Electronic

Circuits

Diode Circuits

Dr Naser Sedghi

nsed@liverpool.ac.uk
 Learning Outcomes

• Diode in forward and reverse bias.

• Analysis of simple diode circuits.
• Methods of diode current and voltage calculation.
• Diode large signal and small signal models.

Electronic Circuits ELEC104 2

 Why is this Lecture Useful?

• Diodes have many applications. You will see them in the

following lectures.
• You need to be able to analyse and design diode circuits.
• Diode is a nonlinear device and analysis of diode circuits is not
always straightforward.
• In this lecture, you will learn various methods to analyse a
simple diode circuit with only one diode.
• You will use these methods later in analysing more
complicated diode circuits.

Electronic Circuits ELEC104 3

 Diode Bias Circuit
VD VD
+ − I − + I

ID
ID
V R V R

Forward bias Reverse bias

• The resistor R, is used to limit the diode current.

• The diode current is measured from A to K and the polarity of voltage is between A
and K (as in forward bias). If the calculated values are negative, it means that the
current or voltage are in opposite direction or polarity (diode is in reverse bias).
• Diode is a nonlinear device. Therefore, the analysis is not always straightforward.
• There are a few methods to calculate the diode voltage and current.

Electronic Circuits ELEC104 4

Analysis Methods
 1. Ideal Diode
ID (mA)
100
VD
+ − I 80

Forward
60
ID Ideal Diode Real Diode
V R 40

Reverse 20

0 VD (V)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

𝐼𝐷 = 0 If 𝑉𝐷 < 0 Reverse Bias

𝑉𝐷 = 0 If 𝐼𝐷 > 0 Forward Bias

Electronic Circuits ELEC104 6

 1. Ideal Diode (Forward Bias)
ID (mA)
+ VD − 100
I
80

Forward
ID 60
V=5V R = 2 kΩ Ideal Diode Real Diode
40

Reverse 20

0 VD (V)
+ VD − -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
I

𝑉𝐷 = 0
ID
V=5V R = 2 kΩ 𝑉 = 𝑉𝐷 + 𝑅𝐼 = 0 + 𝑅𝐼 = 𝑅𝐼
𝑉 5
𝐼𝐷 = 𝐼 = = = 2.5 mA
𝑅 2

Electronic Circuits ELEC104 7

 1. Ideal Diode (Reverse Bias)
ID (mA)
− VD + 100
I
80

Forward
ID 60
V=5V R = 2 kΩ Ideal Diode Real Diode
40

Reverse 20

− VD + -1 -0.8 -0.6 -0.4 -0.2

0
0 0.2 0.4 0.6 0.8 1
VD (V)
I

ID
𝐼𝐷 = −𝐼 = 0
V=5V R = 2 kΩ 𝑉 = −𝑉𝐷 + 𝑅𝐼 = −𝑉𝐷 + 𝑅 × 0 = −𝑉𝐷
𝑉𝐷 = −𝑉 = −5 V

Electronic Circuits ELEC104 8

 1. Ideal Diode
ID (mA)
100
VD
+ − I 80

Forward
60
ID Ideal Diode Real Diode
V R 40

Reverse 20

0 VD (V)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

When we use ideal diode model?

• When we want to have approximate calculations and the precise value is
not important.
• When the applied voltage is much larger than the diode forward voltage
(usually 0.6-0.7 V).

