Chapter1: Diodes 1

sedr42021_0301a.jpg Figure 2.1 The ideal diode: (a) diode circuit symbol; (b) i–v characteristic; (c) equivalent circuit in the reverse direction; (d) equivalent circuit in the forward direction.

Electrostatics of PN Junction NA ND Max Electric Field Depletion width 3

Depletion region expands with reverse bias Diode Connections Reverse bias connection Depletion region expands with reverse bias

Forward connection For silicon diodes, the typical forward voltage is 0.7 volts, For germanium diodes, the forward voltage is only 0.3 volts.

Typical I-V Characteristics Thermal Voltage VT=k*T/q

Figure 2.7 The i–v characteristic of a silicon junction diode. sedr42021_e0305.jpg Figure 2.7 The i–v characteristic of a silicon junction diode.

i=is (ev/nVT -1) (¤) v=n VT ln(i/iS) The forward-Bias Region: It is entered when the terminal voltage v is positive. In the forward region the i-v relationship is closely approximated by: i=is (ev/nVT -1) (¤) Where VT=KT/q k=Boltzmann’s constant= 1.38*10-23 joules/kelvin T=the absolute temperature in kelvins=273+temperature in °C q=The magnitude of electronic charge= 1.6*10-19 coulomb n has a value between 1 and 2 For appreciable current I in the forward direction, specially for i>>Is, (¤) can be approximated by the relationship i=is ev/nVT v=n VT ln(i/iS) Example: A silicon diode said to be a 1mA device displays a forward voltage of 0.7v at a current of 1mA. Evaluate the junction scaling constant IS in the event that n is either 1 or 2. Solution: Since i=Is ev/nVT Then Is=i e-v/nVT n=1: Is= 10-3e-700/25=6.9*10-16A N=2: Is= 10-3e-700/50=8.3*10-10A

Figure 2.10 A simple circuit used to illustrate the analysis of circuits in which the diode is forward conducting. Example: Determine the current ID and the diode voltage VD of the circuit with VDD=5V and R=1kΩ. Assume that the diode has a current of 1mA at a voltage of 0.7V and that its voltage drop changes by 0.1V for every decade change in current. Solution: we assume that VD=0.7V Then , by employing the equation and considering That 2.3nVT =0.1V, we obtain: V1=0.7V, I1=1mA and I2=4.3mA results in V2=0.763V. Thus results permit to us to get: and sedr42021_e0309.jpg

Resistance Levels sedr42021_0312.jpg Figure 2.12 Approximating the diode forward characteristic with two straight lines: the piecewise-linear model.

iD=(vD –VDD)/rD , vD >VDD Figure 2.13 Piecewise-linear model of the diode forward characteristic and its equivalent circuit representation. sedr42021_0313a.jpg The straight-lines (or piecewise linear) model of the fig (a) can be described by: iD=0 , vD <VDD iD=(vD –VDD)/rD , vD >VDD

Application: 1- In case of DC current, Determine the dc resistance levels for the diode at (a) ID=2 mA (b) ID= 20 mA (c) VD=-10 V

sedr42021_0317a.jpg Figure 2.17 Development of the diode small-signal model. Note that the numerical values shown are for a diode with n = 2.

Application 2: In case of AC current : (a) Determine the ac resistance at ID= 2 mA. (b) Determine the ac resistance at ID =25 mA. sedr42021_0314.jpg

Load Line Analysis From the circuit above, Figure 2.11 Graphical analysis of the circuit in Fig. 3.10 using the exponential diode model. sedr42021_0311.jpg From the circuit above, If we consider the 2 equations, we obtain the Q point in the intersection with the curve of the diode response I=f(V)

Series of Diode configurations sedr42021_0302a.jpg Figure 2.2 The two modes of operation of ideal diodes and the use of an external circuit to limit the forward current (a) and the reverse voltage (b).

sedr42021_0305a.jpg Figure 2.5 Diode logic gates: (a) OR gate; (b) NAND gate (in a positive-logic system).

Example: Find the values of I and V in the circuits shown in Fig E2.4 sedr42021_e0304a.jpg Example: Find the values of I and V in the circuits shown in Fig E2.4

Application: 1- Determine Vo, I1, ID1, and ID2 for the parallel diode configuration of the figure shown below 2- Determine I1, I2, and ID2 for the parallel diode configuration of the figure shown below sedr42021_0316a.jpg

Homework: Assuming the diodes to be ideal, find the values of I and V in the circuit sedr42021_0306a.jpg Figure 2.6 Circuits for Example 3.2.

Zener Diode Figure 2.20 Circuit symbol for a zener diode and its Model. sedr42021_0320.jpg Figure 2.21 The diode i–v characteristic with the breakdown region shown in some detail.

