Design and Analysis of Diode Circuits

Diode Circuits Operating in the Reverse Breakdown region. (Zener Diode) In may applications, operation in the reverse breakdown region is highly desirable. The reverse breakdown voltage is relatively insensitive to the current flowing thought the diode (the reverse current). Zener diodes are designed to operate in the reverse breakdown region and circuits containing them provide voltage regulation or voltage referencing. The circuit shown on Figure 1(a) will be used to explore the characteristics of operation in the breakdown region. The i-v characteristic curve of the diode is shown on Figure 1(b). Vz is the reverse breakdown voltage and Vg is the forward voltage drop across the diode. We will focus our analysis in the reverse bias region of the i-v curve. Id Rs Vs D Vz Vd 0 Vg Vd + 1/Rz (a) (b) Figure 1 For the Zener diode we are using a model with a breakdown voltage Vz and an effective resistance Rz in the breakdown as shown on Figure 2 and illustrated on Figure 1. Vz Rz ≡ Iz Iz Figure 2. Zener diode model in the breakdown region 1 With this model for the Zener diode the circuit in the breakdown region is shown on Figure 3. Rs Id Rz Vs + - Vz Figure 3 By applying KVL to the circuit we have Vz + ( R + Rz ) Id = Vs (1.1) Equation (1.1) is also called the load line equation and for operation in the reverse breakdown region the load line expression becomes Id = − Vz Vs + R + Rz R + Rz (1.2) The two points labeled 1 and 2 as shown on Figure 4 define the load line in the i-v operating space. Id Vz Vg Q Point 1 Vd Load line 1/Rz 1/(R+Rz) Vs/(R+Rz) 2 Figure 4 The operating point or Q point1 is defined by the intersection of the load line equation and the i-v curve of the diode 1 Q stands for Quiescent which we will discuss in detail when we investigate transistor amplifiers. 2 Now let’s consider the half wave rectifier circuit examined previously with the addition of a capacitor in parallel with the load resistor as shown on Figure 5. + C Vin R Vo - Figure 5 Initially the capacitor is uncharged (Vo=0 Volts). The signal Vin is a sinusoid with amplitude Vs and period T. The silicon diode has a forward voltage drop of about 0.7 Volts. Therefore the signal Vo will remain at 0 Volts until the voltage Vin exceeds 0.7 Volts as shown on Figure 6. Once Vin becomes greater than 0.7 Volts the diode turns on and the voltage across the capacitor increases until Vin reaches its maximum value Vs. When Vin starts decreasing ( t > T1 ) the diode becomes reverse biased and the capacitor begins to discharge through the resistor R at a rate proportional to e − t / RC . Vo ∝ e − t / RC Vin Vh Vr = Vh − Vl Vl T1 diode turns on at T2 T Figure 6 The voltage Vo for t > T1 is given by Vo(t ) = Vh e − (t −T1 ) / RC (1.3) 3 The voltage Vo continuous to decrease until the voltage drop across the diode becomes greater than 0.7 Volts. On Figure 6 this occurs at t = T2 and the value of Vo at that time is Vl = Vh e− (T2 −T1 ) / RC The difference between the maximum and the minimum value of Vo, Vh and Vl respectively, is called the ripple of the signal and it is given by Vr = Vh − Vl = Vh (1 − e − (T2 −T1 ) / RC ) (1.4) (1.5) In practical situations we usually would like to have a time constant RC large compared to T2 − T1 or equivalently to the period of the input signal Vin. Therefore, for RC  T2 − T1 the Taylor expansion of Equation (1.5) gives T2 − T1 (1.6) RC At this point we see that the time T2 − T1 depends on RC and thus Equation (1.6) cannot be Vr  Vh solved very easily. However, if we assume that T2 − T1 is equal to the period of the input signal (which constraints our treatment to small values of the ripple) equation (1.6) becomes Vr  Vh T RC (1.7) In terms of the signal frequency the expression for the ripple for this half wave rectifier circuit becomes Vr  Vh Vs − 0.7  f RC f RC (1.8) It is now easy by extension to see that for a full wave rectifier arrangement the ripple scales as Vr  Vh Vs − 0.7  2 f RC 2 f RC (1.9) Equations (1.8) and (1.9) show us that the ripple for a full wave rectifier is half of the ripple due to a half wave rectifier, resulting in a more efficient AC to DC converter. As an extension of this analysis the plots shown on Figure 7 present the complete solution for various values to the time constant RC. 4 (a) No capacitor. Half wave rectifier (b) C=5µF, R=300Ω (c) C=5µF, R=1kΩ (d) C=5µF, R=10kΩ (e) C=5µF, R= infinite Figure 7 5 Light Emitting Diodes (LED) LEDs are pn junction diodes that emit light at various frequencies. The light could be visible or infrared. The LED is active when it is forward biased. The i-v characteristics of an LED diode are similar to that of a regular diode except that the forward voltage may vary from 0.5 Volts to 2.5Volts depending on the type of semiconductor used. The current that flows through the diode controls the intensity of the emitted light. When using such a diode provisions have to be taken for its protection from excessive current through it. The protection is accomplished by using a current limiting resistor as shown on Figure 8. The value of the current limiting resistor is determined by the forward voltage drop of the diode, Vg, the maximum current through it, Im, and the source voltage Vs. The relationship is obtained by applying KVL and it is R= Vs − Vg Im (1.10) R I + Vs - Figure 8. LED diode circuit. By using an LED and a Zener diode we can create a circuit which gives turns on the LED when a voltage exceeds a certain value. Consider the circuit shown on Figure 9. The LED will turn on when the voltage Vs becomes greater than Vz + Vg R Vz I Vs Figure 9. voltage level indication circuit 6 Photodiodes When the pn junction of a diode is exposed to light of sufficiently high frequency the energy of the photons causes the electrons to move, thereby creating electron-hole pairs. The motion of these pairs results in a current through the diode. The symbol, for the photodiode is hv Figure 10. Photodiode symbol Consider the circuit on Figure 11 where the photodiode is reverse biased. When the light intensity is zero, the current that flows through he diode is the reverse –saturation current which is typically very low. When the energy of the light increases, electrons are separated and there is a current flowing in the reverse bias direction. The output voltage Vo is proportional to the current Ip Vo = Ip R (1.11) hv Ip + + Vs - R Vo - Figure 11. Photodiode circuit 7 Schottky Diodes When a diode with a low forward voltage drop is required the Schottky diode may be used. The Schottky diode turns on at about 0.2 Volts compared to 0.7 Volts for the Si diode and it is characterized by a very fast switching times. The symbol, for the Schottky diode is I + Vd - Figure 12. Symbol of Schottky diode The fabrication process of the Schottky diode is different that that of the standard pn junction Si diode. The Schottky diode has a metallic layer in the place of the p region. 8