Electronic Circuits ELEC104 9

 2. Constant Voltage Model
ID (mA)
100
VD Model
+ − I 80
Forward
(On)
Ideal Diode
60
ID Real Diode
V R 40

Reverse 20 Forward
(Off) (Off)
0 VD (V)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
VF

𝐼𝐷 = 0 If 𝑉𝐷 < 𝑉𝐹 Diode Off (Reverse and forward)

𝑉𝐷 = 𝑉𝐹 If 𝐼𝐷 > 0 Diode On (Forward)

VF

Electronic Circuits ELEC104 10

 2. Constant Voltage Model
ID (mA)
100
VD Model
+ − I 80
Forward
(On)

60
ID Real Diode
V R 40

Reverse 20 Forward
(Off) (Off)
0 VD (V)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
VF

• Forward voltage is assumed constant ( 0.6 – 0.7 V)

and the reverse current is assumed zero.
• Not very different from the actual diode, except in
the region close to the knee. VF

Electronic Circuits ELEC104 11

 2. Constant Voltage Model (Forward Bias)
ID (mA)
100
Model
+ VD − Forward
I 80
(On)

60
ID Real Diode
V=5V R = 2 kΩ 40

Reverse 20 Forward
(Off) (Off)
0 VD (V)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
+ VD − VF

I
𝑉𝐷 = 𝑉𝐹 ≈ 0.6 to 0.7 V
VF

ID 𝑉 = 𝑉𝐷 + 𝑅𝐼 = 𝑉𝐹 + 𝑅𝐼
V=5V R = 2 kΩ
𝑉 − 𝑉𝐹 5 − 0.6
𝐼𝐷 = 𝐼 = = = 2.2 mA
𝑅 2

Electronic Circuits ELEC104 12

 2. Constant Voltage Model (Reverse Bias)
− VD +
I
ID (mA)
100
Model
Forward
80
(On)
ID
V=5V R = 2 kΩ 60

Real Diode
40

Reverse 20 Forward
(Off) (Off)
0 VD (V)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
− VD + VF
I
𝐼𝐷 = −𝐼 = 0
ID
V=5V R = 2 kΩ 𝑉 = −𝑉𝐷 + 𝑅𝐼 = −𝑉𝐷 + 𝑅 × 0 = −𝑉𝐷
𝑉𝐷 = −𝑉 = −5 V

Electronic Circuits ELEC104 13

 2. Constant Voltage Model
ID (mA)
100
VD Model
+ − I 80
Forward
(On)

60
ID Real Diode
V R 40

Reverse 20 Forward
(Off) (Off)
0 VD (V)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
VF

When we use constant voltage model?

• Most of the time.
• It is fairly accurate, except at small diode currents (close to the knee).
• However, the error is not significant if the applied voltage is large (much
larger than 𝑉𝐹 ).

Electronic Circuits ELEC104 14

 3. Piecewise Linear Model
ID (mA)
100
VD Model 1
Slope =
+ − I 80
Forward 𝑅𝑓
(On)

60
ID Real Diode
V R 40

Reverse 20 Forward
(Off) (Off)
0 VD (V)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
V0

𝐼𝐷 = 0 If 𝑉𝐷 < 𝑉0 Diode Off (Reverse and forward)

V0 Rf
𝑉𝐷 = 𝑉𝐹 = 𝑉0 + 𝑅𝑓 𝐼𝐷 If 𝐼𝐷 > 0 (𝑉𝐷 > 𝑉0 ) Diode On (Forward)
𝑉𝐷 − 𝑉0 𝑉0 1
𝐼𝐷 = = − + 𝑉𝐷
𝑅𝑓 𝑅𝑓 𝑅𝑓

Electronic Circuits ELEC104 15

 3. Piecewise Linear Model (Forward Bias)
+ VD − ID (mA)
100
Model 1
Slope =
Forward 𝑅𝑓
80
(On)
ID
V=5V R = 2 kΩ 60

Real Diode
40

𝑉0 = 0.6 V 𝑅𝑓 = 20 Ω Reverse 20 Forward

(Off) (Off)
+ VD − -1 -0.8 -0.6 -0.4 -0.2
0
0 0.2 0.4 0.6 0.8 1
VD (V)

