Waveshaping Diodes

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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



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)



Rectifier Circuit


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



Rectifier Circuit: vo is the positive portion v

i


0 and OFFDiode ,For

and ONDiode ,For

0

00

=<

−=≥

o Di

Dio Di

vV v

V vvV v



Application of Rectifier Circuit: AC to DC

convertor for power supply


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




Clipper or Limiter Circuit

(open-loop transfer function)


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



Clipper Circuit

does not allow vo > V D0 to go through


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



Rectifier & clipper circuits are the same

but vo is taken at different locations


Half-wave

Rectifier

Clipper



Clipper circuit limits vo

when the diode is ON


By adjusting “V D0 ” we can adjust limiting voltage!





Bottom portion of signal can also be clipped


vo

limited to ≥ V D0 V DC

vo limited ≥ V D0 V Z



vo

limited to ≤V D0 + V DC1 and ≥ V D0 V DC2

Both top & bottom portions of the signal

can be clipped simultaneously


vo limited to ≤V D0 + V Z1

and ≥ V D0 V Z2



“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,)


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!



“Ideal” Peak Detector Circuit(open-loop transfer function)


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



Response of the “Ideal” Peak Detector (1)


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



Response of the “Ideal” Peak Detector (2)


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





Practical Peak Detector Circuit (1)


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)



Practical Peak Detector Circuit (2)


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



])/(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)


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





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



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)

sound carrier T RC T <<=<<τ



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 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



Clamp Circuit


“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!





Voltage shift in a clamp circuit can be adjusted!


Peak detector circuit:

vc = V + A − V D0

vc = V + − V DC − V D0


“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 −−−= +



Clamp circuit can also introduce a “positive” shift


Peak detector (diode is reversed):

vo = vc = (V−

V D0)

)(

)(

0

0

Dici Do

Dc

V V vvvvv

V V v

−+=−==

−−=

−

−


“upward” by (V

−

− V D0 )

Clamp circuit (diode reversed):

vo = v D



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 )

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Waveshaping Diodes