv/dtdv
coDci
DicoDcii
==+<−==+=≥
00
00
OFF, Diode :For , ON Diode : & 0For
0 0
)( 0
0
≥→≥=
=−
===
−==
dtdvii
dtdvC
dtVvdC
dtdvCii
Vvvv
icD
iDiccD
Dico
Because state of diode depends on vc , we cannot produce a universal plot vo vs vi
Response of the “Ideal” Peak Detector (1)
F. Najmabadi, ECE65, Winter 2012
constvvVvvVvvvVvv/dtdv
coDci
DicoDcii
==+<−==+=≥
00
00
OFF, Diode :For , ON Diode : & 0For
When vi = vc0 + VD0 = VD0 , diode turns ON (since dvi/dt > 0)
Capacitor starts to charge and vc tracks vi o vo = vc = vi - VD0
Start at t = 0 with vc= 0 For t > 0, dvi/dt > 0. For vi < vc0 + VD0 = VD0 ,
diode remains OFF. o vo = vc0 = 0
Response of the “Ideal” Peak Detector (2)
F. Najmabadi, ECE65, Winter 2012
constvvVvvVvvvVvv/dtdv
coDci
DicoDcii
==+<−==+=≥
000
00
OFF, Diode :For , ON Diode : & 0For
Even when vi starts to increase (dvi/dt > 0) diode remains OFF as vo < vc0 + VD0 o vc0 + VD0 = V + − VD0 +VD0 = V + !
Diode turns ON vi = V + and immediately turns OFF vi starts to decrease (dvi/dt < 0)
Cap continue to charge until vi = V + (vc = V + - VD0 )
Afterward vi starts to decrease (dvi/dt < 0) and diode turns OFF. o vo = vc0 = V + − VD0
Response of the “Ideal” Peak Detector (3)
F. Najmabadi, ECE65, Winter 2012
vo is the “peak” value of input waveform (V + – VD0 ): “Peak Detector” o Note vo did not “drop” after the peak was decreased in the 3rd cycle.
Exercise: Show that if the diode direction is reversed, circuit detects the “negative” peak value, −V − (i.e., lowest voltage of the wave form which should be negative)
Practical Peak Detector Circuit (1)
F. Najmabadi, ECE65, Winter 2012
00
00
)( ])/( exp[ )(
DciDciD
cco
VtvvVvvvtt-vtvv
+<→<−=−== τ
0 and 0 :OFF Diode DDD Vvi <=
Capacitor discharges into the resistor with a time constant of τ = RC
A resistor is added in parallel to the capacitor! (It can be the load for the circuit)
Practical Peak Detector Circuit (2)
F. Najmabadi, ECE65, Winter 2012
0 and :ON Diode 0 ≥= DDD iVv
])/( exp[ )( OFF, Diode :For , ON Diode : ,& 0For
000
00
τtt-vtvvVvvVvvvVvv/dtdv
ccoDci
DicoDcii
−==+<−==+=≥
0 0
)( 0
0
≥→≥=
=−
===
−==
dtdvii
dtdvC
dtVvdC
dtdvCii
Vvvv
icD
iDiccD
Dico
])/( exp[ )( OFF, Diode :For , ON Diode : ,& 0For
000
00
τtt-vtvvVvvVvvvVvv/dtdv
ccoDci
DicoDcii
−==+<−==+=≥
Response of the Practical Peak Detector (1)
F. Najmabadi, ECE65, Winter 2012
When vi = vc0 + VD0 = VD0 , diode turns ON (since dvi/dt > 0)
Capacitor starts to charge and vc tracks vi o vo = vc = vi - VD0
Start at t = 0 with vc= 0 For t > 0, dvi/dt > 0. For vi < vc0 + VD0 = VD0 ,
diode remains OFF. o vo = vc0 = 0
])/( exp[ )( OFF, Diode :For , ON Diode : ,& 0For
000
00
τtt-vtvvVvvVvvvVvv/dtdv
ccoDci
DicoDcii
−==+<−==+=≥
Response of the Practical Peak Detector (2)
F. Najmabadi, ECE65, Winter 2012
Even when vi starts to increase (dvi/dt > 0) diode remains OFF as long as vo < vc + VD0
Diode turns ON when vi = vc + VD0 and charges capacitor until vi = V + is reached)
Cap continue to charge until vi = V + (vc = V + - VD0 )
