Diodes Waveform shaping Circuits Lecture notes: page 2-20 to 2-31 - - PowerPoint PPT Presentation

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)
• “Open-loop” Transfer function (RL → ∞ or io = 0)

Rectifier Circuit

• F. Najmabadi, ECE65, Winter 2012

L

• D

D i

• D

i D

• R

v i v v v v v v i i / : Law : KVL : KCL = Ω − = → + = = and : OFF Diode

D i

• i

D D D L

• D

D D

V v v v V v i R v V v i < = − → < = = < = / and : ON Diode

D i D i

• L
• D

D i D i

• D

D D

V v v v v R v i V v v v v i V v ≥ → ≥ − = → ≥ = − = − = ≥ = and OFF Diode , For and ON Diode , For = < − = ≥

• D

i D i

• D

i

v V v V v v V v

Rectifier Circuit: vo is the positive portion vi

• F. Najmabadi, ECE65, Winter 2012

and OFF Diode , For and ON Diode , For = < − = ≥

• D

i D i

• D

i

v V v V v v V v

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

• f the cycle
• F. Najmabadi, ECE65, Winter 2012

Clipper or Limiter Circuit (open-loop transfer function)

• F. Najmabadi, ECE65, Winter 2012

R

D i D D i

• i

V v V v v v v v < → < = → + × = / ) (

D i D i D D

• V

v R V v i V v ≥ → ≥ − = = and : OFF Diode

D D D

V v i < = and : ON Diode ≥ =

D D D

i V v

i

• D

i D

• D

i

v v V v V v V v = < = ≥ and OFF Diode , For and ON Diode , For

Clipper Circuit does not allow vo > VD0 to go through

• F. Najmabadi, ECE65, Winter 2012

i

• D

i D

• D

i

v v V v V v V v = < = ≥ and OFF Diode , For and ON Diode , For

• 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

const.

D c i D c i D c

• V

v v V v v v v v + < → < − = = = and : OFF Diode

D D D

V v i < =

• 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

and : ON Diode ≥ =

D D D

i V v const v v V v v V v v v V v v /dt dv

c

• D

c i D i c

• D

c i i

= = + < − = = + = ≥ OFF, Diode : For , ON Diode : & For ) ( ≥ → ≥ = = − = = = − = = dt dv i i dt dv C dt V v d C dt dv C i i V v v v

i c D i D i c c D D i c

• 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

const v v V v v V v v v V v v /dt dv

c

• D

c i D i c

• D

c i i

= = + < − = = + = ≥ OFF, Diode : For , ON Diode : & For

• When vi = vc0 + VD0 = VD0 , diode

turns ON (since dvi/dt > 0)

• Capacitor starts to charge and vc

tracks vi

• 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.

• vo = vc0 = 0

Response of the “Ideal” Peak Detector (2)

• F. Najmabadi, ECE65, Winter 2012

const v v V v v V v v v V v v /dt dv

c

• D

c i D i c

• D

c i i

= = + < − = = + = ≥ OFF, Diode : For , ON Diode : & For

• Even when vi starts to increase (dvi/dt > 0)

diode remains OFF as vo < vc0 + VD0

• 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.

• 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”
• 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

) ( ] )/ ( exp[ ) (

D c i D c i D c c

• V

t v v V v v v t t

• v

t v v + < → < − = − = = τ and : OFF Diode

D D D

V v i < =

• 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

and : ON Diode ≥ =

D D D

i V v ] )/ ( exp[ ) ( OFF, Diode : For , ON Diode : , & For τ t t

• v

t v v V v v V v v v V v v /dt dv

c c

• D

c i D i c

• D

c i i

− = = + < − = = + = ≥ ) ( ≥ → ≥ = = − = = = − = = dt dv i i dt dv C dt V v d C dt dv C i i V v v v

i c D i D i c c D D i c

] )/ ( exp[ ) ( OFF, Diode : For , ON Diode : , & For τ t t

• v

t v v V v v V v v v V v v /dt dv

c c

• D

c i D i c

• D

c i i

− = = + < − = = + = ≥

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

• 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.

• vo = vc0 = 0

] )/ ( exp[ ) ( OFF, Diode : For , ON Diode : , & For τ t t

• v

t v v V v v V v v v V v v /dt dv

c c

• D

c i D i c

• D

c i i

− = = + < − = = + = ≥

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[ ) ( τ t t

• v

t v v

c c

• −

= =

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)

sound carrier

T RC T << = <<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).

• 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

L sound carrier

R R T RC T << << = << and τ

Clamp Circuit

• F. Najmabadi, ECE65, Winter 2012

“Ideal” peak detector: vo = vc = V + − VD0 ) (

D i c i D

• D

c

V V v v v v v V V v − − = − = = − =

+ +

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

) (

D DC i c i

• D

DC c

V V V v v v v V V V v − − − = − = − − =

+ +

) (

D Z i

• V

V V v v − − − =

+

Clamp circuit can also introduce a “positive” shift

• F. Najmabadi, ECE65, Winter 2012

Peak detector (diode is reversed): vo = vc = − (V − − VD0) ) ( ) (

D i c i D

• D

c

V V v v v v v V V v − + = − = = − − =

− −

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

) (

D Z i

• V

V V v v − − + =

−

) (

D DC i

• V

V V v v − − + =

−

How to find response of clipper or clamp circuits:

• Assume diode is ON and calculate vc .
• If vc = +vi …, replace vi with V+ (peak positive value)
• 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 )