V0

I
𝑉 = 𝑉0 + 𝑅𝑓 𝐼 + 𝑅𝐼 = 𝑉0 + 𝑅𝑓 + 𝑅 𝐼
V0 Rf

R = 2 kΩ
𝑉 − 𝑉0 5 − 0.6
V=5V ID 𝐼𝐷 = 𝐼 = = = 2.18 mA
𝑅 + 𝑅𝑓 2 + 0.020
𝑉𝐷 = 𝑉0 + 𝑅𝑓 𝐼 = 0.6 + 0.020 × 2.18 = 0.64 𝑉
𝑉0 = 0.6 V 𝑅𝑓 = 20 Ω
Electronic Circuits ELEC104 16
 3. Piecewise Linear Model (Reverse Bias)
ID (mA)
− VD +
I 100
Model 1
Slope =
Forward 𝑅𝑓
80
(On)
ID
60
V=5V R = 2 kΩ
Real Diode
40

Reverse 20 Forward
(Off) (Off)
0 VD (V)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

− VD + V0
I
𝐼𝐷 = −𝐼 = 0
ID
V=5V R = 2 kΩ 𝑉 = −𝑉𝐷 + 𝑅𝐼 = −𝑉𝐷 + 𝑅 × 0 = −𝑉𝐷
𝑉𝐷 = −𝑉 = −5 V

Electronic Circuits ELEC104 17

 3. Piecewise Linear Model
ID (mA)
VD
100
+ − I Model
Slope =
Forward
80
(On) 1
𝑅𝑓
ID 60
V R Real Diode
40

Reverse 20 Forward
(Off) (Off)
0 VD (V)
• The value of 𝑅𝑓 depends on the -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6
V0
0.8 1

nominal current, but is very small, in

range of ohms to tens of ohms. Constant voltage model is a special case of
piecewise linear model when forward resistance
• By increasing the current, 𝑅𝑓 is
is zero.
decreased.
• At large currents the diode series Ideal diode model is a special case of piecewise
resistance becomes dominant. linear model when both 𝑽𝟎 and 𝑹𝒇 are zero.
Electronic Circuits ELEC104 18
 3. Piecewise Linear Model
ID (mA)
VD 100
+ − I Model
Slope =
Forward
80
(On) 1
𝑅𝑓
ID 60

V R Real Diode
40

Reverse 20 Forward
(Off) (Off)
0 VD (V)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
V0

When we use piecewise linear model?

• When the effect of forward resistance is significant.
• This usually happens at high currents in power diodes when the series
resistance is dominant.
• In low or medium currents, forward resistance is negligible and the constant
voltage model is adequate.
Electronic Circuits ELEC104 19
 4. Precise Solution
VD
+ −
𝐼𝐷 = 𝐼0 𝑒 𝑉𝐷 Τ𝜂𝑉𝑇 − 1 Diode equation
ID ൞
V R 𝑉 = 𝑉𝐷 + 𝑅𝐼𝐷 KVL circuit equation

1. Start with an initial guess, for example

• The exact solution can be found by for 𝐼𝐷 .
solving two simultaneous equations. 2. Find 𝑉𝐷 from one equation.
• However, diode equation is nonlinear (no 3. Use this value in the other equation to
analytical solution). find 𝐼𝐷 .
• The equations can be solved by 4. Calculate the difference (error) and
numerical methods (trial and error). adjust the initial guess.
5. Repeat until the error is minimum.
Electronic Circuits ELEC104 20
 4. Precise Solution
VD
+ − I 𝐼𝐷 = 𝐼0 𝑒 𝑉𝐷 Τ𝜂𝑉𝑇 − 1 (1) Diode equation
൞
ID 𝑉 = 𝑉𝐷 + 𝑅𝐼𝐷 (2) KVL circuit equation
V=5V R = 2 kΩ

i Guessed 𝐼𝐷 𝑉𝐷 from (1) 𝐼𝐷 from (2) Error

𝐼𝑆 = 0.1 pA 𝜂=1 1 2.5 mA 0.622 V 2.189 mA 0.311 mA

• We know that the forward voltage 2 2.1 mA 0.618 V 2.220 mA -0.120 mA

of diode is very small. 3 2.15 mA 0.619 V 2.191 mA -0.041 mA
• A good initial guess is assuming it as
4 2.2 mA 0.619 V 2.191 mA 0.009 mA
zero (ideal diode):
5 2.19 mA 0.619 V 2.191 mA -0.001 mA
5
𝐼𝐷 = = 2.5 mA 6 2.191 mA 0.619 V 2.190 mA 0.0005 mA
2