Afterward vi starts to decrease (dvi/dt < 0) and diode turns OFF. Capacitor discharges:
])/( exp[ )( 00 τtt-vtvv cco −==
Response of the Practical Peak Detector (3)
F. Najmabadi, ECE65, Winter 2012
Shape of output signal depends on the ratio of τ/T “ideal” peak detector: τ/T → ∞ “Good” peak detector: τ/T >> 1 As τ/T decreases, the circuit departs from a peak detector. For τ/T << 1, capacitor discharges very fast and circuit resembles a rectifier
circuit
Decreasing τ/T
Peak detector is used in AM receivers
F. Najmabadi, ECE65, Winter 2012
Carrier wave amplitude is modulated with the sound data (sound signal is the “envelop” of the carrier wave)
soundcarrier TRCT <<=<<τ
Peak-Detector with a “load”
F. Najmabadi, ECE65, Winter 2012
A clipper circuit with a load RL is similar to the open-loop clipper with R → R || RL
Examples of Design Choices: As a peak detector (want τ/T → ∞) R is NOT needed and we should set
C RL to be large (>>T). o Peak detector circuit is used to “smooth” out the output voltage of a
rectifier for the power supply circuit (Need a large C!). For applications such as AM receiver when the peak detector is used as
separate the signal from a carrier, R and C should be chosen such that
Lsoundcarrier RRTRCT <<<<=<< and τ
Clamp Circuit
F. Najmabadi, ECE65, Winter 2012
“Ideal” peak detector: vo = vc = V + − VD0
)(
0
0
DiciDo
Dc
VVvvvvvVVv
−−=−==
−=+
+
vo is equal to vi but shifted “downward” by − (V + − VD0)
Clamp circuit: vo = vD
If amplitude of vi (V + ) changes, the shift would changes and vo becomes distorted!
Clamp Circuit with a Load
F. Najmabadi, ECE65, Winter 2012
Capacitor charges when the diode is ON:
vc = V + − VD0 Capacitor remains charged
when diode is OFF.
Capacitor charges when the diode is ON:
vc = V + − VD0 Capacitor discharges into RL
when diode is OFF. As long as τ = RLC >> T
capacitor discharges little and clamp circuits works fine!
Voltage shift in a clamp circuit can be adjusted!
F. Najmabadi, ECE65, Winter 2012
Peak detector circuit: vc = V +A − VD0
vc = V + − VDC − VD0
vo is equal to vi but shifted
“downward” by − (V + − VDC − VD0)
vA = vi − VDC
V + : peak of vi
V +A : peak of vA
V +A = V + − VDC
)(
0
0
DDCicio
DDCc
VVVvvvvVVVv
−−−=−=
−−=+
+
)( 0DZio VVVvv −−−= +
Clamp circuit can also introduce a “positive” shift
F. Najmabadi, ECE65, Winter 2012
Peak detector (diode is reversed): vo = vc = − (V − − VD0)
)(
)(
0
0
DiciDo
Dc
VVvvvvvVVv
−+=−==
−−=−
−
vo is equal to vi but shifted “upward” by (V − − VD0)
Clamp circuit (diode reversed): vo = vD
The positive shift can also be adjusted.
F. Najmabadi, ECE65, Winter 2012
)( 0DZio VVVvv −−+= − )( 0DDCio VVVvv −−+= −
How to find response of clipper or clamp circuits: Assume diode is ON and calculate vc .
o If vc = +vi …, replace vi with V+ (peak positive value) o If vc = −vi …, replace vi with −V− (peak negative value)
If clipper, vo = vc . If Clamp, use KVL to find vo (e.g., , vo = vi − vc )
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