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Diode sketch

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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
 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)
F. Najmabadi, ECE65, Winter 2012
Rectifier Circuit
KCL :
io = iD
KVL :
vi = vD + vo → vo = vi − vD
Ω Law : iD = vo / RL
Diode OFF : iD = 0 and vD < VD 0
vo = RL iD = 0
vD < VD 0
→ vi − vo = vi < VD 0
Diode ON :
vD = VD 0
and
iD ≥ 0
vo = vi − vD = vi − VD 0
iD = vo / RL ≥ 0
→ vo = vi − vD ≥ 0 → vi ≥ VD 0
For vi ≥ VD 0 , Diode ON
and
For vi < VD 0 , Diode OFF and
F. Najmabadi, ECE65, Winter 2012
vo = vi − VD 0
vo = 0
Rectifier Circuit: vo is the positive portion vi
For vi ≥ VD 0 , Diode ON
and
For vi < VD 0 , Diode OFF and
F. Najmabadi, ECE65, Winter 2012
vo = vi − VD 0
vo = 0
Application of Rectifier Circuit: AC to DC
convertor for power supply
Half-wave rectifier (only converts half of AC input to DC value)
Full-wave rectifier (converts all of AC input to DC value)
F. Najmabadi, ECE65, Winter 2012
Each pair of diodes conduct only for half
of the cycle
F. Najmabadi, ECE65, Winter 2012
Clipper or Limiter Circuit
(open-loop transfer function)
vD = VD 0
Diode OFF : iD = 0 and vD < VD 0
Diode ON :
vi = R × 0 + vo → vo = vi
vo = VD 0
vD < VD 0
iD = (vi − VD 0 ) / R ≥ 0
→ vi < VD 0
For vi ≥ VD 0 , Diode ON
F. Najmabadi, ECE65, Winter 2012
and
For vi < VD 0 , Diode OFF and
vo = VD 0
vo = vi
and
iD ≥ 0
→ vi ≥ VD 0
Clipper Circuit
does not allow vo > VD0 to go through
For vi ≥ VD 0 , Diode ON
and
For vi < VD 0 , Diode OFF and
F. Najmabadi, ECE65, Winter 2012
vo = VD 0
vo = vi
 Impact of RL is discussed as an exercise problem
Rectifier & clipper circuits are the same
but vo is taken at different locations
Half-wave
Rectifier
Clipper
F. Najmabadi, ECE65, Winter 2012
Clipper circuit limits vo when the diode is ON
 By adjusting “VD0 ” we can adjust limiting voltage!
F. Najmabadi, ECE65, Winter 2012
Limiting voltage can be adjusted
vo limited to ≤ VD0 + VDC
F. Najmabadi, ECE65, Winter 2012
vo limited to ≤ VD0 + VZ
Bottom portion of signal can also be clipped
vo limited to ≥ − VD0 − VDC
vo limited ≥ − VD0 −VZ
F. Najmabadi, ECE65, Winter 2012
Both top & bottom portions of the signal
can be clipped simultaneously
vo limited to ≤ VD0 + VDC1 and ≥ − VD0 − VDC2
vo limited to ≤ VD0 + VZ1
and ≥ − VD0 − VZ2
F. Najmabadi, ECE65, Winter 2012
“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,)
Diode OFF : iD = 0 and vD < VD 0
 Capacitor does not charge or discharge!
 vc (t) = vc0 where vc0 is the capacitor voltage at
the moment diode turned OFF!
vo = vc 0 = const.
