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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. ∆ =

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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

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Figure 3.20 Model for the zener diode.

𝑉𝑧 = 𝑉𝑧0 + 𝑟𝑧𝐼𝑧

𝐼𝑍 > 𝐼𝑍𝐾, 𝑉𝑍 > 𝑉𝑍0

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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.

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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

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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 .

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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

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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

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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

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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…

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When instantaneous source voltage is positive, D1

conducts while D2 blocks…

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when instantaneous source voltage is negative, D2

conducts while D1 blocks

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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

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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.

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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

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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

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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.

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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

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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

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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

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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

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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

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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

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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

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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

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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)

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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

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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.

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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

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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.

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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

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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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.