The Science of Electronics: Analog Devices

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The Science of Electronics Analog Devices
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Chapter Two Diode Circuits and Applications

• Contents
• 2.1 The Diode as a Network Element
• 2.2 Direct Methods of Analysis
• 2.3 Piecewise linear Models of Diode Behavior
• 2.4 Diode Applications

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2.1 The Diode as a Network Element

• The circuit symbol of the diode in the
  networks
• The characteristic of the diode element
• The expression for the characteristic
• Where IS is the reverse saturation current,
  VT is a potential related to the temperature

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2.2  Direct Methods of Analysis (1)

• The diode is a nonlinear element in the
  networks. Therefore, we cannot use the methods
  discussed before to analyze the network
  containing the diode. Generally, there are two
  kinds of methods for the analysis of nonlinear
  network, graphical method and algebraic method.
• 2.2.1 Graphical Methods The Load Line
• If there is only one nonlinear element in
  the network, the network can be separated to two
  parts nonlinear element and its linear
  companion. The linear circuit part is considered
  as the "load" (equivalent) of the nonlinear
  element.

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2.2  Direct Methods of Analysis (2)

• The "load" and the nonlinear element have the
  same voltage and current (by the KVL and KCL). On
  the other words, the terminal voltage and current
  must satisfy two characteristics, one is linear
  and another is nonlinear.
• Therefore, in order to find the terminal voltage
  and current we should determine the cross point
  (operating point) of two characteristics in one
  plane. This method is called graphical method.

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2.2  Direct Methods of Analysis (3)

• 2.2.2  Example Calculation

The following figure shows a circuit consisting
of a diode connected to a linear network of
resistors and voltage sources.
Notice that once the voltage and current in the
nonlinear element is found, only linear equations
were required to solve for the remaining voltages
and currents in the linear network. They may be
calculated straightforward.
First find the Thévenin equivalent for the linear
network.
Draw the v-i characteristic of this equivalent
and the diode in one plane.
The operating point is found in the figure that
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2.2  Direct Methods of Analysis (4)

• 2.2.4 Networks with More than One Nonlinear
  Element If a circuit contains more than one
  nonlinear element, graphical solutions, while
  possible, become more complex. First, it is not
  possible to separate the circuit into a linear
  part and a single nonlinear element. Thus the
  network facing a given nonlinear element contains
  at least one nonlinear element, and the v-i
  characteristic at its terminals will produce a
  nonlinear load line. Of course, the intersection
  of the nonlinear load line with the remaining
  nonlinear characteristic produces the desired
  operating point the difficulty is with the
  construction of the nonlinear load line. If the
  network contains only two nonlinear elements, a
  graphical solution can be obtained with only a
  modest increase in complexity. For cases with
  more than two nonlinear elements, the effort
  required for graphical solutions is seldom
  justified. For this reason we seek alternate
  methods of solution to networks with nonlinear
  elements, some of which we will now describe.

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2.2  Direct Methods of Analysis (5)

• 2.2.5 Algebraic Methods The Exponential and
  Logarithmic Amplifier

Because the diode has an exponential
characteristic, it is possible to construct the
exponential or logarithmic amplifier using the
diode and op-amps.
If the element A has characteristic     
i f1(vi)
and the element F has characteristic
   vof2(i).
Then the output voltage would be vof2(f1(vi))
According to the selection of components A and F,
two special amplifiers can be constructed.
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2.2  Direct Methods of Analysis (6)

• 1. Exponential amplifier

Let element A be a diode
element F a resistor R
The transfer characteristic of the circuit is
Circuit Demo
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2.2  Direct Methods of Analysis (7)

• 2. Logarithmic amplifier

Let element A be a resistance R
element F a diode D
Circuit Demo
The transfer characteristic of the circuit is
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2.3 Piecewise linear Models of Diode Behavior (1)

• In networks with several nonlinear elements, the
  graphical and algebraic methods become very
  complex. Furthermore, in a network containing an
  energy storage element, the graphical technique
  cannot handle adequately the dynamic responses to
  time-varying inputs.
• An alternate and very useful approach is to
  represent the nonlinear v-i characteristic in
  pieces with a set of approximate but linear v-i
  characteristics, each one valid over a suitably
  restricted range of voltage and current. In fact,
  we have already used this approach in discussing
  op-amps. The complete op-amp transfer
  characteristic was represented in three linear
  segments a linear gain region and two saturation
  regions. As long as we were careful to check that
  the voltages and currents in the proper ranges,
  it was possible to represent the nonlinear op-amp
  with a piecewise linear model.

