Early Effect & BJT Biasing

Transcription

1 Early Effect & BJT Biasing Early Effect DC BJT Behavior DC Biasing the BJT 1

2 ESE319 Introduction to Microelectronics Early Effect Saturation region Forward-Active region 4 3 Ideal NPN BJT Transfer V Characteristic BE2 -V V A BE1 0 2

3 Early Effect - Continued Collector voltage has some effect on collector current it increases slightly with increases in voltage. This phenomenon is called the Early Effect and is modeled as a linear increase in total current with increases in v CE : i C =I S e v BE V T 1 v CE V A NMOS transistor n = 1 V A V A = is called the Early voltage and ranges from about 15 V to 150 V. 3

4 Early Effect - Continued Saturation region =... Fwd-Active slope=1/ r o region =... Observed by James Early from BTL =... =... -V A 15 V V A 150 V 4

5 Early Effect - Continued Total (bias+signal) quantities: i C =I S e i C = i c v BE = v be v CE = v ce Consider dc (bias) condition (signal = 0): i C = v BE = v CE = v BE V T 1 v CE V A =I S e V T 1 V A =I 1 V CE C V A Lets call the idealized collector bias current (no Early Effect) I C, i.e. =I S e V T 5

6 Early Effect - Continued Rearranging slightly: We shall define: r o = V A =I S e = V T 1 V CE V A => r o = f( ) =I C V A r o = V A I D The dc current due to both and is: r o MOS transistor I D = 1 2 k n W L V GS V t 2 = r o 6

7 Early Effect - Continued Although the bias current is better modeled by including the Early effect = r o We almost always will ignore the second term above in hand calculations and use our ideal expression for the bias current: =I S e V T 7

8 Early Effect - Continued The Early term adds r o to the large signal model: r o r o = I S e v BE /V T = r o = r o 8

9 Early Effect - Continued For typical operating conditions: V A V. 1mA. r o = V A 100 V 10 3 A =100 k We usually can ignore r o since, in practice, r o is in parallel with other resistors, which are much smaller than 100 k. For the time being, you will be specifically told if you must include r o in your circuit analyses and designs. 9

10 (ma) load-line ESE319 Introduction to Microelectronics Simulation Results Early Effect slope = -1/R C r o r o = = 1 dictated by circuit V R CC C R C 4 2 V CC (V) Note: r o is in parallel with R C. 10

11 Active Mode Conditions Base-emitter diode forward-biased: 0.7 V Base-collector diode reverse-biased: V BC = 0.5V Forward-Active (ideal cond.) > 0 V BC < 0 i E = i C + i B v CE = v CB + v BE V 0.2V 11

12 Amplifier Biasing Goals We wish to set a stable value of so that we can apply a signal voltage or signal current to the emitter-base circuit and obtain an amplified (undistorted) version of the signal between the collector and ground. The transistor cannot saturate during operation, i.e. v CE 0.2V. And it cannot cut off during operation, i.e. i C 0 ma. 12

13 Amplifier DC Bias Problem v O cutoff fwd active saturation V CC slope = A v V CC i C R C Q v o = v ce Time v I = v BE v O = v CE 0 sat = 0.2 V v I Time i C = i c v i = v be v BE = v be v CE = v ce Time 13

14 Amplifier Action i C R C i B v CE V CC Source v BE (ac + dc) Base current source: A small ac change in base current results in a large ac collector current ( i b ). This yields a large change in the ac collector voltage v ce. Base voltage source: A small ac change in base voltage results in a large change in the ac collector current (i c = I S exp(v be /V T )). This yields a large change in the ac collector v ce voltage. 14

15 Voltage Source Input With Collector Load (ac + dc) v CE Solution of the simultaneous equations exists where the two curves: the exponential (i C,v BE ) and the straight line (i C,v CE ) intersect: i C =I S e v BE V T BJT V CC v CE R C =I S e v BE V T i C = V CC v CE R C Circuit Load Line 15

16 Scilab Plot of NPN Characteristic //Calculate and plot npn BJT collector //characteristic using active mode model VT=0.025; VTinv=1/VsubT; IsubS=1E-14; vce=0:0.01:10; for vbe=0.58:0.01:0.63 ic=isubs*exp(vtinv*vbe); plot(vce,1000*ic); //Current in ma. end VCC=10; Rc=10000; vload=0:0.01:10; iload=(vcc-vload)/rc; plot(vload,1000*iload); 16

17 Plot Output i Ic (ma.) C (ma) NPN Transistor Load Line v BE =0.63V. Load Line i C = V CC v CE R C V CC =10V v BE =0.62V. v BE =0.04V R C =10k 0.3 v BE =0.60V v CE 7V Vce v (V.) CE (V) =v C 17

18 Amplifier Action Note that as v BE varies from about 0.59 V to 0.63 V, v CE varies from about 1 V to 8 V! A 0.04 V peak-to-peak swing of v BE results in an 7 V peak-topeak swing in v CE - a voltage-gain ratio of 7/0.04, or about 175. The input signal has two components: a dc one called the bias voltage, and an ac one called the (small) signal voltage. For proper operation, let: =V BIAS = v BE MAX v BE MIN /2=0.61V v be =v signal = v BE MAX v BE MIN /2=0.02 V peak 18

19 Candidate Bias Configurations Base current source Base voltage source Emitter current source 19

20 Drive Base With a Base Current Source R c = 10 kω For this collector current: I B I = 5 µa Q1 V CC = 10 V =V CC R C = =5 V Assume: =100 = I B = =0.5 ma. The transistor is almost right in the center of the desired operating region! 20

21 Current Bias Beta Dependence Unfortunately, β is often poorly controlled and may easily vary from 100 to 200. And β is also temperature dependent! For β = 100: = =0.5 ma. For β = 200: = =1.0 ma. =V CC R C = =5V = =0 V The BJT with a = 5 V The BJT is saturated! Base current source biasing BIAS POINT IS UNSTABLE. 21

22 Drive Base with a Base Voltage Source R c = 10 kω V CC = 10 V Q1 Given: I S =10 14 A and: = A =0.025 ln = V =I S e V T For an of 0.5 ma: =V T ln I S = =0.616 V Since = 5 V the transistor is nearly at the center of the desired operating region! OK. Apply volts to the base and we have the desired collector current! 22

23 Voltage Bias I S and Dependence Unfortunately, I S is highly temperature-dependent, doubling for every 5 o C increase in temperature. If the base-emitter voltage is chosen to give = 0.5 ma at 20 o C (68 o F), it will be 2x at 25 o C and 0.5x at 15 o C. is also highly sensitive to. Consider two values and 10 : 10 V T 10 = I V S e BE10 1 =V T ln 10 V I BE1 C 10 1 = =0.058V. V I S e T Less than a 60 mv change in voltage increases by an order of magnitude (10X). BIAS POINT IS UNSTABLE. 23

24 Emitter Current Source This holds collector current close to its desired value since: = I E Changes in due to variations in α in the range determined by the extremes of β are negligible, i.e There is considerable variation in base current, however, but this is usually of no consequence. I B = I E 1 I E 101 I B I E 201 = 1 24

25 Conclusion Biasing a BJT poses potential large bias stability problems, since its characteristics are highly sensitive to temperature and since its electrical properties (principally β) can vary widely from one device to another! The next lecture sequence will cover some techniques for stabilizing the BJT bias. 25