Small Signal Model of the diode
 In certain applications a diode is biased to operate at a point on the forward i-v curve.
 A small AC signal is superimposed on the DC quantities.
1. Determine DC operating point (VD and ID), using one of the models discussed,
2. For small signal operation around the dc bias point:
The diode is modeled by a resistance equal to the inverse of the slope of the tangent
to the i-v curve at the bias point.
Consider the circuit shown:
𝜐𝐷 𝑡 = 𝑉𝐷 + 𝜐𝑑 𝑡 is the total voltage applied:
𝑉𝐷
≡ the dc value
𝜐𝑑 𝑡
≡ the small signal value
𝑖𝐷 𝑡 = 𝐼𝐷 + 𝑖𝑑 𝑡 is the total current:
𝐼𝐷
≡ the dc value
𝑖𝑑 𝑡
≡ the small signal value
1. DC analysis:
iD
Turn off the small signal: ⇒ 𝜐𝐷 𝑡 = 𝑉𝐷
The current through the diode will be only dc:
𝑉𝐷
𝑖𝐷 𝑡 = 𝐼𝐷 = 𝐼𝑆 exp(
)
𝑛𝑉𝑇
Bias Point
Q
ID
vD
0.5
0.6
V
V
VD
0.7
V
0.8
V
When the signal 𝜐𝑑 𝑡 is applied:
 Total voltage across the diode:
𝜐𝐷 𝑡 = 𝑉𝐷 + 𝜐𝑑 𝑡
 Total instantaneous current:
𝑖𝐷 𝑡 = 𝐼𝑆 exp(
𝑖𝐷 𝑡 = 𝐼𝑆 exp
𝑉𝐷 +𝜐 𝑑 𝑡
𝑖𝐷 𝑡 = 𝐼𝐷 exp
𝑛𝑉𝑇
𝜐𝑑 𝑡
𝑛𝑉𝑇
 When 𝜐𝑑 ≪ 𝑛𝑉𝑇 ;
𝑖𝐷 𝑡 = 𝐼𝐷 exp
𝜐𝑑 𝑡
𝑛𝑉𝑇
𝜐𝐷 𝑡
= 𝐼𝑆 exp
:
𝑉𝐷
𝑛𝑉𝑇
× exp
𝜐𝑑 𝑡
𝑛 𝑉𝑇
)
→
𝑛𝑉𝑇
(1)
𝜐𝑑
𝑛 𝑉𝑇
≪ 1 ⇒ exp
≅ 𝐼𝐷 (1 +
𝜐𝑑 𝑡
𝑛𝑉𝑇
):
𝜐𝑑 𝑡
𝑛𝑉𝑇
≅1+
𝜐𝑑 𝑡
𝑛𝑉𝑇
(2)
This represents the small signal approximation: where the
exponential dependence is approximated by a linear relation
𝑖𝐷 𝑡 ≅ 𝐼𝐷 +
𝐼𝐷
𝑛 𝑉𝑇
𝜐𝑑 𝑡 = 𝐼𝐷 + 𝑖𝑑 (𝑡):
Thus we have a small signal current 𝑖𝑑 (𝑡) superimposed on the
dc current 𝐼𝐷
𝐼𝐷
𝑖𝑑 𝑡 ≅
𝜐𝑑 𝑡
𝑛𝑉𝑇
The quantity
𝐼𝐷
𝑛 𝑉𝑇
relating 𝑖𝑑 to 𝑣𝑑 has the dimension of
conductance; it is: the diode small signal conductance
Its inverse: 𝑟𝑑 =
𝑛𝑉𝑇
𝐼𝐷
is the
diode small signal resistance 𝑟𝑑
or
or
incremental resistance 𝑟𝑑
the dynamic resistance 𝑟𝑑
Graphical Interpretation of the small signal approximation
𝑟𝑑 =
1
𝜕 𝑖𝐷
𝜕 𝑣 𝐷 𝑖 =𝐼
𝐷 𝐷
This small signal resistance represents the inverse of the slope of
the 𝑖𝐷 − 𝑣𝑠 − 𝑣𝐷 curve at the operating point Q.
Equivalent circuit model for the diode for
small changes around bias point Q.
The incremental resistance rd is the inverse
of the slope of the tangent at Q, and VD0 is
the intercept of the tangent on the vD axis:
𝜐𝐷 𝑡 = 𝑉𝐷 + 𝜐𝑑 𝑡 = 𝑉𝐷0 + 𝑟𝑑 ∙ 𝑖𝐷 𝑡
𝑉𝐷 + 𝜐𝑑 𝑡 = 𝑉𝐷0 + 𝑟𝑑 ∙ 𝐼𝐷 + 𝑖𝑑 𝑡
𝑉𝐷 + 𝜐𝑑 𝑡 = 𝑉𝐷0 + 𝑟𝑑 ∙ 𝐼𝐷 + 𝑟𝑑 ∙ 𝑖𝑑 𝑡
DC:
𝑉𝐷 = 𝑉𝐷0 + 𝑟𝑑 ∙ 𝐼𝐷
AC:
𝜐𝑑 𝑡 = 𝑟𝑑 ∙ 𝑖𝑑 𝑡
Large Signal
Equivalent Circuit
The Small Signal Equivalent Circuit: is as
shown
Small Signal
Equivalent Circuit
Replace Diode by its large
signal equivalent circuit
dc Analysis
Small signal analysis
High frequency small signal equivalent circuit
We add the capacitance to consider the delay between the signal
voltage applied and the signal current