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8/3/2019 Nonlinear Wave Shaping
http://slidepdf.com/reader/full/nonlinear-wave-shaping 1/17
Presented by APN Rao, Dept ECE, GRIET, Hyderabad. Jan 2012 1
Nonlinear Waveshaping using Diode Circuits
Text Book:
Pulse, Digital and Switching Waveforms
Jacob Millman, Herbert Taub
McGraw-Hill Kogakusha Ltd (1965)
8/3/2019 Nonlinear Wave Shaping
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Practical Diode
V-I Characteristic
Presented by APN Rao, Dept ECE, GRIET, Hyderabad. Jan 2012 2
Diode
Approximation of Diode Characteristics: Considerations
a) Cut-in Voltage (Vγ): 0.3V(Ge), 0.7V(Si)b) Reverse Saturation (Leakage) Current (Is ): few μA
c) Forward Resistance (Rf ): few Ω
d) Reverse Resistance (Rr): many kΩ
e) Diode Capacitance: few pF
f) Effect of Temperature
V
IIdeal Diode
V-I Characteristic
V
I
Vγ
slope = 1/Rf
slope = 1/Rr
Piece-wise linear
approximation for
large signals
8/3/2019 Nonlinear Wave Shaping
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VR +Vγ
VR +Vγ
vi
vo
Transfer Characteristic
Presented by APN Rao, Dept ECE, GRIET, Hyderabad. Jan 2012 3
Diode Clipper Circuits (Positive)
γ s f r
R γ R
γ
γ
R
assumptions: V 0, I = 0, R = 0, R =
D 'OF
D
F' v V +
'ON' v V +V ; v V +
v
V
V ; v
i
o i
o
i
R
VR
Dvi vo
R
VR
D
vi vo
Exercise:
Similarly analyse
Positive Series
Clipper
PositiveShunt
Clipper
t
8/3/2019 Nonlinear Wave Shaping
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Presented by APN Rao, Dept ECE, GRIET, Hyderabad. Jan 2012 4
Diode Clipper Circuits (Negative)
γ s f r
R γ R
γ
γ
R
assumptions: V 0, I = 0, R = 0, R =
D 'OFF' v V V ;
D 'ON' v V V ; v V
v v
Vi o
i o i
R
VR
Dvi vo
VR - Vγ
VR
- Vγ
vi
voTransfer
Characteristic
R
VR
D
vi vo
Exercise:
Similarly analyse
Negative Series
Clipper
t
NegativeShunt
Clipper
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Presented by APN Rao, Dept ECE, GRIET, Hyderabad. Jan 2012 5
Diode Clippers with Rf ≠ 0 & Rr ≠ ∞
γ s f r
i R o i R i
f i R o i
f
r
R R
RD 'ON' v > V ; v = V + v VR + R
RD 'OF
assumptions: V 0, I = 0, R 0, R
F' v < V ; v = v + V vR + R
R
VR
Dvi vo
Choice of External Resistor R: For clipping operation to be close to ideal, we
should choose R >> Rf ; but to minimize distortion of vi passed, R << Rr is to
be chosen. An optimal choice is R = (Rf Rr)1/2
Circuit analysis is done replacing diode with Rf when forward-biased and with Rr
when reverse-biased.
VR
VR
vi
vo0
f
f
Rslope
R R
< 1r
r
Rslope
R R
In forward biased region, imperfect clipping
takes place since slope ≠ 0, and in reverse
biased region waveform distortion occurs since
slope ≠ 1. Ex: Carry out similar analysis for the
other diode clippers.
8/3/2019 Nonlinear Wave Shaping
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Presented by APN Rao, Dept ECE, GRIET, Hyderabad. Jan 2012 6
Effect of Diode Capacitance
Diode capacitance (in pF) shunts the diode, and acts as a short for any discontinuities
in input voltage. High frequency components are passed even when diode is reversebiased. Depending on location of diode in the circuit, waveshape changes will occur.
Portions of the waveform will be depend on charging/discharging process of the
diodecapacitance.
Diode Clippers with Is = non-zero constantR
VR
Dvi vo
γ s f r
i R γ o i
R γ o
s
i R γD 'ON' v > V
assumptio
D
ns: V 0, I 0,
'OFF'
R 0, R
v < V + V
+ V ; v
;
=
v =
V +
+
V
v I R
For Is = non-zero constant, the output when diode is in OFF region gets modified.
Exercise: Analyse the other three diode clipperssimilarly.
