Diodes. Sections

Transcription

1 iodes Sections

2 Modeling iode Characteristics Exponential model nonlinearity makes circuit analysis difficult. Two common approaches are graphical analysis and iterative analysis For simple battery, resistor, diode circuit (see below) graphical analysis can be performed by simply plotting relationship of diode and resistor equations on i-v plane The plot of the straight line resistor equation is commonly referred to as the load line Intersection of diode equation and load line represents the operating point of the circuit Graphical analysis is good for only simple circuits 2

3 I = I S e V / nv T I = V V R Figure 3.10 A simple circuit used to illustrate the analysis of circuits in which the diode is forward conducting. 3

4 Figure 3.11 Graphical analysis of the circuit in Fig using the exponential diode model. 4

5 Iterative Analysis Iterative analysis can be performed using a simple procedure For example consider V =5V and R = 1Kohm. Assume diode current of 1mA at a voltage of 0.7V and assume voltage drop changes 0.1V for every decade drop in current (Ans. V = 0.762V) Gives precise answer but can be time consuming especially if done by hand calculations (note: we can use a circuit simulator like SPICE to help out) 5

6 Piecewise Linear Model Analysis can be greatly simplified if we can find a linear approximation of diode equation We can approximate the diode forward characteristics with two straight lines (see below) The piecewise linear model can be represented by an equivalent circuit that includes a battery and a resistance 6

7 7 ( ) 0 0, / V v r V v i = 0, 0 V v i = Note: V 0 =0.65V and r =20 ohms for above example Figure 3.12 Approximating the diode forward characteristic with two straight lines: the piecewise-linear model.

8 Figure 3.13 Piecewise-linear model of the diode forward characteristic and its equivalent circuit representation. 8

9 Repeating analysis for previous circuit with equivalent circuit substituted for diode I V V R + r 0 = I = = A = 4. 26mA V = V0 + I r = * 20 = V 9

10 Constant Voltage rop Model Even simpler model uses a vertical straight line to approximate fast rising part of exponential curve (i.e. forward biased diode exhibits constant voltage drop typically assumed to be 0.7V) (see below) Because of its simplicity, this model is commonly used in initial stages of analysis and design For previous circuit V = 0.7V and I = 4.3mA I = = A = 4. 3mA

11 Figure 3.15 evelopment of the constant-voltage-drop model of the diode forward characteristics. A vertical straight line (B) is used to approximate the fast-rising exponential. Observe that this simple model predicts V to within ±0.1 V over the current range of 0.1 ma to 10 ma. 11

12 Figure 3.16 The constant-voltage-drop model of the diode forward characteristics and its equivalent-circuit representation. 12

13 Example 1 esign the circuit for figure below to provide an output voltage of 2.4V. Assume diodes have 0.7V drop at 1mA and that V=0.1V/decade change in current Ans: R = 760 ohms Figure E

14 Small Signal Model In many circuit applications a diode is biased at an operating point with some small ac signal superimposed on the dc bias For this situation a good solution is to find dc bias using one of previous methods and then model small signal variations by resistance equal to 1/slope of diode curve at the operating point 14

15 Figure 3.17 evelopment of the diode small-signal model. Note that the numerical values shown are for a diode with n = 2. 15

16 The value of r d can be determined as follows: v I = I S e V / nv T ( t) = V v ( t) + d i i ( t) = T I S e v / nv T ( ) vd / nvt V + vd / nvt V / nvt vd / nvt ( t) = I Se = I se e = vd 1 nv i t) I 1 + v d nv T I e Assume v d is small ( Small Signal appox. 16

17 v i ( t ) I d = I + 1+ nv T I i d ( t) = vd = nvt v r d d i d r = d nv I T Small-signal resistance 17

18 For circuit in (a) R=10Kohms, V + =10V C + 60Hz sine wave with 1V peak amplitude (i.e power supply ripple) Calculate C voltage of diode and amplitude of sinusoidal signal appearing across it. Assume diode to have 0.7V drop at 1mA and n=2. Figure 3.18 (a) Circuit for Example 3.6. (b) Circuit for calculating the dc operating point. (c) Small-signal equivalent circuit. 18

19 I = = 0. 93mA 10 Note: close to 1mA so diode voltage will be close to assumed value of 0.7V r d nvt 2*.025 = = = 53. 8Ω I Note: signal voltage can be found from small-signal model in figure (c) above rd vd( peak) = VS = 1* = 5. 35mV R + rd Note: since signal is small, use of small-signal model is valid 19

20 Example 2 Find the value of the diode small-signal resistance r d at bias currents of 0.1mA, 1mA, and 10mA. Assume n=1 Ans: 250ohms, 25ohms, 2.5ohms 20

21 Example 3 Consider a diode with n=2 biased at 1mA. Find the current as a result of changing the voltage by -20mV. Calculate using smallsignal model and exponential model Ans: -0.40ma, -0.33mA 21