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2.3 Piecewise linear Models of Diode Behavior (2)

• 2.3.1 Ideal Diode
• The p-n junction diode permits large
  forward currents to flow with only a small
  forward voltage, and supports large reverse
  voltages with only a tiny reverse saturation
  current. If we use a diode in a circuit where the
  voltages are much large compared to the diode
  forward voltage and the currents are much large
  compared to the diode reverse saturation current,
  then both the diode forward voltage and diode
  reverse current can be neglected. This is the
  ideal diode, which characteristic is represented
  as

v0 for i gt0 i0 for v lt0
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2.3 Piecewise linear Models of Diode Behavior (3)

• 2.3.2 Examples Rectifier Circuits????

1. Rectifier The rectifier translates an
alternating current with two directions into a
pulsatile current with single direction.  
2. Half-wave rectifier 
vI lt0
vI gt0
Circuit Demo
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2.3 Piecewise linear Models of Diode Behavior (4)
3. Full-wave rectifier
Circuit Demo
vIgt0, diode D1 is forward biased and equivalent
to a short-circuit, while diode D2 is reverse
biased and equivalent to an open-circuit.
vIlt0, diode D1 is reverse biased and equivalent
to an open-circuit, while diode D2 is forward
biased and equivalent to a short-circuit.
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2.3 Piecewise linear Models of Diode Behavior (5)

• 2.3.3 Improved Models for Forward Bias
• In many circuits, the source voltages present are
  not large compared to the threshold voltage (0.6V
  in silicon or 0.3V in germanium). In such
  circuits, the representation of a forward biased
  diode as a perfect short circuit is too drastic a
  simplification. In this case, we should use more
  accurate model (combine an ideal diode and other
  additional elements) to represent the diode.
• 1. Involve the threshold voltage

vVT for i gt0 i0 for v ltVT
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2.3 Piecewise linear Models of Diode Behavior (6)

• 2. Involve the slope of the characteristic

vVT Ri for i gt0       i0 for v ltVT
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2.3 Piecewise linear Models of Diode Behavior (7)

• 2.3.4 Models for Reverse Breakdown

1. not involve zener resistor 
i0 for -VZlt v lt0  v-VZ      for  i lt0
2. involve zener resistor  
i0 for -VZlt v lt0   v-VZ-Rzi    
  for  i lt0
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2.3 Piecewise linear Models of Diode Behavior (8)
3. The full piecewise linear model of an actual
diode
(1) not involve resistances
 (2) involve resistances
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2.4 Diode Applications(1)
2.4.1 Peak Sampler (?????)
1. Peak sampler
The output voltage of a peak sampler is holed the
positive peak of the input voltage.  In circuit
structure, the diode is used as a sampling switch
and a capacitor is a voltage keeper.  When the
input voltage is higher than the output voltage,
the switch is on and the capacitor is charged,
output voltage raises until it reaches the
positive peak of the input voltage.
2. Ideal peak sampler
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2.4 Diode Applications(2)

• As vI goes positive, the diode is forward-biased
  and equivalent to a short circuit. Therefore the
  diode conducts whatever forward current is needed
  to keep the capacitor voltage, vC, exactly equal
  to the source voltage, vI. Once vI reaches its
  maximum begins to decrease, the ideal diode
  becomes reverse biased and is equivalent to an
  open circuit. The capacitor will retain its
  voltage. 
• Thus, once vI passes through its maximum, the
  capacitor cannot discharge, and it therefore
  retains its voltage indefinitely. The only way,
  in this idealized version of the circuit, to
  return the capacitor voltage to zero is to
  connect an external short circuit once again
  across the capacitor terminals

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2.4 Diode Applications(3)

• 3. The effect of forward diode drop and load
  resistor on peak sampler

In practice, there are several ways in which
actual peak samplers depart in their behavior
from the ideal. First, with an actual diode
replacing the ideal diode, the capacitor charges
to a voltage that is smaller than the peak of  vI
by an amount equal to the forward voltage drop on
the diode, roughly 0.6 V for silicon. Second, a
resistor has been added to represent either an
external circuit (such as a voltmeter) or the
leakage resistance of the capacitor.  In either
case, the finite resistance shunting the
capacitor allows the capacitor to discharge with
time constant RC even after the diode becomes
reverse-biased. Thus the peak voltage on the
capacitor is less than the actual waveform peak,
and it decays at a rate dependent on the current
paths for discharge. (The reverse saturation
current of the diode also provides a discharge
path for the capacitor.) 
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2.4 Diode Applications(4)

• Peak samplers in which the above errors are
  largely eliminated can be constructed using
  op-amps and feedback.

Demonstration
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2.4 Diode Applications(5)

• 2.4.2 A Power Supply Rectifier??????