Electronic Circuits ELEC104 21

 4. Precise Solution
VD
+ −
𝐼𝐷 = 𝐼0 𝑒 𝑉𝐷 Τ𝜂𝑉𝑇 − 1 (1) Diode equation
ID ൞
V R (2) KVL circuit equation
𝑉 = 𝑉𝐷 + 𝑅𝐼𝐷

When the precise method is used? Is the method really that precise?
• When we want to have the precise values of • It can be very precise if we know the exact
the diode voltage and current. values of the parameters (𝐼0 and 𝜂).
• We usually don’t need that much accuracy • Ideality factor, 𝜂, varies with current. To have
and the more simplified methods adequate. a precise calculation, we need to know the
• It is useful in devices in which we cannot value of 𝜂 in the region.
easily guess the voltage and current. • The method is the basis of the models in
• The technique is usually used in calculations advanced simulation software.
by programming or simulation.
Electronic Circuits ELEC104 22
 5. Graphical Method
(1) Diode equation ID
𝐼𝐷 = 𝐼0 𝑒 𝑉𝐷Τ𝜂𝑉𝑇 − 1 Diode Characteristics (1)
൞
𝑉 = 𝑉𝐷 + 𝑅𝐼𝐷 (2) KVL circuit equation
V/R
• The solution of the two simultaneous Load line (2)
equations is the point that their curves IDQ Q Slope = − 1/R
intersect.
• By plotting the curves of the equations, we VD
can find the intersection, which is our VDQ V
solution and is called operating point (Q). • To draw the line we need to find two points on the
• The equation for line can be written as line.
𝑉𝐷 = 𝑉 − 𝑅𝐼𝐷 or • The easiest points are the intercepts with the axes.
𝑉 − 𝑉𝐷 1 𝑉
𝐼𝐷 = = − 𝑉𝐷 +
𝑅 𝑅 𝑅 The load line concept is very important to
• It is a line with slope of − 1Τ𝑅 and is called understand the electronic circuits operation. It
load line. is used extensively.
Electronic Circuits ELEC104 23
 5. Graphical Method
VD
+ − I

ID (mA)
ID 10

V = 1.5 V R = 250 Ω
8

V/R 6 Operating point

4 Load line
IDQ 1
𝑄 Slope = −
2
𝑅
𝐼𝐷 = 𝐼𝑆 𝑒 𝑉𝐷 Τ𝜂𝑉𝑇 − 1 Diode Equation 0 VD (V)

ቊ
-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
VDQ V
𝑉 = 𝑉𝐷 + 𝑅𝐼𝐷 Circuit Equation
𝐼𝐷𝑄 = 3.5 mA
𝑉 1
𝐼𝐷 = − 𝑉𝐷 𝑉𝐷𝑄 = 0.62 V
𝑅 𝑅
Electronic Circuits ELEC104 24
 5. Graphical Method
ID (mA)
10
VD
+ − I 8

6
ID
V=5V R = 2 kΩ 4

0 VD (V)
-0.2 0 0.2 0.4 0.6 0.8 1 1.2

𝐼𝐷 = 𝐼𝑆 𝑒 𝑉𝐷 Τ𝜂𝑉𝑇 − 1 Diode Equation

ቊ It is not always possible to draw the
𝑉 = 𝑉𝐷 + 𝑅𝐼𝐷 Circuit Equation load line with the intercept on the
axes, especially when the applied
𝑉 1
𝐼𝐷 = − 𝑉𝐷 voltage is large.
𝑅 𝑅