8/3/2019 Nonlinear Wave Shaping
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Effect of Diode Capacitance: Example
RD
vi vo
C1
C2R
Rf
vi vo
C1
C2 R
Rr
vi vo
C1
C2
C1 = Diode capacitance (pF)
C2 = Input capacitance (pF)
Equivalent Circuit for D ‘ON’ Equivalent Circuit for D ‘OFF’
+5 V
-5 V
vi
5V
0 V
2 V
vo
τ1 = 2.5ns
τ2 = 25μs3 V
Example: C1= 5 pF, C2 = 20
pF, Rf = 100 Ω, R = 1 MΩ, Rr
= ∞. Find and sketch
response to input squarepulse ±10V.
Exercise: Repeat the above problem with diode and R interchanged in the negative
series clipper circuit shown.
8/3/2019 Nonlinear Wave Shaping
http://slidepdf.com/reader/full/nonlinear-wave-shaping 8/17Presented by APN Rao, Dept ECE, GRIET, Hyderabad. Jan 2012 8
Two-level Diode Clippers: ExamplesR
VR1
D1vi vo
VR2
D2
vo
viVR2
VR2
VR1
VR1
Note: Two independent clipping
levels. Above circuit can eliminate
noise riding The peaks of a squarewave.(Assumed VR2 > VR1)
D1 D2 vo
vi ≤ VR1 ON OFF ≈ VR1
VR1 ≤ vi ≤ VR2 OFF OFF vi
vi ≥ VR2 OFF ON ≈ VR2
R
Z1
vi vo
Z2
Zener diode-clipper
Zener voltages VZ1 and VZ2
Z1 Z2 vo
vi ≥ VZ2 + Vγ ON breakdown VZ2 + Vγ
vi ≤ -(VZ1 + Vγ ) breakdown ON -(VZ1 + Vγ )
VZ2 + Vγ
≥ vi ≥ -(VZ1 + Vγ )OFF/ON ON/OFF vi
8/3/2019 Nonlinear Wave Shaping
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Two-level Diode Clippers: Examples
Rvi vo
D1 D2 vo
vi ≤ -Vγ ON OFF vi + Vγ
-Vγ ≤ vi ≤ Vγ OFF OFF 0
vi ≥ Vγ OFF ON vi - Vγ
D1
D2
Vγ ≠ 0
(Exercise: Sketch transfer characteristic.)Noise Clipper: Eliminates noise of small amplitudes.
vi vo
100V25V
200K100K
D1 D2Solution:
Assuming ideal diodes,
vi ≤ 25 V v0 = 50 V
25V ≤ vi ≤ 100 V v0 = v i
v ≥ 100 v0 = 100 V
(Exercise: Sketch the
transfer characteristic)
8/3/2019 Nonlinear Wave Shaping
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Clamping Circuit: Ideal Diode
Analysis assuming ideal diode
t < t 1: D is forward biased. C
charges instantaneously (with
zero time-constant ) to input
voltage. vC = v i ; vo = vi – vC = 0
t = t 1: v i reaches first peak = +V
volts. vC = V
t > t 1: D is reverse biased. C
has no discharge path. vC =
constant = V; vo = vi – V; output
positive peaks are clamped to
0 volt level. Hence called
Positive Clamper
vi
vc
vo = vi - vc
+V
-V
0V
-2V
+V
0V
t
t
t
t1
Exercise: Analyze and verify that
the circuit with diode reversed
operates asa negative clamper.
vi vo
C
D
vc+ -
8/3/2019 Nonlinear Wave Shaping
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Clamping Circuit: Ideal Diode
Increased amplitude peaks are clamped by instantaneous charging ofcapacitor. However, since discharge path is not available, clamping is
ineffective for decreasing amplitude waveforms.
Case of decreasing amplitudeCase of increasing amplitude
vi
vo
0 V
8/3/2019 Nonlinear Wave Shaping
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Clamping Circuit: Non-ideal Diode
With Rf ≠ 0 and Rr ≠∞, the capacitor-diode circuit operates as a high-pass circuit
switching between diode ON/OFF states with effective resistance alternating
between Rf andRr .
Equivalent circuits for analysis
when
diode
forwardbiased
when
diode
reversebiased
Biasing condition of diode depends on polarity of vo = vi – vC.
