waveshaping diodes
TRANSCRIPT
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Diodes Waveform shaping Circuits
Lecture notes: page 2-20 to 2-31
Sedra & Smith (6th
Ed): Sec. 4.5 & 4.6Sedra & Smith (5th Ed): Sec. 3.5 & 3.6
F. Najmabadi, ECE65, Winter 2012
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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)
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Rectifier Circuit
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Lo D
Dioo Di
Do
Rvi
vvvvvv
ii
/ :Law
:KVL :KCL
=Ω
−=→+=
=
00
0
0
and 0 :OFFDiode
Dioi D D
D Lo
D D D
V vvvV v
i Rv
V vi
<=−→<
==
<=
0
0
0
0 0/
0 and :ONDiode
Di Dio Lo D
Di Dio
D D D
V vvvv Rvi
V vvvv
iV v
≥→≥−=→≥=
−=−=
≥=
0 and OFFDiode ,For
and ONDiode ,For
0
00
=<
−=≥
o Di
Dio Di
vV v
V vvV v
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Rectifier Circuit: vo is the positive portion v
i
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0 and OFFDiode ,For
and ONDiode ,For
0
00
=<
−=≥
o Di
Dio Di
vV v
V vvV v
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Application of Rectifier Circuit: AC to DC
convertor for power supply
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Full-wave rectifier (converts all of AC input to DC value)
Half-wave rectifier (only converts half of AC input to DC value)
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Each pair of diodes conduct only for half
of the cycle
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Clipper or Limiter Circuit
(open-loop transfer function)
F. Najmabadi, ECE65, Winter 2012
00
0R
Di D D
iooi
V vV v
vvvv
<→<
=→+×=
00
0
0/)( Di Di D
Do
V v RV vi
V v
≥→≥−=
=
0 and 0 :OFFDiode D D D V vi <= 0 and :ONDiode 0 ≥= D D D iV v
io Di
Do Di
vvV v
V vV v
=<
=≥
and OFFDiode ,For
and ONDiode ,For
0
00
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Clipper Circuit
does not allow vo > V D0 to go through
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io Di
Do Di
vvV v
V vV v
=<
=≥
and OFFDiode ,For
and ONDiode ,For
0
00
Impact of RL is discussed as an exercise problem
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Rectifier & clipper circuits are the same
but vo is taken at different locations
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Half-wave
Rectifier
Clipper
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Clipper circuit limits vo
when the diode is ON
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By adjusting “V D0 ” we can adjust limiting voltage!
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Bottom portion of signal can also be clipped
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vo
limited to ≥ V D0 V DC
vo limited ≥ V D0 V Z
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vo
limited to ≤V D0 + V DC1 and ≥ V D0 V DC2
Both top & bottom portions of the signal
can be clipped simultaneously
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vo limited to ≤V D0 + V Z1
and ≥ V D0 V Z2
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“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.
Dci Dci D
co
V vvV vvv
vv
+<→<−=
==
0 and 0 :OFFDiode D D D
V vi <=
Capacitor does not charge or discharge!
vc (t) = vc0 where vc0 is the capacitor voltage at
the moment diode turned OFF!
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“Ideal” Peak Detector Circuit(open-loop transfer function)
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0 and :ONDiode 0 ≥= D D D
iV v
const vvV vv
V vvvV vv /dt dv
co Dci
Dico Dcii
==+<
−==+=≥
00
00
OFF,Diode :For
, ONDiode : & 0For
0 0
)( 0
0
≥→≥=
=−
===
−==
dt
dvii
dt
dvC
dt
V vd C
dt
dvC ii
V vvv
i
c D
i Dic
c D
Dico
Because state of diode depends on vc , we cannot produce
a universal plot vo vs vi
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Response of the “Ideal” Peak Detector (1)
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const vvV vv
V vvvV vv /dt dv
co Dci
Dico Dcii
==+<
−==+=≥
00
00
OFF,Diode :For, ONDiode : & 0For
When vi = vc0 + V D0 = V D0 , diode
turns ON (since dvi/dt > 0)
Capacitor starts to charge and vc
tracks vi
o vo = vc = vi - V D0
Start at t = 0 with vc= 0
For t > 0, dvi/dt > 0.