Electronic Circuits ELEC104 25

 5. Graphical Method
ID (mA)
VD 10

+ − I
8

6
ID
V=5V R = 2 kΩ 4

2
𝑄
0 VD (V)
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

𝐼𝐷 = 𝐼𝑆 𝑒 𝑉𝐷 Τ𝜂𝑉𝑇 − 1 Diode Equation

ቊ • We can extend the axes to include the
𝑉 = 𝑉𝐷 + 𝑅𝐼𝐷 Circuit Equation intercepts with the load line.
• The operating point is very close to the
𝑉 1
𝐼𝐷 = − 𝑉𝐷 origin (in a small part of the graph).
𝑅 𝑅 • The measurement is not very accurate.
Electronic Circuits ELEC104 26
 5. Graphical Method
ID (mA)
VD 4.0

+ − I 3.5

3.0

ID
2.5 𝑄
2.0
V=5V R = 2 kΩ
1.5

1.0

0.5

0.0 VD (V)
-0.2 0 0.2 0.4 0.6 0.8 1 1.2

𝐼𝐷 = 𝐼𝑆 𝑒 𝑉𝐷 Τ𝜂𝑉𝑇 − 1 Diode Equation

ቊ • Two points to draw the line, do not need
𝑉 = 𝑉𝐷 + 𝑅𝐼𝐷 Circuit Equation to be on the axes.
• We can draw the line between any two
𝑉 1 arbitrary points.
𝐼𝐷 = − 𝑉𝐷
𝑅 𝑅
Measured values: 𝑉𝐷 = 0.62 V, 𝐼𝐷 = 2.2 mA.
Electronic Circuits ELEC104 27
 5. Graphical Method
VD ID (mA)
+ − I 4.0

3.5

3.0
ID
R = 2 kΩ
2.5 𝑄
V=5V 2.0

1.5

1.0

0.5

0.0 VD (V)
When the graphical method is used? -0.2 0 0.2 0.4 0.6 0.8 1 1.2

• When we have the IV characteristics of How accurate is the method?

the diode available. • The accuracy depends on how accurately we
• When we want to explain the circuit can draw the load line or measure the current
operation using the load line concept. and voltage on the graph.
• The load line is particularly important in • Sometimes we use it to have a quick estimate.
explaining the operation of transistor • It can be very accurate if we have the IV
circuits. characteristics in graphical software.
Electronic Circuits ELEC104 28
 6. Circuit Simulation
• Circuit simulation tools are very important in analysis and design of
electronic circuits.
• There are many circuit simulation packages available.
• They differ by accuracy of calculations, accuracy of models, simulation
speed, and flexibility.
• Multisim is a powerful simulation package which is used in our labs.
• A simpler version, but more user friendly, Multisim Live is available
online.
• https://www.multisim.com/content/pTLaxdDhbbBvYFNiPLUJY2/diode-
forward-bias/open/

Electronic Circuits ELEC104 29

 6. Circuit Simulation
How accurate it is?
When circuit simulation is used? • The accuracy of the simulation depends on:
• It is commonly used in industry and 1. Device models,
academia to predict the circuit 2. Simulation settings.
behaviour before fabrication. • For complex circuits, there is a trade off
• The modifications can be easily applied between accuracy and speed.
to achieve the optimum design. • It is the most precise method with the
• It is usually used for complex circuits, right settings and with an accurate model.
particularly integrated circuits. • Experienced users can write or edit the
• It can be used for simple circuits as netlist and in most simulation packages
well to understand the concepts better they can define their own models and
or for learning to work with simulation subcircuits.
software. • Integrated circuit design cannot be
imagined without simulation tools.
Electronic Circuits ELEC104 30
 Which Method and When?

• Most of the time we use constant voltage model.

