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Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
1
3.4. Operation in the Reverse Breakdown
• Under certain circumstances, diodes may be intentionally used in the reverse breakdown region
• These are referred to as Zener Diode or Breakdown Diode
• Voltage regulator• Provide a constant dc voltage between its output terminals
• To remain output as constant as possible in spite of changes in dc power supply voltage and load current
Figure 3.18 Circuit symbol for a zener diode.
∆𝑉 = 𝑟𝑧∆𝐼
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
2
Figure 3.20 Model for the zener diode.
𝑉𝑧 = 𝑉𝑧0 + 𝑟𝑧𝐼𝑧
𝐼𝑍 > 𝐼𝑍𝐾, 𝑉𝑍 > 𝑉𝑍0
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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3.5 Rectifier Circuits
• One important application of diode is the rectifier –
• Electrical device which converts alternating current (AC) to direct current (DC)
• One important application of rectifier is dc power supply.
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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4.5. Rectifier Circuits
• One important application of diode is the rectifier
• Electrical device which converts alternating current (AC) to direct current (DC)
• One important application of rectifier is dc power supply
• Power transformer: • Step down voltage: primary winding (N1) - Secondary winding (N2)
• Electrical isolation
• Diode rectifier: produce pulsating waveform
• Rectifier filter: constant + ripple
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
5Figure 4.20: Block diagram of a dc power supply
step #1: increase / decrease rms magnitude of AC wave via power transformer
step #2: convert full-wave AC to half-wave DC (still time-varying and periodic)
step #3: employ low-pass filter to reduce wave amplitude by > 90%
step #4: employ voltage regulator to eliminate ripple
step #5: supply dc load .
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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3.5.1 Half-Wave Rectifier
• Half-wave rectifier: utilizes only alternate half-cycles of the input sinusoid
• Employ constant voltage drop diode model
• 𝑣𝑂 = 0, 𝑣𝑆 < 𝑉𝐷
• 𝑣𝑂 = 𝑣𝑆 − 𝑉𝐷 , 𝑣𝑆 ≥ 𝑉𝐷
• Selecting a diode• Current-handling capability
(largest current to be conduct)
• Peak inverse voltage (PIV)
(largest reverse voltage without
breakdown)
Figure 4.21: (a) Half-wave rectifier (b) Transfer characteristic of the rectifier circuit (c) Input and output
waveforms
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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3.5.1 Half-Wave Rectifier
• Current-handling capability: maximum forward current diode expected to conduct
• Peak inverse voltage (PIV): maximum reverse voltage it is expected to block without breakdown
• Use of exponential model: It is possible to use the diode exponential model in describing rectifier operation; however, this requires too much work
• Apply small inputs: the rectifier will not operate properly when input voltage is small (< 1V).
→ Require a precision rectifier
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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3.5.2 Full-Wave Rectifier
• Utilize both halves of the input sinusoid
• Provide a unipolar output
• Current through R always flows in the same direction
Figure 4.22: Full-wave rectifier utilizing a transformer with a center-tapped secondary winding
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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Figure 4.22: full-wave rectifier utilizing a transformer with a center-tapped secondary winding: (a) circuit; (b) transfer characteristic
assuming a constant-voltage-drop model for the diodes; (c) input and output waveforms.
The key here is center-tapping of the transformer, allowing “reversal” of certain currents…
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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When instantaneous source voltage is positive, D1
conducts while D2 blocks…
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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when instantaneous source voltage is negative, D2
conducts while D1 blocks
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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3.5.2 Full-Wave Rectifier
• The most important observation
• The direction of current flowing across load never changes (both halves of AC wave are rectified)
• Produces a more “energetic” waveform than half-wave
• PIV for full-wave: PIV = 2𝑉𝑠 − 𝑉𝐷
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
13
3.5.3 Bridge Rectifier
• Advantage• No need for center-tapped transformer
• PIV is half of the full-wave rectifier with a center-tapped transformer
• Disadvantage: • Used 4 diodes
• Series connection of two diodes will reduce output voltage
• Current through R always flows in the same direction
• PIV = 𝑉𝑠 − 𝑉𝐷
Figure 4.23: The bridge rectifier circuit.
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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Figure 4.23: The bridge rectifier circuit.
when instantaneous source voltage is positive, D1
and D2 conduct while D3 and D4 block
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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Figure 4.23: The bridge rectifier circuit.
when instantaneous source voltage is negative, D3
and D4 conduct while D1 and D2 block
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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3.5.4 Rectifier with Filter Capacitor
• Pulsating nature of rectifier output makes unreliable dc supply
• Employed a filter capacitor to remove ripple
• Step 1: • Source voltage is positive,
• Diode is forward biased
• Capacitor charges
• Step 2: • Source voltage is reverse,
• Diode is reverse-biased (blocking),
• Capacitor cannot discharge
• Step 3: • Source voltage is positive,
• Diode is forward biased,
• Capacitor charges (maintains voltage) Figure 4.24: (a) A simple circuit used to illustrate the effect of a filter capacitor. (b) input and output
waveforms assuming an ideal diode.
