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Diodes

Sections 3.3.1 – 3.3.8

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Modeling Diode Characteristics• Exponential model nonlinearity makes circuit analysis

difficult.• Two common approaches are graphical analysis and iterative

analysis• For simple battery, resistor, diode circuit (see below) graphical

analysis can be performed by simply plotting relationship of diode and resistor equations on i-v plane

• The plot of the straight line resistor equation is commonly referred to as the load line

• Intersection of diode equation and load line represents the operating point of the circuit

• Graphical analysis is good for only simple circuits

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TD nVVSD eII /=

RVVI DDD

D−

=

Figure 3.10 A simple circuit used to illustrate the analysis of circuits in which the diode is forward conducting.

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Figure 3.11 Graphical analysis of the circuit in Fig. 3.10 using the exponential diode model.

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Iterative Analysis

• Iterative analysis can be performed using a simple procedure

• For example consider VDD=5V and R = 1Kohm. Assume diode current of 1mA at a voltage of 0.7V and assume voltage drop changes 0.1V for every decade drop in current (Ans. VD = 0.762V)

• Gives precise answer but can be time consuming especially if done by hand calculations (note: we can use a circuit simulator like SPICE to help out)

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Piecewise Linear Model

• Analysis can be greatly simplified if we can find a linear approximation of diode equation

• We can approximate the diode forward characteristics with two straight lines (see below)

• The piecewise linear model can be represented by an equivalent circuit that includes a battery and a resistance

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( ) 00 ,/ DDDDDD VvrVvi ≥−=

0,0 DDD Vvi ≤=

Note: VD0=0.65V and rD=20 ohms for above exampleFigure 3.12 Approximating the diode forward characteristic with two straight lines: the piecewise-linear model.

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Figure 3.13 Piecewise-linear model of the diode forward characteristic and its equivalent circuit representation.

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• Repeating analysis for previous circuit with equivalent circuit substituted for diode

D

DDDD rR

VVI+−

= 0

mAAID 26.400426.0201000

65.05==

+−

=

VrIVV DDDD 735.020*00426.65.00 =+=+=

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Constant Voltage Drop Model

• Even simpler model uses a vertical straight line to approximate fast rising part of exponential curve (i.e. forward biased diode exhibits constant voltage drop typically assumed to be 0.7V) (see below)

• Because of its simplicity, this model is commonly used in initial stages of analysis and design

• For previous circuit VD = 0.7V and ID = 4.3mA

mAAID 3.40043.01000

7.05==

−=

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Figure 3.15 Development of the constant-voltage-drop model of the diode forward characteristics. A vertical straight line (B) is used to approximate the fast-rising exponential. Observe that this simple model predicts VD to within ±0.1 V over the current range of 0.1 mA to 10 mA.

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Figure 3.16 The constant-voltage-drop model of the diode forward characteristics and its equivalent-circuit representation.

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• Example 1• Design the circuit for figure below to provide an output

voltage of 2.4V. Assume diodes have 0.7V drop at 1mA and that ∆V=0.1V/decade change in current

• Ans: R = 760 ohms

Figure E3.12

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Small Signal Model

• In many circuit applications a diode is biased at an operating point with some small ac signal superimposed on the dc bias

• For this situation a good solution is to find dc bias using one of previous methods and then model small signal variations by resistance equal to 1/slope of diode curve at the operating point

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Figure 3.17 Development of the diode small-signal model. Note that the numerical values shown are for a diode with n = 2.

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• The value of rd can be determined as follows:

TD nVVSD eII /=

)()( tvVtv dDD +=

TD nVvSD eIti /)( =

1⟨⟨T

d

nVv

( ) TdTdTDTdD nVvD

nVvnVVs

nVvVSD eIeeIeIti ////)( === +

Assume vd is small

⎟⎟⎠

⎞⎜⎜⎝

⎛+≅

T

dDD nV

vIti 1)( Small Signal appox.

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dDT

dDD iI

nVvIti +=⎟⎟

⎠

⎞⎜⎜⎝

⎛+≅ 1)(

d

dd

T

Dd r

vvnVIti ==)(

D

Td I

nVr = Small-signal resistance

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For circuit in (a) R=10Kohms, V+=10V DC + 60Hz sine wave with 1V peak amplitude (i.e power supply ripple) Calculate DC voltage of diode and amplitude of sinusoidal signal appearing across it. Assume diode to have 0.7V drop at 1mA and n=2.

Figure 3.18 (a) Circuit for Example 3.6. (b) Circuit for calculating the dc operating point. (c) Small-signal equivalent circuit.

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mAID 93.010

7.010=

−=

Note: close to 1mA so diode voltage will be close to assumed value of 0.7V

Ω=== 8.5300093.0

025.*2

D

Td I

nVr

Note: signal voltage can be found from small-signal model in figure (c) above

mVrR

rVpeakvd

dSd 35.5

0538.0100538.0*1)( =

+=

+=

Note: since signal is small, use of small-signal model is valid

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Example 2

• Find the value of the diode small-signal resistance rd at bias currents of 0.1mA, 1mA, and 10mA. Assume n=1

• Ans: 250ohms, 25ohms, 2.5ohms

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Example 3

• Consider a diode with n=2 biased at 1mA. Find the current as a result of changing the voltage by -20mV. Calculate using small-signal model and exponential model

• Ans: -0.40ma, -0.33mA