Diode modeling(Approximation)
1. Ideal Model (high Voltage > 100v)
2. Constant model(few voltage up to 10-20V)
3. Piecewise linear model (for linear
amplification)
4. Small signal model(small signals less than Vp-
p=0.1V
5. Complete model( considering the
capacitance of diode)
Diode modeling
• Models are very often used in engineering. A model is a way
of describing the behavior of a system, often by using
mathematical formulae for given condition.
• Models are used to make predictions and calculations. In fact,
the exponential law that relates the diode current to the
diode voltage is a model
• High precision is not always needed. When designing a circuit,
an approximate calculation suffices. In a later stage, the
circuit can be simulated or even built, to get an idea of the
‘digits behind the comma’. Therefore, models will be used
that approximate the behavior of the diode.
• The purpose of these models is not to explain the physics of
the working device. Their purpose is to simplify calculations.
The simpler the model, the simpler the calculation. The more
complex the model, the higher the precision of the
calculation.
1.Ideal model
• Ideal means ideally act as normal switch of electric line
where the switch is conductor path and not takes any
voltage drop.
• Practically no diode and components are ideal but for
comparison of high voltage 0vr 100V the voltage drop
across the diode is less than 1V for example around 0.7
V for silicon diode so can be ignored and works as one
way switch.
• Here when diode is switched ON the voltage across
diode is considered as zero and current through the
diode is maximum and when the diode is reverse bias
then it is considered as switch OFF and the current is
zero and voltage across the diode is input voltage of
circuit.
• Mathematically, 𝑉𝑂𝑁 (OUT)= 0 V, 𝐼𝑂𝑁 =𝐼𝑀𝐴𝑋 ,𝑅𝐹 = 0 ohm,
• 𝑉𝑂𝐹𝐹 (out)= 𝑉𝑖𝑛 , 𝐼𝑂𝐹𝐹 =0 ,𝑅𝐹 =∞
• When the input is positive it provides the diode conducts
as forward bias and when the voltage is negative or zero
the diode simply not conducts or goes in reverse bias
and no current flow.
• When we calculate the current in this model we consider
𝑉𝑑 = 0𝑉
𝐸−𝑉𝑑 𝐸−0 5−0
𝐼𝑑 = = = = 0.05𝐴
𝑅 𝑅 100
Ideal Diode
Constant Voltage Model
When forward bias voltage applied exceeds
0.7 volts the Diode is in ON mode. If it is
below the minimum voltage then the diode is
in OFF mode. Therefore, in this way diode
acts as a switch.
used below 100V or few up to 10-20V and
the breakdown voltage should consider for
calculation for this model and often used in
low voltage circuits.
When the FB voltage is beyond 0.7V the
diode conducts and when the diode forward
bias is low than 0.7 V then the diode does
not conduct
Mathematically
In ON condition , Vd=0.7V,Id= Id (max),𝑅𝐷 =0
In OFF condition, Vd=Vin, Id=0,𝑅𝐷 =∞
When we calculate in this model
𝐸−𝑉𝐷 5−0.7 4.3
𝐼𝐷 = = = 100 = 0.043𝐴
𝑅 100
Piecewise Linear method
• The cut-off voltage along with some Internal Resistance across the
Diode is observed.
• This condition exists in the practical application in the design of circuits.
This type of resistance can be referred to as Bulk Resistance. It is
dependent upon the amount of the Forward Voltages and Forward
Currents applied to the diode.
• When the forward bias voltage exceeds then the current starts to
increase as the internal resistance decreases and in reality it increases
as exponentially but here we consider that the resistance decreases
1
linearly so we get a linear line with slope of .
𝑅𝐷
• In practical when we need linear action , used the linear piece of
characteristics considering the current increment is linear
• Since there is resistance then some voltage drop internally which is
equal to product of current and the diode internal resistance.
• The total internal voltage equal to the voltage drop across the internal
resistance.