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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Practical Situation
• When load resistor is placed in series with capacitor
• Consider the discharging of capacitor across load
output voltage for state #1
output voltage for state #2
O I D
t
RCO peak
v t v t v
v t V e
circuit state #2
circuit state #1
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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Figure 4.25: Voltage and Current Waveforms in the Peak Rectifier Circuit WITH RC >> T. The diode is assumed ideal.
output voltage for state #1
output voltage for state #2
O I
t
RCO peak
v t v t
v t V e
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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Observations
• The diode conducts for a brief interval (∆𝑡) near the peak of the input sinusoid and supplies the capacitor with charge equal to that lost during the much longer discharge interval (T)
• Assuming an ideal diode, the diode conduction begins at time 𝑡1 (at which the input 𝑣𝐼 equals the exponentially decaying output 𝑣𝑂). Diode conduction stops at time 𝑡2 shortly after the peak of 𝑣𝐼 (the exact value of 𝑡2 is determined by setting of 𝐼𝐷 = 0)
• During the diode off-interval, the capacitor C discharges through R causing an exponential decay in the output voltage (𝑣𝑂). At the end of the discharge interval, which lasts for almost the entire period T, voltage output is defined as follows 𝑣𝑂 = 𝑉𝑝-𝑉𝑟
• When the ripple voltage (𝑉𝑟) is small, the output (𝑣𝑂) is almost constant and equal to the peak of the input (𝑉𝑃). the average output voltage may be defined as below…
(eq4.27) if is s1
ll 2
ma O peak r peak rV V V V V avg
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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• Step 1: • Analyze circuit state #1
• When diode is forward biased and conducting
• Step 2: • Input voltage (𝑣𝐼) will be applied to
output (𝑣𝑂), minus 0.7V drop across diode
• Step 3: • Define output voltage for state #1
: define capacitorcurrent differentially
OL
D C L
ID L
vi
R
i i i
dvi C i
dt
action
circuit state #1
output voltage for state #1
O I Dv v v
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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• Step 4: • Analyze circuit state #2
• When diode is blocking and capacitor is discharging
• Step 5: • Define KVL and KCL for this circuit
• 𝑣𝑂 = 𝑅𝑖𝐿
• 𝑖𝐿 = −𝑖𝐶
• Step 6: • Use combination of circuit and
Laplace Analysis to solve for 𝑣𝑂(𝑡)in terms of initial condition and time…
circuit state #2
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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3.5.4 Rectifier with Filter Capacitor
: take Laplace transform
: replace with -
: define differentially
: change sides
0
0
L C
C
C
OO L O
O C
OO
i
O
i
i
i
O
dvv Ri v RC
dt
v Ri
dvv R C
dt
dvv RC
dt
action
action
action
action
L
: take Laplace transform
tra
: seperate disalike / collect alike ter
nsform of
initial1 ( )conditio
s
n
m
0 0
0
O
O
dv
dt
RCs
O O O
O O
V s
O
V s RC sV s V
V s RCsV s RCV
action
action
: eliminate from both sides
: solve for
: pull out C
(
1
1)
R
10
10
1
10
1/
1 0
O
O
O O
O O
O O
O
RC s V s
RC
s
R
V
O
C
s V s VRC
V s V
sRC
V s Vs RC
RCs V s RCV
RC RC
action
action
action
L
: take inverse Laplace
: solve
0t
RCO Ov t V e
action
action
Use Laplace transform
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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• Step 7: • Define output voltage for states #1
and #2
output voltage for state #1
output voltage for state #2
O I D
t
RCO peak
v t v t v
v t V e
circuit state #2
circuit state #1
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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3.5.4 Rectifier with Filter Capacitor
• Q: What is 𝑉𝑂(0)?
• A: Peak of 𝑣𝑖, because the transition between state #1 and state #2 (aka. diode begins blocking) approximately as 𝑣𝑖 drops below 𝑣𝐶
• Q: How is ripple voltage (𝑉𝑟) defined?
• step 1: Begin with transient response of output during “off interval”
• step 2: Note T is discharge interval
• step 3: Simplify using assumption that RC >> T
• step 4: Solve for ripple voltage 𝑉𝑟
is discharge interval
because ,we
:
can assume...
1
1 1
solve forripple voltage
(eq4.28)
)
(
T
RC
r
t
RCO peak
peak r O
T
RCpeak r peak
r pea
T
RC T
Te
R
C
k
C
T
R
V
v t V e
V V v T
V V V e
TV V
RC
action
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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• step 5: Put expression in terms of frequency (f = 1/T)
• Observe that, as long as 𝑉𝑟 << 𝑉𝑃𝑒𝑎𝑘, the capacitor discharges as constant current source (𝐼𝐿 = 𝑉𝑝/𝑅).
• Q: How is conduction interval (∆𝑡) defined?
• A: See following slides…
(eq4.29)
peak
pea
V
L
R
k
r
V IV
fRC fC
expression to define ripple voltage (Vr)
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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• step 1: Assume that diode conduction stops (very close to when) 𝑣𝑖 approaches its peak
• step 2: With this assumption, one may define expression to the right.