Application: 1- (a) For the Zener diode network, determine VL, VR, IZ, and PZ. (b) Repeat part (a) with RL = 3 k. Homework: Ex 42 P130

Find V0 with no load and with V+ at its nominal value Figure 2.23 (a) Circuit for Example 2.8. (b) The circuit with the zener diode replaced with its equivalent circuit model. The -6.8v zener diode in the circuit is specified to have Vz =6.8v at Iz=5.mA. rs=20, and Izk=20mA. The supply voltage V+ is nominally 10v but can vary by ±1v Find V0 with no load and with V+ at its nominal value Find the change in V0 resulting from the ±1 vchange in V+ . Note that (ΔV0/ΔV+), usually expressed in mV/V, is known line regulation Find the change in V0 resulting from connecting a load resistance RL that draws a current IL=1mA, and hence find the load regulation (ΔV0/ΔIL), in mV/mA. Find the change inV0 when RL=2kΩ Find the value of V0 when RL=0.5kΩ What is the minimum value of RL for which the diode still operates in the breakdown region sedr42021_0323a.jpg

Diodes in AC analysis with Ac source sedr42021_0303a.jpg Figure 2.3 (a) Rectifier circuit. (b) Input waveform. (c) Equivalent circuit when vI  0. (d) Equivalent circuit when vI  0. (e) Output waveform.

Figure E2.1 sedr42021_e0301.jpg Figure E2.2

Figure 2.4 Circuit and waveforms for Example 3.1. Example: (a) shows a circuit for charging a -12v battery. If Vs is a sinusoid with 24v peak amplitude. Find the fraction of each cycle during which the diode conducts. Also, find the peak value of the diode current and the maximum reverse-bias voltage that appears across the diode Solution: The diode conducts when Vs exceeds 12v. As shown in Fig2.4 (b). The conduction angle is 2θ, where θ is given by: 24 cosθ= 12 Thus θ=60° and the conduction angle is 120°, or one-third of a cycle. The peak value of the diode current is given by The maximum reverse voltage across the diode occurs when Vs is at its negative peak and is equal to 24+12=36V sedr42021_0304a.jpg

Figure 2.24 Block diagram of a dc power supply. APPLICATIONS OF DIODES: Diodes are used in so many ways that we will not be able to discuss all of them. The major applications of the diodes that will be discussed are: Rectifiers Clippers or Limiters Clampers Voltage Multipliers sedr42021_0324.jpg Figure 2.24 Block diagram of a dc power supply.

Half-wave rectifier Conduction region (0 T/2).

No conduction region (T/2 T). Half-wave rectified signal

Effect of VK on half-wave rectified signal. If we consider a network for the example

The resulting vo for the circuit If we consider the effect of VK on output of Figure

Full-wave bridge rectifier Network of this Figure for the period 0 T/2 of the input voltage vi.

Conduction path for the positive region of vi. +

That’s why if we consider the Input and output waveforms for a full-wave rectifier, we will obtain the following result Determining VOmax for silicon diodes in the bridge configuration.

Full-Wave Rectifier using a center-tapped secondary Network conditions for the positive region of vi.

Series clipper with a dc supply: if we consider the following figure Network conditions for the negative region of vi. Series clipper with a dc supply: if we consider the following figure

sedr42021_0325a.jpg Figure 2.25 (a) Half-wave rectifier. (b) Equivalent circuit of the half-wave rectifier with the diode replaced with its battery-plus-resistance model. (c) Transfer characteristic of the rectifier circuit. (d) Input and output waveforms, assuming that rD ! R.

sedr42021_0326a.jpg Figure 2.26 Full-wave rectifier utilizing a transformer with a center-tapped secondary winding: (a) circuit; (b) transfer characteristic assuming a constant-voltage-drop model for the diodes; (c) input and output waveforms.

sedr42021_0327a.jpg Figure 2.27 The bridge rectifier: (a) circuit; (b) input and output waveforms.

sedr42021_0328a.jpg Figure 2.28 (a) A simple circuit used to illustrate the effect of a filter capacitor. (b) Input and output waveforms assuming an ideal diode. Note that the circuit provides a dc voltage equal to the peak of the input sine wave. The circuit is therefore known as a peak rectifier or a peak detector.

sedr42021_0329a.jpg Figure 2.29 Voltage and current waveforms in the peak rectifier circuit with CR @ T. The diode is assumed ideal.

Figure 2.30 Waveforms in the full-wave peak rectifier. sedr42021_0330.jpg

Applications: Voltage doubler sedr42021_0338a.jpg Figure 2.38 Voltage doubler: (a) circuit; (b) waveform of the voltage across D1.