What is Diode Approximation : Types and Diode Models

Diodes are mainly unidirectional devices. It offers low resistance when a forward or positive voltage is applied and has high resistance when the diode is reverse biased. An ideal diode has zero forward resistance and zero voltage drop. The diode offers high reverse resistance, resulting in zero reverse currents. Though ideal diodes do not exist, near-ideal diodes are used in some applications. The supply voltages are generally much larger than the forward voltage of a diode and thus  V_F is assumed to be constant. Mathematical models are used to approximate characteristics of silicon and germanium diode when the load resistance is typically high or very low. These methods help to solve real-world problems. This article discusses what is diode approximation, types of approximations, problems and approximate diode models.

What is a Diode?

A diode is a simple semiconductor with two terminals called as anode and cathode. It allows the flow of current in one direction (forward direction) and restricts the current flow in the opposite direction (the reverse direction). It has low or zero resistance when forward biased and high or infinite resistance when reverse biased. The terminals anode refers to positive lead and cathode refers to the negative lead. Most of the diodes conduct or allow current to flow when the anode is connected with a positive voltage. Diodes are used as rectifiers in power supply.

What is Diode Approximation?

Diode approximation is a mathematical method used to approximate the nonlinear behavior of real diodes to enable calculations and circuit analysis. There are three different approximations used to analyze the diode circuits.

First Diode Approximation

In the first approximation method, the diode is considered as a forward-biased diode and as a closed switch with zero voltage drop. It is not apt to use in real-life circumstances but used only for general approximations where preciseness is not required.

Second Diode Approximation

In the second approximation, the diode is considered as a forward-biased diode in series with a battery to turn on the device. For a silicon diode to turn on, it needs 0.7V. A voltage of 0.7V or greater is fed to turn on the forward-biased diode. The diode turns off if the voltage is less than 0.7V.

Third Diode Approximation

The third approximation of a diode includes voltage across the diode and voltage across bulk resistance, R_B. The bulk resistance is low, such as less than 1 ohm and always less than 10 ohms. The bulk resistance, R_B corresponds to the resistance of p and n materials. This resistance changes based on the amount of forwarding voltage and the current flowing through the diode at any given time.

The voltage drop across the diode is calculated using the formula

V_d  = 0.7V + I_d *R_B

And if R_B < 1/100 R_Th  or R_B < 0.001 R_Th, we neglect that

Diode Approximation Problems with Solutions

Let’s now look at two 2 examples of diode approximation problems with solutions

1). Look at the circuit below and use the second approximation of diode and find the current flowing through the diode.

I_D =(V_s – V_D)/R = (4-0.7)/8 = 0.41A

2). Look at both of the circuits and calculate using the third approximation method of diode

For fig (a)

Adding 1kΩ resistor with bulk resistor 0.2Ω doesn’t make any difference in current flowing

I_D = 9.3/1000.2= 0.0093 A

If we don’t count 0.2Ω, then

I_D = 9.3/1000=0.0093 A

For fig (b)

For load resistance of 5Ω, ignoring bulk resistance of 0.2Ω brings a difference in current flow.

Therefore, bulk resistance has to be considered and the correct value of current is 1.7885 A.

I_D=9.3/5.2=1.75885 A

If we don’t count 0.2Ω, then

I_D=9.3/5=1.86 A

Summarizing, if the load resistance is small, the bulk resistance is taken into effect. However, if the load resistance is very high (ranging to several kilo-ohms), then bulk resistance has no effect on the current.

Approximate Diode Models

The diode models are mathematical models used for the approximation of diode’s actual behavior. We shall discuss the modeling of p-n junction connected in a forward-biased direction using various techniques.

Shockley Diode Model

In the Shockley diode model equation, the diode current I of a p-n junction diode is related to the diode voltage VD. Assuming that VS>0.5V and ID is much higher than IS, we represent the VI characteristic of a diode by

i_D = i_S  (e ^{VD /ηVT} – 1) —— (i)

With Kirchhoff’s loop equation, we obtain the following equation

i_D = (V_S – V_D/R) ———- (ii)

Assuming that the diode parameters are and η are known, while ID and IS are unknown quantities. These can be found using two techniques – Graphical analysis and Iterative analysis

Iterative Analysis

An iterative analysis method is used to find diode voltage VD with respect to VS for any given series of values using a computer or calculator. The equation (i) can be reorganized by dividing it by IS and adding 1.

  e^VD/ηVT = I/I_S +1

By applying the natural log on both sides of an equation, the exponential can be removed. The equation reduces to

          V_D/ηV_T = ln(I/I_S +1)

Substituting for (i) from (ii) as it satisfies Kirchhoff’s law and the equation reduces to

  V_D /ηV_T = (ln(V_S –V_D)/RI_S ) +1

Or

    V_D = ηV_T ln((V_S – V_D)/RI_S +1)

As Vs is known to value, VD can be guessed and the value is put in the right-hand side of the equation and performing continuous operations, a new value for VD can be found. Once VD is found, Kirchhoff’s law is used to find I.

Graphical Solution

By plotting the equations (i) and (ii) on the I-V curve, an approximate graphical solution is obtained at the intersection of two graphs. This intersecting point on the graph satisfies equations (i) and (ii). The straight line on the graph represents the load line and the curve on the graph represents the diode characteristic equation.

Piecewise Linear Model

As the graphical solution method is highly complicated for composite circuits, an alternative approach of diode modeling is used, known as piecewise linear modeling. In this method, a function is broken down into multiple linear segments and used as a diode approximation characteristic curve.

The graph shows the VI curve of a real diode that is approximated using a two-segment piecewise linear model. A real diode is classified into three elements in series: an ideal diode, the voltage source, and a resistor. The tangent drawn at the Q-point to the diode curve and the slope of this line is equal to the reciprocal of the diode’s resistance at the Q-point.

Mathematically Idealized Diode

A mathematically idealized diode refers to an ideal diode. In this type of an ideal diode, the current flowing is equal to zero when the diode is reverse biased. The characteristic of an ideal diode is to conduct at 0V when a positive voltage is applied and the current flow would be infinite and diode behaves like a short circuit. The characteristic curve of an ideal diode is shown.

FAQs

1). Which diode model represents the most accurate approximation?

The third approximation is the most accurate approximation as it includes a diode voltage of 0.7V, voltage across internal bulk resistance of a diode, and reverse resistance offered by a diode.

2). What is the breakdown voltage of the diode?

The breakdown voltage of a diode is the minimum reverse voltage applied to make the diode breakdown and conduct in the reverse direction.

3). How do you test a diode?

To test a diode, use a digital multimeter

• Change the multimeter selector switch to diode check mode
• Connect the anode to the positive lead of multimeter and cathode to the negative lead
• Multimeter shows a voltage reading between 0.6V to 0.7V and knows that the diode is working
• Now reverse the connections of multimeter
• If the multimeter displays an infinite resistance (over range) and knows that the diode is working

4). Is diode a current?

A diode is neither a current-controlled nor a voltage-controlled device. It conducts if positive and negative voltages are given correctly.

This article discussed the three types of diode approximation method. We discussed how a diode can be approximated when the diode acts as a switch with few numerical. Finally, we discussed various types of approximate diode models. Here is a question for you, what is the function of a diode?