The rectifiers are already shown in 8.3.2. In
this section we discuss the power supply
rectifier with a capacitance load and sin-wave
input voltage.
1. Full-Wave rectifier without the capacitor
When the secondary voltage of the transformer,
v1, is positive (gt0), the diode D1 is
forward-bias and D2 is reverse-bias. Then a
current flows through D1 and RL. While the
secondary voltage of the transformer, v1, is
negative (lt0), the diode D2 is forward-bias and
D1 is reverse-bias. A current flows through D2
and RL. 
In either cases, the current through the load,
RL, is from top to bottom in the circuit.
Therefore, the voltage on the load resistance
should be always positive ( single polarity but
identity).
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2.4 Diode Applications(6)
The average output voltage, DC voltage, is
Where, V1 is the virtual value (r-m-s) of
secondary voltage, v1, of the transformer.
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2.4 Diode Applications(7)
2. Full-Wave rectifier with the capacitor
When v1 exceeds the capacitor voltage vo. diode
D1 will conduct, charging up the capacitor.
When -vo lt v1 lt vo, diodes D1 and D2 will
cut-off, discharging the capacitor through the
resistance RL
When v1 lt -vo, diode D2 will conduct, charging up
the capacitor again.
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2.4 Diode Applications(8)
The operating waveform of the Full-Wave rectifier
with the capacitor is shown as follows
The average output voltage, DC voltage, is
determined by the time constant of capacitor and
Where, V1 is the virtual value (r-m-s) of
secondary voltage, v1, of the transformer. In
engineering, if the ?RLCgt10???it may be
calculated approximately
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2.4 Diode Applications(9)

• 2.4.3 Diode Clamps and Limiters ??????????

1. Ideal diode limiter
Since diode become strongly conducting when the
forward voltage exceeds the threshold, diodes can
be used to limit or clamp the excursion of
voltages in a network. In the circuit bellow the
diode will conduct a forward current whenever the
input voltage vI exceeds the battery voltage V.
When vI gtV, the diode is forward bias and
equivalent to a short-circuit. Then,
When vI ltV, the diode is reverse bias and
equivalent to a open-circuit. Then,
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2.4 Diode Applications(10)
2. Bipolar limiter
By reversing the diode, the limiter can be made
to prevent the output voltage from ever becoming
less than the battery voltage. Also, by reversing
the polarity of the battery, limiting can be made
to occur for negative values of output voltage.
This circuit and its variations are used as
protection circuits to prevent burnout of
semiconductor devices through excessive voltage,
and to produce waveforms of constant amplitude
for FM and digital signal applications.
Negative limiter
Positive limiter
Bipolar limiter
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2.4 Diode Applications(11)

• 3. Diode protection circuit

A dc source is connected to a relay coil (modeled
as an inductor). When the switch is opened, the
current in the inductor must drop rapidly to
zero, producing a strongly negative transient in
vL. If an alternate path is not provided for this
current, the transient will get big enough to
produce a spark across the switch (this principle
is used to ignite the spark plug in an automobile
engine). 
The diode provides an alternate path for the
current, limiting the negative excursion of vL to
the threshold voltage of the diode. Sparks across
the switch are prevented, and the current in the
inductor decays smoothly, dissipating the
inductive stored energy in diode. Often, a small
resistor is put in series with the diode.
This diode is often called "free-wheeling" diode.
?????
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2.4 Diode Applications(12)

• 2.4.4 A DC Power Supply Employing a Zener Diode
  Regulator

???????????
1. The purpose of regulating?
In practice, the load of a DC power may be
uncertain usually.  The ripple is varied with the
load current, or load resistance.  On the other
hand, the output DC voltage will be changed by AC
voltage and the load current. This uncertain
output DC voltage is not expected in
applications. Therefore, the output of a power
rectifier should be regulated in order to obtain
a unchanged (or constant) DC voltage.  
The output of a power rectifier with capacitor
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2.4 Diode Applications(13)

• 2. How to regulate?
• As we know, the terminal voltage of a reverse
  breakdown zener diode is fixed. If a zener diode
  is connected in parallel across the output
  terminals, as long as the diode is reverse
  breakdown the output must be fixed to the
  breakdown voltage of the diode in spite of
  changing of input voltage and load.

A Zener Diode Regulator
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2.4 Diode Applications(14)
The changeable components (ripple and
instability) of the rectifier are absorbed by
resistance R. R also protects the excess current
through the zener diode, so it is called current-
limit resistance. Here is the operating waveforms
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2.4 Diode Applications(15)

• 3. Determination of current-limit resistance
• In the circuit, there are two worst cases 
• The input voltage is maximum and the load current
  is minimum. In this case, the zener diode carries
  maximum current, which should less than the
  maximum allowable current of the diode
• The input voltage is minimum and the load current
  is maximum. In this case, the zener diode carries
  minimum current, which should greater than the
  minimum stabilized current of the diode

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2.4 Diode Applications(16)
where, VC is the average (DC component) of the
capacitor voltage, which can be calculated by
1.2V1. Therefore, the allowable range of the
current-limit resistance R can be determined as
If this inequality has no solution, the zener
diode should be replaced by one which has higher
IZmax. Otherwise, the circuit configuration
should be changed.
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Chapter Two Diode Circuits And Applications
End of Chapter Two