• When the applied voltage is much larger than 𝑉𝐹 or accuracy is not very
important, even we can use the ideal diode model.
• Piecewise linear model is usually used at high currents in power diodes.
• Precise solution is used mainly in programming algorithms. They are used
in some simulation models.
• Graphical method is mainly used to explain or understand the concepts.
• Simulation is used to have a better understanding of the circuit operation
or in circuit design to achieve the optimum design.

Electronic Circuits ELEC104 31

 Comparison of Methods

𝑅 = 2 kΩ 𝑽 = 𝟏. 𝟓 𝐕 𝑽 = 𝟏𝟐 𝐕 𝑽 = 𝟏𝟎𝟎 𝐕
Ideal Diode 0.75 mA 6 mA 50 mA
Constant Voltage 0.4 mA 5.65 mA 49.65 mA
Piecewise Linear Model 0.44 mA 5.69 mA 49.69 mA
Using Diode Equation 0.50 mA 5.72 mA 49.69 mA
Graphical Method 0.5 mA 5.7 mA 50 mA
Circuit Simulation 0.50 mA 5.72 mA 49.69 mA

Electronic Circuits ELEC104 32

 Comparison of Methods

What is your conclusion about the table on the previous slide?

Electronic Circuits ELEC104 33

 Analysis of Diode Circuits

What you need to know:

• Using various methods to analyse simple diode circuits.
• Comparing accuracy of different analysis methods.
• Deciding on which method to use based on the application and
the input voltage.

Electronic Circuits ELEC104 34

Diode Models
 Small Signal Model
ID
v
Vm Vm sin (ωt)

V Slope gd
diD IDQ Q

0 t
VD
dvD VDQ V
𝑣 = 𝑉 + 𝑉𝑚 sin 𝜔𝑡
2Vm
𝑔𝑑 : Dynamic conductance.
• A small ac signal is superimposed to a dc voltage. 𝑖𝐷 = 𝐼𝑆 𝑒 𝑣𝐷Τ𝜂𝑉𝑇 − 1
• It changes the load line around the operating point, Q. 𝑑𝑖𝐷 1 𝑣𝐷 Τ𝜂𝑉𝑇
𝐼𝐷𝑄
𝑔𝑑 = = 𝐼𝑒 ≈
• Slope of diode characteristics around the operating 𝑑𝑣𝐷 𝜂𝑉𝑇 𝑆 𝜂𝑉𝑇
point: 𝑔𝑑 = 𝑑𝑖𝐷 Τ𝑑𝑣𝐷 . 1 𝜂𝑉𝑇
𝑟𝑑 = = Dynamic resistance.
𝑔𝑑 𝐼𝐷𝑄

Electronic Circuits ELEC104 36

Dynamic Resistance and Forward Resistance
ID

• At currents well above the knee

𝜂𝑉𝑇
𝑅𝑓 = 𝑟𝑑 = 1
𝐼𝐷
𝑅𝑓
• To be more precise:
𝑅𝑓 = 𝑟𝑑 + 𝑅𝑆 VD
V0
• 𝑅𝑆 : Series resistance.
V0
• At low and medium currents, 𝑅𝑆 is Rf

much smaller than 𝑟𝑑 and is negligible:

𝑅𝑓 ≈ 𝑟𝑑 . Large signal piecewise linear model
at forward bias.
• At high currents (power diodes), 𝑅𝑆 is rd
dominant.
Small signal model at forward bias.

Electronic Circuits ELEC104 37

 Diode Models

What you need to know:

• Diode small signal and large signal models.
• Concept of dynamic resistance and its equation.
• Calculating the diode dynamic resistance.
• Diode forward resistance.

Electronic Circuits ELEC104 38

 Overview
• Diode simple circuit analysis:
1. Ideal diode,
2. Constant voltage model,
3. Piecewise linear model,
4. Using the diode equation,
5. Graphical method,
6. Circuit simulation.
• Comparison of methods.
• Diode dynamic resistance.
• Diode large signal and small signal models.

Electronic Circuits ELEC104 39