vD = vi − vc < VD 0 → vi < vc 0 + VD 0
F. Najmabadi, ECE65, Winter 2012
“Ideal” Peak Detector Circuit
(open-loop transfer function)
Diode ON :
vD = VD 0
and
iD ≥ 0
vo = vc = vi − VD 0
dvc
d (vi − VD 0 )
dv
=C
=C i
dt
dt
dt
dvi
≥0
iD = ic ≥ 0 →
dt
iD = ic = C
For dvi /dt ≥ 0 & vi = vc + VD 0 : Diode ON , vo = vc = vi − VD 0
For vi < vc + VD 0 :
Diode OFF, vo = vc 0 = const
 Because state of diode depends on vc , we cannot produce
a universal plot vo vs vi
F. Najmabadi, ECE65, Winter 2012
Response of the “Ideal” Peak Detector (1)
For dvi /dt ≥ 0 & vi = vc + VD 0 : Diode ON , vo = vc = vi − VD 0
For vi < vc + VD 0 :
 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
F. Najmabadi, ECE65, Winter 2012
Diode OFF, vo = vc 0 = const
 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
Response of the “Ideal” Peak Detector (2)
For dvi /dt ≥ 0 & vi = vc + VD 0 : Diode ON , vo = vc = vi − VD 0
For vi < vc 0 + VD 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
F. Najmabadi, ECE65, Winter 2012
Diode OFF, vo = vc 0 = const
 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)
Response of the “Ideal” Peak Detector (3)
 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)
F. Najmabadi, ECE65, Winter 2012
Practical Peak Detector Circuit (1)
 A resistor is added in parallel
to the capacitor! (It can be
the load for the circuit)
Diode OFF : iD = 0 and vD < VD 0
 Capacitor discharges into the resistor
with a time constant of τ = RC
F. Najmabadi, ECE65, Winter 2012
vo = vc (t ) = vc 0 exp[ - (t − t0 )/τ ]
vD = vi − vc < VD 0 → vi < vc (t ) + VD 0
Practical Peak Detector Circuit (2)
Diode ON :
vD = VD 0
and
iD ≥ 0
vo = vc = vi − VD 0
dvc
d (vi − VD 0 )
dv
=C
=C i
dt
dt
dt
dvi
≥0
iD = ic ≥ 0 →
dt
iD = ic = C
For dvi /dt ≥ 0 &, vi = vc + VD 0 : Diode ON , vo = vc = vi − VD 0
For vi < vc + VD 0 :
F. Najmabadi, ECE65, Winter 2012
Diode OFF, vo = vc (t ) = vc 0 exp[ - (t − t0 )/τ ]
Response of the Practical Peak Detector (1)
For dvi /dt ≥ 0 &, vi = vc + VD 0 : Diode ON , vo = vc = vi − VD 0
For vi < vc + VD 0 :
 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
F. Najmabadi, ECE65, Winter 2012
Diode OFF, vo = vc (t ) = vc 0 exp[ - (t − t0 )/τ ]
 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
Response of the Practical Peak Detector (2)
For dvi /dt ≥ 0 &, vi = vc + VD 0 : Diode ON , vo = vc = vi − VD 0
For vi < vc + VD 0 :
 Cap continue to charge until
vi = V + (vc = V + - VD0 )
 Afterward vi starts to decrease
(dvi/dt < 0) and diode turns
OFF. Capacitor discharges:
vo = vc (t ) = vc 0 exp[ - (t − t0 )/τ ]
F. Najmabadi, ECE65, Winter 2012
Diode OFF, vo = vc (t ) = vc 0 exp[ - (t − t0 )/τ ]
 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)
Response of the Practical Peak Detector (3)
 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
F. Najmabadi, ECE65, Winter 2012
Peak detector is used in AM receivers
Carrier wave amplitude is
modulated with the sound data
(sound signal is the “envelop” of
the carrier wave)
Tcarrier << τ = RC << Tsound
F. Najmabadi, ECE65, Winter 2012
Peak-Detector with a “load”
 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
Tcarrier << τ = RC << Tsound
and
R << RL
F. Najmabadi, ECE65, Winter 2012
Clamp Circuit
“Ideal” peak detector:
vo = vc = V + − VD0
Clamp circuit: vo = vD
vc = V + − VD 0
vo = vD = vi − vc = vi − (V + − VD 0 )
vo is equal to vi but shifted
“downward” by − (V + − VD0)
 If amplitude of vi (V + ) changes, the shift would
changes and vo becomes distorted!
F. Najmabadi, ECE65, Winter 2012
Clamp Circuit with a Load
 Capacitor charges when
the diode is ON:
 Capacitor charges when the diode
is ON:
vc = V + − VD0
 Capacitor remains charged
when diode is OFF.
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!
F. Najmabadi, ECE65, Winter 2012
Voltage shift in a clamp circuit can be adjusted!
vA = vi − VDC
V + : peak of vi
V +A : peak of vA
V +A = V + − VDC
F. Najmabadi, ECE65, Winter 2012
Peak detector circuit:
vc = V +A − VD0
vc = V + − VDC − VD0
vc = V + − VDC − VD 0
vo = vi − vc = vi − (V + − VDC − VD 0 )
 vo is equal to vi but shifted
“downward” by − (V + − VDC − VD0)
vo = vi − (V + − VZ − VD 0 )
Clamp circuit can also introduce a “positive” shift
Peak detector (diode is reversed):
vo = vc = − (V − − VD0)
Clamp circuit (diode reversed):
v o = vD
vc = − (V − − VD 0 )
vo = vD = vi − vc = vi + (V − − VD 0 )
vo is equal to vi but shifted
“upward” by (V − − VD0)
F. Najmabadi, ECE65, Winter 2012
The positive shift can also be adjusted.
vo = vi + (V − − VDC − VD 0 )
vo = vi + (V − − VZ − VD 0 )
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 )
F. Najmabadi, ECE65, Winter 2012
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