For vi < vc0 + V D0 = V D0 ,
diode remains OFF.
o vo = vc0 = 0
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Response of the “Ideal” Peak Detector (2)
F. Najmabadi, ECE65, Winter 2012
const vvV vv
V vvvV vv /dt dv
co Dci
Dico Dcii
==+<
−==+=≥
000
00
OFF,Diode :For, ONDiode : & 0For
Even when vi starts to increase (dvi/dt > 0)
diode remains OFF as vo < vc0 + V D0
o vc0 + V D0 = V + − V D0 +V D0 = 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 + - V D0 )
Afterward vi starts todecrease (dvi/dt < 0) and
diode turns OFF.
o vo = vc0 = V + − V D0
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Practical Peak Detector Circuit (1)
F. Najmabadi, ECE65, Winter 2012
00
00
)(
])/(exp[)(
Dci Dci D
cco
V t vvV vvv
t t -vt vv
+<→<−=
−== τ
0 and 0 :OFFDiode D D D
V vi <=
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)
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Practical Peak Detector Circuit (2)
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0 and :ONDiode 0 ≥= D D D
iV v
])/(exp[)( OFF,Diode :For
, ONDiode : ,& 0For
000
00
τ t t -vt vvV vv
V vvvV vv /dt dv
cco Dci
Dico Dcii
−==+<
−==+=≥
0 0
)( 0
0
≥→≥=
=−
===
−==
dt
dvii
dt
dvC
dt
V vd C
dt
dvC ii
V vvv
i
c D
i Dic
c D
Dico
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])/(exp[)( OFF,Diode :For, ONDiode : ,& 0For
000
00
τ t t -vt vvV vv
V vvvV vv /dt dv
cco Dci
Dico Dcii
−==+<
−==+=≥
Response of the Practical Peak Detector (1)
F. Najmabadi, ECE65, Winter 2012
When vi = vc0 + V D0 = V D0 , diode
turns ON (since dvi/dt > 0)
Capacitor starts to charge and vc
tracks vi
o vo = vc = vi - V D0
Start at t = 0 with vc= 0
For t > 0, dvi/dt > 0.
For vi < vc0 + V D0 = V D0 ,
diode remains OFF.
o vo = vc0 = 0
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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
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Peak detector is used in AM receivers
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Carrier wave amplitude is
modulated with the sound data
(sound signal is the “envelop” of
the carrier wave)
sound carrier T RC T <<=<<τ
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Peak-Detector with a “load”
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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 arectifier 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
Lsound carrier R RT RC T <<<<=<< and τ
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Clamp Circuit
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“Ideal” peak detector:
vo = vc = V + V D0
)(
0
0
Dici Do
Dc
V V vvvvv
V V v
−−=−==
−=
+
+
vo is equal to vi but shifted
“downward” by − (V
+
− V D0 )
Clamp circuit: vo = v D
If amplitude of vi (V + ) changes, the shift would
changes and vo
becomes distorted!
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Voltage shift in a clamp circuit can be adjusted!
F. Najmabadi, ECE65, Winter 2012
Peak detector circuit:
vc = V + A − V D0
vc = V + − V DC − V D0
vo is equal to vi but shifted
“downward” by − (V + − V DC − V D0)
v A = vi − V DC
V + : peak of vi
V + A : peak of v A
V + A = V + − V DC
)(
0
0
D DC icio
D DC c
V V V vvvv
V V V v
−−−=−=
−−=+
+
)( 0 D Z io V V V vv −−−= +
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Clamp circuit can also introduce a “positive” shift
F. Najmabadi, ECE65, Winter 2012
Peak detector (diode is reversed):
vo = vc = (V−
V D0)
)(
)(
0
0
Dici Do
Dc
V V vvvvv
V V v
−+=−==
−−=
−
−
vo is equal to vi but shifted
“upward” by (V
−
− V D0 )
Clamp circuit (diode reversed):
vo = v D
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The positive shift can also be adjusted.
)( 0 D Z io V V V vv −−+=
− )( 0 D DC io V V V vv −−+=
−
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 )