9/14/2004
Zener Diode Models.doc
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Zener Diode Models
The conventional diode models we studied earlier were based
on junction diode behavior in the forward and reverse bias
regions—they did not “match” the junction diode behavior in
breakdown!
iD
−VZK
vD
0.7V
CVD
Model
Junction
Diode
Breakdown
However, we assume that Zener diodes most often operate in
breakdown—we need new diode models!
Specifically, we need models that match junction/Zener diode
behavior in the reverse bias and breakdown regions.
New
Zener
Model
iZ
vZ
VZK
Jim Stiles
The Univ. of Kansas
Dept. of EECS
9/14/2004
Zener Diode Models.doc
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We will study two important zener diode models, each with
familiar names!
1.
The Constant Voltage Drop (CVD) Zener Model
The Piece-Wise Linear (PWL) Zener Model
2.
The Zener CVD Model
Let’s see, we know that a Zener Diode in reverse bias can be
described as:
iZ ≈ I s ≈ 0
and v Z < VZK
Whereas a Zener in breakdown is approximately stated as:
iZ > 0
and
v Z ≈VZK
Q: Can we construct a model which behaves in a similar
manner??
A: Yes! The Zener CVD model behaves precisely in this way!
iz
Replace:
vz
_
Jim Stiles
iz
+
with:
Ideal
diode
+
vz
+
VZK
_
The Univ. of Kansas
Note the
direction
of ideal
diode !
_
Zener
CVD
Model
Dept. of EECS
9/14/2004
iZ = 0
Zener Diode Models.doc
Analyzing this Zener CVD model, we
find that if the model voltage vZ is less
than VZK (i.e., v Z < VZK ), then the ideal
+
+
vdi < 0
−
+
v Z <VZK
VZK
_
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diode will be in reverse bias, and thus
the model current iZ will equal zero.
In other words:
iZ = 0
_
and
v Z <VZK
Just like a Zener diode in reverse bias!
Likewise, we find that if the model
current is positive (iZ >0), then the ideal
diode must be forward biased, and thus
the model voltage must be vZ =VZK. In
other words:
iZ > 0
and
v Z = VZK
Just like a Zener diode in breakdown!
iz > 0
+
+
vdi = 0
−
v Z = VZK
+
VZK
_
_
Problem: The voltage across a zener diode in breakdown is
NOT EXACTLY equal to VZK for all iz > 0 . The CVD is an
approximation.
Jim Stiles
The Univ. of Kansas
Dept. of EECS
9/14/2004
Zener Diode Models.doc
4/6
In reality, vZ increases a very small (tiny) amount as iZ
increases.
iZ
Real zener diode
characteristic
CVD
model
vZ
VZK
Thus, the CVD model causes a small error, usually
acceptable—but for some cases not!
For these cases, we require a better model:
The Zener (PWL) Piece-Wise Linear model.
The Zener Piecewise Linear Model
iZ
Replace:
iz
+
VZ
with:
Ideal
diode
+
vz
+
VZ0
_
Jim Stiles
Note the
direction
of ideal
diode!
_
rZ
The Univ. of Kansas
_
Zener
PWL
Model
Dept. of EECS
9/14/2004
Zener Diode Models.doc
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Please Note:
* The PWL model includes a very small series resistor,
such that the voltage across the model vz increases
slightly with increasing iz .
* This small resistance rZ is called the dynamic
resistance.
* The voltage source VZ0 is not equal to the zener
breakdown voltage VZK, however, it is typically very close!
iZ = 0
+
+
vdi < 0
−
+
VZ0
v Z <VZ 0
_
rz
_
Analyzing this Zener PWL model, we find
that if the model voltage vZ is less than
VZ0 (i.e., v Z <VZ 0 ), then the ideal diode
will be in reverse bias, and the model
current iZ will equal zero. In other
words:
iZ = 0 and v Z < VZ 0 ≈VZK
Just like a Zener diode in reverse bias!
Likewise, we find that if the model
current is positive ( iZ > 0), then the ideal
diode must be forward biased, and thus:
iZ > 0 and v Z =VZ 0 + iZ rZ
Note that the model voltage vZ will be
nearVZK, but will increase slightly as the
model current increases.
Just like a Zener diode in breakdown!
Jim Stiles
The Univ. of Kansas
iz > 0
+
+
vdi = 0
vZ =
VZ 0 + iz rz
−
+
VZ0
_
rz
_
Dept. of EECS
9/14/2004
Zener Diode Models.doc
CVD
model
iZ
Comparison between
CVD and PWL models
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Zener
Diode
PWL model
VZ0
vZ
VZK
Q: How do we construct this PWL model (i.e., find VZ 0 and rz )?
A: Pick two points on the zener diode curve (v1, i1) and (v2, i2),
and then select rz and VZ0 so that the PWL model line
intersects them.
iZ
i2
1/rz
i1
vZ
VZ0
i.e.,
rz =
v1
v2
v 2 − v1
i2 − i1
and
Vz 0 = v1 − i1rz
Jim Stiles
or
Vz 0 = v2 − i2rz
The Univ. of Kansas
Dept. of EECS