Resistance & Nonlinearity of Diode AC & DC Approach Engr . Fazal Ur Rehman

Contents Linear & Nonlinear Devices V-I Curves of Linear & Nonlinear Devices AC & DC Resistances

Linear Elements The elements which have a linear relation between the voltage applied across them and current through them, are known as linear devices V = aI + b I = cV + d a, b, c and d are constants For example; voltage and current for resistor are related to each other as: V = IR a = R b = 0 or I = VG c = G d = 0 G = 1/R Resistor, capacitor and inductor are linear devices and their equations are given as: R  V = IR R is resistance C  V = IXC XC is capacitive reactance L  V = IXL XL is inductive reactance Current through linear devices does not alter its linearity property.

Graphs of Linear Elements V V2 ΔV ΔV = V2 – V1 V1 ΔI I1 I2 I ΔV / ΔI = R ΔI = I2 – I1

Nonlinear Elements The elements which have a nonlinear relation between the current through them and voltage applied across them are known as nonlinear elements. For example, the diode equation is given as: This is a nonlinear equation and hence the element is nonlinear one

Graph of Diode Behavior Forward Bias Region ID r2 ΔI ΔV r1 ΔI ΔV VD r1 > r2 Reverse Bias Region

Nonlinear Elements Unlike linear device, the resistance of a nonlinear device depends on the voltage across it (or current through it) I-V characteristics becomes very nearly horizontal at low values of current and in the reverse-biased region. So, in these regions, large change in voltage create very small change in current so the value of “r” is very large. The region on the I-V curve where the transition from high resistance to low resistance takes place is called the Knee of the curve.

AC & DC Resistance ΔV/ΔI is called ac (dynamic) resistance of the diode because we consider small change in voltage We would not want to calculate ac resistance between V=0.55V and V=0.65V rd= ΔV/ΔI ohms The dc resistance of a diode is found by dividing the dc voltage across it by dc current through it. DC resistance also called the static resistance. Rd=V/I ohms Diode is nonlinear in both the dc & the ac sense, that is, both its dc & c resistance change over a wide range.

AC & DC Resistance I (mA) rD = VT / I 40 30 DC Resistance AC Resistance RD = V / I 20 rD = ΔV / ΔI ΔI 10 ΔV 0.1 0.2 0.3 0.4 0.5 0.6 V (V)

AC & DC Resistance The DC current in the diode has a value somewhere above the knee. When the dc current in the diode has a value somewhere above the knee, the ac resistance is closely approximate by rd=Vt/I, so at room temp rd=0.026/I ohms

Bulk Resistance Resistance between the contacts and semiconductor material is called “Bulk Resistance”. Its value is less than 1 Ω - + P N + -

Bulk Resistance Total AC resistance=AC resistance + Bulk resistance At low current bulk resistance can be neglected. At high currents Bulk resistance is typically on the order of 0.1 Ω When diode is connected in a circuit in a way that results in the diode being forward biased, there should always be resistance in series with the diode to limit the current that flows through it.

An Example R VD 6312 0.55 4269 0.56 2877 0.57 599 0.61 405 0.62 274 0.63 85 0.66 57.5 0.67 39 0.68 5V R Find the approximate ac resistance when the diode voltages are 0.56 V, 0.62 V, and 0.67 V. Assume bulk resistances of 0.8 Ω, 0.5 Ω and 0.1 Ω respectively. Find the dc resistance of the diode when the voltage across it is 0.56, 0.62, and 0.67 V Find the ac resistance presented by the diode to an ac signal generator that causes the voltage across the diode to vary between 0.55 V and 0.57 V, between 0.61 V and 0.63 V, and between 0.66 V and 0.68 V

Ideal Diode Model Equivalent Circuit + - ON Short Circuit - + OFF Open Circuit

Practical Diode Model Equivalent Circuit + - ON 0.7 V - + OFF Open Circuit

Actual Diode Model Equivalent Circuit + - ON rD 0.7 V - + OFF Reverse Biased Resistance

Loop Equation 0.7 V E R E = 0.7 + IR I

Home Work Example: 3.1 End Problems: 3.1  3.13

Any Questions?