• step 3: Solve for 𝜔∆𝑡
cos(0O)
Onote that peak of vI represents cos(0 ),therefore represents variationaround this value
as assumed, conductioninterval will be smallwhen
(eq 2 /4.30)
t
t
peak
r peak
peak rV t V V
t V V
cos
cos
r peakV V
cos 𝜔∆𝑡 ≅ 1 − 12(𝜔∆𝑡)2
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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3.5.5 Precision HW Rectifier
• Precision rectifier – is a device which facilitates rectification of low-voltage input waveforms
Figure 4.27: The “Superdiode” Precision Half-Wave Rectifier and its almost-ideal transfer characteristic.
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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3.6 Limiting and Clamping Circuits
• Limiter circuit: limits voltage output
• Passive limiter circuit (K < 1)• has linear range
• has nonlinear range
• Examples include• Single limiter operate in unipolar manner
• Double limiter operate in bipolar manner
Figure 3.30: General transfer characteristic for a limiter circuit
over linear range
outside linear range
-
constant value(s)
I
O
O
I
I
I
I
Kvv
L
v Kv
Lv
KL L
vK K
Lv
KL
over linear range
outside linear range
-
constant value(s)
I
O
O
I
I
I
I
Kvv
L
v Kv
Lv
KL L
vK K
Lv
KL
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
29
3.6 Limiting and Clamping Circuits
• Soft vs. Hard limiter
• How are limiter circuits applied?
• A: Signal processing, used to prevent breakdown of transistors within various devices
Figure 3.32: Hard vs. Soft Limiting.
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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Figure 3.33: Variety of basic limiting circuits.
single limiters employ one
diode
double limiters employ two
diodes of opposite polarity
linear range may be controlled via
string of diodes and dc sources
zener diodes may be used to
implement soft limiting
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
31
3.6.2 Clamped Capacitor or DC Restorer
• DC restorer: Circuit which removes the dc component of an AC wave
• 𝑣𝐶 will charge equal to the magnitude of the most negative peak of the input signal
• 𝑣𝑂 = 𝑣𝐼 + 𝑣𝐶
Figure 3.34: The clamped capacitor or dc restorer with a square-wave input and no
load
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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3.6.3 Voltage Doubler
• Clamped capacitor + peak rectifier
• Output voltage = double the input peak
Figure 3.36: Voltage doubler: (a) circuit; (b) waveform of the voltage across D1.
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
33
Summary (1)
• In the forward direction, the ideal diode conducts any current forced by the external circuit while displaying a zero-voltage drop. The ideal diode does not conduct in reverse direction; any applied voltage appears as reverse bias across the diode.
• The unidirectional current flow property makes the diode useful in the design of rectifier circuits.
• The forward conduction of practical silicon-junction diodes is accurately characterized by the relationship i = ISe
V/VT.
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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Summary (2)
• A silicon diode conducts a negligible current until the forward voltage is at least 0.5V. Then, the current increases rapidly with the voltage drop increasing by 60mV for every decade of current change.
• In the reverse direction, a silicon diode conducts a current on the order of 10-9A. This current is much greater than IS
and increases with the magnitude of reverse voltage.
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
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Summary (3)
• Beyond a certain value of reverse voltage (that depends on the diode itself), breakdown occurs and current increases rapidly with a small corresponding increase in voltage.
• Diodes designed to operate in the breakdown region are called zener diodes. They are employed in the design of voltage regulators whose function is to provide a constant dc voltage that varies little with variations in power supply voltage and / or load current.
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
36
Summary (4)
• In many applications, a conducting diode is modeled as having a constant voltage drop – usually with value of approximately 0.7V.
• A diode biased to operate at a dc current ID has small signal resistance rd = VT/ID.
• Rectifiers covert ac voltage into unipolar voltages. Half-wave rectifiers do this by passing the voltage in half of each cycle and blocking the opposite-polarity voltage in the other half of the cycle.
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
37
Summary (5)
• The bridge-rectifier circuit is the preferred full-wave rectifier configuration.
• The variation of the output waveform of the rectifier is reduced considerably by connecting a capacitor C across the output load resistance R. The resulting circuit is the peak rectifier. The output waveform then consists of a dc voltage almost equal to the peak of the input sine wave, Vp, on which is superimposed a ripple component of frequency 2f (in the full-wave case) and of peak-to-peak amplitude Vr = Vp/2fRC.
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
38
Summary (6)
• Combination of diodes, resistors, and possible reference voltage can be used to design voltage limiters that prevent one or both extremities of the output waveform from going beyond predetermined values – the limiting levels.
• Applying a time-varying waveform to a circuit consisting of a capacitor in series with a diode and taking the output across the diode provides a clamping function.
• By cascading a clamping circuit with a peak-rectifier circuit, a voltage doubler is realized.
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016
39
Summary (6)
• Beyond a certain value of reverse voltage (that depends on the diode itself), breakdown occurs and current increases rapidly with a small corresponding increase in voltage.
• Diodes designed to operate in the breakdown region are called zener diodes. They are employed in the design of voltage regulators whose function is to provide a constant dc voltage that varies little with variations in power supply voltage and / or load current.
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