• Mathematically
• When the diode is OFF Id=0,Vd=Vin,R=∞
𝐸𝑠 −𝑉𝐷 𝐸𝑠 −𝑉𝐷
• When the diode is ON- 𝐼𝐷 = , 𝐸𝐷 > 𝑉𝐷 ,𝑅𝐷 = , 𝑉𝐷 =𝐼𝐷 𝑥 𝑅𝐷 or
𝑅𝐷 𝐼𝐷
𝐼𝐷 1 𝑉𝐷
= or 𝑅𝐷 =
𝑉𝐷 𝑅𝐷 𝐼𝐷
• If the E ,Id,Vd are known we can calculate the internal resistance
𝐸 −𝑉 5−0.75 4.25
• 𝐼𝐷 = 𝑠 𝐷 𝑜𝑟 0.01 = 𝑜𝑟 100 + 𝑅𝐷 = 𝑜𝑟 𝑅𝐷 = 425 −
𝑅𝑆 +𝑅𝐷 100+𝑅𝐷 0.010
100=325 ohm
Piecewise
linear
modeling
• When the diode is OFF Id=0,Vd=Vin ,R =∞
𝐸𝑠 −𝑉𝐷
• When the diode is ON- 𝐼𝐷 =
𝑅𝐷 +𝑅𝑆
For diode only when the voltage increases 𝑅𝐷 decreases
𝑉𝐷 1
• 𝑅𝐷 = and the curve goes in straight by value
𝐼𝐷 𝑅𝐷
• If the E ,Id , Vd are known we can calculate the internal
resistance
𝐸𝑠 −𝑉𝐷
• 𝐼𝐷 = 𝑜𝑟 0.01 =
𝑅𝑆 +𝑅𝐷
5−0.75 4.25
𝑜𝑟 100 + 𝑅𝐷 = 𝑜𝑟 𝑅𝐷 = 425 − 100 =325
100+𝑅𝐷 0.010
ohm
Small signal model(AC model)
• Small signal means it may be the V p-p
voltage signal from few mV to some 0.1V
or so around as if it is increased than that
exceeds linear part of diode
characteristics.
• Since the small voltage cannot be applied
to diode directly as the negative half will
be cutoff and most of the signal in
positive half also lies in nonlinear part
before breakdown voltage.
• So the small signal(𝑉𝑑 ) always associates a
DC voltage(𝑉𝐷 ) supply so that the diode
voltage will be in breakdown voltage near
around 0.7V.
• small-signal diode model
• Diode is modeled as variable resistor.
• Whose value is defined via
linearization of exponential model.
• Around bias point defined by constant
voltage drop model.VD(0) = 0.7V
• The diode model also taken as piecewise
linear model for small signal
Small Signal Model
Small Signal Model
Mathematical analysis
The total voltage at any time t is the sum of the DC and AC
componentsvD (t ) = VD+vd (t )
As, taken 𝐼𝐷 (t ) >> 𝐼𝑆 such that
𝑉𝐷 +𝑉𝑑 𝑉𝐷 (𝑡) 𝑉𝑑 (𝑡) 𝑉𝑑 (𝑡)
𝑖𝐷 (t ) » 𝐼𝑆 𝑒 = 𝐼𝑆 𝑒
𝑛𝑉𝑇 𝑛𝑉𝑇 .𝑒 𝑛𝑉𝑇 =𝐼𝐷 . 𝑒 𝑛𝑉𝑇
Comparing to series
𝑋2
e=1+X+ 2 +..
𝑉𝐷 (𝑡)
𝑛𝑉𝑇
Since the value of < < 2 so taken two
ternms only
𝑉𝐷 (𝑡)
𝑉 (𝑡)
𝐷
𝑒 𝑛𝑉𝑇 = 1+ 𝑛𝑉 putting this value in equation
𝑇
𝑉𝑑 (𝑡) 𝑉𝐷 (𝑡)
𝐷 𝑉 (𝑡)
𝑖𝐷 (t )=𝐼𝐷 . 𝑒 𝑛𝑉𝑇 = 𝐼𝐷 (𝑒 𝑛𝑉𝑇 )= 𝐼𝐷 (1+ 𝑛𝑉 )= 𝐼𝐷 +
𝑇
𝑉𝐷 (𝑡)
𝐼𝐷 𝑛𝑉 ,Here the term
𝑇
The changing value is second part so we
𝑛𝑉
compare in ohms law and 𝑟𝑑 = 𝐼𝑑𝑇
If the R is given and the signal voltage given and
supply voltage is given then we can calculate
the current as normal diode for DC so then
putting the value of I(D) can value r(d)
Complete Model
• AC Diode Model The diode model under ac conditions is quite a bit
more complicated. For now, keep in mind that whenever you have a
charge separation there is a capacitive effect. This charge separation
comes about in the diode due to the depletion region, which is in
turn dependent on the applied bias.
• To add insult to injury, it turns out that the frequency of operation
introduces an additional consideration for forward bias operation.
• In forward bias there exist the forward diode resistance and
associated two capacitances as C(d) and C(j)
• Since current flow is moving charge, we’ve got charges moving in
the semiconductor material. Charges cannot move instantaneously,
so there is a “charge storage” effect that leads to a diffusion
capacitance C(d).
• The junction capacitance is exist due to the depletion layer of the
diode and depends upon the bias voltage on it.
• The forward bias resistance is also a function of frequency, so the
dynamic resistance, rd and here referred as Rf term
• Put this all together and the ac diode model under forward bias
conditions is represented.
• For reverse bias the diffusion capacitance not existed where as the
highly effected by junction capacitance.