(ON if vo positive and OFF if negative)
vi vo
C
Rf D ‘ON’
τf = Rf C
vi vo
C
RrD ‘OFF’
τr = Rr C
With finite Rf and Rr ,the capacitor at any instant is either charging or discharging,
hence is vC is never constant. The dc (average) level of input waveform gets shifted
by the dc (average) level of capacitor voltage.
For effective clamping of increasing or decreasing amplitude waveform-peaks, bothcharging and discharging time-constants have to be reasonably small. For this
purpose, the diode is shunted with an external resistance R such that Rf << R << Rr .
Analysis at input discontinuities: If the discontinuity includes both forward and
reverse-biased conditions, both the above circuits need to be used, using the
principlethat capacitor voltage does not change during the transition.
8/3/2019 Nonlinear Wave Shaping
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Practical Clamping Circuit: with Rs ≠ 0
Charging/ discharging time-constantsDiode ON (vo > 0) : (Rf +Rs)C
Diode OFF (vo < 0) : (R+Rs)C
Example: Rs = Rf = 100 Ω, R = 1 0 K , C = 1
μF. Find response (first two cycles) to a
symmetric square wave input 0-10 V,frequency = 5 kHz. Capacitor uncharged at
t = 0 .
vs vo
C
D R
vs
vo
C
Rf
D ‘ON’
τf =
(Rf +Rs)C
Rs
vs
vo
C
R
D ‘OFF’
τr =
(R +Rs)C
Rs
Rs
53 3 1.8 1.8 1.1
− 4
− 6.4
− 7.8
10
t0
100 μs100 μs
vo
8/3/2019 Nonlinear Wave Shaping
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Steady State Analysis: Clamping Circuit TheoremThe capacitor voltage varies continuously, as charging / discharging current is always
present. The average (dc) level of input periodic waveform is biased by the average
(dc) level of the capacitor v
at steady state
oltage. Steady
, the net charg
state is reached when average
e acquired by the capacitor
ov
capacitor voltage
r
er a cycle must be
eaches a st
zero.
eady value. Thus,
This principle is the ba .sis of Clamping Circuit Theorem
vs vo
C
D
R
if ir
r f f
f o r o
As R >> R >> R , effective resistance = R while charging and R while discharging.
Let charging current = i (D "ON", v > 0) & discharging current = i (D"OFF",v < 0)At steady state, net charge gaine
" " " "
d by C should = 0 f r
D ON D OFF
i dt i dt
0 0
0 0
" " " "
(with D "ON"), (with D"OFF")
Define A , and A
Then
o o
f r f r
f
f of r or
v v
f r
D ON D OFF
f f
r
v vi i
R R
v dt v dt
i dt i dt A R
A R
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V′ V′
V′′ V′′ V′′
V1
V2
V1′
V2′ V2′
V1
V2
V1′
vs
vo
T1 T2V
Presented by APN Rao, Dept ECE, GRIET, Hyderabad. Jan 2012 15
Steady State Response to Square Wave Input
1
f s
2
s
T
R + R C1 1
T
R + R C
2 2
f s s1 2
f
f s s1 2
f
V V e (1)
V V e (2)
R + R R + RV = V V (3)
R R
R + R R + RV = V V (4)
R R
Equations 3 and 4 are derived using the principle that capacitor voltage is unaffected during
discontinuous changes at input.
sf
f s
1 1 2 2From 3 & 4, and defining f V V and r V V
R + RRf r If R 0, f r
R +R
, we get
.R
s
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R
f R 1 f
r R 2
R
A Rholds if A and A are computed
A R
with respect to dc level V . If A and A are
with respect to zero level, the relatio
Positive peaks are clamped at V
A V T R=
n beco
A + V T
e
R
m s
f f
f r
r
f r
Presented by APN Rao, Dept ECE, GRIET, Hyderabad. Jan 2012 16
Introducing Fixed VR
vs vo
C
DR
if ir
VR
vs vo
C
D
R
if ir
VR
X
X
f R 1
f
f
r
R
At x-x, dc level of waveform is zero
(highpass effect). With the conditions that
the amplitude is at least V and R >> R ,
and V 0, clam
A
ping the
V
ore
+V
m becom
T R=A
e
R
s
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Transmission (Attenuation) Factors
o s o s
o s
s
f
f s
s
v (R 0) v (R 0) when diode is forward biased.
= v (R 0) when diode is reverse biased.
Non-zero R causes unequal attenuation to different parts of
wavef
R
R + RR
R
orm and
+
t r
R
he ef
o i
ore causes distortion.
(Note: This attenuation is on v , not on v )